Raeli, Alice; Bergmann, Michel; Iollo, Angelo
2018-02-01
We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.
Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team
2017-11-01
We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).
Descartes, Cartesianism, and Theology
Goudriaan, A.; Lehner, Ulrich; Muller, Richard A.; Roeber, Gregory
2015-01-01
While insisting on the need to separate theology from philosophy, Descartes developed a philosophical theology that was intensely debated in the early modern period. This article asks the question how the receptions of Cartesian philosophy were related to different confessional profiles.
Non Standard Finite Difference Scheme for Mutualistic Interaction Description
Gabbriellini, Gianluca
2012-01-01
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the o...
Baryon number dissipation at finite temperature in the standard model
International Nuclear Information System (INIS)
Mottola, E.; Raby, S.; Starkman, G.
1990-01-01
We analyze the phenomenon of baryon number violation at finite temperature in the standard model, and derive the relaxation rate for the baryon density in the high temperature electroweak plasma. The relaxation rate, γ is given in terms of real time correlation functions of the operator E·B, and is directly proportional to the sphaleron transition rate, Γ: γ preceq n f Γ/T 3 . Hence it is not instanton suppressed, as claimed by Cohen, Dugan and Manohar (CDM). We show explicitly how this result is consistent with the methods of CDM, once it is recognized that a new anomalous commutator is required in their approach. 19 refs., 2 figs
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
On the fate of the Standard Model at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Rose, Luigi Delle; Marzo, Carlo [Università del Salento, Dipartimento di Matematica e Fisica “Ennio De Giorgi' ,Via Arnesano, 73100 Lecce (Italy); INFN - Sezione di Lecce,via Arnesano, 73100 Lecce (Italy); Urbano, Alfredo [SISSA - International School for Advanced Studies,via Bonomea 256, 34136 Trieste (Italy)
2016-05-10
In this paper we revisit and update the computation of thermal corrections to the stability of the electroweak vacuum in the Standard Model. At zero temperature, we make use of the full two-loop effective potential, improved by three-loop beta functions with two-loop matching conditions. At finite temperature, we include one-loop thermal corrections together with resummation of daisy diagrams. We solve numerically — both at zero and finite temperature — the bounce equation, thus providing an accurate description of the thermal tunneling. Assuming a maximum temperature in the early Universe of the order of 10{sup 18} GeV, we find that the instability bound excludes values of the top mass M{sub t}≳173.6 GeV, with M{sub h}≃125 GeV and including uncertainties on the strong coupling. We discuss the validity and temperature-dependence of this bound in the early Universe, with a special focus on the reheating phase after inflation.
Grebenev, Igor V.; Lebedeva, Olga V.; Polushkina, Svetlana V.
2018-07-01
The article proposes a new research object for a general physics course—the vapour Cartesian diver, designed to study the properties of saturated water vapour. Physics education puts great importance on the study of the saturated vapour state, as it is related to many fundamental laws and theories. For example, the temperature dependence of the saturated water vapour pressure allows the teacher to demonstrate the Le Chatelier’s principle: increasing the temperature of a system in a dynamic equilibrium favours the endothermic change. That means that increasing the temperature increases the amount of vapour present, and so increases the saturated vapour pressure. The experimental setup proposed in this paper can be used as an example of an auto-oscillatory system, based on the properties of saturated vapour. The article describes a mathematical model of physical processes that occur in the experiment, and proposes a numerical solution method for the acquired system of equations. It shows that the results of numerical simulation coincide with the self-oscillation parameters from the real experiment. The proposed installation can also be considered as a model of a thermal engine.
SPECTRAL SETS AND TILES IN CARTESIAN PRODUCTS OVER ...
Indian Academy of Sciences (India)
41
Spectral set conjecture: A Borel set Ω ⊂ Rd of positive and finite. Lebesgue measure is a spectral set if and only if it ... Ω ⊂ G of positive and finite Haar measure is a spectral set if and only if it is a translational tile. ... Key words and phrases. p-adic number field, Cartesian product, tile, spectral set. This work was supported by ...
Finite element analyses for seismic shear wall international standard problem
International Nuclear Information System (INIS)
Park, Y.J.; Hofmayer, C.H.
1998-04-01
Two identical reinforced concrete (RC) shear walls, which consist of web, flanges and massive top and bottom slabs, were tested up to ultimate failure under earthquake motions at the Nuclear Power Engineering Corporation's (NUPEC) Tadotsu Engineering Laboratory, Japan. NUPEC provided the dynamic test results to the OECD (Organization for Economic Cooperation and Development), Nuclear Energy Agency (NEA) for use as an International Standard Problem (ISP). The shear walls were intended to be part of a typical reactor building. One of the major objectives of the Seismic Shear Wall ISP (SSWISP) was to evaluate various seismic analysis methods for concrete structures used for design and seismic margin assessment. It also offered a unique opportunity to assess the state-of-the-art in nonlinear dynamic analysis of reinforced concrete shear wall structures under severe earthquake loadings. As a participant of the SSWISP workshops, Brookhaven National Laboratory (BNL) performed finite element analyses under the sponsorship of the U.S. Nuclear Regulatory Commission (USNRC). Three types of analysis were performed, i.e., monotonic static (push-over), cyclic static and dynamic analyses. Additional monotonic static analyses were performed by two consultants, F. Vecchio of the University of Toronto (UT) and F. Filippou of the University of California at Berkeley (UCB). The analysis results by BNL and the consultants were presented during the second workshop in Yokohama, Japan in 1996. A total of 55 analyses were presented during the workshop by 30 participants from 11 different countries. The major findings on the presented analysis methods, as well as engineering insights regarding the applicability and reliability of the FEM codes are described in detail in this report. 16 refs., 60 figs., 16 tabs
Stability and non-standard finite difference method of the generalized Chua's circuit
Radwan, Ahmed G.; Moaddy, K.; Momani, Shaher M.
2011-01-01
In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well
Shattering a Cartesian Sceptical Dream
Directory of Open Access Journals (Sweden)
Stephen Hetherington
2004-06-01
Full Text Available Scepticism about external world knowledge is frequently claimed to emerge from Descartes’s dreaming argument. That argument supposedly challenges one to have some further knowledge — the knowledge that one is not dreaming that p — if one is to have even one given piece of external world knowledge that p. The possession of that further knowledge can seem espe-cially important when the dreaming possibility is genuinely Cartesian (with one’s dreaming that p being incompatible with the truth of one’s accompany-ing belief that p. But this paper shows why that Cartesian use of that possi-bility is not at all challenging. It is because that putative sceptical challenge reduces to a triviality which is incompatible with the sceptic’s having de-scribed some further piece of knowledge which is needed, if one is to have the knowledge that p.
Non-Cartesian parallel imaging reconstruction.
Wright, Katherine L; Hamilton, Jesse I; Griswold, Mark A; Gulani, Vikas; Seiberlich, Nicole
2014-11-01
Non-Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non-Cartesian trajectories can enable more efficient coverage of k-space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be used to reconstruct images from undersampled Cartesian data, non-Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the nonhomogeneous sensitivities of multi-coil phased arrays. This review will begin with an overview of non-Cartesian k-space trajectories and their sampling properties, followed by an in-depth discussion of several selected non-Cartesian parallel imaging algorithms. Three representative non-Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non-Cartesian generalized autocalibrating partially parallel acquisition (GRAPPA), and Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non-Cartesian parallel imaging will be covered. © 2014 Wiley Periodicals, Inc.
Finite element analyses for Seismic Shear Wall International Standard Problem
International Nuclear Information System (INIS)
Park, Y.; Hofmayer, C.; Chokshi, N.
1997-01-01
In the seismic design of shear wall structures, e.g., nuclear reactor buildings, a linear FEM analysis is frequently used to quantify the stresses under the design loading condition. The final design decisions, however, are still based on empirical design rules established over decades from accumulated laboratory test data. This paper presents an overview of the state-of-the-art on the application of nonlinear FEM analysis to reinforced concrete (RC) shear wall structures under severe earthquake loadings based on the findings obtained during the Seismic Shear Wall International Standard Problem (SSWISP) Workshop in 1996. Also, BNL's analysis results of the International Standard Problem (ISP) shear walls under monotonic static, cyclic static and dynamic loading conditions are described
Zernike Basis to Cartesian Transformations
Mathar, R. J.
2009-12-01
The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle) defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.
Standard Model Extension and Casimir effect for fermions at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Santos, A.F., E-mail: alesandroferreira@fisica.ufmt.br [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso (Brazil); Department of Physics and Astronomy, University of Victoria, 3800 Finnerty Road, Victoria, BC (Canada); Khanna, Faqir C., E-mail: khannaf@uvic.ca [Department of Physics and Astronomy, University of Victoria, 3800 Finnerty Road, Victoria, BC (Canada); Department of Physics, University of Alberta, T6J 2J1, Edmonton, Alberta (Canada)
2016-11-10
Lorentz and CPT symmetries are foundations for important processes in particle physics. Recent studies in Standard Model Extension (SME) at high energy indicate that these symmetries may be violated. Modifications in the lagrangian are necessary to achieve a hermitian hamiltonian. The fermion sector of the standard model extension is used to calculate the effects of the Lorentz and CPT violation on the Casimir effect at zero and finite temperature. The Casimir effect and Stefan–Boltzmann law at finite temperature are calculated using the thermo field dynamics formalism.
Zernike Basis to Cartesian Transformations
Directory of Open Access Journals (Sweden)
Mathar, R. J.
2009-12-01
Full Text Available The radial polynomials of the 2D (circular and 3D (spherical Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.
Zernike basis to cartesian transformations
Directory of Open Access Journals (Sweden)
Mathar R.J.
2009-01-01
Full Text Available The radial polynomials of the 2D (circular and 3D (spherical Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.
Directory of Open Access Journals (Sweden)
W.R. Azzam
2015-08-01
Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Cartesian product of hypergraphs: properties and algorithms
Directory of Open Access Journals (Sweden)
Alain Bretto
2009-09-01
Full Text Available Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspects of Cartesian products of hypergraphs. We also extend a classical prime factorization algorithm initially designed for graphs to connected conformal hypergraphs using 2-sections of hypergraphs.
Stability and non-standard finite difference method of the generalized Chua's circuit
Radwan, Ahmed G.
2011-08-01
In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua\\'s circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles\\' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.
Analyzing correlation functions with tesseral and Cartesian spherical harmonics
International Nuclear Information System (INIS)
Danielewicz, Pawel; Pratt, Scott
2007-01-01
The dependence of interparticle correlations on the orientation of particle relative momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real Cartesian harmonics. Mathematical properties of the lesser known Cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regard to determining angular features of emission regions is investigated. The considered final-state effects include identity interference, strong interactions, and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of Gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs
Casimir effect at finite temperature for pure-photon sector of the minimal Standard Model Extension
Energy Technology Data Exchange (ETDEWEB)
Santos, A.F., E-mail: alesandroferreira@fisica.ufmt.br [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso (Brazil); Department of Physics and Astronomy, University of Victoria, 3800 Finnerty Road Victoria, BC (Canada); Khanna, Faqir C., E-mail: khannaf@uvic.ca [Department of Physics and Astronomy, University of Victoria, 3800 Finnerty Road Victoria, BC (Canada)
2016-12-15
Dynamics between particles is governed by Lorentz and CPT symmetry. There is a violation of Parity (P) and CP symmetry at low levels. The unified theory, that includes particle physics and quantum gravity, may be expected to be covariant with Lorentz and CPT symmetry. At high enough energies, will the unified theory display violation of any symmetry? The Standard Model Extension (SME), with Lorentz and CPT violating terms, has been suggested to include particle dynamics. The minimal SME in the pure photon sector is considered in order to calculate the Casimir effect at finite temperature.
Agarwal, P.; El-Sayed, A. A.
2018-06-01
In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
Vogman, Genia
Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space
Advances in non-Cartesian parallel magnetic resonance imaging using the GRAPPA operator
Energy Technology Data Exchange (ETDEWEB)
Seiberlich, Nicole
2008-07-21
This thesis has presented several new non-Cartesian parallel imaging methods which simplify both gridding and the reconstruction of images from undersampled data. A novel approach which uses the concepts of parallel imaging to grid data sampled along a non-Cartesian trajectory called GRAPPA Operator Gridding (GROG) is described. GROG shifts any acquired k-space data point to its nearest Cartesian location, thereby converting non-Cartesian to Cartesian data. The only requirements for GROG are a multi-channel acquisition and a calibration dataset for the determination of the GROG weights. Then an extension of GRAPPA Operator Gridding, namely Self-Calibrating GRAPPA Operator Gridding (SC-GROG) is discussed. SC-GROG is a method by which non-Cartesian data can be gridded using spatial information from a multi-channel coil array without the need for an additional calibration dataset, as required in standard GROG. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. Thereafter a simple, novel method for performing modified Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG to arrive at a non-aliased image is introduced. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. Finally a novel method of using GROG to mimic the bunched phase encoding acquisition (BPE) scheme is discussed. In MRI, it is generally assumed that an artifact-free image can be reconstructed only from sampled points which fulfill the Nyquist criterion. However, the BPE reconstruction is based on the Generalized Sampling Theorem of Papoulis, which states that a continuous signal can be reconstructed from sampled points as long as the points are on average sampled at the Nyquist frequency. A novel
Advances in non-Cartesian parallel magnetic resonance imaging using the GRAPPA operator
International Nuclear Information System (INIS)
Seiberlich, Nicole
2008-01-01
This thesis has presented several new non-Cartesian parallel imaging methods which simplify both gridding and the reconstruction of images from undersampled data. A novel approach which uses the concepts of parallel imaging to grid data sampled along a non-Cartesian trajectory called GRAPPA Operator Gridding (GROG) is described. GROG shifts any acquired k-space data point to its nearest Cartesian location, thereby converting non-Cartesian to Cartesian data. The only requirements for GROG are a multi-channel acquisition and a calibration dataset for the determination of the GROG weights. Then an extension of GRAPPA Operator Gridding, namely Self-Calibrating GRAPPA Operator Gridding (SC-GROG) is discussed. SC-GROG is a method by which non-Cartesian data can be gridded using spatial information from a multi-channel coil array without the need for an additional calibration dataset, as required in standard GROG. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. Thereafter a simple, novel method for performing modified Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG to arrive at a non-aliased image is introduced. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. Finally a novel method of using GROG to mimic the bunched phase encoding acquisition (BPE) scheme is discussed. In MRI, it is generally assumed that an artifact-free image can be reconstructed only from sampled points which fulfill the Nyquist criterion. However, the BPE reconstruction is based on the Generalized Sampling Theorem of Papoulis, which states that a continuous signal can be reconstructed from sampled points as long as the points are on average sampled at the Nyquist frequency. A novel
Directory of Open Access Journals (Sweden)
Bo Li
2014-01-01
Full Text Available The lack of evaluation standard for safety coefficient based on finite element method (FEM limits the wide application of FEM in roller compacted concrete dam (RCCD. In this paper, the strength reserve factor (SRF method is adopted to simulate gradual failure and possible unstable modes of RCCD system. The entropy theory and catastrophe theory are used to obtain the ultimate bearing resistance and failure criterion of the RCCD. The most dangerous sliding plane for RCCD failure is found using the Latin hypercube sampling (LHS and auxiliary analysis of partial least squares regression (PLSR. Finally a method for determining the evaluation standard of RCCD safety coefficient based on FEM is put forward using least squares support vector machines (LSSVM and particle swarm optimization (PSO. The proposed method is applied to safety coefficient analysis of the Longtan RCCD in China. The calculation shows that RCCD failure is closely related to RCCD interface strength, and the Longtan RCCD is safe in the design condition. Considering RCCD failure characteristic and combining the advantages of several excellent algorithms, the proposed method determines the evaluation standard for safety coefficient of RCCD based on FEM for the first time and can be popularized to any RCCD.
Sibonga, J. D.; Feiveson, A. H.
2014-01-01
This work was accomplished in support of the Finite Element [FE] Strength Task Group, NASA Johnson Space Center [JSC], Houston, TX. This group was charged with the task of developing rules for using finite-element [FE] bone-strength measures to construct operating bands for bone health that are relevant to astronauts following exposure to spaceflight. FE modeling is a computational tool used by engineers to estimate the failure loads of complex structures. Recently, some engineers have used this tool to characterize the failure loads of the hip in population studies that also monitored fracture outcomes. A Directed Research Task was authorized in July, 2012 to investigate FE data from these population studies to derive these proposed standards of bone health as a function of age and gender. The proposed standards make use of an FE-based index that integrates multiple contributors to bone strength, an expanded evaluation that is critical after an astronaut is exposed to spaceflight. The current index of bone health used by NASA is the measurement of areal BMD. There was a concern voiced by a research and clinical advisory panel that the sole use of areal BMD would be insufficient to fully evaluate the effects of spaceflight on the hip. Hence, NASA may not have a full understanding of fracture risk, both during and after a mission, and may be poorly estimating in-flight countermeasure efficacy. The FE Strength Task Group - composed of principal investigators of the aforementioned population studies and of FE modelers -donated some of its population QCT data to estimate of hip bone strength by FE modeling for this specific purpose. Consequently, Human Health Countermeasures [HHC] has compiled a dataset of FE hip strengths, generated by a single FE modeling approach, from human subjects (approx.1060) with ages covering the age range of the astronauts. The dataset has been analyzed to generate a set of FE strength cutoffs for the following scenarios: a) Qualify an
Energy Technology Data Exchange (ETDEWEB)
Batalin, Igor A. [P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Pedagogical University, Tomsk (Russian Federation); Bering, Klaus [Masaryk University, Faculty of Science, Brno (Czech Republic); Lavrov, Peter M. [Tomsk State Pedagogical University, Tomsk (Russian Federation); National Research Tomsk State University, Tomsk (Russian Federation)
2016-03-15
Finite BRST-BV transformations are studied systematically within the W-X formulation of the standard and the Sp(2)-extended field-antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie equations. The corresponding finite change of the gauge-fixing master action X and the corresponding Ward identity are derived. (orig.)
Watanabe, Takao; Stoorvogel, Antonie Arij
2001-01-01
A relation between the finite zero structure of the plant and the standard $H_\\infty$ controller was studied. The mechanism was also investigated using the ARE-based $H_\\infty$ controller that is represented by a free parameter. It was observed that the mechanism of the controller reduction is
Solving the incompressible surface Navier-Stokes equation by surface finite elements
Reuther, Sebastian; Voigt, Axel
2018-01-01
We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.
Free breathing whole-heart 3D CINE MRI with self-gated Cartesian trajectory.
Usman, M; Ruijsink, B; Nazir, M S; Cruz, G; Prieto, C
2017-05-01
To present a method that uses a novel free-running self-gated acquisition to achieve isotropic resolution in whole heart 3D Cartesian cardiac CINE MRI. 3D cardiac CINE MRI using navigator gating results in long acquisition times. Recently, several frameworks based on self-gated non-Cartesian trajectories have been proposed to accelerate this acquisition. However, non-Cartesian reconstructions are computationally expensive due to gridding, particularly in 3D. In this work, we propose a novel highly efficient self-gated Cartesian approach for 3D cardiac CINE MRI. Acquisition is performed using CArtesian trajectory with Spiral PRofile ordering and Tiny golden angle step for eddy current reduction (so called here CASPR-Tiger). Data is acquired continuously under free breathing (retrospective ECG gating, no preparation pulses interruption) for 4-5min and 4D whole-heart volumes (3D+cardiac phases) with isotropic spatial resolution are reconstructed from all available data using a soft gating technique combined with temporal total variation (TV) constrained iterative SENSE reconstruction. For data acquired on eight healthy subjects and three patients, the reconstructed images using the proposed method had good contrast and spatio-temporal variations, correctly recovering diastolic and systolic cardiac phases. Non-significant differences (P>0.05) were observed in cardiac functional measurements obtained with proposed 3D approach and gold standard 2D multi-slice breath-hold acquisition. The proposed approach enables isotropic 3D whole heart Cartesian cardiac CINE MRI in 4 to 5min free breathing acquisition. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
Explicitly computing geodetic coordinates from Cartesian coordinates
Zeng, Huaien
2013-04-01
This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.
An adaptive Cartesian control scheme for manipulators
Seraji, H.
1987-01-01
A adaptive control scheme for direct control of manipulator end-effectors to achieve trajectory tracking in Cartesian space is developed. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for online implementation with high sampling rates.
Predoi, Mihai Valentin
2014-09-01
The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.
Cartesian anisotropic mesh adaptation for compressible flow
International Nuclear Information System (INIS)
Keats, W.A.; Lien, F.-S.
2004-01-01
Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This paper discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for compressible flow. This technique, developed for laminar flow by Ham, Lien and Strong, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this paper the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. The convection scheme used is the Advective Upstream Splitting Method (Plus), and the refinement/ coarsening criteria are based on work done by Ham et al. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant. (author)
Kim, Seungil
2010-01-01
In this paper, we study the spectrum of the operator which results when the Perfectly Matched Layer (PML) is applied in Cartesian geometry to the Laplacian on an unbounded domain. This is often thought of as a complex change of variables or "complex stretching." The reason that such an operator is of interest is that it can be used to provide a very effective domain truncation approach for approximating acoustic scattering problems posed on unbounded domains. Stretching associated with polar or spherical geometry lead to constant coefficient operators outside of a bounded transition layer and so even though they are on unbounded domains, they (and their numerical approximations) can be analyzed by more standard compact perturbation arguments. In contrast, operators associated with Cartesian stretching are non-constant in unbounded regions and hence cannot be analyzed via a compact perturbation approach. Alternatively, to show that the scattering problem PML operator associated with Cartesian geometry is stable for real nonzero wave numbers, we show that the essential spectrum of the higher order part only intersects the real axis at the origin. This enables us to conclude stability of the PML scattering problem from a uniqueness result given in a subsequent publication. © 2009 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Rek Václav
2016-11-01
Full Text Available In this paper, the form of modifications of the existing sequential code written in C or C++ programming language for the calculation of various kind of structures using the explicit form of the Finite Element Method (Dynamic Relaxation Method, Explicit Dynamics in the NEXX system is introduced. The NEXX system is the core of engineering software NEXIS, Scia Engineer, RFEM and RENEX. It has the possibilities of multithreaded running, which can now be supported at the level of native C++ programming language using standard libraries. Thanks to the high degree of abstraction that a contemporary C++ programming language provides, a respective library created in this way can be very generalized for other purposes of usage of parallelism in computational mechanics.
Analysis of a Cartesian PML approximation to acoustic scattering problems in and
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.
Standard Model CP-violation and baryon asymmetry; 2, finite temperature
Gavela-Legazpi, Maria Belen; Orloff, J; Pène, O; Quimbay, C
1994-01-01
We consider the scattering of quasi-particles off the boundary created during a first order electroweak phase transition. Spatial coherence is lost due to the quasi-quark damping rate, and we show that reflection on the boundary is suppressed, even at tree-level. Simply on CP considerations, we argue against electroweak baryogenesis in the Standard Model via the charge transport mechanism. A CP asymmetry is produced in the reflection properties of quarks and antiquarks hitting the phase boundary. An effect is present at order \\alpha_W^2 in rate and a regular GIM behaviour is found, which can be expressed in terms of two unitarity triangles. A crucial role is played by the damping rate of quasi-particles in a hot plasma, which is a relevant scale together with M_W and the temperature. The effect is many orders of magnitude below what observation requires.
Non-Cartesian MRI scan time reduction through sparse sampling
Wajer, F.T.A.W.
2001-01-01
Non-Cartesian MRI Scan-Time Reduction through Sparse Sampling Magnetic resonance imaging (MRI) signals are measured in the Fourier domain, also called k-space. Samples of the MRI signal can not be taken at will, but lie along k-space trajectories determined by the magnetic field gradients. MRI
High-order discrete ordinate transport in non-conforming 2D Cartesian meshes
International Nuclear Information System (INIS)
Gastaldo, L.; Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J. M.
2009-01-01
We present in this paper a numerical scheme for solving the time-independent first-order form of the Boltzmann equation in non-conforming 2D Cartesian meshes. The flux solution technique used here is the discrete ordinate method and the spatial discretization is based on discontinuous finite elements. In order to have p-refinement capability, we have chosen a hierarchical polynomial basis based on Legendre polynomials. The h-refinement capability is also available and the element interface treatment has been simplified by the use of special functions decomposed over the mesh entities of an element. The comparison to a classical S N method using the Diamond Differencing scheme as spatial approximation confirms the good behaviour of the method. (authors)
A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
Johansen, Hans; Colella, Phillip
1998-11-01
We present a numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. We treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservative differencing of second-order accurate fluxes on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multigrid iterations with a simple point relaxation strategy. We have combined this with an adaptive mesh refinement (AMR) procedure. We provide evidence that the algorithm is second-order accurate on various exact solutions and compare the adaptive and nonadaptive calculations.
International Nuclear Information System (INIS)
Crevoisier, D.; Voltz, M.; Chanzy, A.
2009-01-01
Ross [Ross PJ. Modeling soil water and solute transport - fast, simplified numerical solutions. Agron J 2003;95:1352-61] developed a fast, simplified method for solving Richards' equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins: 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions. The Ross method is compared with the standard finite element model, Hydrus-1D [Simunek J, Sejna M, Van Genuchten MTh. The HYDRUS-1D and HYDRUS-2D codes for estimating unsaturated soil hydraulic and solutes transport parameters. Agron Abstr 357; 1999]. Computing time, accuracy of results and robustness of numerical schemes are monitored in 1D simulations involving different types of homogeneous soils, grids and hydrological conditions. The Ross method associated with modified Van Genuchten hydraulic functions [Vogel T, Cislerova M. On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport Porous Media 1988:3:1-15] proves in every tested scenario to be more robust numerically, and the compromise of computing time/accuracy is seen to be particularly improved on coarse grids. Ross method run from 1.25 to 14 times faster than Hydrus-1D. (authors)
International Nuclear Information System (INIS)
Scheurich, H.
1986-01-01
From the projective Dirac equation in a six-dimensional Kleinian space R(3, 3) are derived finite-rotation-group models as self-interaction models of virtual leptons and quarks. The quaternion group underlying them is considered as a substructure group of projective spacetime. A finite hyperspherical carrier of the self-interaction models is embedded into projective spacetime by means of the Planck length L 0 = (hG/c 3 )/sup 1/2/ as a physical unit length. The corresponding modification of metrics in the Planck domain becomes apparent to be equivalent to the role of the Higgs field in the electroweak GWS standard model. (author)
The Thickness of Amalgamations and Cartesian Product of Graphs
Directory of Open Access Journals (Sweden)
Yang Yan
2017-08-01
Full Text Available The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n.
The Louvain printers and the establishment of the Cartesian curriculum
Directory of Open Access Journals (Sweden)
Geert Vanpaemel
2012-03-01
Full Text Available With regard to the public circulation of knowledge, universities are often regarded as privileged institutions where information and ideas are formally transmitted through regulated didactic experiences. University life, however, provided a more complex environment in which various parallel and perhaps contradictory processes of transmission were at work. In this paper, we analyse a set of 55 engravings with scientific images, which started to appear around 1670 in student notebooks at the University of Louvain. These engravings, produced and sold by the Louvain printers Michael Hayé and Lambert Blendeff, were related to the philosophy curriculum of the Faculty of Arts but did not correspond entirely to the actual topics or doctrine taught. In fact, the obvious Cartesian orientation of the images was not in line with the more prudent position of the Faculty. This paper offers a preliminary analysis of the set of engravings and their role in the Cartesian reforms at Louvain.
Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces
Yukawa, Masahiro
2014-01-01
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed to contain multiple components such as (i) linear and nonlinear components, (ii) high- and low- frequency components etc. In this case, the use of multiple RKHSs permits a compact representation of multicomponent functions. The proposed algorithm is where t...
Naturalism and un-naturalism among the Cartesian physicians
Manning, Gideon
2008-01-01
Highlighting early modern medicine's program of explanation and intervention, I claim that there are two distinctive features of the physician's naturalism. These are, first, an explicit recognition that each patient had her own individual and highly particularized nature and, second, a self-conscious use of normative descriptions when characterizing a patient's nature as healthy (ordered) or unhealthy (disordered). I go on to maintain that in spite of the well documented Cartesian rejection ...
Development of a Cartesian grid based CFD solver (CARBS)
International Nuclear Information System (INIS)
Vaidya, A.M.; Maheshwari, N.K.; Vijayan, P.K.
2013-12-01
Formulation for 3D transient incompressible CFD solver is developed. The solution of variable property, laminar/turbulent, steady/unsteady, single/multi specie, incompressible with heat transfer in complex geometry will be obtained. The formulation can handle a flow system in which any number of arbitrarily shaped solid and fluid regions are present. The solver is based on the use of Cartesian grids. A method is proposed to handle complex shaped objects and boundaries on Cartesian grids. Implementation of multi-material, different types of boundary conditions, thermo physical properties is also considered. The proposed method is validated by solving two test cases. 1 st test case is that of lid driven flow in inclined cavity. 2 nd test case is the flow over cylinder. The 1 st test case involved steady internal flow subjected to WALL boundaries. The 2 nd test case involved unsteady external flow subjected to INLET, OUTLET and FREE-SLIP boundary types. In both the test cases, non-orthogonal geometry was involved. It was found that, under such a wide conditions, the Cartesian grid based code was found to give results which were matching well with benchmark data. Convergence characteristics are excellent. In all cases, the mass residue was converged to 1E-8. Based on this, development of 3D general purpose code based on the proposed approach can be taken up. (author)
Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.
Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H
2013-05-01
In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction. Copyright © 2012 Wiley Periodicals, Inc.
Hegel's Solution to Cartesian Dualism of Mind and Body
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Farzad
2015-10-01
Full Text Available In this paper, I am going to review the Hegelian solution to solve Cartesian doctrine of the mind body dualism. Such a dichotomy refers to the fact that in the recognition we are dealing with two completely different and separate domains, i.e., the internal world (ideas, beliefs, concepts, and mentalities, and the external world (the domain of objects that which refers to the first domain. Hegel believes that Cartesian dualism arises from a categorical mistake. He says that subjectivism is the starting point that fundamentally is wrong. Hegel argues that a genuine philosophy could overcome the dichotomy. According to Hegel, it is only by the idea of "absolute" and “identity in differences” that could be possible to go out of this dualism. The role of philosophy, for him, is theorizing "about the real world”. Hegel says that these contradictions are within the "structure of consciousness." By adopting the right approach in explaining Cartesian doctrine of the mind body dualism from a phenomenological perspective, it can be possible to show the mind’s Odyssey within reality.
Finite-volume scheme for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: bramiozo@gmail.com [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands)
2016-02-01
In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.
Single-breath-hold 3-D CINE imaging of the left ventricle using Cartesian sampling.
Wetzl, Jens; Schmidt, Michaela; Pontana, François; Longère, Benjamin; Lugauer, Felix; Maier, Andreas; Hornegger, Joachim; Forman, Christoph
2018-02-01
Our objectives were to evaluate a single-breath-hold approach for Cartesian 3-D CINE imaging of the left ventricle with a nearly isotropic resolution of [Formula: see text] and a breath-hold duration of [Formula: see text]19 s against a standard stack of 2-D CINE slices acquired in multiple breath-holds. Validation is performed with data sets from ten healthy volunteers. A Cartesian sampling pattern based on the spiral phyllotaxis and a compressed sensing reconstruction method are proposed to allow 3-D CINE imaging with high acceleration factors. The fully integrated reconstruction uses multiple graphics processing units to speed up the reconstruction. The 2-D CINE and 3-D CINE are compared based on ventricular function parameters, contrast-to-noise ratio and edge sharpness measurements. Visual comparisons of corresponding short-axis slices of 2-D and 3-D CINE show an excellent match, while 3-D CINE also allows reformatting to other orientations. Ventricular function parameters do not significantly differ from values based on 2-D CINE imaging. Reconstruction times are below 4 min. We demonstrate single-breath-hold 3-D CINE imaging in volunteers and three example patient cases, which features fast reconstruction and allows reformatting to arbitrary orientations.
A finite difference method for free boundary problems
Fornberg, Bengt
2010-01-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax
ψ -ontology result without the Cartesian product assumption
Myrvold, Wayne C.
2018-05-01
We introduce a weakening of the preparation independence postulate of Pusey et al. [Nat. Phys. 8, 475 (2012), 10.1038/nphys2309] that does not presuppose that the space of ontic states resulting from a product-state preparation can be represented by the Cartesian product of subsystem state spaces. On the basis of this weakened assumption, it is shown that, in any model that reproduces the quantum probabilities, any pair of pure quantum states |ψ >,|ϕ > with ≤1 /√{2 } must be ontologically distinct.
Cartesian oval representation of freeform optics in illumination systems.
Michaelis, D; Schreiber, P; Bräuer, A
2011-03-15
The geometrical method for constructing optical surfaces for illumination purpose developed by Oliker and co-workers [Trends in Nonlinear Analysis (Springer, 2003)] is generalized in order to obtain freeform designs in arbitrary optical systems. The freeform is created by a set of primitive surface elements, which are generalized Cartesian ovals adapted to the given optical system. Those primitives are determined by Hamiltonian theory of ray optics. The potential of this approach is demonstrated by some examples, e.g., freeform lenses with collimating front elements.
Connection between Fourier coefficient and Discretized Cartesian path integration
International Nuclear Information System (INIS)
Coalson, R.D.
1986-01-01
The relationship between so-called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier-like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on-diagonal statistical density matrix elements for a number of prototypical 1-d potentials. A consistent convergence order among these prescriptions is established
Application of finite Fourier transformation for the solution of the diffusion equation
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1991-01-01
The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)
Energy Technology Data Exchange (ETDEWEB)
Zanette, Rodrigo; Petersen, Caudio Zen [Univ. Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcello [Univ. Federal de Pelotas (Brazil). Centro de Engenharias; Zabadal, Jorge Rodolfo [Univ. Federal do Rio Grande do Sul, Tramandai (Brazil)
2017-05-15
In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.
Finite-volume discretizations and immersed boundaries
Y.J. Hassen (Yunus); B. Koren (Barry)
2009-01-01
htmlabstractIn this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed `Cartesian' grid. The essence of the present method
Finite-volume discretizations and immersed boundaries
Y.J. Hassen (Yunus); B. Koren (Barry)
2010-01-01
textabstractIn this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is
Study guide for applied finite mathematics
Macri, Nicholas A
1982-01-01
Study Guide for Applied Finite Mathematics, Third Edition is a study guide that introduces beginners to the fundamentals of finite mathematics and its various realistic and relevant applications. Some applications of probability, game theory, and Markov chains are given. Each chapter includes exercises, and each set begins with basic computational ""drill"" problems and then progresses to problems with more substance.Comprised of 10 chapters, this book begins with exercises related to set theory and concepts such as the union and intersection of sets. Exercises on Cartesian coordinate
International Nuclear Information System (INIS)
Palmiotti, G.; Carrico, C.B.; Lewis, E.E.
1995-10-01
The theoretical basis, implementation information and numerical results are presented for VARIANT (VARIational Anisotropic Neutron Transport), a FORTRAN module of the DIF3D code system at Argonne National Laboratory. VARIANT employs the variational nodal method to solve multigroup steady-state neutron diffusion and transport problems. The variational nodal method is a hybrid finite element method that guarantees nodal balance and permits spatial refinement through the use of hierarchical complete polynomial trial functions. Angular variables are expanded with complete or simplified P 1 , P 3 or P 5 5 spherical harmonics approximations with full anisotropic scattering capability. Nodal response matrices are obtained, and the within-group equations are solved by red-black or four-color iteration, accelerated by a partitioned matrix algorithm. Fission source and upscatter iterations strategies follow those of DIF3D. Two- and three-dimensional Cartesian and hexagonal geometries are implemented. Forward and adjoint eigenvalue, fixed source, gamma heating, and criticality (concentration) search problems may be performed
Direct adaptive control of manipulators in Cartesian space
Seraji, H.
1987-01-01
A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.
Consent: a Cartesian ideal? Human neural transplantation in Parkinson's disease.
Lopes, Manuel; Meningaud, Jean-Paul; Behin, Anthony; Hervé, Christian
2003-01-01
The grafting of human embryonic cells in Parkinson's disease is an innovative and hopefully useful therapeutic approach. However, it still concerns a very small number of patients and is only suggested as a research protocol. We present here a study of the problems of information and consent to research within the framework of this disease in which the efficacy of medical treatment is shortlived. The only French center to use this treatment (Hôpital H. Mondor in Créteil) has received authorization from the Comité Consultatif National d'Ethique (Consultative National Committee on Ethics). Eleven patients were treated between 1991 and 1998. The study of the results of a questionnaire sent to those patients showed the difficulties met in evaluating the perception of information despite intact intellectual capacities in people "prepared to risk everything." In France, the duty to inform patients during research procedures is regulated by the Huriet Act. However, it is not easy to guarantee genuine consent when preliminary information is given to patients psychologically impaired by the slow and ineluctable course of their disease. In these borderline cases, a valid consent seems to be a myth in terms of pure autonomy when considered with the Cartesian aim of elimination of uncertainty. The relevance of this concept of genuine consent probably makes more sense as aiming at a Cartesian ideal which is perhaps more in the spirit rather than in the letter. It is in that same spirit that, from the outset, we propose to define t he practical ways of answering the patients' request for information, even sometimes after consent has been given.
A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity
Energy Technology Data Exchange (ETDEWEB)
Thornburg, Jonathan [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany)
2004-01-21
In 3 + 1 numerical simulations of dynamic black-hole spacetimes, it is useful to be able to find the apparent horizon(s) (AH) in each slice of a time evolution. A number of AH finders are available, but they often take many minutes to run, so they are too slow to be practically usable at each time step. Here I present a new AH finder, AHFINDERDIRECT, which is very fast and accurate: at typical resolutions it takes only a few seconds to find an AH {approx} 10{sup -5}m accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlkoerper ('star-shaped region') with respect to some local origin, and so parametrize the AH shape by r = h(angle) for some single-valued function h:S{sup 2} {yields} R{sup 2}. The AH equation then becomes a nonlinear elliptic PDE in h on S{sup 2}, whose coefficients are algebraic functions of g{sub ij}, K{sub ij}, and the Cartesian-coordinate spatial derivatives of g{sub ij}. I discretize S{sup 2} using six angular patches (one each in the neighbourhood of the {+-}x, {+-} y, and {+-}z axes) to avoid coordinate singularities, and finite difference the AH equation in the angular coordinates using fourth-order finite differencing. I solve the resulting system of nonlinear algebraic equations (for h at the angular grid points) by Newton's method, using a 'symbolic differentiation' technique to compute the Jacobian matrix. AHFINDERDIRECT is implemented as a thorn in the CACTUS computational toolkit, and is freely available by anonymous CVS checkout.
Directory of Open Access Journals (Sweden)
Serkan Dundar
2016-01-01
Full Text Available The aim of this study was to examine the stress distributions with three different loads in two different geometric and threaded types of dental implants by finite element analysis. For this purpose, two different implant models, Nobel Replace and Nobel Active (Nobel Biocare, Zurich, Switzerland, which are currently used in clinical cases, were constructed by using ANSYS Workbench 12.1. The stress distributions on components of the implant system under three different static loadings were analysed for the two models. The maximum stress values that occurred in all components were observed in FIII (300 N. The maximum stress values occurred in FIII (300 N when the Nobel Replace implant is used, whereas the lowest ones, in the case of FI (150 N loading in the Nobel Active implant. In all models, the maximum tensions were observed to be in the neck region of the implants. Increasing the connection between the implant and the bone surface may allow more uniform distribution of the forces of the dental implant and may protect the bone around the implant. Thus, the implant could remain in the mouth for longer periods. Variable-thread tapered implants can increase the implant and bone contact.
Anderson, Christian E; Wang, Charlie Y; Gu, Yuning; Darrah, Rebecca; Griswold, Mark A; Yu, Xin; Flask, Chris A
2018-04-01
The regularly incremented phase encoding-magnetic resonance fingerprinting (RIPE-MRF) method is introduced to limit the sensitivity of preclinical MRF assessments to pulsatile and respiratory motion artifacts. As compared to previously reported standard Cartesian-MRF methods (SC-MRF), the proposed RIPE-MRF method uses a modified Cartesian trajectory that varies the acquired phase-encoding line within each dynamic MRF dataset. Phantoms and mice were scanned without gating or triggering on a 7T preclinical MRI scanner using the RIPE-MRF and SC-MRF methods. In vitro phantom longitudinal relaxation time (T 1 ) and transverse relaxation time (T 2 ) measurements, as well as in vivo liver assessments of artifact-to-noise ratio (ANR) and MRF-based T 1 and T 2 mean and standard deviation, were compared between the two methods (n = 5). RIPE-MRF showed significant ANR reductions in regions of pulsatility (P Reson Med 79:2176-2182, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Tolerating Correlated Failures for Generalized Cartesian Distributions via Bipartite Matching
International Nuclear Information System (INIS)
Ali, Nawab; Krishnamoorthy, Sriram; Halappanavar, Mahantesh; Daily, Jeffrey A.
2011-01-01
Faults are expected to play an increasingly important role in how algorithms and applications are designed to run on future extreme-scale systems. A key ingredient of any approach to fault tolerance is effective support for fault tolerant data storage. A typical application execution consists of phases in which certain data structures are modified while others are read-only. Often, read-only data structures constitute a large fraction of total memory consumed. Fault tolerance for read-only data can be ensured through the use of checksums or parities, without resorting to expensive in-memory duplication or checkpointing to secondary storage. In this paper, we present a graph-matching approach to compute and store parity data for read-only matrices that are compatible with fault tolerant linear algebra (FTLA). Typical approaches only support blocked data distributions with each process holding one block with the parity located on additional processes. The matrices are assumed to be blocked by a cartesian grid with each block assigned to a process. We consider a generalized distribution in which each process can be assigned arbitrary blocks. We also account for the fact that multiple processes might be part of the same failure unit, say an SMP node. The flexibility enabled by our novel application of graph matching extends fault tolerance support to data distributions beyond those supported by prior work. We evaluate the matching implementations and cost to compute the parity and recover lost data, demonstrating the low overhead incurred by our approach.
Shared memory parallelism for 3D cartesian discrete ordinates solver
International Nuclear Information System (INIS)
Moustafa, S.; Dutka-Malen, I.; Plagne, L.; Poncot, A.; Ramet, P.
2013-01-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multi-core + SIMD - Single Instruction on Multiple Data) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46*10 6 spatial cells and 1*10 12 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40.74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool. (authors)
Solus Secedo and Sapere Aude: Cartesian Meditation as Kantian Enlightenment
Directory of Open Access Journals (Sweden)
Suma Rajiva
2015-11-01
Full Text Available Recently Samuel Fleischacker has developed Kant’s model of enlightenment as a “minimalist enlightenment” in the tradition of a relatively thin proceduralism focused on the form of public debate and interaction. I want to discuss the possibility that such a minimalism, endorsed by Fleischacker, Habermas, Rawls, and others, benefits from a metaphysics of critical individual subjectivity as a prerequisite for the social proceduralism of the minimalist enlightenment. I argue that Kant’s enlightenment, metaphysically thicker than much contemporary proceduralism, constitutes a recovery and transformation of a subjective interiority deeply Cartesian in spirit and central to the reciprocity of the community of subjects in What is Enlightenment. This opens a space for a site of resistance to the social. Descartes’ solus secedo describes the analogical space of such a resistance for Kant’s sapere aude. The Meditations thus point forward implicitly to how a rational subject might achieve critical distance from tradition in its various forms, epistemic, ethical, moral, and political.
High-Reynolds Number Viscous Flow Simulations on Embedded-Boundary Cartesian Grids
2016-05-05
AFRL-AFOSR-VA-TR-2016-0192 High- Reynolds Number Viscous Flow Simulations on Embedded-Boundary Cartesian Grids Marsha Berger NEW YORK UNIVERSITY Final...TO THE ABOVE ORGANIZATION. 1. REPORT DATE (DD-MM-YYYY) 30/04/2016 2. REPORT TYPE Final 3. DATES COVERED (From - To) High- Reynolds 4. TITLE AND...SUBTITLE High- Reynolds Number Viscous Flow Simulations on Embedded-Boundary Cartesian Grids 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-13-1
On the research of flow around obstacle using the viscous Cartesian grid technique
Directory of Open Access Journals (Sweden)
Liu Yan-Hua
2012-01-01
Full Text Available A new 2-D viscous Cartesian grid is proposed in current research. It is a combination of the existent body-fitted grid and Cartesian grid technology. On the interface of the two different type of grid, a fined triangular mesh is used to connect the two grids. Tests with flow around the cylinder and aerofoil NACA0012 show that the proposed scheme is easy for implement with high accuracy.
Directory of Open Access Journals (Sweden)
S. Knitel
2016-12-01
Full Text Available A new inverse method was developed to derive the plastic flow properties of non-standard disk tensile specimens, which were so designed to fit irradiation rods used for spallation irradiations in SINQ (Schweizer Spallations Neutronen Quelle target at Paul Scherrer Institute. The inverse method, which makes use of MATLAB and the finite element code ABAQUS, is based upon the reconstruction of the load-displacement curve by a succession of connected small linear segments. To do so, the experimental engineering stress/strain curve is divided into an elastic and a plastic section, and the plastic section is further divided into small segments. Each segment is then used to determine an associated pair of true stress/plastic strain values, representing the constitutive behavior. The main advantage of the method is that it does not rely on a hypothetic analytical expression of the constitutive behavior. To account for the stress/strain gradients that develop in the non-standard specimen, the stress and strain were weighted over the volume of the deforming elements. The method was validated with tensile tests carried out at room temperature on non-standard flat disk tensile specimens as well as on standard cylindrical specimens made of the reduced-activation tempered martensitic steel Eurofer97. While both specimen geometries presented a significant difference in terms of deformation localization during necking, the same true stress/strain curve was deduced from the inverse method. The potential and usefulness of the inverse method is outlined for irradiated materials that suffer from a large uniform elongation reduction.
Multiscale geometric modeling of macromolecules I: Cartesian representation
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2014-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Multiscale geometric modeling of macromolecules I: Cartesian representation
Energy Technology Data Exchange (ETDEWEB)
Xia, Kelin [Department of Mathematics, Michigan State University, MI 48824 (United States); Feng, Xin [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Chen, Zhan [Department of Mathematics, Michigan State University, MI 48824 (United States); Tong, Yiying [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Mathematics, Michigan State University, MI 48824 (United States); Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824 (United States)
2014-01-15
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
A finite difference method for free boundary problems
Fornberg, Bengt
2010-04-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Barros, R.C.; Filho, H.A.; Oliveira, F.B.S.; Silva, F.C. da
2004-01-01
Presented here are the advances in spectral nodal methods for discrete ordinates (SN) eigenvalue problems in Cartesian geometry. These coarse-mesh methods are based on three ingredients: (i) the use of the standard discretized spatial balance SN equations; (ii) the use of the non-standard spectral diamond (SD) auxiliary equations in the multiplying regions of the domain, e.g. fuel assemblies; and (iii) the use of the non-standard spectral Green's function (SGF) auxiliary equations in the non-multiplying regions of the domain, e.g., the reflector. In slab-geometry the hybrid SD-SGF method generates numerical results that are completely free of spatial truncation errors. In X,Y-geometry, we obtain a system of two 'slab-geometry' SN equations for the node-edge average angular fluxes by transverse-integrating the X,Y-geometry SN equations separately in the y- and then in the x-directions within an arbitrary node of the spatial grid set up on the domain. In this paper, we approximate the transverse leakage terms by constants. These are the only approximations considered in the SD-SGF-constant nodal method, as the source terms, that include scattering and eventually fission events, are treated exactly. Moreover, we describe in this paper the progress of the approximate SN albedo boundary conditions for substituting the non-multiplying regions around the nuclear reactor core. We show numerical results to typical model problems to illustrate the accuracy of spectral nodal methods for coarse-mesh SN criticality calculations. (Author)
LES of Internal Combustion Engine Flows Using Cartesian Overset Grids
Directory of Open Access Journals (Sweden)
Falkenstein Tobias
2017-11-01
Full Text Available Accurate computations of turbulent flows using the Large-Eddy Simulation (LES technique with an appropriate SubFilter Scale (SFS model require low artificial dissipation such that the physical energy cascade process is not perturbed by numerical artifacts. To realize this in practical simulations, energy-conserving numerical schemes and high-quality computational grids are needed. If unstructured meshes are used, the latter requirement often makes grid generation for complex geometries very difficult. Structured Cartesian grids offer the advantage that uncertainties in mesh quality are reduced to choosing appropriate resolution. However, two intrinsic challenges of the structured approach are local mesh refinement and representation of complex geometries. In this work, the effectiveness of numerical methods which can be expected to reduce both drawbacks is assessed in engine flows, using a multi-physics inhouse code. The overset grid approach is utilized to arbitrarily combine grid patches of different spacing to a flow domain of complex shape during mesh generation. Walls are handled by an Immersed Boundary (IB method, which is combined with a wall function to treat underresolved boundary layers. A statistically stationary Spark Ignition (SI engine port flow is simulated at Reynolds numbers typical for engine operation. Good agreement of computed and measured integral flow quantities like overall pressure loss and tumble number is found. A comparison of simulated velocity fields to Particle Image Velocimetry (PIV measurement data concludes the validation of the enhanced numerical framework for both mean velocity and turbulent fluctuations. The performance of two SFS models, the dynamic Smagorinsky model with Lagrangian averaging along pathlines and the coherent structure model, is tested on different grids. Sensitivity of pressure loss and tumble ratio to the wall treatment and mesh refinement is presented. It is shown that increased wall
Finite element solution of two dimensional time dependent heat equation
International Nuclear Information System (INIS)
Maaz
1999-01-01
A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)
Recursive generation of Cartesian angular momentum coupling trees for SO(3)
International Nuclear Information System (INIS)
Sherborne, B.S.; Stedman, G.E.
1990-01-01
Two computer algorithms are evaluated for the reduction of angular momentum coupling trees with vector (j=1) terminals with a Cartesian choice of basis as used in nonlinear optics. Rather than employ advanced tensor algebra, both methods essentially iterate in distinct ways the basic techniques of angular momentum coupling. Turbo Pascal programs implementing these algorithms are presented and compared. The accompanying analysis integrates the Cartesian tensor approach and the diagrammatic approach to the solution of problems in nonlinear optics. The programs generate TeX files for the relevant angular momentum diagrams. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Deister, F.; Hirschel, E.H. [Univ. Stuttgart, IAG, Stuttgart (Germany); Waymel, F.; Monnoyer, F. [Univ. de Valenciennes, LME, Valenciennes (France)
2003-07-01
An automatic adaptive hybrid Cartesian grid generation and simulation system is presented together with applications. The primary computational grid is an octree Cartesian grid. A quasi-prismatic grid may be added for resolving the boundary layer region of viscous flow around the solid body. For external flow simulations the flow solver TAU from the ''deutsche zentrum fuer luft- und raumfahrt (DLR)'' is integrated in the simulation system. Coarse grids are generated automatically, which are required by the multilevel method. As an application to an internal problem the thermal and dynamic modeling of a subway station is presented. (orig.)
Random subspaces for encryption based on a private shared Cartesian frame
International Nuclear Information System (INIS)
Bartlett, Stephen D.; Hayden, Patrick; Spekkens, Robert W.
2005-01-01
A private shared Cartesian frame is a novel form of private shared correlation that allows for both private classical and quantum communication. Cryptography using a private shared Cartesian frame has the remarkable property that asymptotically, if perfect privacy is demanded, the private classical capacity is three times the private quantum capacity. We demonstrate that if the requirement for perfect privacy is relaxed, then it is possible to use the properties of random subspaces to nearly triple the private quantum capacity, almost closing the gap between the private classical and quantum capacities
Embodying Learning: Post-Cartesian Pedagogy and the Academic Study of Religion
Lelwica, Michelle Mary
2009-01-01
This paper explores the concept and practice of "embodied pedagogy" as an alternative to the Cartesian approach to knowledge that is tacitly embedded in traditional modes of teaching and learning about religion. My analysis highlights a class I co-teach that combines the study of Aikido (a Japanese martial art) with seminar-style discussions of…
Numerical Computation of a Viscous Flow around a Circular Cylinder on a Cartesian Grid
Verstappen, R.W.C.P.; Veldman, A.E.P.
2000-01-01
We introduce a novel cut-cell Cartesian grid method that preserves the spectral properties of convection and diffusion. That is, convection is discretised by a skew-symmetric operator and diffusion is approximated by a symmetric positive-definite coefficient matrix. Such a symmetry-preserving
[Odontology and the beginning of cartesianism (1673--1650) (Rene Descartes)].
Gysel, C
1979-01-01
In the seventeenth century the universities of the Netherlands underwent the influence of Descartes in all the faculties. In medicine three periods can be distinguished: in the first, pathology and therapy are still galenic; the second, by the application of the cartesian method, triumphs in physiology; and the third, corrected by the views of Newton is integrated in a moderate biomechanism.
Peano—A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids
Weinzierl, Tobias; Mehl, Miriam
2011-01-01
-dimensional Cartesian grids represented by a (k = 3)- spacetree, a generalization of the well-known octree concept, and it also shows the correctness of the approach. These grids may change their adaptive structure throughout the traversal. The algorithm uses 2d + 4
Earnest, Darrell Steven
2012-01-01
This dissertation explores fifth and eighth grade students' interpretations of three kinds of mathematical representations: number lines, the Cartesian plane, and graphs of linear functions. Two studies were conducted. In Study 1, I administered the paper-and-pencil Linear Representations Assessment (LRA) to examine students'…
"Mens Sana in Corpore Sano": Cartesian Dualism and the Marginalisation of Sex Education
Paechter, Carrie
2004-01-01
Cartesian dualism has left a heavy legacy in terms of how we think about ourselves, so that we treat humans as minds within bodies rather than mind/body unities. This has far-reaching effects on our conceptualisation of the sex/gender distinction and on the relationship between bodies and identities. Related to this is a dualism that is embedded…
Non-Cartesian Parallel Imaging Reconstruction of Undersampled IDEAL Spiral 13C CSI Data
DEFF Research Database (Denmark)
Hansen, Rie Beck; Hanson, Lars G.; Ardenkjær-Larsen, Jan Henrik
scan times based on spatial information inherent to each coil element. In this work, we explored the combination of non-cartesian parallel imaging reconstruction and spatially undersampled IDEAL spiral CSI1 acquisition for efficient encoding of multiple chemical shifts within a large FOV with high...
Solution of 3-dimensional diffusion equation by finite Fourier transformation
International Nuclear Information System (INIS)
Krishnani, P.D.
1978-01-01
Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)
Sprague, Mark W; Luczkovich, Joseph J
2016-01-01
This finite-difference time domain (FDTD) model for sound propagation in very shallow water uses pressure and velocity grids with both 3-dimensional Cartesian and 2-dimensional cylindrical implementations. Parameters, including water and sediment properties, can vary in each dimension. Steady-state and transient signals from discrete and distributed sources, such as the surface of a vibrating pile, can be used. The cylindrical implementation uses less computation but requires axial symmetry. The Cartesian implementation allows asymmetry. FDTD calculations compare well with those of a split-step parabolic equation. Applications include modeling the propagation of individual fish sounds, fish aggregation sounds, and distributed sources.
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
International Nuclear Information System (INIS)
Zhang Wen; Haas, Stephan
2009-01-01
An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in Cartesian coordinates, which is considerably simpler. Under open boundary conditions, an expression for multipole moments of point dipoles in a cell is derived. These make the program appropriate for nanomagnetic simulations, including magnetic nanoparticles and ferrofluids. The performance is optimized in terms of cell size and parameter set (expansion order and opening angle) and the trade off between computing time and accuracy is quantitatively studied. A rule of thumb is proposed to decide the appropriate average number of dipoles in the smallest cells, and an optimal choice of parameter set is suggested. Finally, the superiority of Cartesian coordinate FMM is demonstrated by comparison to spherical harmonics FMM and FFT.
A Cartesian Adaptive Level Set Method for Two-Phase Flows
Ham, F.; Young, Y.-N.
2003-01-01
In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.
Trost, Nico; Jiménez, Javier; Imke, Uwe; Sanchez, Victor
2014-06-01
TWOPORFLOW is a thermo-hydraulic code based on a porous media approach to simulate single- and two-phase flow including boiling. It is under development at the Institute for Neutron Physics and Reactor Technology (INR) at KIT. The code features a 3D transient solution of the mass, momentum and energy conservation equations for two inter-penetrating fluids with a semi-implicit continuous Eulerian type solver. The application domain of TWOPORFLOW includes the flow in standard porous media and in structured porous media such as micro-channels and cores of nuclear power plants. In the latter case, the fluid domain is coupled to a fuel rod model, describing the heat flow inside the solid structure. In this work, detailed profiling tools have been utilized to determine the optimization potential of TWOPORFLOW. As a result, bottle-necks were identified and reduced in the most feasible way, leading for instance to an optimization of the water-steam property computation. Furthermore, an OpenMP implementation addressing the routines in charge of inter-phase momentum-, energy- and mass-coupling delivered good performance together with a high scalability on shared memory architectures. In contrast to that, the approach for distributed memory systems was to solve sub-problems resulting by the decomposition of the initial Cartesian geometry. Thread communication for the sub-problem boundary updates was accomplished by the Message Passing Interface (MPI) standard.
Optimized respiratory-resolved motion-compensated 3D Cartesian coronary MR angiography.
Correia, Teresa; Ginami, Giulia; Cruz, Gastão; Neji, Radhouene; Rashid, Imran; Botnar, René M; Prieto, Claudia
2018-04-22
To develop a robust and efficient reconstruction framework that provides high-quality motion-compensated respiratory-resolved images from free-breathing 3D whole-heart Cartesian coronary magnetic resonance angiography (CMRA) acquisitions. Recently, XD-GRASP (eXtra-Dimensional Golden-angle RAdial Sparse Parallel MRI) was proposed to achieve 100% scan efficiency and provide respiratory-resolved 3D radial CMRA images by exploiting sparsity in the respiratory dimension. Here, a reconstruction framework for Cartesian CMRA imaging is proposed, which provides respiratory-resolved motion-compensated images by incorporating 2D beat-to-beat translational motion information to increase sparsity in the respiratory dimension. The motion information is extracted from interleaved image navigators and is also used to compensate for 2D translational motion within each respiratory phase. The proposed Optimized Respiratory-resolved Cartesian Coronary MR Angiography (XD-ORCCA) method was tested on 10 healthy subjects and 2 patients with cardiovascular disease, and compared against XD-GRASP. The proposed XD-ORCCA provides high-quality respiratory-resolved images, allowing clear visualization of the right and left coronary arteries, even for irregular breathing patterns. Compared with XD-GRASP, the proposed method improves the visibility and sharpness of both coronaries. Significant differences (p respiratory phases with larger motion amplitudes and subjects with irregular breathing patterns. A robust respiratory-resolved motion-compensated framework for Cartesian CMRA has been proposed and tested in healthy subjects and patients. The proposed XD-ORCCA provides high-quality images for all respiratory phases, independently of the regularity of the breathing pattern. © 2018 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.
Directory of Open Access Journals (Sweden)
Karachevtseva Larysа Mykolaivna
2013-06-01
Full Text Available The article analyses the polemics between Michel Foucault and Jacques Derrida that took place in the sixties of the 20th century. This polemics was dedicated to the elucidation of the role of reason and madness within Cartesian radical doubt – that thought experiment maintained the formula ego cogito ergo sum. The article also examines Emmanuel Levinas's interpretation of Descartes' idea of the infinite. It is shown that the idea of the infinite constitutes cogito.
Cyclones and Vortices: Alejo Carpentier's Reasons of State as Cartesian Discourse
Directory of Open Access Journals (Sweden)
Joseph F. O'Neill
1978-01-01
Full Text Available Alejo Carpentier's Reasons of State is a reconstruction of Cartesian discourse that is paradoxically both fantastic and baroque in its implications. Building upon the assumption that Cartesianism is typically baroque and therefore a dynamism, rather than a dichotomy of subject and object, the novel proceeds in the form of a retrospective deathbed narrative to suggest the radically anti-Cartesian polarization of subject and object in fin de siècle Latin America by portraying its dictator/narrator as a man whose world-view, like his culture's, is schizophrenically divided between magical realism and positivist progressivism. This ambiguous narrative perception is comparable to that of the literary genre known as the fantastic, whose several subjective themes are found to be operative in Reasons of State . Their working-out in the novel, however, is not exclusively psychological or socio-psychological. Ultimately they assume in the narrator's retrospective reflections a metaphorical character that effects a paradoxical synthesis of the prevailing opposed epistemologies: a self-aware folk consciousness that, in its dependence upon contradiction, is indisputably baroque.
Many-particle hydrodynamic interactions in parallel-wall geometry: Cartesian-representation method
International Nuclear Information System (INIS)
Blawzdziewicz, J.; Wajnryb, E.; Bhattacharya, S.
2005-01-01
This talk will describe the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose an efficient algorithm for evaluating many-particle friction matrix in this system-no Stokesian-dynamics algorithm of this kind has been available so far. Our approach involves expanding the fluid velocity field in the wall-bounded suspension into spherical and Cartesian fundamental sets of Stokes flows. The spherical set is used to describe the interaction of the fluid with the particles and the Cartesian set to describe the interaction with the walls. At the core of our method are transformation relations between the spherical and Cartesian fundamental sets. Using the transformation formulas, we derive a system of linear equations for the force multipoles induced on the particle surfaces; the coefficients in these equations are given in terms of lateral Fourier integrals corresponding to the directions parallel to the walls. The force-multipole equations have been implemented in a numerical algorithm for the evaluation of the multiparticle friction matrix in the wall-bounded system. The algorithm involves subtraction of the particle-wall and particle-particle lubrication contributions to accelerate the convergence of the results with the spherical-harmonics order, and a subtraction of the single-wall contributions to accelerate the convergence of the Fourier integrals. (author)
Spatial pattern of Amazonian timber species using cartesian and spatial coordinates method
Directory of Open Access Journals (Sweden)
Tiago Monteiro Condé
2016-06-01
Full Text Available Geographic information system (GIS applied to forest analysis permit the recognition and analysis of spatial patterns of species in two and three dimensional. The aim of this study to demonstrate the efficiency of cartesian and spatial coordinates method (MCCE, method of correcting UTM coordinates of trees location in accordance with the location of field or Cartesian (X ,Y, combined with natural neighbor index (ANND in recognition and analysis of spatial distribution patterns of four commercial timber species in forest management in Caracaraí, Roraima State, Brazil. Simulations were performed on 9 ha, divided into 100 plots of 100 m2 each. Collected data were DBH > 10 cm, commercial and total heights, cartesian coordinates (X,Y and spatial coordinates (UTM. Random spatial patterns were observed in Eschweilera bracteosa and Manilkara huberi. The dispersed and rare spatial patterns were observed in Dinizia excelsa and Cedrelinga cateniformis. MCCE proved to be an efficient method in the recognition and analysis of spatial patterns of native species from Amazon rain forest, as forest planning becomes easier by 2D and 3D simulations.
International Nuclear Information System (INIS)
Wu Hongchun; Xie Zhongsheng; Zhu Xuehua
1994-01-01
The nodal discrete-ordinate transport calculating model of anisotropy scattering problem in three-dimensional cartesian geometry is given. The computing code NOTRAN/3D has been encoded and the satisfied conclusion is gained
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.
Directory of Open Access Journals (Sweden)
Monica Fernandes Abreu
2010-09-01
Full Text Available Esta reflexão pretende mostrar o discurso racional cartesiano na segunda prova da existência de Deus. Para tanto, Descartes se depara com uma pergunta central: qual a causa da existência da res cogitans que é finita e possui a ideia de infinito? A resposta é encontrada na desproporcionalidade ontológica entre o finito e o infinito. Essa desproporcionalidade é elucidada mediante dois conceitos: o princípio de causalidade que determina que a causa deve ser igual ou superior a coisa causada e o princípio de criação contínua em que a causa que criou o ser não é menor do que aquela que o conserva em sua existência. As objeções destacadas no texto contra os argumentos cartesianos foram escolhas deliberadas que servem para elucidar a importância da racionalidade como fundamento para a prova da existência de Deus. A relação entre o entendimento e a liberdade, apresentada no texto sucintamente, justifica a impossibilidade da res cogitans ser causa de si mesma.Palavras-chave: Infinito; finito; causalidade; criação contínua AbstractThis essay aims to show the rational Cartesian discourse on the second proof of God’s existence. In order to do so, Descartes faces a core question: which is the cause for the existence of the res cogitans that is finite in front of the idea of the infinite? The answer is found in the ontological disproportionality between the finite and the infinite. This disproportionality is elucidated through a couple crucial concepts: the principle of causality, which determines that the cause must be equal or superior to the caused thing and the principle of continuous creation, in which the cause that created the being is not inferior than the one that preserves its existence. The objections highlighted in the text against the Cartesian arguments were deliberated choices, to elucidate the relevance of rationality as the foundation for the proof of God’s existence. The relation between the understanding
An analytic interface dynamo over a shear layer of finite depth
Petrovay, K.; Kerekes, A.; Erdélyi, R.
2010-01-01
Parker's analytic Cartesian interface dynamo is generalized to the case of a shear layer of finite thickness and low resistivity ("tachocline"), bounded by a perfect conductor ("radiative zone") on the one side, and by a highly diffusive medium ("convective zone") supporting an $\\alpha$-effect on the other side. In the limit of high diffusivity contrast between the shear layer and the diffusive medium, thought to be relevant for the Sun, a pair of exact dispersion relations for the growth rat...
International Nuclear Information System (INIS)
Biondo, Elliott D.; Davis, Andrew; Wilson, Paul P.H.
2016-01-01
Highlights: • A CAD-based shutdown dose rate analysis workflow has been implemented. • Cartesian and superimposed tetrahedral mesh are fully supported. • Biased and unbiased photon source sampling options are available. • Hybrid Monte Carlo/deterministic techniques accelerate photon transport. • The workflow has been validated with the FNG-ITER benchmark problem. - Abstract: In fusion energy systems (FES) high-energy neutrons born from burning plasma activate system components to form radionuclides. The biological dose rate that results from photons emitted by these radionuclides after shutdown—the shutdown dose rate (SDR)—must be quantified for maintenance planning. This can be done using the Rigorous Two-Step (R2S) method, which involves separate neutron and photon transport calculations, coupled by a nuclear inventory analysis code. The geometric complexity and highly attenuating configuration of FES motivates the use of CAD geometry and advanced variance reduction for this analysis. An R2S workflow has been created with the new capability of performing SDR analysis directly from CAD geometry with Cartesian or tetrahedral meshes and with biased photon source sampling, enabling the use of the Consistent Adjoint Driven Importance Sampling (CADIS) variance reduction technique. This workflow has been validated with the Frascati Neutron Generator (FNG)-ITER SDR benchmark using both Cartesian and tetrahedral meshes and both unbiased and biased photon source sampling. All results are within 20.4% of experimental values, which constitutes satisfactory agreement. Photon transport using CADIS is demonstrated to yield speedups as high as 8.5·10"5 for problems using the FNG geometry.
Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20.
Michael, J Robert; Volkov, Anatoliy
2015-03-01
The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle-Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.
Generic multiset programming with discrimination-based joins and symbolic Cartesian products
DEFF Research Database (Denmark)
Henglein, Fritz; Larsen, Ken Friis
2010-01-01
This paper presents GMP, a library for generic, SQL-style programming with multisets. It generalizes the querying core of SQL in a number of ways: Multisets may contain elements of arbitrary first-order data types, including references (pointers), recur- sive data types and nested multisets......: symbolic (term) repre- sentations of multisets, specifically for Cartesian products, for facilitating dynamic symbolic computation, which intersperses algebraic simplification steps with conventional data pro- cessing; and discrimination-based joins, a generic technique for computing equijoins based...
International Nuclear Information System (INIS)
Schlegel, H.B.; Binkley, J.S.; Pople, J.A.
1984-01-01
Formulas are developed for the first and second derivatives of two electron integrals over Cartesian Gaussians. Integrals and integral derivatives are evaluated by the Rys polynomial method. Higher angular momentum functions are not used to calculate the integral derivatives; instead the integral formulas are differentiated directly to produce compact and efficient expressions for the integral derivatives. The use of this algorithm in the ab initio molecular orbital programs gaussIan 80 and gaussIan 82 is discussed. Representative timings for some small molecules with several basis sets are presented. This method is compared with previously published algorithms and its computational merits are discussed
Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft
Directory of Open Access Journals (Sweden)
Yuma Fukushima
2015-01-01
Full Text Available The linearized Euler equations (LEEs solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.
International Nuclear Information System (INIS)
Goncalves, Glenio Aguiar
2003-01-01
In this work, we are reported analytical solutions for the transport equation for neutral particles in cylindrical and cartesian geometry. For the cylindrical geometry, it is applied the Hankel transform of order zero in the S N approximation of the one-dimensional cylindrical transport equation, assuming azimuthal symmetry and isotropic scattering. This procedure is coined HTSN method. The anisotropic problem is handled using the decomposition method, generating a recursive approach, which the HTSN solution is used as initial condition. For cartesian geometry, the one and two dimensional transport equation is derived in the angular variable as many time as the degree of the anisotropic scattering. This procedure leads to set of integro-differential plus one differential equation that can be really solved by the variable separation method. Following this procedure, it was possible to come out with the Case solution for the one-dimensional problem. Numerical simulations are reported for the cylindrical transport problem both isotropic and anisotropic case of quadratic degree. (author)
Large-eddy simulation of wind turbine wake interactions on locally refined Cartesian grids
Angelidis, Dionysios; Sotiropoulos, Fotis
2014-11-01
Performing high-fidelity numerical simulations of turbulent flow in wind farms remains a challenging issue mainly because of the large computational resources required to accurately simulate the turbine wakes and turbine/turbine interactions. The discretization of the governing equations on structured grids for mesoscale calculations may not be the most efficient approach for resolving the large disparity of spatial scales. A 3D Cartesian grid refinement method enabling the efficient coupling of the Actuator Line Model (ALM) with locally refined unstructured Cartesian grids adapted to accurately resolve tip vortices and multi-turbine interactions, is presented. Second order schemes are employed for the discretization of the incompressible Navier-Stokes equations in a hybrid staggered/non-staggered formulation coupled with a fractional step method that ensures the satisfaction of local mass conservation to machine zero. The current approach enables multi-resolution LES of turbulent flow in multi-turbine wind farms. The numerical simulations are in good agreement with experimental measurements and are able to resolve the rich dynamics of turbine wakes on grids containing only a small fraction of the grid nodes that would be required in simulations without local mesh refinement. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the National Science Foundation under Award number NSF PFI:BIC 1318201.
Aligning Spinoza with Descartes: An informed Cartesian account of the truth bias.
Street, Chris N H; Kingstone, Alan
2017-08-01
There is a bias towards believing information is true rather than false. The Spinozan account claims there is an early, automatic bias towards believing. Only afterwards can people engage in an effortful re-evaluation and disbelieve the information. Supporting this account, there is a greater bias towards believing information is true when under cognitive load. However, developing on the Adaptive Lie Detector (ALIED) theory, the informed Cartesian can equally explain this data. The account claims the bias under load is not evidence of automatic belief; rather, people are undecided, but if forced to guess they can rely on context information to make an informed judgement. The account predicts, and we found, that if people can explicitly indicate their uncertainty, there should be no bias towards believing because they are no longer required to guess. Thus, we conclude that belief formation can be better explained by an informed Cartesian account - an attempt to make an informed judgment under uncertainty. © 2016 The British Psychological Society.
Semantyczne założenia sceptycyzmu kartezjańskiego (Semantic Presuppositions of Cartesian Skepticism
Directory of Open Access Journals (Sweden)
Krzysztof Posłajko
2010-12-01
Full Text Available The paper purports to show that in order to formulate the hypothesis that all our beliefs are collectively false – which is taken to be the core of Cartesian skepticism – one must accept the presumption that semantic properties of subject`s beliefs locally supervene on “internal” properties of said subject. In order to show that the responses to skepticism from semantic externalism, i.e. those formulated by Putnam and Davidson, are analyzed. It is argued that even though these arguments are controversial they indicate that Cartesian skeptic must assume that subject beliefs` semantic properties can remain the same in different surroundings, which is exactly what the supervenience thesis amounts to. Finally, it is pointed out that the skepticism introduced by Kripke in his discussion of rule-following is indeed more radical than traditional, Cartesian one, as the former denies the very thesis that the latter must assume.
Leamer, Micah J.
2004-01-01
Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS
Locally Finite Root Supersystems
Yousofzadeh, Malihe
2013-01-01
We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.
Domain decomposition methods for mortar finite elements
Energy Technology Data Exchange (ETDEWEB)
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis
2016-11-01
A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates
A simplified presentation of the multigroup analytic nodal method in 2-D Cartesian geometry
International Nuclear Information System (INIS)
Hebert, Alain
2008-01-01
The nodal diffusion algorithms used in many production reactor simulation codes are originating from a common ancestry developed in the 1970s, the analytic nodal method (ANM) of the QUANDRY code. However, this original presentation of the ANM is complex and makes difficult the calculation of the nodal coupling matrices. Moreover, QUANDRY is limited to two-energy groups and its generalization to more groups appears laborious. We are presenting a simplified implementation of the ANM requiring only limited programming work. This formulation is consistent with the initial QUANDRY implementation and is easily generalizable to arbitrary G-group problems. A Matlab script is provided to highlight the simplicity of our presentation. For the sake of clarity, our implementation is limited to G-group, 2-D Cartesian geometry
Directory of Open Access Journals (Sweden)
Eduardo Izaguirre
2011-09-01
Full Text Available This paper presents a kinematic cartesian control scheme of 3 degree of freedom parallel robot driven by electro-pneumatic actuators based on exteroceptive pose measurement system. The inverse kinematics model is used to obtain the desired joint position coordinates from the time-varying trajectory given in task space. The proposal cascade control scheme in task space is based in two loops, the inner loop consisting in a decoupled joint position control and the outer loop which is designed to obtain an appropriate task space trajectory tracking. In order to avoid the on-line computation of direct kinematics an arrangement of inertial sensor and optical encoders are employed to provide the accurate pose measurement of end-effector. The experiment's results demonstrate the great performance of the proposed control scheme in industrial motion tracking application.
Cartesian coupled coherent states simulations: Ne(n)Br2 dissociation as a test case.
Reed, Stewart K; González-Martínez, Maykel L; Rubayo-Soneira, Jesús; Shalashilin, Dmitrii V
2011-02-07
In this article, we describe coupled coherent states (CCS) simulations of vibrational predissociation of weakly bounded complexes. The CCS method is implemented in the Cartesian frame in a manner that is similar to classical molecular dynamics. The calculated lifetimes of the vibrationally excited Ne-Br(2)(ν) complexes agree with experiment and previous calculations. Although the CCS method is, in principle, a fully quantum approach, in practice it typically becomes a semiclassical technique at long times. This is especially true following dissociation events. Consequently, it is very difficult to converge the quantum calculations of the final Br(2) vibrational distributions after predissociation and of the autocorrelation functions. However, the main advantage of the method is that it can be applied with relative ease to determine the lifetimes of larger complexes and, in order to demonstrate this, preliminary results for tetra- and penta-atomic clusters are reported.
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.
2009-01-01
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
A Comparative Study on Evaluation Methods of Fluid Forces on Cartesian Grids
Directory of Open Access Journals (Sweden)
Taku Nonomura
2017-01-01
Full Text Available We investigate the accuracy and the computational efficiency of the numerical schemes for evaluating fluid forces in Cartesian grid systems. A comparison is made between two different types of schemes, namely, polygon-based methods and mesh-based methods, which differ in the discretization of the surface of the object. The present assessment is intended to investigate the effects of the Reynolds number, the object motion, and the complexity of the object surface. The results show that the mesh-based methods work as well as the polygon-based methods, even if the object surface is discretized in a staircase manner. In addition, the results also show that the accuracy of the mesh-based methods is strongly dependent on the evaluation of shear stresses, and thus they must be evaluated by using a reliable method, such as the ghost-cell or ghost-fluid method.
Wu, Bofeng; Huang, Chao-Guang
2018-04-01
The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.
Dakin, Gautier; Després, Bruno; Jaouen, Stéphane
2018-01-01
We propose a new high-order accurate numerical boundary treatment for solving hyperbolic systems of conservation laws and Euler equations using a Lagrange-remap approach on Cartesian grids in cases of physical boundaries not aligned with the mesh. The method is an adaptation of the Inverse Lax-Wendroff procedure [34-38] to the Lagrange-remap approach, which considerably alleviates the algebra. High-order accurate ghost values of conservative variables are imposed using Taylor expansions whose coefficients are found by inverting a (linear or non-linear) system which is well posed in all our examples. For 2D problems, a least-square procedure is added to prevent extrapolation instabilities. The Lagrange-remap formalism also provides a simpler fluid-structure coupling which is also described. Numerical examples are given for the linear case and Euler equations in 1D and 2D.
The impact of susceptibility gradients on cartesian and spiral EPI for BOLD fMRI
DEFF Research Database (Denmark)
Sangill, Ryan; Wallentin, Mikkel; Østergaard, Leif
2006-01-01
, with special emphasis on spiral EPI (spiral) and cartesian EPI (EPI) and their performance under influence of induced field gradients (SFGs) and stochastic noise. A numerical method for calculating synthetic MR images is developed and used to simulate BOLD fMRI experiments using EPI and spirals. The data...... is then examined for activation using a pixel-wise t test. Nine subjects are scanned with both techniques while performing a motor task. SPM99 is used for analysing the experimental data. The simulated spirals provide generally higher t scores at low SFGs but lose more strength than EPI at higher SFGs, where EPI...... activation is offset from the true position. In the primary motor area spirals provide significantly higher t scores (P SFG areas spirals provide stronger activation than...
Wade, Derick
2006-03-01
Adjectives are supposed to describe the associated noun more fully or definitively, and the adjective physical is sometimes added to words such as medicine, rehabilitation and disability. What increase in description does its use allow? The adjective was probably added when rehabilitation started to develop for several reasons: it contrasted the mode of treatment with pharmacology and surgery; it contrasted the nature of the supposed aetiology with emotionally generated disorders, especially shell-shock; and it justified the presence of rehabilitation within the profession of medicine. Its continued use, however, perpetuates a Cartesian, dualist philosophy. This editorial uses the World Health Organization International Classification of Functioning (WHO ICF) model of illness to analyse its continued use, and concludes that its continued use may disadvantage both patients and the practice of rehabilitation.
Nataf, Pierre; Mila, Frédéric
2018-04-01
We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.
A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.
2001-01-01
This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.
Y.J. Hassen (Yunus); B. Koren (Barry)
2008-01-01
textabstractIn this paper, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is
Geometry-invariant GRIN lens: finite ray tracing.
Bahrami, Mehdi; Goncharov, Alexander V
2014-11-17
The refractive index distribution of the geometry-invariant gradient refractive index lens (GIGL) model is derived as a function of Cartesian coordinates. The adjustable external geometry of the GIGL model aims to mimic the shape of the human and animal crystalline lens. The refractive index distribution is based on an adjustable power-law profile, which provides additional flexibility of the model. An analytical method for layer-by-layer finite ray tracing through the GIGL model is developed and used to calculate aberrations of the GIGL model. The result of the finite ray tracing aberrations of the GIGL model are compared to those obtained with paraxial ray tracing. The derived analytical expression for the refractive index distribution can be employed in the reconstruction processes of the eye using the conventional ray tracing methods. The layer-by-layer finite ray tracing approach would be an asset in ray tracing through a modified GIGL model, where the refractive index distribution cannot be described analytically. Using the layer-by-layer finite ray-tracing method, the potential of the GIGL model in representing continuous as well as shell-like layered structures is illustrated and the results for both cases are presented and analysed.
Cerezo, Javier; Santoro, Fabrizio
2016-10-11
Vertical models for the simulation of spectroscopic line shapes expand the potential energy surface (PES) of the final state around the equilibrium geometry of the initial state. These models provide, in principle, a better approximation of the region of the band maximum. At variance, adiabatic models expand each PES around its own minimum. In the harmonic approximation, when the minimum energy structures of the two electronic states are connected by large structural displacements, adiabatic models can breakdown and are outperformed by vertical models. However, the practical application of vertical models faces the issues related to the necessity to perform a frequency analysis at a nonstationary point. In this contribution we revisit vertical models in harmonic approximation adopting both Cartesian (x) and valence internal curvilinear coordinates (s). We show that when x coordinates are used, the vibrational analysis at nonstationary points leads to a deficient description of low-frequency modes, for which spurious imaginary frequencies may even appear. This issue is solved when s coordinates are adopted. It is however necessary to account for the second derivative of s with respect to x, which here we compute analytically. We compare the performance of the vertical model in the s-frame with respect to adiabatic models and previously proposed vertical models in x- or Q 1 -frame, where Q 1 are the normal coordinates of the initial state computed as combination of Cartesian coordinates. We show that for rigid molecules the vertical approach in the s-frame provides a description of the final state very close to the adiabatic picture. For sizable displacements it is a solid alternative to adiabatic models, and it is not affected by the issues of vertical models in x- and Q 1 -frames, which mainly arise when temperature effects are included. In principle the G matrix depends on s, and this creates nonorthogonality problems of the Duschinsky matrix connecting the normal
International Nuclear Information System (INIS)
Acharya, B.S.; Douglas, M.R.
2006-06-01
We present evidence that the number of string/M theory vacua consistent with experiments is finite. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems. (author)
Nilpotent -local finite groups
Cantarero, José; Scherer, Jérôme; Viruel, Antonio
2014-10-01
We provide characterizations of -nilpotency for fusion systems and -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
International Nuclear Information System (INIS)
Lee, Byeong Hae
1992-02-01
This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.
Alabdulmohsin, Ibrahim M.
2018-01-01
In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.
Alabdulmohsin, Ibrahim M.
2018-03-07
In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.
A Trajectory Generation Method Based on Edge Detection for Auto-Sealant Cartesian Robot
Directory of Open Access Journals (Sweden)
Eka Samsul Maarif
2014-07-01
Full Text Available This paper presents algorithm ingenerating trajectory for sealant process using captured image. Cartesian robot as auto-sealant in manufacturing process has increased productivity, reduces human error and saves time. But, different sealant path in many engine models means not only different trajectory but also different program. Therefore robot with detection ability to generate its own trajectory is needed. This paper describes best lighting technique in capturing image and applies edge detection in trajectory generation as the solution. The algorithm comprises image capturing, Canny edge detection, integral projection in localizing outer most edge, scanning coordinates, and generating vector direction codes. The experiment results show that the best technique is diffuse lighting at 10 Cd. The developed method gives connected point to point trajectory which forms sealant path with a point to next point distance is equal to 90° motor rotation. Directional movement for point to point trajectory is controlled by generated codes which are ready to be sent by serial communication to robot controller as instruction for motors which actuate axes X and Y directions.
Path Planning of Free-Floating Robot in Cartesian Space Using Direct Kinematics
Directory of Open Access Journals (Sweden)
Wenfu Xu
2007-03-01
Full Text Available Dynamic singularities make it difficult to plan the Cartesian path of free-floating robot. In order to avoid its effect, the direct kinematic equations are used for path planning in the paper. Here, the joint position, rate and acceleration are bounded. Firstly, the joint trajectories are parameterized by polynomial or sinusoidal functions. And the two parametric functions are compared in details. It is the first contribution of the paper that polynomial functions can be used when the joint angles are limited(In the similar work of other researchers, only sinusoidla functions could be used. Secondly, the joint functions are normalized and the system of equations about the parameters is established by integrating the differential kinematics equations. Normalization is another contribution of the paper. After normalization, the boundary of the parameters is determined beforehand, and the general criterion to assign the initial guess of the unknown parameters is supplied. The criterion is independent on the planning conditions such as the total time tf. Finally, the parametes are solved by the iterative Newtonian method. Modification of tf may not result in the recalculation of the parameters. Simulation results verify the path planning method.
Peano—A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids
Weinzierl, Tobias
2011-01-01
Almost all approaches to solving partial differential equations (PDEs) are based upon a spatial discretization of the computational domain-a grid. This paper presents an algorithm to generate, store, and traverse a hierarchy of d-dimensional Cartesian grids represented by a (k = 3)- spacetree, a generalization of the well-known octree concept, and it also shows the correctness of the approach. These grids may change their adaptive structure throughout the traversal. The algorithm uses 2d + 4 stacks as data structures for both cells and vertices, and the storage requirements for the pure grid reduce to one bit per vertex for both the complete grid connectivity structure and the multilevel grid relations. Since the traversal algorithm uses only stacks, the algorithm\\'s cache hit rate is continually higher than 99.9 percent, and the runtime per vertex remains almost constant; i.e., it does not depend on the overall number of vertices or the adaptivity pattern. We use the algorithmic approach as the fundamental concept for a mesh management for d-dimensional PDEs and for a matrix-free PDE solver represented by a compact discrete 3 d-point operator. In the latter case, one can implement a Jacobi smoother, a Krylov solver, or a geometric multigrid scheme within the presented traversal scheme which inherits the low memory requirements and the good memory access characteristics directly. © 2011 Society for Industrial and Applied Mathematics.
A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows
Das, Pratik; Sen, Oishik; Jacobs, Gustaaf; Udaykumar, H. S.
2017-09-01
A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid-fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid-fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.
The Dirac equation in external fields: Variable separation in Cartesian coordinates
International Nuclear Information System (INIS)
Shishkin, G.V.; Cabos, W.D.
1991-01-01
The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 30, 2132 (1989)] is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational [Theor. Math. Phys. 70, 204 (1987)] or vector fields [J. Math. Phys. 30, 2132 (1989)], permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
International Nuclear Information System (INIS)
Khoromskij, B.N.; Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.
2009-01-01
In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h 3 ) convergence in the grid-size h=O(n -1 ). Moreover, this requires O(3rn+r 3 ) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH 4 molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10 -6 hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.
On the adequacy of Cartesian geometry discrete ordinates solutions for assembly calculations
International Nuclear Information System (INIS)
Schunert, S.; Azmy, Y. Y.
2009-01-01
The current generation of lattice codes employs the method of Collision Probabilities (CP), the Method of Characteristics (MOC) or methods derived thereof to solve the two-dimensional multigroup transport equation on the assembly level. We compare the attainable solution accuracy of the lattice code DRAGON to the accuracy of the Discrete Ordinates (DO) code DORT on the basis of the two-dimensional GE-13 assembly in order to determine if the DO on Cartesian meshes is suitable as flux solver in future lattice codes. If DO exhibits high accuracy for assembly configurations, the next question is at what computational expense compared to traditional assembly codes. For this purpose DORT and DRAGON are required to converge to a reference solution, obtained by a multigroup MCNP calculation, with increasing angular quadrature order and decreasing spatial cell size; additionally for DRAGON the reference solution must be approached with increasing tracking density. The convergence of the two codes is judged via the multiplication factor, the pin wise relative error in the fission production rate, it's RMS and the maximum of it's absolute value over all pins. Additionally the computational cost of the obtained solutions is judged via the user CPU time. Although the multiplication factor computed by both codes converges with refinement of the employed meshes, the maximum deviation error of the fission production rate in the central region of the assembly remains unsatisfactorily high for CP and MOC. (authors)
International Nuclear Information System (INIS)
Warnock, R.L.; Ellison, J.A.; Univ. of New Mexico, Albuquerque, NM
1997-08-01
Data from orbits of a symplectic integrator can be interpolated so as to construct an approximation to the generating function of a Poincare map. The time required to compute an orbit of the symplectic map induced by the generator can be much less than the time to follow the same orbit by symplectic integration. The construction has been carried out previously for full-turn maps of large particle accelerators, and a big saving in time (for instance a factor of 60) has been demonstrated. A shortcoming of the work to date arose from the use of canonical polar coordinates, which precluded map construction in small regions of phase space near coordinate singularities. This paper shows that Cartesian coordinates can also be used, thus avoiding singularities. The generator is represented in a basis of tensor product B-splines. Under weak conditions the spline expansion converges uniformly as the mesh is refined, approaching the exact generator of the Poincare map as defined by the symplectic integrator, in some parallelepiped of phase space centered at the origin
Viability of Bioprinted Cellular Constructs Using a Three Dispenser Cartesian Printer.
Dennis, Sarah Grace; Trusk, Thomas; Richards, Dylan; Jia, Jia; Tan, Yu; Mei, Ying; Fann, Stephen; Markwald, Roger; Yost, Michael
2015-09-22
Tissue engineering has centralized its focus on the construction of replacements for non-functional or damaged tissue. The utilization of three-dimensional bioprinting in tissue engineering has generated new methods for the printing of cells and matrix to fabricate biomimetic tissue constructs. The solid freeform fabrication (SFF) method developed for three-dimensional bioprinting uses an additive manufacturing approach by depositing droplets of cells and hydrogels in a layer-by-layer fashion. Bioprinting fabrication is dependent on the specific placement of biological materials into three-dimensional architectures, and the printed constructs should closely mimic the complex organization of cells and extracellular matrices in native tissue. This paper highlights the use of the Palmetto Printer, a Cartesian bioprinter, as well as the process of producing spatially organized, viable constructs while simultaneously allowing control of environmental factors. This methodology utilizes computer-aided design and computer-aided manufacturing to produce these specific and complex geometries. Finally, this approach allows for the reproducible production of fabricated constructs optimized by controllable printing parameters.
The Cartesian doctor, François Bayle (1622-1709), on psychosomatic explanation.
Easton, Patricia
2011-06-01
There are two standing, incompatible accounts of Descartes' contributions to the study of psychosomatic phenomena that pervade histories of medicine, psychology, and psychiatry. The first views Descartes as the father of "rational psychology" a tradition that defines the soul as a thinking, unextended substance. The second account views Descartes as the father of materialism and the machine metaphor. The consensus is that Descartes' studies of optics and motor reflexes and his conception of the body-machine metaphor made early and important contributions to physiology and neuroscience but otherwise his impact was minimal. These predominately negative assessments of Descartes' contributions give a false impression of the role his philosophy played in the development of medicine and psychiatry in seventeenth-century France and beyond. I explore Descartes' influence in the little-known writings of a doctor from Toulouse, François Bayle (1622-1709). A study of Bayle gives us occasion to rethink the nature and role of psychosomatic explanation in Descartes' philosophy. The portrait I present is of a Cartesian science that had an actual and lasting effect on medical science and practice, and may offer something of value to practitioners today. Copyright © 2010 Elsevier Ltd. All rights reserved.
Häyrynen, Teppo; Osterkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels
2017-09-01
Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform k-space discretization was introduced for rotationally symmetric structures, providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)JOAOD61084-752910.1364/JOSAA.33.001298]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates, allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier k space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence, enabling more accurate and efficient modeling of open 3D nanophotonic structures.
Path Planning of Free-Floating Robot in Cartesian Space Using Direct Kinematics
Directory of Open Access Journals (Sweden)
Wenfu Xu
2008-11-01
Full Text Available Dynamic singularities make it difficult to plan the Cartesian path of freefloating robot. In order to avoid its effect, the direct kinematic equations are used for path planning in the paper. Here, the joint position, rate and acceleration are bounded. Firstly, the joint trajectories are parameterized by polynomial or sinusoidal functions. And the two parametric functions are compared in details. It is the first contribution of the paper that polynomial functions can be used when the joint angles are limited(In the similar work of other researchers, only sinusoidla functions could be used. Secondly, the joint functions are normalized and the system of equations about the parameters is established by integrating the differential kinematics equations. Normalization is another contribution of the paper. After normalization, the boundary of the parameters is determined beforehand, and the general criterion to assign the initial guess of the unknown parameters is supplied. The criterion is independent on the planning conditions such as the total time tf. Finally, the parametes are solved by the iterative Newtonian method. Modification of tf may not result in the recalculation of the parameters. Simulation results verify the path planning method.
A second order penalized direct forcing for hybrid Cartesian/immersed boundary flow simulations
International Nuclear Information System (INIS)
Introini, C.; Belliard, M.; Fournier, C.
2014-01-01
In this paper, we propose a second order penalized direct forcing method to deal with fluid-structure interaction problems involving complex static or time-varying geometries. As this work constitutes a first step toward more complicated problems, our developments are restricted to Dirichlet boundary condition in purely hydraulic context. The proposed method belongs to the class of immersed boundary techniques and consists in immersing the physical domain in a Cartesian fictitious one of simpler geometry on fixed grids. A penalized forcing term is added to the momentum equation to take the boundary conditions around/inside the obstacles into account. This approach avoids the tedious task of re-meshing and allows us to use fast and accurate numerical schemes. In contrary, as the immersed boundary is described by a set of Lagrangian points that does not generally coincide with those of the Eulerian grid, numerical procedures are required to reconstruct the velocity field near the immersed boundary. Here, we develop a second order linear interpolation scheme and we compare it to a simpler model of order one. As far as the governing equations are concerned, we use a particular fractional-step method in which the penalized forcing term is distributed both in prediction and correction equations. The accuracy of the proposed method is assessed through 2-D numerical experiments involving static and rotating solids. We show in particular that the numerical rate of convergence of our method is quasi-quadratic. (authors)
Directory of Open Access Journals (Sweden)
Panou G.
2017-02-01
Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.
Issack, Bilkiss B; Roy, Pierre-Nicholas
2005-08-22
An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.
The Cartesian intervention in body and mind through the notions of «habit» and «memory»
Directory of Open Access Journals (Sweden)
Sergio García Rodríguez
2017-06-01
Full Text Available The Cartesian habit is the key element that enables the implementation of certain regularities in mind and body, allowing the intervention of the subject in both dimensions. Habits play a central role in important Cartesian proposals ―the assumption of the method, the prejudices of childhood or the education of passions—, for that reason, the present article will elucidate the meaning of habit. This aim will require a distinction between types of movements which generate different habits and an analysis of the kinds of memory which preserve the connections of habits. Once offered this explanation about how habits are produced, it will be proposed a categorization of them appealing to Descartes’s distinction between soul and body.
An interior-point method for the Cartesian P*(k-linear complementarity problem over symmetric cones
Directory of Open Access Journals (Sweden)
B Kheirfam
2014-06-01
Full Text Available A novel primal-dual path-following interior-point algorithm for the Cartesian P*(k-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-update approach is the best-available bound.
Higher Order Lagrange Finite Elements In M3D
International Nuclear Information System (INIS)
Chen, J.; Strauss, H.R.; Jardin, S.C.; Park, W.; Sugiyama, L.E.; Fu, G.; Breslau, J.
2004-01-01
The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles
NAMMU: finite element program for coupled heat and groundwater flow problems
International Nuclear Information System (INIS)
Rae, J.; Robinson, P.C.
1979-11-01
NAMMU is a computer program which will calculate the evolution in time of coupled water and heat flow in a porous medium. It is intended to be used primarily for modelling studies of underground nuclear waste repositories. NAMMU is based on the Galerkin-Finite-element method and has self-adjusting time stepping. The present version is written for 2-dimensional cartesian or cylindrical coordinate systems. It has been checked against two calculations from the KBS study and an exact solution by Hodgkinson for a very idealised repository design. (author)
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald
2013-12-01
We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.
International Nuclear Information System (INIS)
Schunck, N.; Dobaczewski, J.
2017-01-01
Here, we describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree–Fock or Skyrme Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.
Fractional finite Fourier transform.
Khare, Kedar; George, Nicholas
2004-07-01
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)
International Nuclear Information System (INIS)
Souza, Manoelito M. de
1997-01-01
We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)
Batty, Christopher
2017-02-01
This paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighboring cells, use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation. To properly recover second order accuracy in the resulting numerical gradients, prior work addressing block-structured grids and graded trees has shown that quadratic, rather than linear, interpolation is required; the gradients otherwise exhibit only first order convergence, which limits potential applications such as fluid flow. However, previous schemes fail or lose accuracy in the presence of the more complex T-junction geometries arising in the case of general non-graded quadtrees, which place no restrictions on the resolution of neighboring cells. We therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed. The method handles complex tree topologies and large resolution jumps between neighboring cells, even along the domain boundary, and both Dirichlet and Neumann boundary conditions are supported. Numerical experiments confirm the overall second order accuracy of the method in the L∞ norm.
Sman, van der R.G.M.
2006-01-01
In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Supersymmetric theories and finiteness
International Nuclear Information System (INIS)
Helayel-Neto, J.A.
1989-01-01
We attempt here to present a short survey of the all-order finite Lagrangian field theories known at present in four-and two-dimensional space-times. The question of the possible relevance of these ultraviolet finite models in the formulation of consistent unified frameworks for the fundamental forces is also addressed to. (author)
Jiang, Wenwen; Larson, Peder E Z; Lustig, Michael
2018-03-09
To correct gradient timing delays in non-Cartesian MRI while simultaneously recovering corruption-free auto-calibration data for parallel imaging, without additional calibration scans. The calibration matrix constructed from multi-channel k-space data should be inherently low-rank. This property is used to construct reconstruction kernels or sensitivity maps. Delays between the gradient hardware across different axes and RF receive chain, which are relatively benign in Cartesian MRI (excluding EPI), lead to trajectory deviations and hence data inconsistencies for non-Cartesian trajectories. These in turn lead to higher rank and corrupted calibration information which hampers the reconstruction. Here, a method named Simultaneous Auto-calibration and Gradient delays Estimation (SAGE) is proposed that estimates the actual k-space trajectory while simultaneously recovering the uncorrupted auto-calibration data. This is done by estimating the gradient delays that result in the lowest rank of the calibration matrix. The Gauss-Newton method is used to solve the non-linear problem. The method is validated in simulations using center-out radial, projection reconstruction and spiral trajectories. Feasibility is demonstrated on phantom and in vivo scans with center-out radial and projection reconstruction trajectories. SAGE is able to estimate gradient timing delays with high accuracy at a signal to noise ratio level as low as 5. The method is able to effectively remove artifacts resulting from gradient timing delays and restore image quality in center-out radial, projection reconstruction, and spiral trajectories. The low-rank based method introduced simultaneously estimates gradient timing delays and provides accurate auto-calibration data for improved image quality, without any additional calibration scans. © 2018 International Society for Magnetic Resonance in Medicine.
Alabdulmohsin, Ibrahim M.
2018-03-07
We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.
Alabdulmohsin, Ibrahim M.
2018-01-01
We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.
Finite fields and applications
Mullen, Gary L
2007-01-01
This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications. The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of error-correcting codes and cryptographic systems using finite fields. Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises rel...
Lyusternik, L A
1965-01-01
Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates contains Tables of mathematical functions up to ten-decimal value. These tables are compiled in the Department for Approximate Computations of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The computations are carried out by this department in conjunction with the Computational-Experimental Laboratory of the Institute.This book will be of value to mathematicians and researchers.
International Nuclear Information System (INIS)
Anderson, D.V.; Breazeal, J.; Finan, C.H.; Johnston, B.M.
1976-01-01
ABCXYZ is a computer code for obtaining the Cartesian components of the vector potential and the magnetic field on an observed grid from an arrangement of current-carrying wires. Arbitrary combinations of straight line segments, arcs, and loops are allowed in the specification of the currents. Arbitrary positions and orientations of the current-carrying elements are also allowed. Specification of the wire diameter permits the computation of well-defined fields, even in the interiors of the conductors. An optical feature generates magnetic field lines. Extensive graphical and printed output is available to the user including contour, grid-line, and field-line plots. 12 figures, 1 table
International Nuclear Information System (INIS)
Yan-Jun, Gong; Zhen-Sen, Wu; Jia-Ji, Wu
2009-01-01
We present an analytical model of Doppler spectra in backscattering from arbitrary rough convex bodies of revolution rotating around their axes in the global Cartesian coordinate system. This analytical model is applied to analyse Doppler spectra in backscatter from two cones and two cylinders, as well as two ellipsoids of revolution. We numerically analyse the influences of attitude and geometry size of objects on Doppler spectra. The analytical model can give contribution of the surface roughness, attitude and geometry size of convex bodies of revolution to Doppler spectra and may contribute to laser Doppler velocimetry as well as ladar applications
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
Introduction to finite temperature and finite density QCD
International Nuclear Information System (INIS)
Kitazawa, Masakiyo
2014-01-01
It has been pointed out that QCD (Quantum Chromodynamics) in the circumstances of medium at finite temperature and density shows numbers of phenomena similar to the characteristics of solid state physics, e.g. phase transitions. In the past ten years, the very high temperature and density matter came to be observed experimentally at the heavy ion collisions. At the same time, the numerical QCD analysis at finite temperature and density attained quantitative level analysis possible owing to the remarkable progress of computers. In this summer school lecture, it has been set out to give not only the recent results, but also the spontaneous breaking of the chiral symmetry, the fundamental theory of finite temperature and further expositions as in the following four sections. The first section is titled as 'Introduction to Finite Temperature and Density QCD' with subsections of 1.1 standard model and QCD, 1.2 phase transition and phase structure of QCD, 1.3 lattice QCD and thermodynamic quantity, 1.4 heavy ion collision experiments, and 1.5 neutron stars. The second one is 'Equilibrium State' with subsections of 2.1 chiral symmetry, 2.2 vacuum state: BCS theory, 2.3 NJL (Nambu-Jona-Lasinio) model, and 2.4 color superconductivity. The third one is 'Static fluctuations' with subsections of 3.1 fluctuations, 3.2 moment and cumulant, 3.3 increase of fluctuations at critical points, 3.4 analysis of fluctuations by lattice QCD and Taylor expansion, and 3.5 experimental exploration of QCD phase structure. The fourth one is 'Dynamical Structure' with 4.1 linear response theory, 4.2 spectral functions, 4.3 Matsubara function, and 4.4 analyses of dynamical structure by lattice QCD. (S. Funahashi)
Simulating QCD at finite density
de Forcrand, Philippe
2009-01-01
In this review, I recall the nature and the inevitability of the "sign problem" which plagues attempts to simulate lattice QCD at finite baryon density. I present the main approaches used to circumvent the sign problem at small chemical potential. I sketch how one can predict analytically the severity of the sign problem, as well as the numerically accessible range of baryon densities. I review progress towards the determination of the pseudo-critical temperature T_c(mu), and towards the identification of a possible QCD critical point. Some promising advances with non-standard approaches are reviewed.
Finite elements and approximation
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
International Nuclear Information System (INIS)
Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.
2011-01-01
We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)
International Nuclear Information System (INIS)
Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.
2010-01-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
A short note on the use of the red-black tree in Cartesian adaptive mesh refinement algorithms
Hasbestan, Jaber J.; Senocak, Inanc
2017-12-01
Mesh adaptivity is an indispensable capability to tackle multiphysics problems with large disparity in time and length scales. With the availability of powerful supercomputers, there is a pressing need to extend time-proven computational techniques to extreme-scale problems. Cartesian adaptive mesh refinement (AMR) is one such method that enables simulation of multiscale, multiphysics problems. AMR is based on construction of octrees. Originally, an explicit tree data structure was used to generate and manipulate an adaptive Cartesian mesh. At least eight pointers are required in an explicit approach to construct an octree. Parent-child relationships are then used to traverse the tree. An explicit octree, however, is expensive in terms of memory usage and the time it takes to traverse the tree to access a specific node. For these reasons, implicit pointerless methods have been pioneered within the computer graphics community, motivated by applications requiring interactivity and realistic three dimensional visualization. Lewiner et al. [1] provides a concise review of pointerless approaches to generate an octree. Use of a hash table and Z-order curve are two key concepts in pointerless methods that we briefly discuss next.
Indian Academy of Sciences (India)
IAS Admin
wavelength, they are called shallow water waves. In the ... Deep and intermediate water waves are dispersive as the velocity of these depends on wavelength. This is not the ..... generation processes, the finite amplitude wave theories are very ...
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
International Nuclear Information System (INIS)
Rittenberg, V.
1983-01-01
Fischer's finite-size scaling describes the cross over from the singular behaviour of thermodynamic quantities at the critical point to the analytic behaviour of the finite system. Recent extensions of the method--transfer matrix technique, and the Hamiltonian formalism--are discussed in this paper. The method is presented, with equations deriving scaling function, critical temperature, and exponent v. As an application of the method, a 3-states Hamiltonian with Z 3 global symmetry is studied. Diagonalization of the Hamiltonian for finite chains allows one to estimate the critical exponents, and also to discover new phase transitions at lower temperatures. The critical points lambda, and indices v estimated for finite-scaling are given
Supersymmetry at finite temperature
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.
1983-01-01
Finite-temperature supersymmetry (SUSY) is characterized by unbroken Ward identities for SUSY variations of ensemble averages of Klein-operator inserted imaginary time-ordered products of fields. Path-integral representations of these products are defined and the Feynman rules in superspace are given. The finite-temperature no-renormalization theorem is derived. Spontaneously broken SUSY at zero temperature is shown not to be restored at high temperature. (orig.)
Finite-size scaling of survival probability in branching processes
Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Alvaro
2014-01-01
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival probability for a given branching process ruled by a probability distribution of the number of offspring per element whose standard deviation is finite, obtaining the exact scaling function as well as the critical exponents. Our findings prove the universal behavi...
Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media
Jiang, L.; Copeland, D.; Moulton, J. D.
2012-01-01
We develop a family of expanded mixed multiscale finite element methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed multiscale finite element formulation in the sense that four
International Nuclear Information System (INIS)
Ragusa, J. C.
2004-01-01
In this paper, a method for performing spatially adaptive computations in the framework of multigroup diffusion on 2-D and 3-D Cartesian grids is investigated. The numerical error, intrinsic to any computer simulation of physical phenomena, is monitored through an a posteriori error estimator. In a posteriori analysis, the computed solution itself is used to assess the accuracy. By efficiently estimating the spatial error, the entire computational process is controlled through successively adapted grids. Our analysis is based on a finite element solution of the diffusion equation. Bilinear test functions are used. The derived a posteriori error estimator is therefore based on the Hessian of the numerical solution. (authors)
Lagrangian Finite-Element Method for the Simulation of K-BKZ Fluids with Third Order Accuracy
DEFF Research Database (Denmark)
Marin, José Manuel Román; Rasmussen, Henrik K.
2009-01-01
system attached to the particles is discretized by ten-node quadratic tetrahedral elements using Cartesian coordinates and the pressure by linear interpolation inside these elements. The spatial discretization of the governing equations follows the mixed Galerkin finite element method. The time integral...... is discretized by a quadratic interpolation in time. The convergence of the method in time and space was demonstrated on the free surface problem of a filament stretched between two plates, considering the axisymmetric case as well as the growth of non-axisymmetric disturbances on the free surface. The scheme...
Finite element formulation for dynamics of planar flexible multi-beam system
International Nuclear Information System (INIS)
Liu Zhuyong; Hong Jiazhen; Liu Jinyang
2009-01-01
In some previous geometric nonlinear finite element formulations, due to the use of axial displacement, the contribution of all the elements lying between the reference node of zero axial displacement and the element to the foreshortening effect should be taken into account. In this paper, a finite element formulation is proposed based on geometric nonlinear elastic theory and finite element technique. The coupling deformation terms of an arbitrary point only relate to the nodal coordinates of the element at which the point is located. Based on Hamilton principle, dynamic equations of elastic beams undergoing large overall motions are derived. To investigate the effect of coupling deformation terms on system dynamic characters and reduce the dynamic equations, a complete dynamic model and three reduced models of hub-beam are prospected. When the Cartesian deformation coordinates are adopted, the results indicate that the terms related to the coupling deformation in the inertia forces of dynamic equations have small effect on system dynamic behavior and may be neglected, whereas the terms related to coupling deformation in the elastic forces are important for system dynamic behavior and should be considered in dynamic equation. Numerical examples of the rotating beam and flexible beam system are carried out to demonstrate the accuracy and validity of this dynamic model. Furthermore, it is shown that a small number of finite elements are needed to obtain a stable solution using the present coupling finite element formulation
Recurrent Artificial Neural Networks and Finite State Natural Language Processing.
Moisl, Hermann
It is argued that pessimistic assessments of the adequacy of artificial neural networks (ANNs) for natural language processing (NLP) on the grounds that they have a finite state architecture are unjustified, and that their adequacy in this regard is an empirical issue. First, arguments that counter standard objections to finite state NLP on the…
International Nuclear Information System (INIS)
Schunck, Nicolas F.; McDonnell, J.; Sheikh, J.A.; Staszczak, A.; Stoitsov, Mario; Dobaczewski, J.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.
International Nuclear Information System (INIS)
Feinsilver, Philip; Schott, Rene
2009-01-01
We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.
Hoang, P. D.; Andonian, G.; Gadjev, I.; Naranjo, B.; Sakai, Y.; Sudar, N.; Williams, O.; Fedurin, M.; Kusche, K.; Swinson, C.; Zhang, P.; Rosenzweig, J. B.
2018-04-01
Photonic structures operating in the terahertz (THz) spectral region enable the essential characteristics of confinement, modal control, and electric field shielding for very high gradient accelerators based on wakefields in dielectrics. We report here an experimental investigation of THz wakefield modes in a three-dimensional photonic woodpile structure. Selective control in exciting or suppressing of wakefield modes with a nonzero transverse wave vector is demonstrated by using drive beams of varying transverse ellipticity. Additionally, we show that the wakefield spectrum is insensitive to the offset position of strongly elliptical beams. These results are consistent with analytic theory and three-dimensional simulations and illustrate a key advantage of wakefield systems with Cartesian symmetry: the suppression of transverse wakes by elliptical beams.
International Nuclear Information System (INIS)
Grundmann, U.
1995-11-01
The code DYN3D/M2 was developed for 3-dimensional steady-state and transient analyses of reactor cores with hexagonal fuel assemblies. The neutron kinetics of the new version DYN3DR is based on a nodal method for the solution of the 3-dimensional 2-group neutron diffusion equation for Cartesian geometry. The thermal-hydraulic model FLOCAL simulating the two phase flow of coolant and the fuel rod behaviour is used in the two versions. The fundamentals for the solution of the neutron diffusion equations in DYN3DR are described. The 3-dimensional NEACRP benchmarks for rod ejections in LWR with quadratic fuel assemblies were calculated and the results were compared with the published solutions. The developed algorithm for neutron kinetics are suitable for using parallel processing. The behaviour of speed-up versus the number of processors is demonstrated for calculations of a static neutron flux distribution using a workstation with 4 processors. (orig.) [de
Gillies, Val; Harden, Angela; Johnson, Katherine; Reavey, Paula; Strange, Vicki; Willig, Carla
2004-03-01
The research presented in this paper uses memory work as a method to explore six women's collective constructions of two embodied practices, sweating and pain. The paper identifies limitations in the ways in which social constructionist research has theorized the relationship between discourse and materiality, and it proposes an approach to the study of embodiment which enjoins, rather than bridges, the discursive and the non-discursive. The paper presents an analysis of 25 memories of sweating and pain which suggests that Cartesian dualism is central to the women's accounts of their experiences. However, such dualism does not operate as a stable organizing principle. Rather, it offers two strategies for the performance of a split between mind and body. The paper traces the ways in which dualism can be both functional and restrictive, and explores the tensions between these two forms. The paper concludes by identifiying opportunities and limitations associated with memory work as a method for studying embodiment.
Crack Propagation by Finite Element Method
Directory of Open Access Journals (Sweden)
Luiz Carlos H. Ricardo
2018-01-01
Full Text Available Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FDandE SAE Keyhole Specimen Test Load Histories by finite element analysis. To understand the crack propagation processes under variable amplitude loading, retardation effects are observed
Hamilton, Scott; Hamilton, Trevor J.
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes’s “radical” or “mind-body” dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes’s famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student’s understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student’s understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur. PMID:26321981
Directory of Open Access Journals (Sweden)
Ali Gunes
2015-12-01
Full Text Available The Deconstruction of the Cartesian Dichotomy of Black and Whitein William Blake’s The Little Black Boy Abstract This paper discusses English Romantic Poet William Blake’s anti-racial views in his poem The Little Black Boy. In so doing, it focuses upon how Blake attempts to deconstruct the Cartesian dichotomy of Western world view, a dichotomy which has usually been based on “the theory that the universe has been ruled from its origins by two conflicting powers, one good and one evil, both existing as equally ultimate first causes.” In this binary and hierarchal relationship, there are two essential terms in which one term is absolutely regarded as primary or fundamental in its essence, whereas the other term is considered secondary or something that lacks originality and presence. Once this equation is applied to the relationship between black and white people, it will easily be seen in the Western world that white people are always primary or fundamental to black-skinned people, and thus the perception behind this binary and hierarchal relationship seems the root of all the racial problems between black and white. This paper argues that Blake strives to deconstruct radically in The Little Black Boy the basis of this binary and hierarchal relationship which has been carried out for centuries in the Western world to segregate and then control the lives of black people. Finally, the paper maintains that Blake also shows a strong aspiration for creating an egalitarian society free of discrimination and injustices at a time when anti-slavery campaigns hit the top on both sides of Atlantic.
Hamilton, Scott; Hamilton, Trevor J
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes's "radical" or "mind-body" dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes's famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student's understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student's understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur.
Finite temperature field theory
Das, Ashok
1997-01-01
This book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. Applications of the formalisms are worked out in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The question of gauge dependence of the effective potential and the Nielsen identities are explained. The nonrestoration of some symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are al
International Nuclear Information System (INIS)
Wachspress, E.
2009-01-01
Triangles and rectangles are the ubiquitous elements in finite element studies. Only these elements admit polynomial basis functions. Rational functions provide a basis for elements having any number of straight and curved sides. Numerical complexities initially associated with rational bases precluded extensive use. Recent analysis has reduced these difficulties and programs have been written to illustrate effectiveness. Although incorporation in major finite element software requires considerable effort, there are advantages in some applications which warrant implementation. An outline of the basic theory and of recent innovations is presented here. (authors)
Directory of Open Access Journals (Sweden)
Isabel G. Gamero Cabrera
2017-07-01
Full Text Available In this paper, I analyse Judith Butler’s recent critics against the Cartesian scepticism and the posTmodern constructivism (indentified by Preciado and Haraway’s works, in order to explain Butler’s distance from constructivism and, at the same time, to assert the ethical and potentially universal dimension of her defence of the precarious lives.
Phase transitions in finite systems
Energy Technology Data Exchange (ETDEWEB)
Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), DSM-CEA / IN2P3-CNRS, 14 - Caen (France); Gulminelli, F. [Caen Univ., 14 (France). Lab. de Physique Corpusculaire
2002-07-01
In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermo-statistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent. (authors)
Finite groups and quantum physics
International Nuclear Information System (INIS)
Kornyak, V. V.
2013-01-01
Concepts of quantum theory are considered from the constructive “finite” point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution—only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers—a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories—in particular, within the Standard Model.
Phase transitions in finite systems
International Nuclear Information System (INIS)
Chomaz, Ph.; Gulminelli, F.
2002-01-01
In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermo-statistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent. (authors)
International Nuclear Information System (INIS)
Meszaros, A.
1984-05-01
In case the graviton has a very small non-zero mass, the existence of six additional massive gravitons with very big masses leads to a finite quantum gravity. There is an acausal behaviour on the scales that is determined by the masses of additional gravitons. (author)
Finite lattice extrapolation algorithms
International Nuclear Information System (INIS)
Henkel, M.; Schuetz, G.
1987-08-01
Two algorithms for sequence extrapolation, due to von den Broeck and Schwartz and Bulirsch and Stoer are reviewed and critically compared. Applications to three states and six states quantum chains and to the (2+1)D Ising model show that the algorithm of Bulirsch and Stoer is superior, in particular if only very few finite lattice data are available. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Kapetanakis, D. (Technische Univ. Muenchen, Garching (Germany). Physik Dept.); Mondragon, M. (Technische Univ. Muenchen, Garching (Germany). Physik Dept.); Zoupanos, G. (National Technical Univ., Athens (Greece). Physics Dept.)
1993-09-01
We present phenomenologically viable SU(5) unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV. (orig.)
International Nuclear Information System (INIS)
Kapetanakis, D.; Mondragon, M.; Zoupanos, G.
1993-01-01
We present phenomenologically viable SU(5) unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV. (orig.)
International Nuclear Information System (INIS)
Kapetanakis, D.; Mondragon, M.
1993-01-01
It is shown how to obtain phenomenologically viable SU(5) unified models which are finite to all orders before the spontaneous symmetry breaking. A very interesting feature of the models with three families is that they predict the top quark mass to be around 178 GeV. 16 refs
Czech Academy of Sciences Publication Activity Database
Šorel, Michal; Šíma, Jiří
2004-01-01
Roč. 62, - (2004), s. 93-110 ISSN 0925-2312 R&D Projects: GA AV ČR IAB2030007; GA MŠk LN00A056 Keywords : radial basis function * neural network * finite automaton * Boolean circuit * computational power Subject RIV: BA - General Mathematics Impact factor: 0.641, year: 2004
Weiser, Martin
2016-01-01
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.
Poirot, Jordan; De Luna, Paolo; Rainer, Gregor
2016-04-01
We comprehensively characterize spiking and visual evoked potential (VEP) activity in tree shrew V1 and V2 using Cartesian, hyperbolic, and polar gratings. Neural selectivity to structure of Cartesian gratings was higher than other grating classes in both visual areas. From V1 to V2, structure selectivity of spiking activity increased, whereas corresponding VEP values tended to decrease, suggesting that single-neuron coding of Cartesian grating attributes improved while the cortical columnar organization of these neurons became less precise from V1 to V2. We observed that neurons in V2 generally exhibited similar selectivity for polar and Cartesian gratings, suggesting that structure of polar-like stimuli might be encoded as early as in V2. This hypothesis is supported by the preference shift from V1 to V2 toward polar gratings of higher spatial frequency, consistent with the notion that V2 neurons encode visual scene borders and contours. Neural sensitivity to modulations of polarity of hyperbolic gratings was highest among all grating classes and closely related to the visual receptive field (RF) organization of ON- and OFF-dominated subregions. We show that spatial RF reconstructions depend strongly on grating class, suggesting that intracortical contributions to RF structure are strongest for Cartesian and polar gratings. Hyperbolic gratings tend to recruit least cortical elaboration such that the RF maps are similar to those generated by sparse noise, which most closely approximate feedforward inputs. Our findings complement previous literature in primates, rodents, and carnivores and highlight novel aspects of shape representation and coding occurring in mammalian early visual cortex. Copyright © 2016 the American Physiological Society.
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Jin; Seo, Jeong Moon
2000-08-01
The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel.
International Nuclear Information System (INIS)
Lee, Sang Jin; Seo, Jeong Moon
2000-08-01
The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel
Strong interaction at finite temperature
Indian Academy of Sciences (India)
Quantum chromodynamics; finite temperature; chiral perturbation theory; QCD sum rules. PACS Nos 11.10. ..... at finite temperature. The self-energy diagrams of figure 2 modify it to ..... method of determination at present. Acknowledgement.
Supersymmetry at finite temperature
International Nuclear Information System (INIS)
Oliveira, M.W. de.
1986-01-01
The consequences of the incorporation of finite temperature effects in fields theories are investigated. Particularly, we consider the sypersymmetric non-linear sigma model, calculating the effective potencial in the large N limit. Initially, we present the 1/N expantion formalism and, for the O(N) model of scalar field, we show the impossibility of spontaneous symmetry breaking. Next, we study the same model at finite temperature and in the presence of conserved charges (the O(N) symmetry's generator). We conclude that these conserved charges explicitly break the symmetry. We introduce a calculation method for the thermodynamic potential of the theory in the presence of chemical potentials. We present an introduction to Supersymmetry in the aim of describing some important concepts for the treatment at T>0. We show that Suppersymmetry is broken for any T>0, in opposition to what one expects, by the solution of the Hierachy Problem. (author) [pt
Directory of Open Access Journals (Sweden)
M.H.R. Ghoreishy
2008-02-01
Full Text Available This research work is devoted to the footprint analysis of a steel-belted radial tyre (185/65R14 under vertical static load using finite element method. Two models have been developed in which in the first model the tread patterns were replaced by simple ribs while the second model was consisted of details of the tread blocks. Linear elastic and hyper elastic (Arruda-Boyce material models were selected to describe the mechanical behavior of the reinforcing and rubbery parts, respectively. The above two finite element models of the tyre were analyzed under inflation pressure and vertical static loads. The second model (with detailed tread patterns was analyzed with and without friction effect between tread and contact surfaces. In every stage of the analysis, the results were compared with the experimental data to confirm the accuracy and applicability of the model. Results showed that neglecting the tread pattern design not only reduces the computational cost and effort but also the differences between computed deformations do not show significant changes. However, more complicated variables such as shape and area of the footprint zone and contact pressure are affected considerably by the finite element model selected for the tread blocks. In addition, inclusion of friction even in static state changes these variables significantly.
Belytschko, Ted; Wing, Kam Liu
1987-01-01
In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.
Crack Propagation by Finite Element Method
H. Ricardo, Luiz Carlos
2017-01-01
Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FD&E SAE Keyh...
Directory of Open Access Journals (Sweden)
J. Ju
2017-07-01
Full Text Available The flexible Cartesian robotic manipulator (FCRM is coming into widespread application in industry. Because of the feeble rigidity and heavy deflection, the dynamic characteristics of the FCRM are easily influenced by external disturbances which mainly concentrate in the driving end and the load end. Thus, with the influence of driving base disturbance and terminal load considered, the motion differential equations of the FCRM under the plane motion of the base are constructed, which contain the forced and non-linear parametric excitations originated from the disturbances of base lateral and axial motion respectively. Considering the relationship between the coefficients of the motion differential equations and the mode shapes of the flexible manipulator, the analytic expressions of the mode shapes with terminal load are deduced. Then, based on multiple scales method and rectangular coordinate transformation, the average equations of the FCRM are derived to analyze the influence mechanism of base disturbance and terminal load on the system parametric vibration stability. The results show that terminal load mainly affects the node locations of mode shapes and mode frequencies of the FCRM, and the axial motion disturbance of the driving base introduces parametric excitation while the lateral motion disturbance generates forced excitation for the transverse vibration model of the FCRM. Furthermore, with the increase of the base excitation acceleration and terminal load, the parametric vibration instability region of the FCRM increases significantly. This study will be helpful for the dynamic characteristics analysis and vibration control of the FCRM.
International Nuclear Information System (INIS)
Ceolin, Celina
2010-01-01
The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)
An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry
International Nuclear Information System (INIS)
Bernard-Champmartin, Aude; Ghidaglia, Jean-Michel; Braeunig, Jean-Philippe
2013-01-01
In this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable h), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific up-winding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity uh. (authors)
A finite volume procedure for fluid flow, heat transfer and solid-body stress analysis
Jagad, P. I.
2018-04-12
A unified cell-centered unstructured mesh finite volume procedure is presented for fluid flow, heat transfer and solid-body stress analysis. An in-house procedure (A. W. Date, Solution of Transport Equations on Unstructured Meshes with Cell-Centered Colocated Variables. Part I: Discretization, International Journal of Heat and Mass Transfer, vol. 48 (6), 1117-1127, 2005) is extended to include the solid-body stress analysis. The transport terms for a cell-face are evaluated in a structured grid-like manner. The Cartesian gradients at the center of each cell-face are evaluated using the coordinate transformation relations. The accuracy of the procedure is demonstrated by solving several benchmark problems involving different boundary conditions, source terms, and types of loading.
Optical Finite Element Processor
Casasent, David; Taylor, Bradley K.
1986-01-01
A new high-accuracy optical linear algebra processor (OLAP) with many advantageous features is described. It achieves floating point accuracy, handles bipolar data by sign-magnitude representation, performs LU decomposition using only one channel, easily partitions and considers data flow. A new application (finite element (FE) structural analysis) for OLAPs is introduced and the results of a case study presented. Error sources in encoded OLAPs are addressed for the first time. Their modeling and simulation are discussed and quantitative data are presented. Dominant error sources and the effects of composite error sources are analyzed.
Anderson, Ian
2011-01-01
Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. ""An excellent text for a topics course in discrete mathematics."" - Bulletin of the Ame
International Nuclear Information System (INIS)
McGavin, Dennis G; Tennant, W Craighead
2009-01-01
In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS 3 and BS 5 . Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, 1-bar Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
Yang, R; Zelyak, O; Fallone, B G; St-Aubin, J
2018-01-30
Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.
Yang, R.; Zelyak, O.; Fallone, B. G.; St-Aubin, J.
2018-02-01
Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.
Inoue, Yuuji; Yoneyama, Masami; Nakamura, Masanobu; Takemura, Atsushi
2018-06-01
The two-dimensional Cartesian turbo spin-echo (TSE) sequence is widely used in routine clinical studies, but it is sensitive to respiratory motion. We investigated the k-space orders in Cartesian TSE that can effectively reduce motion artifacts. The purpose of this study was to demonstrate the relationship between k-space order and degree of motion artifacts using a moving phantom. We compared the degree of motion artifacts between linear and asymmetric k-space orders. The actual spacing of ghost artifacts in the asymmetric order was doubled compared with that in the linear order in the free-breathing situation. The asymmetric order clearly showed less sensitivity to incomplete breath-hold at the latter half of the imaging period. Because of the actual number of partitions of the k-space and the temporal filling order, the asymmetric k-space order of Cartesian TSE was superior to the linear k-space order for reduction of ghosting motion artifacts.
Kalita, Jiten C.; Biswas, Sougata; Panda, Swapnendu
2018-04-01
Till date, the sequence of vortices present in the solid corners of steady internal viscous incompressible flows was thought to be infinite. However, the already existing and most recent geometric theories on incompressible viscous flows that express vortical structures in terms of critical points in bounded domains indicate a strong opposition to this notion of infiniteness. In this study, we endeavor to bridge the gap between the two opposing stream of thoughts by diagnosing the assumptions of the existing theorems on such vortices. We provide our own set of proofs for establishing the finiteness of the sequence of corner vortices by making use of the continuum hypothesis and Kolmogorov scale, which guarantee a nonzero scale for the smallest vortex structure possible in incompressible viscous flows. We point out that the notion of infiniteness resulting from discrete self-similarity of the vortex structures is not physically feasible. Making use of some elementary concepts of mathematical analysis and our own construction of diametric disks, we conclude that the sequence of corner vortices is finite.
Measuring Item Fill-Rate Performance in a Finite Horizon
Douglas J. Thomas
2005-01-01
The standard treatment of fill rate relies on stationary and serially independent demand over an infinite horizon. Even if demand is stationary, managers are held accountable for performance over a finite horizon. In a finite horizon, the fill rate is a random variable. Studying the distribution is relevant because a vendor may be subject to financial penalty if she fails to achieve her target fill rate over a specified finite period. It is known that for a zero lead time, base-stock model, t...
Finite-State Complexity and the Size of Transducers
Directory of Open Access Journals (Sweden)
Cristian Calude
2010-08-01
Full Text Available Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our main result, we show that the state-size hierarchy with respect to a standard encoding is infinite. We consider also hierarchies yielded by more general computable encodings.
The Determining Finite Automata Process
Directory of Open Access Journals (Sweden)
M. S. Vinogradova
2017-01-01
Full Text Available The theory of formal languages widely uses finite state automata both in implementation of automata-based approach to programming, and in synthesis of logical control algorithms.To ensure unambiguous operation of the algorithms, the synthesized finite state automata must be deterministic. Within the approach to the synthesis of the mobile robot controls, for example, based on the theory of formal languages, there are problems concerning the construction of various finite automata, but such finite automata, as a rule, will not be deterministic. The algorithm of determinization can be applied to the finite automata, as specified, in various ways. The basic ideas of the algorithm of determinization can be most simply explained using the representations of a finite automaton in the form of a weighted directed graph.The paper deals with finite automata represented as weighted directed graphs, and discusses in detail the procedure for determining the finite automata represented in this way. Gives a detailed description of the algorithm for determining finite automata. A large number of examples illustrate a capability of the determinization algorithm.
Finite energy electroweak dyon
Energy Technology Data Exchange (ETDEWEB)
Kimm, Kyoungtae [Seoul National University, Faculty of Liberal Education, Seoul (Korea, Republic of); Yoon, J.H. [Konkuk University, Department of Physics, College of Natural Sciences, Seoul (Korea, Republic of); Cho, Y.M. [Konkuk University, Administration Building 310-4, Seoul (Korea, Republic of); Seoul National University, School of Physics and Astronomy, Seoul (Korea, Republic of)
2015-02-01
The latest MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss three different ways to estimate the mass of the electroweak monopole. We first present the dimensional and scaling arguments which indicate the monopole mass to be around 4 to 10 TeV. To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strength at short distance. Our result demonstrates that a genuine electroweak monopole whose mass scale is much smaller than the grand unification scale can exist, which can actually be detected at the present LHC. (orig.)
Probabilistic fracture finite elements
Liu, W. K.; Belytschko, T.; Lua, Y. J.
1991-05-01
The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress.
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)
Axial anomaly at finite temperature and finite density
International Nuclear Information System (INIS)
Qian Zhixin; Su Rukeng; Yu, P.K.N.
1994-01-01
The U(1) axial anomaly in a hot fermion medium is investigated by using the real time Green's function method. After calculating the lowest order triangle diagrams, we find that finite temperature as well as finite fermion density does not affect the axial anomaly. The higher order corrections for the axial anomaly are discussed. (orig.)
Meson spectral functions at finite temperature
International Nuclear Information System (INIS)
Wetzorke, I.; Karsch, F.; Laermann, E.; Petreczky, P.; Stickan, S.
2001-10-01
The Maximum Entropy Method provides a Bayesian approach to reconstruct the spectral functions from discrete points in Euclidean time. The applicability of the approach at finite temperature is probed with the thermal meson correlation function. Furthermore the influence of fuzzing/smearing techniques on the spectral shape is investigated. We present first results for meson spectral functions at several temperatures below and above T c . The correlation functions were obtained from quenched calculations with Clover fermions on large isotropic lattices of the size (24 - 64) 3 x 16. We compare the resulting pole masses with the ones obtained from standard 2-exponential fits of spatial and temporal correlation functions at finite temperature and in the vacuum. The deviation of the meson spectral functions from free spectral functions is examined above the critical temperature. (orig.)
Meson spectral functions at finite temperature
International Nuclear Information System (INIS)
Wetzorke, I.; Karsch, F.; Laermann, E.; Petreczky, P.; Stickan, S.
2002-01-01
The Maximum Entropy Method provides a Bayesian approach to reconstruct the spectral functions from discrete points in Euclidean time. The applicability of the approach at finite temperature is probed with the thermal meson correlation function. Furthermore the influence of fuzzing/smearing techniques on the spectral shape is investigated. We present first results for meson spectral functions at several temperatures below and above T c . The correlation functions were obtained from quenched calculations with Clover fermions on large isotropic lattices of the size (24 - 64) 3 x 16. We compare the resulting pole masses with the ones obtained from standard 2-exponential fits of spatial and temporal correlation functions at finite temperature and in the vacuum. The deviation of the meson spectral functions from free spectral functions is examined above the critical temperature
Multicomplementary operators via finite Fourier transform
International Nuclear Information System (INIS)
Klimov, Andrei B; Sanchez-Soto, Luis L; Guise, Hubert de
2005-01-01
A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail
Meson spectral functions at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Wetzorke, I.; Karsch, F.; Laermann, E.; Petreczky, P.; Stickan, S
2002-03-01
The Maximum Entropy Method provides a Bayesian approach to reconstruct the spectral functions from discrete points in Euclidean time. The applicability of the approach at finite temperature is probed with the thermal meson correlation function. Furthermore the influence of fuzzing/smearing techniques on the spectral shape is investigated. We present first results for meson spectral functions at several temperatures below and above T{sub c}. The correlation functions were obtained from quenched calculations with Clover fermions on large isotropic lattices of the size (24 - 64){sup 3} x 16. We compare the resulting pole masses with the ones obtained from standard 2-exponential fits of spatial and temporal correlation functions at finite temperature and in the vacuum. The deviation of the meson spectral functions from free spectral functions is examined above the critical temperature.
Meson spectral functions at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Wetzorke, I.; Karsch, F.; Laermann, E.; Petreczky, P.; Stickan, S. [Bielefeld Univ. (Germany). Fakultaet fuer Physik
2001-10-01
The Maximum Entropy Method provides a Bayesian approach to reconstruct the spectral functions from discrete points in Euclidean time. The applicability of the approach at finite temperature is probed with the thermal meson correlation function. Furthermore the influence of fuzzing/smearing techniques on the spectral shape is investigated. We present first results for meson spectral functions at several temperatures below and above T{sub c}. The correlation functions were obtained from quenched calculations with Clover fermions on large isotropic lattices of the size (24 - 64){sup 3} x 16. We compare the resulting pole masses with the ones obtained from standard 2-exponential fits of spatial and temporal correlation functions at finite temperature and in the vacuum. The deviation of the meson spectral functions from free spectral functions is examined above the critical temperature. (orig.)
Finite element analysis of human joints
Energy Technology Data Exchange (ETDEWEB)
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
Quark bag coupling to finite size pions
International Nuclear Information System (INIS)
De Kam, J.; Pirner, H.J.
1982-01-01
A standard approximation in theories of quark bags coupled to a pion field is to treat the pion as an elementary field ignoring its substructure and finite size. A difficulty associated with these treatments in the lack of stability of the quark bag due to the rapid increase of the pion pressure on the bad as the bag size diminishes. We investigate the effects of the finite size of the qanti q pion on the pion quark bag coupling by means of a simple nonlocal pion quark interaction. With this amendment the pion pressure on the bag vanishes if the bag size goes to zero. No stability problems are encountered in this description. Furthermore, for extended pions, no longer a maximum is set to the bag parameter B. Therefore 'little bag' solutions may be found provided that B is large enough. We also discuss the possibility of a second minimum in the bag energy function. (orig.)
Finite element analysis of human joints
International Nuclear Information System (INIS)
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described
Kaltenbach, Benjamin; Bucher, Andreas M; Wichmann, Julian L; Nickel, Dominik; Polkowski, Christoph; Hammerstingl, Renate; Vogl, Thomas J; Bodelle, Boris
2017-11-01
The aim of this study was to assess the feasibility of a free-breathing dynamic liver imaging technique using a prototype Cartesian T1-weighted volumetric interpolated breathhold examination (VIBE) sequence with compressed sensing and simultaneous acquisition of a navigation signal for hard-gated and motion state-resolved reconstruction. A total of 43 consecutive oncologic patients (mean age, 66 ± 11 years; 44% female) underwent free-breathing dynamic liver imaging for the evaluation of liver metastases from colorectal cancer using a prototype Cartesian VIBE sequence (field of view, 380 × 345 mm; image matrix, 320 × 218; echo time/repetition time, 1.8/3.76 milliseconds; flip angle, 10 degrees; slice thickness, 3.0 mm; acquisition time, 188 seconds) with continuous data sampling and additionally acquired self-navigation signal. Data were iteratively reconstructed using 2 different approaches: first, a hard-gated reconstruction only using data associated to the dominating motion state (CS VIBE, Compressed Sensing VIBE), and second, a motion-resolved reconstruction with 6 different motion states as additional image dimension (XD VIBE, eXtended dimension VIBE). Continuous acquired data were grouped in 16 subsequent time increments with 11.57 seconds each to resolve arterial and venous contrast phases. For image quality assessment, both CS VIBE and XD VIBE were compared with the patient's last staging dynamic liver magnetic resonance imaging including a breathhold (BH) VIBE as reference standard 4.5 ± 1.2 months before. Representative quality parameters including respiratory artifacts were evaluated for arterial and venous phase images independently, retrospectively and blindly by 3 experienced radiologists, with higher scores indicating better examination quality. To assess diagnostic accuracy, same readers evaluated the presence of metastatic lesions for XD VIBE and CS VIBE compared with reference BH examination in a second session. Compared with CS VIBE, XD VIBE
Axial anomaly at finite temperature
International Nuclear Information System (INIS)
Chaturvedi, S.; Gupte, Neelima; Srinivasan, V.
1985-01-01
The Jackiw-Bardeen-Adler anomaly for QED 4 and QED 2 are calculated at finite temperature. It is found that the anomaly is independent of temperature. Ishikawa's method [1984, Phys. Rev. Lett. vol. 53 1615] for calculating the quantised Hall effect is extended to finite temperature. (author)
Finite flavour groups of fermions
International Nuclear Information System (INIS)
Grimus, Walter; Ludl, Patrick Otto
2012-01-01
We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations and character tables. In a specialized part, we attempt to give a fairly comprehensive review of finite subgroups of SO(3) and SU(3), in which we apply and illustrate the general theory. Moreover, we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of U(3) and finite subgroups of SU(3). Although in this review we give a detailed description of a wide range of finite groups, the main focus is on the methods which allow the exploration of their different aspects. (topical review)
On finite quantum field theories
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.
1984-01-01
The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Massively Parallel Finite Element Programming
Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang
2010-01-01
Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Czech Academy of Sciences Publication Activity Database
Glombíček, Petr
2010-01-01
Roč. 24, č. 24 (2010), s. 133-141 ISSN 0231-5955 R&D Projects: GA AV ČR(CZ) KJB900090704 Institutional research plan: CEZ:AV0Z90090514 Keywords : le bon sens * Seneca * sensus communis Subject RIV: AA - Philosophy ; Religion
Mimetic finite difference method
Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail
2014-01-01
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Energy Technology Data Exchange (ETDEWEB)
Akherraz, B.; Lautard, J.J. [CEA Saclay, Dept. Modelisation de Systemes et Structures, Serv. d' Etudes des Reacteurs et de Modelisation Avancee (DMSS/SERMA), 91 - Gif sur Yvette (France); Erhard, P. [Electricite de France (EDF), Dir. de Recherche et Developpement, Dept. Sinetics, 92 - Clamart (France)
2003-07-01
In this paper we present two applications of the Nodal finite elements developed by Hennart and del Valle, first to three-dimensional Cartesian meshes and then to two-dimensional Hexagonal meshes. This work has been achieved within the framework of the DESCARTES project, which is a co-development effort by the 'Commissariat a l'Energie Atomique' (CEA) and 'Electricite de France' (EDF) for the development of a toolbox for reactor core calculations based on object oriented programming. The general structure of this project is based on the object oriented method. By using a mapping technique proposed in Schneider's thesis and del Valle, Mund, we show how this structuration allows us an easy implementation of the hexagonal case from the Cartesian case. The main attractiveness of this methodology is the possibility of a pin-by-pin representation by division of each lozenge into smaller ones. Furthermore, we will explore the use of non structured quadrangles to treat the circular geometry within a hexagon. It remains nevertheless, in the hexagonal case, the implementation of the acceleration of the internal iterations by the DSA (Diffusion Synthetic Acceleration) or the TSA. (authors)
Institute of Scientific and Technical Information of China (English)
Daciberg Lima GON(C)ALVES; John GUASCHI
2017-01-01
Let X be a topological space.In this survey the authors consider severaltypes of configuration spaces,namely,the classical (usual) configuration spaces Fn(X)and Dn(X),the orbit configuration spaces FGn(X) and FGn(X)/Sn with respect to a freeaction of a group G on X,and the graph configuration spaces FΓn(X) and FΓn(X)/H,where F is a graph and H is a suitable subgroup of the symmetric group Sn.The orderedconfiguration spaces Fn (X),FGn (X),FΓn(X) are all subsets of the n-fold Cartesian productnП1 X of X with itself,and satisfy FGn(X) (C) Fn(X) (C) Frn(X) (C) nП1 X.If A denotes one of these configuration spaces,the authors analyse the difference between A and nП1 X from a topological and homotopical point of view.The principal results known in the literature concern the usual configuration spaces.The authors are particularly interested in the homomorphism on the level of the homotopy groups of the spaces induced by the inclusion (ι):A → nП1 X,the homotopy type of the homotopy fibre I(ι) of the map (ι) via certain constructions on various spaces that depend on X,and the long exact sequence in homotopy of the fibration involving I(ι) and arising from the inclusion (ι).In this respect,if X is either a surface without boundary,in particular if X is the 2-sphere or the real projective plane,or a space whose universal covering is contractible,or an orbit space Sk/G of the k-dimensional sphere by a free action of a Lie group G,the authors present recent results obtained by themselves for the first case,and in collaboration with Golasi(n)ski for the second and third cases.The authors also briefly indicate some older results relative to the homotopy of these spaces that are related to the problems of interest.In order to motivate various questions,for the remaining types of configuration spaces,a few of their basic properties are described and proved.A list of open questions and problems is given at the end of the paper.
Muralidharan, Balaji; Menon, Suresh
2018-03-01
A high-order adaptive Cartesian cut-cell method, developed in the past by the authors [1] for simulation of compressible viscous flow over static embedded boundaries, is now extended for reacting flow simulations over moving interfaces. The main difficulty related to simulation of moving boundary problems using immersed boundary techniques is the loss of conservation of mass, momentum and energy during the transition of numerical grid cells from solid to fluid and vice versa. Gas phase reactions near solid boundaries can produce huge source terms to the governing equations, which if not properly treated for moving boundaries, can result in inaccuracies in numerical predictions. The small cell clustering algorithm proposed in our previous work is now extended to handle moving boundaries enforcing strict conservation. In addition, the cell clustering algorithm also preserves the smoothness of solution near moving surfaces. A second order Runge-Kutta scheme where the boundaries are allowed to change during the sub-time steps is employed. This scheme improves the time accuracy of the calculations when the body motion is driven by hydrodynamic forces. Simple one dimensional reacting and non-reacting studies of moving piston are first performed in order to demonstrate the accuracy of the proposed method. Results are then reported for flow past moving cylinders at subsonic and supersonic velocities in a viscous compressible flow and are compared with theoretical and previously available experimental data. The ability of the scheme to handle deforming boundaries and interaction of hydrodynamic forces with rigid body motion is demonstrated using different test cases. Finally, the method is applied to investigate the detonation initiation and stabilization mechanisms on a cylinder and a sphere, when they are launched into a detonable mixture. The effect of the filling pressure on the detonation stabilization mechanisms over a hyper-velocity sphere launched into a hydrogen
Directory of Open Access Journals (Sweden)
Emílio Borges
2007-04-01
Full Text Available A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational analysis. Examples are given for diatomic and triatomic molecules.
Energy Technology Data Exchange (ETDEWEB)
Eisenbach, Sven; Friedrich, Rainer [Fachgebiet Stroemungsmechanik, Technische Universitaet Muenchen, Garching (Germany)
2008-05-15
Incompressible flow separating from the upper surface of an airfoil at an 18 angle of attack and a Reynolds number of Re=10{sup 5}, based on the freestream velocity and chord length c, is studied by the means of large-eddy simulation (LES). The numerical method is based on second-order central spatial discretization on a Cartesian grid using an immersed boundary technique. The results are compared with an LES using body-fitted nonorthogonal grids and with experimental data. (orig.)
Gribov gap equation at finite temperature
International Nuclear Information System (INIS)
Canfora, Fabrizio; Pais, Pablo; Salgado-Rebolledo, Patricio
2014-01-01
In this paper the Gribov gap equation at finite temperature is analyzed. The solutions of the gap equation (which depend explicitly on the temperature) determine the structure of the gluon propagator within the semi-classical Gribov approach. The present analysis is consistent with the standard confinement scenario for low temperatures, while for high enough temperatures, deconfinement takes place and a free gluon propagator is obtained. An intermediate regime in between the confined and free phases can be read off from the resulting gluon propagator, which appears to be closely related to partial deconfinement. (orig.)
Gribov gap equation at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Canfora, Fabrizio; Pais, Pablo [Centro de Estudios Cientificos (CECS), Valdivia (Chile); Universidad Andres Bello, Santiago (Chile); Salgado-Rebolledo, Patricio [Centro de Estudios Cientificos (CECS), Valdivia (Chile); Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile); Universite Libre de Bruxelles and International Solvay Insitutes, Physique Theorique et Mathematique, Bruxelles (Belgium)
2014-05-15
In this paper the Gribov gap equation at finite temperature is analyzed. The solutions of the gap equation (which depend explicitly on the temperature) determine the structure of the gluon propagator within the semi-classical Gribov approach. The present analysis is consistent with the standard confinement scenario for low temperatures, while for high enough temperatures, deconfinement takes place and a free gluon propagator is obtained. An intermediate regime in between the confined and free phases can be read off from the resulting gluon propagator, which appears to be closely related to partial deconfinement. (orig.)
Quantum fields at finite temperature and density
International Nuclear Information System (INIS)
Blaizot, J.P.
1991-01-01
These lectures are an elementary introduction to standard many-body techniques applied to the study of quantum fields at finite temperature and density: perturbative expansion, linear response theory, quasiparticles and their interactions, etc... We emphasize the usefulness of the imaginary time formalism in a wide class of problems, as opposed to many recent approaches based on real time. Properties of elementary excitations in an ultrarelativistic plasma at high temperature or chemical potential are discussed, and recent progresses in the study of the quark-gluon plasma are briefly reviewed
Mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods
International Nuclear Information System (INIS)
Baker, A.R.
1982-07-01
A study has been performed of mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods. As the objective was to illuminate the issues, the study was performed for a 1D slab model of a reactor with one neutron-energy group for which analytical solutions were possible. A computer code SLAB was specially written to perform the finite-difference and finite-element calculations and also to obtain the analytical solutions. The standard finite-difference equations were obtained by starting with an expansion of the neutron current in powers of the mesh size, h, and keeping terms as far as h 2 . It was confirmed that these equations led to the well-known result that the criticality parameter varied with the square of the mesh size. An improved form of the finite-difference equations was obtained by continuing the expansion for the neutron current as far as the term in h 4 . In this case, the critical parameter varied as the fourth power of the mesh size. The finite-element solutions for 2 and 3 nodes per element revealed that the criticality parameter varied as the square and fourth power of the mesh size, respectively. Numerical results are presented for a bare reactive core of uniform composition with 2 zones of different uniform mesh and for a reactive core with an absorptive reflector. (author)
Finite spatial volume approach to finite temperature field theory
International Nuclear Information System (INIS)
Weiss, Nathan
1981-01-01
A relativistic quantum field theory at finite temperature T=β -1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned. (auth)
Automatic Construction of Finite Algebras
Institute of Scientific and Technical Information of China (English)
张健
1995-01-01
This paper deals with model generation for equational theories,i.e.,automatically generating (finite)models of a given set of (logical) equations.Our method of finite model generation and a tool for automatic construction of finite algebras is described.Some examples are given to show the applications of our program.We argue that,the combination of model generators and theorem provers enables us to get a better understanding of logical theories.A brief comparison betwween our tool and other similar tools is also presented.
Photon propagators at finite temperature
International Nuclear Information System (INIS)
Yee, J.H.
1982-07-01
We have used the real time formalism to compute the one-loop finite temperature corrections to the photon self energies in spinor and scalar QED. We show that, for a real photon, only the transverse components develop the temperature-dependent masses, while, for an external static electromagnetic field applied to the finite temperature system, only the static electric field is screened by thermal fluctuations. After showing how to compute systematically the imaginary parts of the finite temperature Green functions, we have attempted to give a microscopic interpretation of the imaginary parts of the self energies. (author)
Sound radiation from finite surfaces
DEFF Research Database (Denmark)
Brunskog, Jonas
2013-01-01
A method to account for the effect of finite size in acoustic power radiation problem of planar surfaces using spatial windowing is developed. Cremer and Heckl presents a very useful formula for the power radiating from a structure using the spatially Fourier transformed velocity, which combined...... with spatially windowing of a plane waves can be used to take into account the finite size. In the present paper, this is developed by means of a radiation impedance for finite surfaces, that is used instead of the radiation impedance for infinite surfaces. In this way, the spatial windowing is included...
Observations on finite quantum mechanics
International Nuclear Information System (INIS)
Balian, R.; Itzykson, C.
1986-01-01
We study the canonical transformations of the quantum mechanics on a finite phase space. For simplicity we assume that the configuration variable takes an odd prime number 4 K±1 of distinct values. We show that the canonical group is unitarily implemented. It admits a maximal abelian subgroup of order 4 K, commuting with the finite Fourier transform F, a finite analogue of the harmonic oscillator group. This provides a natural construction of F 1/K and of an orthogonal basis of eigenstates of F [fr
Finite element computational fluid mechanics
International Nuclear Information System (INIS)
Baker, A.J.
1983-01-01
This book analyzes finite element theory as applied to computational fluid mechanics. It includes a chapter on using the heat conduction equation to expose the essence of finite element theory, including higher-order accuracy and convergence in a common knowledge framework. Another chapter generalizes the algorithm to extend application to the nonlinearity of the Navier-Stokes equations. Other chapters are concerned with the analysis of a specific fluids mechanics problem class, including theory and applications. Some of the topics covered include finite element theory for linear mechanics; potential flow; weighted residuals/galerkin finite element theory; inviscid and convection dominated flows; boundary layers; parabolic three-dimensional flows; and viscous and rotational flows
Spacecraft formation control using analytical finite-duration approaches
Ben Larbi, Mohamed Khalil; Stoll, Enrico
2018-03-01
This paper derives a control concept for formation flight (FF) applications assuming circular reference orbits. The paper focuses on a general impulsive control concept for FF which is then extended to the more realistic case of non-impulsive thrust maneuvers. The control concept uses a description of the FF in relative orbital elements (ROE) instead of the classical Cartesian description since the ROE provide a direct insight into key aspects of the relative motion and are particularly suitable for relative orbit control purposes and collision avoidance analysis. Although Gauss' variational equations have been first derived to offer a mathematical tool for processing orbit perturbations, they are suitable for several different applications. If the perturbation acceleration is due to a control thrust, Gauss' variational equations show the effect of such a control thrust on the Keplerian orbital elements. Integrating the Gauss' variational equations offers a direct relation between velocity increments in the local vertical local horizontal frame and the subsequent change of Keplerian orbital elements. For proximity operations, these equations can be generalized from describing the motion of single spacecraft to the description of the relative motion of two spacecraft. This will be shown for impulsive and finite-duration maneuvers. Based on that, an analytical tool to estimate the error induced through impulsive maneuver planning is presented. The resulting control schemes are simple and effective and thus also suitable for on-board implementation. Simulations show that the proposed concept improves the timing of the thrust maneuver executions and thus reduces the residual error of the formation control.
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Finite Size Scaling of Perceptron
Korutcheva, Elka; Tonchev, N.
2000-01-01
We study the first-order transition in the model of a simple perceptron with continuous weights and large, bit finite value of the inputs. Making the analogy with the usual finite-size physical systems, we calculate the shift and the rounding exponents near the transition point. In the case of a general perceptron with larger variety of inputs, the analysis only gives bounds for the exponents.
Incompleteness in the finite domain
Czech Academy of Sciences Publication Activity Database
Pudlák, Pavel
2017-01-01
Roč. 23, č. 4 (2017), s. 405-441 ISSN 1079-8986 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : finite domain Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.742, year: 2016 https://www.cambridge.org/core/journals/bulletin-of-symbolic-logic/article/incompleteness-in-the-finite-domain/D239B1761A73DCA534A4805A76D81C76
Symbolic computation with finite biquandles
Creel, Conrad; Nelson, Sam
2007-01-01
A method of computing a basis for the second Yang-Baxter cohomology of a finite biquandle with coefficients in Q and Z_p from a matrix presentation of the finite biquandle is described. We also describe a method for computing the Yang-Baxter cocycle invariants of an oriented knot or link represented as a signed Gauss code. We provide a URL for our Maple implementations of these algorithms.
International Nuclear Information System (INIS)
Kirkpatrick, M.P.; Armfield, S.W.; Kent, J.H.
2003-01-01
A method is presented for representing curved boundaries for the solution of the Navier-Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel 'cell-linking' method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re=40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow
Directory of Open Access Journals (Sweden)
Fábio V. Magalhães
2005-01-01
Full Text Available A non-informative cue (C elicits an inhibition of manual reaction time (MRT to a visual target (T. We report an experiment to examine if the spatial distribution of this inhibitory effect follows Polar or Cartesian coordinate systems. C appeared at one out of 8 isoeccentric (7o positions, the C-T angular distances (in polar coordinates were 0º or multiples of 45º and ISI were 100 or 800ms. Our main findings were: (a MRT was maximal when C- T distance was 0o and minimal when C-T distance was 180o and (b besides an angular distance effect, there is a meridian effect. When C and T occurred in the same quadrant, MRT was longer than when T and C occurred at the same distance (45o but on different sides of vertical or horizontal meridians. The latter finding indicates that the spatial distribution of the cue inhibitory effects is based on a Cartesian coordinate system.
Directory of Open Access Journals (Sweden)
Kuczyński Paweł
2014-06-01
Full Text Available The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD. The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.
Brodsky, Ethan K.; Klaers, Jessica L.; Samsonov, Alexey A.; Kijowski, Richard; Block, Walter F.
2014-01-01
Non-Cartesian imaging sequences and navigational methods can be more sensitive to scanner imperfections that have little impact on conventional clinical sequences, an issue which has repeatedly complicated the commercialization of these techniques by frustrating transitions to multi-center evaluations. One such imperfection is phase errors caused by resonant frequency shifts from eddy currents induced in the cryostat by time-varying gradients, a phenomemon known as B0 eddy currents. These phase errors can have a substantial impact on sequences that use ramp sampling, bipolar gradients, and readouts at varying azimuthal angles. We present a method for measuring and correcting phase errors from B0 eddy currents and examine the results on two different scanner models. This technique yields significant improvements in image quality for high-resolution joint imaging on certain scanners. The results suggest that correction of short time B0 eddy currents in manufacturer provided service routines would simplify adoption of non-Cartesian sampling methods. PMID:22488532
Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids
DEFF Research Database (Denmark)
Román Marín, José Manuel; Rasmussen, Henrik K.
2009-01-01
equation is replaced with a temperature dependent pseudo time. The spatial coordinate system attached to the particles is discretized by 10-node quadratic tetrahedral elements using Cartesian coordinates. The temperature and the pressure are discretized by 10-node quadratic and linear interpolation...... utilizing an implicit variable step backwards differencing (BDF2) scheme, obtaining second order convergence of the temperature in time. A quadratic interpolation in time is applied to approximate the time integral in the K-BKZ equation. This type of scheme ensures third order accuracy with respect......, respectively, in the tetrahedral particle elements. The spatial discretization of the governing equations follows a mixed Galerkin finite element method. This type of scheme ensures third order accuracy with respect to the discretization of spatial dimension. The temperature equation is solved in time...
International Nuclear Information System (INIS)
Wang Yue; Wang Jian-Guo; Chen Zai-Gao
2015-01-01
Based on conformal construction of physical model in a three-dimensional Cartesian grid, an integral-based conformal convolutional perfectly matched layer (CPML) is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain (ECT-CFDTD) method is used to simulate the wave propagation inside a perfect electric conductor (PEC) waveguide. The algorithm has the same numerical stability as the ECT-CFDTD method. For the long-time propagation problems of an evanescent wave in a waveguide, several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML. Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide. (paper)
3D finite element simulation of optical modes in VCSELs
Rozova, M.; Pomplun, J.; Zschiedrich, L.; Schmidt, F.; Burger, S.
2011-01-01
We present a finite element method (FEM) solver for computation of optical resonance modes in VCSELs. We perform a convergence study and demonstrate that high accuracies for 3D setups can be attained on standard computers. We also demonstrate simulations of thermo-optical effects in VCSELs.
Complex finite element sensitivity method for creep analysis
International Nuclear Information System (INIS)
Gomez-Farias, Armando; Montoya, Arturo; Millwater, Harry
2015-01-01
The complex finite element method (ZFEM) has been extended to perform sensitivity analysis for mechanical and structural systems undergoing creep deformation. ZFEM uses a complex finite element formulation to provide shape, material, and loading derivatives of the system response, providing an insight into the essential factors which control the behavior of the system as a function of time. A complex variable-based quadrilateral user element (UEL) subroutine implementing the power law creep constitutive formulation was incorporated within the Abaqus commercial finite element software. The results of the complex finite element computations were verified by comparing them to the reference solution for the steady-state creep problem of a thick-walled cylinder in the power law creep range. A practical application of the ZFEM implementation to creep deformation analysis is the calculation of the skeletal point of a notched bar test from a single ZFEM run. In contrast, the standard finite element procedure requires multiple runs. The value of the skeletal point is that it identifies the location where the stress state is accurate, regardless of the certainty of the creep material properties. - Highlights: • A novel finite element sensitivity method (ZFEM) for creep was introduced. • ZFEM has the capability to calculate accurate partial derivatives. • ZFEM can be used for identification of the skeletal point of creep structures. • ZFEM can be easily implemented in a commercial software, e.g. Abaqus. • ZFEM results were shown to be in excellent agreement with analytical solutions
Finiteness of quantum field theories and supersymmetry
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We study the consequences of finiteness for a general renormalizable quantum field theory by analysing the finiteness conditions resulting from the requirement of absence of divergent contributions to the renormalizations of the parameters of an arbitrary gauge theory. In all cases considered, the well-known two-loop finite supersymmetric theories prove to be the unique solution of the finiteness criterion. (Author)
Toward finite quantum field theories
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.
1986-01-01
The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)
On characters of finite groups
Broué, Michel
2017-01-01
This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups. The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).
Finite and profinite quantum systems
Vourdas, Apostolos
2017-01-01
This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and ...
Preservation theorems on finite structures
International Nuclear Information System (INIS)
Hebert, M.
1994-09-01
This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs
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)
Ghost-free, finite, fourth-order D = 3 gravity.
Deser, S
2009-09-04
Canonical analysis of a recently proposed linear + quadratic curvature gravity model in D = 3 establishes its pure, irreducibly fourth derivative, quadratic curvature limit as both ghost-free and power-counting UV finite, thereby maximally violating standard folklore. This limit is representative of a generic class whose kinetic terms are conformally invariant in any dimension, but it is unique in simultaneously avoiding the transverse-traceless graviton ghosts plaguing D > 3 quadratic actions as well as double pole propagators in its other variables. While the two-term model is also unitary, its additional mode's second-derivative nature forfeits finiteness.
Different radiation impedance models for finite porous materials
DEFF Research Database (Denmark)
Nolan, Melanie; Jeong, Cheol-Ho; Brunskog, Jonas
2015-01-01
The Sabine absorption coefficients of finite absorbers are measured in a reverberation chamber according to the international standard ISO 354. They vary with the specimen size essentially due to diffraction at the specimen edges, which can be seen as the radiation impedance differing from...... the infinite case. Thus, in order to predict the Sabine absorption coefficients of finite porous samples, one can incorporate models of the radiation impedance. In this study, different radiation impedance models are compared with two experimental examples. Thomasson’s model is compared to Rhazi’s method when...
A program for constructing finitely presented Lie algebras and superalgebras
International Nuclear Information System (INIS)
Gerdt, V.P.; Kornyak, V.V.
1997-01-01
The purpose of this paper is to describe a C program FPLSA for investigating finitely presented Lie algebras and superalgebras. The underlying algorithm is based on constructing the complete set of relations called also standard basis or Groebner basis of ideal of free Lie (super) algebra generated by the input set of relations. The program may be used, in particular, to compute the Lie (super)algebra basis elements and its structure constants, to classify the finitely presented algebras depending on the values of parameters in the relations, and to construct the Hilbert series. These problems are illustrated by examples. (orig.)
Finite difference computation of Casimir forces
International Nuclear Information System (INIS)
Pinto, Fabrizio
2016-01-01
In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing
Finite element analysis of a finite-strain plasticity problem
International Nuclear Information System (INIS)
Crose, J.G.; Fong, H.H.
1984-01-01
A finite-strain plasticity analysis was performed of an engraving process in a plastic rotating band during the firing of a gun projectile. The aim was to verify a nonlinear feature of the NIFDI/RB code: plastic large deformation analysis of nearly incompressible materials using a deformation theory of plasticity approach and a total Lagrangian scheme. (orig.)
FINITE ELEMENT ANALYSIS OF STRUCTURES
Directory of Open Access Journals (Sweden)
PECINGINA OLIMPIA-MIOARA
2015-05-01
Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.
Variational collocation on finite intervals
International Nuclear Information System (INIS)
Amore, Paolo; Cervantes, Mayra; Fernandez, Francisco M
2007-01-01
In this paper, we study a set of functions, defined on an interval of finite width, which are orthogonal and which reduce to the sinc functions when the appropriate limit is taken. We show that these functions can be used within a variational approach to obtain accurate results for a variety of problems. We have applied them to the interpolation of functions on finite domains and to the solution of the Schroedinger equation, and we have compared the performance of the present approach with others
Finite elements of nonlinear continua
Oden, John Tinsley
1972-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Finite connectivity attractor neural networks
International Nuclear Information System (INIS)
Wemmenhove, B; Coolen, A C C
2003-01-01
We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric approximation. A bifurcation analysis of this equation reveals the locations of the paramagnetic to recall and paramagnetic to spin-glass transition lines in the phase diagram. The line separating the retrieval phase from the spin-glass phase is calculated at zero temperature. All phase transitions are found to be continuous
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
Energy Technology Data Exchange (ETDEWEB)
Borges, Volnei; Vilhena, Marco Tullio, E-mail: borges@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Fernandes, Julio Cesar Lombaldo, E-mail: julio.lombaldo@ufrgs.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada
2011-07-01
In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two dimensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTS{sub N} method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTS{sub N} nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature. (author)
Van Gorder, Robert A
2013-04-01
We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.
International Nuclear Information System (INIS)
Borges, Volnei; Vilhena, Marco Tullio; Fernandes, Julio Cesar Lombaldo
2011-01-01
In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two dimensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTS N method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTS N nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature. (author)
International Nuclear Information System (INIS)
Takeda, H.; Isha, H.
1981-01-01
The paper is concerned with the displacement-assumed-finite elements by applying the reduced numerical integration technique in structural problems. The first part is a general consideration on the technique. Its purpose is to examine a variational interpretation of the finite element displacement formulation with the reduced integration technique in structural problems. The formulation is critically studied from a standpoint of the natural stiffness approach. It is shown that these types of elements are equivalent to a certain type of displacement and stress assumed mixed elements. The rank deficiency of the stiffness matrix of these elements is interpreted as a problem in the transformation from the natural system to a Cartesian system. It will be shown that a variational basis of the equivalent mixed formulation is closely related to the Hellinger-Reissner's functional. It is presented that for simple elements, e.g. bilinear quadrilateral plane stress and plate bending there are corresponding mixed elements from the functional. For relatively complex types of these elements, it is shown that they are equivalent to localized mixed elements from the Hellinger-Reissner's functional. In the second part, typical finite elements with the reduced integration technique are studied to demonstrate this equivalence. A bilinear displacement and rotation assumed shear beam element, a bilinear displacement assumed quadrilateral plane stress element and a bilinear deflection and rotation assumed quadrilateral plate bending element are examined to present equivalent mixed elements. Not only the theoretical consideration is presented but numerical studies are shown to demonstrate the effectiveness of these elements in practical analysis. (orig.)
The finite element response Matrix method
International Nuclear Information System (INIS)
Nakata, H.; Martin, W.R.
1983-01-01
A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed
Differential equations and finite groups
Put, Marius van der; Ulmer, Felix
2000-01-01
The classical solution of the Riemann-Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois
Symmetric relations of finite negativity
Kaltenbaeck, M.; Winkler, H.; Woracek, H.; Forster, KH; Jonas, P; Langer, H
2006-01-01
We construct and investigate a space which is related to a symmetric linear relation S of finite negativity on an almost Pontryagin space. This space is the indefinite generalization of the completion of dom S with respect to (S.,.) for a strictly positive S on a Hilbert space.
International Nuclear Information System (INIS)
Bovier, A.; Lueling, M.; Wyler, D.
1980-12-01
We present a new class of finite subgroups of SU(3) of the form Zsub(m) s zsub(n) (semidirect product). We also apply the methods used to investigate semidirect products to the known SU(3) subgroups Δ(3n 2 ) and Δ(6n 2 ) and give analytic formulae for representations (characters) and Clebsch-Gordan coefficients. (orig.)
On symmetric pyramidal finite elements
Czech Academy of Sciences Publication Activity Database
Liu, L.; Davies, K. B.; Yuan, K.; Křížek, Michal
2004-01-01
Roč. 11, 1-2 (2004), s. 213-227 ISSN 1492-8760 R&D Projects: GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z1019905 Keywords : mesh generation * finite element method * composite elements Subject RIV: BA - General Mathematics Impact factor: 0.108, year: 2004
Finite length Taylor Couette flow
Streett, C. L.; Hussaini, M. Y.
1987-01-01
Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cylinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.
Finite-temperature confinement transitions
International Nuclear Information System (INIS)
Svetitsky, B.
1984-01-01
The formalism of lattice gauge theory at finite temperature is introduced. The framework of universality predictions for critical behavior is outlined, and recent analytic work in this direction is reviewed. New Monte Carlo information for the SU(4) theory are represented, and possible results of the inclusion of fermions in the SU(3) theory are listed
Ward identities at finite temperature
International Nuclear Information System (INIS)
DOlivo, J.C.; Torres, M.; Tututi, E.
1996-01-01
The Ward identities for QED at finite temperature are derived using the functional real-time formalism. They are verified by an explicit one-loop calculation. An effective causal vertex is constructed which satisfy the Ward identity with the associated retarded self-energy. copyright 1996 American Institute of Physics
Finite-Temperature Higgs Potentials
International Nuclear Information System (INIS)
Dolgopolov, M.V.; Gurskaya, A.V.; Rykova, E.N.
2016-01-01
In the present article we consider the short description of the “Finite-Temperature Higgs Potentials” program for calculating loop integrals at vanishing external momenta and applications for extended Higgs potentials reconstructions. Here we collect the analytic forms of the relevant loop integrals for our work in reconstruction of the effective Higgs potential parameters in extended models (MSSM, NMSSM and etc.)
Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model
Directory of Open Access Journals (Sweden)
Oluwaseun Egbelowo
2017-05-01
Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.
Testing Linear Temporal Logic Formulae on Finite Execution Traces
Havelund, Klaus; Rosu, Grigore; Norvig, Peter (Technical Monitor)
2001-01-01
We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.
Finite element program Lamcal. (User's manual)
International Nuclear Information System (INIS)
Lamain, L.G.; Blanckenburg, J.F.G.
1982-01-01
The present user's manual gives the input formats, job control and an input example for the finite element part of the Lamcal program. The input data have been organized in a more or less self explaining way, using keywords and standard input formats and is printed at the beginning of every run. To simplify the use of the whole program and to avoid unecessary data handling, all three parts of the Lamcal program, meshgeneration, plotting and, FE, are combined into one load module. This setup allows to do all calculations in one single run. However, preprocessing, postprocessing and restarts can be made in separate runs as well. The same reserved space for the dynamic core storage is used in all three parts, if the available space is not sufficient the FE program will stop
International Nuclear Information System (INIS)
Fenstermacher, T.E.
1981-01-01
The solution of the neutron transport equation has long been a subject of intense interest to nuclear engineers. Present computer codes for the solution of this equation, however, are expensive to run for large, multidimensional problems, and also suffer from computational problems such as the ray effect. A method has been developed which eliminates many of these problems. It consists of transforming the transport equation into a set of linear partial differential equations by the use of spherical harmonics. The problem volume is divided into mesh boxes, and the flux components are approximated within each mesh box by spatially orthogonal quadratic polynomials, which need not be continuous at mesh box interfaces. A variational principle is developed, and used to solve for the unknown coefficients of these polynomials. Both one dimensional and two dimensional computer codes using this method have been written. The codes have each been tested on several test cases, and the solutions checked against solutions obtained by other methods. While the codes have some difficulty in modeling sharp transients, they produce excellent results on problems where the characteristic lengths are many mean free paths. On one test case, the two dimensional code, SHOP/2D, required only one-fourth the computer time required by the finite difference, discrete ordinates code TWOTRAN to produce a solution. In addition, SHOP/2D converged much better than TWOTRAN and produced more physical-appearing results
Gavela, M.B.; Orloff, J.; Pene, O
1994-01-01
Simply on CP arguments, we argue against a Standard Model explanation of baryogenesis via the charge transport mechanism. A CP-asymmetry is found in the reflection coefficients of quarks hitting the electroweak phase boundary created during a first order phase transition. The problem is analyzed both in an academic zero temperature case and in the realistic finite temperature one. At finite temperature, a crucial role is played by the damping rate of quasi-quarks in a hot plasma, which induces loss of spatial coherence and suppresses reflection on the boundary even at tree-level. The resulting baryon asymmetry is many orders of magnitude below what observation requires. We comment as well on related works.
Hadronic electroweak processes in a finite volume
International Nuclear Information System (INIS)
Agadjanov, Andria
2017-01-01
In the present thesis, we study a number of hadronic electroweak processes in a finite volume. Our work is motivated by the ongoing and future lattice simulations of the strong interaction theory called quantum chromodynamics. According to the available computational resources, the numerical calculations are necessarily performed on lattices with a finite spatial extension. The first part of the thesis is based on the finite volume formalism which is a standard method to investigate the processes with the final state interactions, and in particular, the elastic hadron resonances, on the lattice. Throughout the work, we systematically apply the non-relativistic effective field theory. The great merit of this approach is that it encodes the low-energy dynamics directly in terms of the effective range expansion parameters. After a brief introduction into the subject, we formulate a framework for the extraction of the ΔNγ * as well as the B→K * transition form factors from lattice data. Both processes are of substantial phenomenological interest, including the search for physics beyond the Standard Model. Moreover, we provide a proper field-theoretical definition of the resonance matrix elements, and advocate it in comparison to the one based on the infinitely narrow width approximation. In the second part we consider certain aspects of the doubly virtual nucleon Compton scattering. The main objective of the work is to answer the question whether there is, in the Regge language, a so-called fixed pole in the process. To answer this question, the unknown subtraction function, which enters one of the dispersion relations for the invariant amplitudes, has to be determined. The external field method provides a feasible approach to tackle this problem on the lattice. Considering the nucleon in a periodic magnetic field, we derive a simple relation for the ground state energy shift up to a second order in the field strength. The obtained result encodes the value of the
Hadronic electroweak processes in a finite volume
Energy Technology Data Exchange (ETDEWEB)
Agadjanov, Andria
2017-11-07
In the present thesis, we study a number of hadronic electroweak processes in a finite volume. Our work is motivated by the ongoing and future lattice simulations of the strong interaction theory called quantum chromodynamics. According to the available computational resources, the numerical calculations are necessarily performed on lattices with a finite spatial extension. The first part of the thesis is based on the finite volume formalism which is a standard method to investigate the processes with the final state interactions, and in particular, the elastic hadron resonances, on the lattice. Throughout the work, we systematically apply the non-relativistic effective field theory. The great merit of this approach is that it encodes the low-energy dynamics directly in terms of the effective range expansion parameters. After a brief introduction into the subject, we formulate a framework for the extraction of the ΔNγ{sup *} as well as the B→K{sup *} transition form factors from lattice data. Both processes are of substantial phenomenological interest, including the search for physics beyond the Standard Model. Moreover, we provide a proper field-theoretical definition of the resonance matrix elements, and advocate it in comparison to the one based on the infinitely narrow width approximation. In the second part we consider certain aspects of the doubly virtual nucleon Compton scattering. The main objective of the work is to answer the question whether there is, in the Regge language, a so-called fixed pole in the process. To answer this question, the unknown subtraction function, which enters one of the dispersion relations for the invariant amplitudes, has to be determined. The external field method provides a feasible approach to tackle this problem on the lattice. Considering the nucleon in a periodic magnetic field, we derive a simple relation for the ground state energy shift up to a second order in the field strength. The obtained result encodes the
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...
African Journals Online (AJOL)
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL STRESSES IN ... the transverse residual stress in the x-direction (σx) had a maximum value of 375MPa ... the finite element method are in fair agreement with the experimental results.
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Finite elements methods in mechanics
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...
Representation theory of finite monoids
Steinberg, Benjamin
2016-01-01
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional ...
Structural modeling techniques by finite element method
International Nuclear Information System (INIS)
Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong
1991-01-01
This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.
$\\delta$-Expansion at Finite Temperature
Ramos, Rudnei O.
1996-01-01
We apply the $\\delta$-expansion perturbation scheme to the $\\lambda \\phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\\delta$-expansion the interaction term is written as $\\lambda (\\phi^{2})^{ 1 + \\delta}$ and $\\delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $\\delta$. The results are compared with the usual loop-expansion at finite temperature.
Finite temperature instability for compactification
International Nuclear Information System (INIS)
Accetta, F.S.; Kolb, E.W.
1986-03-01
We consider finite temperature effects upon theories with extra dimensions compactified via vacuum stress energy (Casimir) effects. For sufficiently high temperature, a static configuration for the internal space is impossible. At somewhat lower temperatures, there is an instability due to thermal fluctuations of radius of the compact dimensions. For both cases, the Universe can evolve to a de Sitter-like expansion of all dimensions. Stability to late times constrains the initial entropy of the universe. 28 refs., 1 fig., 2 tabs
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Quantum Chromodynamic at finite temperature
International Nuclear Information System (INIS)
Magalhaes, N.S.
1987-01-01
A formal expression to the Gibbs free energy of topological defects of quantum chromodynamics (QCD)by using the semiclassical approach in the context of field theory at finite temperature and in the high temperature limit is determined. This expression is used to calculate the free energy of magnetic monopoles. Applying the obtained results to a method in which the free energy of topological defects of a theory may indicate its different phases, its searched for informations about phases of QCD. (author) [pt
Perturbative QCD at finite temperature
International Nuclear Information System (INIS)
Altherr, T.
1989-03-01
We discuss an application of finite temperature QCD to lepton-pair production in a quark-gluon plasma. The perturbative calculation is performed within the realtime formalism. After cancellation of infrared and mass singularities, the corrections at O (α s ) are found to be very small in the region where the mass of the Drell-Yan pair is much larger than the temperature of the plasma. Interesting effects, however, appear at the annihilation threshold of the thermalized quarks
Spinor pregeometry at finite temperature
International Nuclear Information System (INIS)
Yoshimoto, Seiji.
1985-10-01
We derive the effective action for gravity at finite temperature in spinor pregeometry. The temperature-dependent effective potential for the vierbein which is parametrized as e sub(kμ) = b.diag(1, xi, xi, xi) has the minimum at b = 0 for fixed xi, and behaves as -xi 3 for fixed b. These results indicate that the system of fundamental matters in spinor pregeometry cannot be in equilibrium. (author)
Finite Metric Spaces of Strictly negative Type
DEFF Research Database (Denmark)
Hjorth, Poul G.
If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance...
Characterization of finite spaces having dispersion points
International Nuclear Information System (INIS)
Al-Bsoul, A. T
1997-01-01
In this paper we shall characterize the finite spaces having dispersion points. Also, we prove that the dispersion point of a finite space with a dispersion points fixed under all non constant continuous functions which answers the question raised by J. C obb and W. Voxman in 1980 affirmatively for finite space. Some open problems are given. (author). 16 refs
A finite element method for SSI time history calculation
International Nuclear Information System (INIS)
Ni, X.; Gantenbein, F.; Petit, M.
1989-01-01
The method which is proposed is based on a finite element modelization for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method is presented, then applications are given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior are described
A finite element method for SSI time history calculations
International Nuclear Information System (INIS)
Ni, X.M.; Gantenbein, F.; Petit, M.
1989-01-01
The method which is proposed is based on a finite element modelisation for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method will be presented, then applications will be given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior will be described
Finite-temperature behavior of mass hierarchies in supersymmetric theories
International Nuclear Information System (INIS)
Ginsparg, P.
1982-01-01
It is shown that Witten's mechanism for producing a large gauge hierarchy in supersymmetric theories leads to a novel symmetry behavior at finite temperature. The exponentially large expectation value in such models develops at a critical temperature of order of the small (supersymmetry-breaking) scale. The phase transition can proceed without need of vacuum tunnelling. Models based on Witten's mechanism thus require a reexamination of the standard cosmological treatment of grand unified theories. (orig.)
Directory of Open Access Journals (Sweden)
Francesco Tornabene
2017-07-01
Full Text Available The authors are presenting a novel formulation based on the Differential Quadrature (DQ method which is used to approximate derivatives and integrals. The resulting scheme has been termed strong and weak form finite elements (SFEM or WFEM, according to the numerical scheme employed in the computation. Such numerical methods are applied to solve some structural problems related to the mechanical behavior of plates and shells, made of isotropic or composite materials. The main differences between these two approaches rely on the initial formulation – which is strong or weak (variational – and the implementation of the boundary conditions, that for the former include the continuity of stresses and displacements, whereas in the latter can consider the continuity of the displacements or both. The two methodologies consider also a mapping technique to transform an element of general shape described in Cartesian coordinates into the same element in the computational space. Such technique can be implemented by employing the classic Lagrangian-shaped elements with a fixed number of nodes along the element edges or blending functions which allow an “exact mapping” of the element. In particular, the authors are employing NURBS (Not-Uniform Rational B-Splines for such nonlinear mapping in order to use the “exact” shape of CAD designs.
Energy Technology Data Exchange (ETDEWEB)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G., E-mail: ansar.calloo@cea.fr, E-mail: jean-francois.vidal@cea.fr, E-mail: romain.le-tellier@cea.fr, E-mail: gerald.rimpault@cea.fr [CEA, DEN, DER/SPRC/LEPh, Saint-Paul-lez-Durance (France)
2011-07-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S{sub n} method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
Accelerated cardiac cine MRI using locally low rank and finite difference constraints.
Miao, Xin; Lingala, Sajan Goud; Guo, Yi; Jao, Terrence; Usman, Muhammad; Prieto, Claudia; Nayak, Krishna S
2016-07-01
To evaluate the potential value of combining multiple constraints for highly accelerated cardiac cine MRI. A locally low rank (LLR) constraint and a temporal finite difference (FD) constraint were combined to reconstruct cardiac cine data from highly undersampled measurements. Retrospectively undersampled 2D Cartesian reconstructions were quantitatively evaluated against fully-sampled data using normalized root mean square error, structural similarity index (SSIM) and high frequency error norm (HFEN). This method was also applied to 2D golden-angle radial real-time imaging to facilitate single breath-hold whole-heart cine (12 short-axis slices, 9-13s single breath hold). Reconstruction was compared against state-of-the-art constrained reconstruction methods: LLR, FD, and k-t SLR. At 10 to 60 spokes/frame, LLR+FD better preserved fine structures and depicted myocardial motion with reduced spatio-temporal blurring in comparison to existing methods. LLR yielded higher SSIM ranking than FD; FD had higher HFEN ranking than LLR. LLR+FD combined the complimentary advantages of the two, and ranked the highest in all metrics for all retrospective undersampled cases. Single breath-hold multi-slice cardiac cine with prospective undersampling was enabled with in-plane spatio-temporal resolutions of 2×2mm(2) and 40ms. Highly accelerated cardiac cine is enabled by the combination of 2D undersampling and the synergistic use of LLR and FD constraints. Copyright © 2016 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G.
2011-01-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S_n method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
Directory of Open Access Journals (Sweden)
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Hamilton, Nicholas; Cal, Raúl Bayoán
2015-01-01
A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean
SU-F-J-158: Respiratory Motion Resolved, Self-Gated 4D-MRI Using Rotating Cartesian K-Space Sampling
Energy Technology Data Exchange (ETDEWEB)
Han, F; Zhou, Z; Yang, Y; Sheng, K; Hu, P [UCLA School of Medicine, Los Angeles, CA (United States)
2016-06-15
Purpose: Dynamic MRI has been used to quantify respiratory motion of abdominal organs in radiation treatment planning. Many existing 4D-MRI methods based on 2D acquisitions suffer from limited slice resolution and additional stitching artifacts when evaluated in 3D{sup 1}. To address these issues, we developed a 4D-MRI (3D dynamic) technique with true 3D k-space encoding and respiratory motion self-gating. Methods: The 3D k-space was acquired using a Rotating Cartesian K-space (ROCK) pattern, where the Cartesian grid was reordered in a quasi-spiral fashion with each spiral arm rotated using golden angle{sup 2}. Each quasi-spiral arm started with the k-space center-line, which were used as self-gating{sup 3} signal for respiratory motion estimation. The acquired k-space data was then binned into 8 respiratory phases and the golden angle ensures a near-uniform k-space sampling in each phase. Finally, dynamic 3D images were reconstructed using the ESPIRiT technique{sup 4}. 4D-MRI was performed on 6 healthy volunteers, using the following parameters (bSSFP, Fat-Sat, TE/TR=2ms/4ms, matrix size=500×350×120, resolution=1×1×1.2mm, TA=5min, 8 respiratory phases). Supplemental 2D real-time images were acquired in 9 different planes. Dynamic locations of the diaphragm dome and left kidney were measured from both 4D and 2D images. The same protocol was also performed on a MRI-compatible motion phantom where the motion was programmed with different amplitude (10–30mm) and frequency (3–10/min). Results: High resolution 4D-MRI were obtained successfully in 5 minutes. Quantitative motion measurements from 4D-MRI agree with the ones from 2D CINE (<5% error). The 4D images are free of the stitching artifacts and their near-isotropic resolution facilitates 3D visualization and segmentation of abdominal organs such as the liver, kidney and pancreas. Conclusion: Our preliminary studies demonstrated a novel ROCK 4D-MRI technique with true 3D k-space encoding and respiratory
International Nuclear Information System (INIS)
Adamik, V.; Matejovic, P.
1989-01-01
The problems are discussed of nonstationary, nonlinear dynamics of the continuum. A survey is presented of calculation methods in the given area with emphasis on the area of impact problems. A description is presented of the explicit finite elements method and its application to two-dimensional Cartesian and cylindrical configurations. Using the method the explicit calculation code FINEDAN was written which was tested in a series of verification calculations for different configurations and different types of continuum. The main characteristics are presented of the code and of some, of its practical applications. Envisaged trends of the development of the code and its possible applications in the technology of nuclear reactors are given. (author). 9 figs., 4 tabs., 10 refs
Directory of Open Access Journals (Sweden)
Hassan Badreddine
2017-01-01
Full Text Available The current work focuses on the development and application of a new finite volume immersed boundary method (IBM to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities
Romero, Ignacio; Segurado, Javier; LLorca, Javier
2008-04-01
The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.
Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities
International Nuclear Information System (INIS)
Romero, Ignacio; Segurado, Javier; LLorca, Javier
2008-01-01
The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix
Functionals of finite Riemann surfaces
Schiffer, Menahem
1954-01-01
This advanced monograph on finite Riemann surfaces, based on the authors' 1949-50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of ""a plethora of ideas, each interesting in its own right,"" noting that ""the patient reader will be richly rewarded."" Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theo
International Nuclear Information System (INIS)
Barbarin, F.; Sorba, P.; Ragoucy, E.
1996-01-01
The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G ≅ so (4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G approx=(2, R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) k is briefly presented. (authors)
Finite temperature approach to confinement
International Nuclear Information System (INIS)
Gave, E.; Jengo, R.; Omero, C.
1980-06-01
The finite temperature treatment of gauge theories, formulated in terms of a gauge invariant variable as in a Polyakov method, is used as a device for obtaining an effective theory where the confinement test takes the form of a correlation function. The formalism is discussed for the abelian CPsup(n-1) model in various dimensionalities and for the pure Yang-Mills theory in the limit of zero temperature. In the latter case a class of vortex like configurations of the effective theory which induce confinement correspond in particular to the instanton solutions. (author)
Linear and Nonlinear Finite Elements.
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 +y , (1-y)’ 1-y’ 2 - y" (6) that change eq. (5) to V) = , [yŖ(1 + y") - Qy
Covariant gauges at finite temperature
Landshoff, Peter V
1992-01-01
A prescription is presented for real-time finite-temperature perturbation theory in covariant gauges, in which only the two physical degrees of freedom of the gauge-field propagator acquire thermal parts. The propagators for the unphysical degrees of freedom of the gauge field, and for the Faddeev-Popov ghost field, are independent of temperature. This prescription is applied to the calculation of the one-loop gluon self-energy and the two-loop interaction pressure, and is found to be simpler to use than the conventional one.
Kedia, Kushal S.; Safta, Cosmin; Ray, Jaideep; Najm, Habib N.; Ghoniem, Ahmed F.
2014-01-01
In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A "buffer zone" methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed. © 2014 Elsevier Inc.
Wilde-Piorko, M.; Polkowski, M.
2016-12-01
Seismic wave travel time calculation is the most common numerical operation in seismology. The most efficient is travel time calculation in 1D velocity model - for given source, receiver depths and angular distance time is calculated within fraction of a second. Unfortunately, in most cases 1D is not enough to encounter differentiating local and regional structures. Whenever possible travel time through 3D velocity model has to be calculated. It can be achieved using ray calculation or time propagation in space. While single ray path calculation is quick it is complicated to find the ray path that connects source with the receiver. Time propagation in space using Fast Marching Method seems more efficient in most cases, especially when there are multiple receivers. In this presentation final release of a Python module pySeismicFMM is presented - simple and very efficient tool for calculating travel time from sources to receivers. Calculation requires regular 2D or 3D velocity grid either in Cartesian or geographic coordinates. On desktop class computer calculation speed is 200k grid cells per second. Calculation has to be performed once for every source location and provides travel time to all receivers. pySeismicFMM is free and open source. Development of this tool is a part of authors PhD thesis. Source code of pySeismicFMM will be published before Fall Meeting. National Science Centre Poland provided financial support for this work via NCN grant DEC-2011/02/A/ST10/00284.
Kedia, Kushal S.
2014-09-01
In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A "buffer zone" methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed. © 2014 Elsevier Inc.
A particle finite element method for machining simulations
Sabel, Matthias; Sator, Christian; Müller, Ralf
2014-07-01
The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.
Biset functors for finite groups
Bouc, Serge
2010-01-01
This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.
Supersymmetry breaking at finite temperature
International Nuclear Information System (INIS)
Kratzert, K.
2002-11-01
The mechanism of supersymmetry breaking at finite temperature is still only partly understood. Though it has been proven that temperature always breaks supersymmetry, the spontaneous nature of this breaking remains unclear, in particular the role of the Goldstone fermion. The aim of this work is to unify two existing approaches to the subject. From a hydrodynamic point of view, it has been argued under very general assumptions that in any supersymmetric quantum field theory at finite temperature there should exist a massless fermionic collective excitation, named phonino because of the analogy to the phonon. In the framework of a self-consistent resummed perturbation theory, it is shown for the example of the Wess-Zumino model that this mode fits very well into the quantum field theoretical framework pursued by earlier works. Interpreted as a bound state of boson and fermion, it contributes to the supersymmetric Ward-Takahashi identities in a way showing that supersymmetry is indeed broken spontaneously with the phonino playing the role of the Goldstone fermion. The second part of the work addresses the case of supersymmetric quantum electrodynamics. It is shown that also here the phonino exists and must be interpreted as the Goldstone mode. This knowledge allows a generalization to a wider class of models. (orig.)
Some aspects of the quality assurance of personnel carrying out finite element analysis
International Nuclear Information System (INIS)
Dickenson, P.W.
1990-01-01
In this paper, the need to assess the competence of personnel carrying out finite element analysis is emphasised. In carrying out its regulatory role on behalf of the Health and Safety Executive, the Nuclear Installations Inspectorate (NII) must be satisfied that appropriate standards are developed and maintained by the licensee. Since finite element methods have an important bearing on the acceptance of a safety case, it follows that relevant codes should be adequately validated and the personnel applying the code should be competent. Attention is drawn to the work of the Quality Assurance Working Group of the National Agency for Finite Element Methods and Standards (NAFEMS) who are active in this area. The paper also considers the methods that are available to assess the competence of personnel engaged in finite element methods. (author)
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien
2017-06-01
Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which-as shown on the contact process-provides a significant improvement of the large deviation function estimators compared to the standard one.
Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien
2017-06-01
Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which—as shown on the contact process—provides a significant improvement of the large deviation function estimators compared to the standard one.
The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation
Jin, Bangti; Lazarov, Raytcho; Liu, Yikan; Zhou, Zhi
2014-01-01
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite...
Wigner distributions for finite dimensional quantum systems: An ...
Indian Academy of Sciences (India)
2005-07-11
Jul 11, 2005 ... 5Centre for High Energy Physics, Indian Institute of Science, Bangalore ... one has to take the Cartesian product of the elementary solutions. ... tor of translations in configuration space, with mass not playing an explicit role. .... with a distinguished 'origin' corresponding to the identity element e ∈ G. In turn,.
Characterization of resonances using finite size effects
International Nuclear Information System (INIS)
Pozsgay, B.; Takacs, G.
2006-01-01
We develop methods to extract resonance widths from finite volume spectra of (1+1)-dimensional quantum field theories. Our two methods are based on Luscher's description of finite size corrections, and are dubbed the Breit-Wigner and the improved ''mini-Hamiltonian'' method, respectively. We establish a consistent framework for the finite volume description of sufficiently narrow resonances that takes into account the finite size corrections and mass shifts properly. Using predictions from form factor perturbation theory, we test the two methods against finite size data from truncated conformal space approach, and find excellent agreement which confirms both the theoretical framework and the numerical validity of the methods. Although our investigation is carried out in 1+1 dimensions, the extension to physical 3+1 space-time dimensions appears straightforward, given sufficiently accurate finite volume spectra
['Gold standard', not 'golden standard'
Claassen, J.A.H.R.
2005-01-01
In medical literature, both 'gold standard' and 'golden standard' are employed to describe a reference test used for comparison with a novel method. The term 'gold standard' in its current sense in medical research was coined by Rudd in 1979, in reference to the monetary gold standard. In the same
Finite size scaling and lattice gauge theory
International Nuclear Information System (INIS)
Berg, B.A.
1986-01-01
Finite size (Fisher) scaling is investigated for four dimensional SU(2) and SU(3) lattice gauge theories without quarks. It allows to disentangle violations of (asymptotic) scaling and finite volume corrections. Mass spectrum, string tension, deconfinement temperature and lattice β-function are considered. For appropriate volumes, Monte Carlo investigations seem to be able to control the finite volume continuum limit. Contact is made with Luescher's small volume expansion and possibly also with the asymptotic large volume behavior. 41 refs., 19 figs
Finite element application to global reactor analysis
International Nuclear Information System (INIS)
Schmidt, F.A.R.
1981-01-01
The Finite Element Method is described as a Coarse Mesh Method with general basis and trial functions. Various consequences concerning programming and application of Finite Element Methods in reactor physics are drawn. One of the conclusions is that the Finite Element Method is a valuable tool in solving global reactor analysis problems. However, problems which can be described by rectangular boxes still can be solved with special coarse mesh programs more efficiently. (orig.) [de
A first course in finite elements
Fish, Jacob
2007-01-01
Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts
Features of finite quantum field theories
International Nuclear Information System (INIS)
Boehm, M.; Denner, A.
1987-01-01
We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)
International Nuclear Information System (INIS)
Crofford, W.N.
1980-01-01
EPA has agreed to establish a series of environmental standards for the safe disposal of radioactive waste through participation in the Interagency Review Group on Nuclear Waste Management (IRG). One of the standards required under the IRG is the standard for decommissioning of radioactive contaminated sites, facilities, and materials. This standard is to be proposed by December 1980 and promulgated by December 1981. Several considerations are important in establishing these standards. This study includes discussions of some of these considerations and attempts to evaluate their relative importance. Items covered include: the form of the standards, timing for decommissioning, occupational radiation protection, costs and financial provisions. 4 refs
Burnside structures of finite subgroups
International Nuclear Information System (INIS)
Lysenok, I G
2007-01-01
We establish conditions guaranteeing that a group B possesses the following property: there is a number l such that if elements w, x -1 wx,...,x -l+1 wx l-1 of B generate a finite subgroup G then x lies in the normalizer of G. These conditions are of a quite special form. They hold for groups with relations of the form x n =1 which appear as approximating groups for the free Burnside groups B(m,n) of sufficiently large even exponent n. We extract an algebraic assertion which plays an important role in all known approaches to substantial results on the groups B(m,n) of large even exponent, in particular, to proving their infiniteness. The main theorem asserts that when n is divisible by 16, B has the above property with l=6
Learning Extended Finite State Machines
Cassel, Sofia; Howar, Falk; Jonsson, Bengt; Steffen, Bernhard
2014-01-01
We present an active learning algorithm for inferring extended finite state machines (EFSM)s, combining data flow and control behavior. Key to our learning technique is a novel learning model based on so-called tree queries. The learning algorithm uses the tree queries to infer symbolic data constraints on parameters, e.g., sequence numbers, time stamps, identifiers, or even simple arithmetic. We describe sufficient conditions for the properties that the symbolic constraints provided by a tree query in general must have to be usable in our learning model. We have evaluated our algorithm in a black-box scenario, where tree queries are realized through (black-box) testing. Our case studies include connection establishment in TCP and a priority queue from the Java Class Library.
Phase transition in finite systems
International Nuclear Information System (INIS)
Chomaz, Ph.; Duflot, V.; Duflot, V.; Gulminelli, F.
2000-01-01
In this paper we present a review of selected aspects of Phase transitions in finite systems applied in particular to the liquid-gas phase transition in nuclei. We show that the problem of the non existence of boundary conditions can be solved by introducing a statistical ensemble with an averaged constrained volume. In such an ensemble the microcanonical heat capacity becomes negative in the transition region. We show that the caloric curve explicitly depends on the considered transformation of the volume with the excitation energy and so does not bear direct informations on the characteristics of the phase transition. Conversely, partial energy fluctuations are demonstrated to be a direct measure of the equation of state. Since the heat capacity has a negative branch in the phase transition region, the presence of abnormally large kinetic energy fluctuations is a signal of the liquid gas phase transition. (author)
Finite-time braiding exponents
Budišić, Marko; Thiffeault, Jean-Luc
2015-08-01
Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.
Finite-volume cumulant expansion in QCD-colorless plasma
Energy Technology Data Exchange (ETDEWEB)
Ladrem, M. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); Physics Department, Algiers (Algeria); ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Ahmed, M.A.A. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Taiz University in Turba, Physics Department, Taiz (Yemen); Alfull, Z.Z. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); Cherif, S. [ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Ghardaia University, Sciences and Technologies Department, Ghardaia (Algeria)
2015-09-15
Due to the finite-size effects, the localization of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite-volume transition point T{sub 0}(V) of the QCD deconfinement phase transition to a colorless QGP, we have developed a new approach using the finite-size cumulant expansion of the order parameter and the L{sub mn}-method. The first six cumulants C{sub 1,2,3,4,5,6} with the corresponding under-normalized ratios (skewness Σ, kurtosis κ, pentosis Π{sub ±}, and hexosis H{sub 1,2,3}) and three unnormalized combinations of them, (O = σ{sup 2}κΣ{sup -1},U = σ{sup -2}Σ{sup -1},N = σ{sup 2}κ) are calculated and studied as functions of (T, V). A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed.Anumerical FSS analysis of the obtained results has allowed us to locate accurately the finite-volume transition point. The extracted transition temperature value T{sub 0}(V) agrees with that expected T{sub 0}{sup N}(V) from the order parameter and the thermal susceptibility χ{sub T} (T, V), according to the standard procedure of localization to within about 2%. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable. (orig.)
Finite-Q22 Corrections to Parity-Violating DIS
International Nuclear Information System (INIS)
T. Hobbs; W. Melnitchouk
2008-01-01
Parity-violating deep inelastic scattering (PVDIS) has been proposed as an important new tool to extract the flavor and isospin dependence of parton distributions in the nucleon. We discuss finite-Q 2 effects in PVDIS asymmetries arising from subleading kinematical corrections and longitudinal contributions to the gamma Z interference. For the proton, these need to be accounted for when extracting the d/u ratio at large x. For the deuteron, the finite-Q 2 corrections can distort the effects of charge symmetry violation in parton distributions, or signals for physics beyond the standard model. We further explore the dependence of PVDIS asymmetries for polarized targets on the u and d helicity distributions at large x
Reduction of parameters in Finite Unified Theories and the MSSM
Heinemeyer, Sven; Mondragón, Myriam; Tracas, Nicholas; Zoupanos, George
2018-02-01
The method of reduction of couplings developed by W. Zimmermann, combined with supersymmetry, can lead to realistic quantum field theories, where the gauge and Yukawa sectors are related. It is the basis to find all-loop Finite Unified Theories, where the β-function vanishes to all-loops in perturbation theory. It can also be applied to the Minimal Supersymmetric Standard Model, leading to a drastic reduction in the number of parameters. Both Finite Unified Theories and the reduced MSSM lead to successful predictions for the masses of the third generation of quarks and the Higgs boson, and also predict a heavy supersymmetric spectrum, consistent with the non-observation of supersymmetry so far.
Finite element predictions of active buckling control of stiffened panels
Thompson, Danniella M.; Griffin, O. H., Jr.
1993-04-01
Materials systems and structures that can respond 'intelligently' to their environment are currently being proposed and investigated. A series of finite element analyses was performed to investigate the potential for active buckling control of two different stiffened panels by embedded shape memory alloy (SMA) rods. Changes in the predicted buckling load increased with the magnitude of the actuation level for a given structural concept. Increasing the number of actuators for a given concept yielded greater predicted increases in buckling load. Considerable control authority was generated with a small number of actuators, with greater authority demonstrated for those structural concepts where the activated SMA rods could develop greater forces and moments on the structure. Relatively simple and inexpensive analyses were performed with standard finite elements to determine such information, indicating the viability of these types of models for design purposes.
Finite Cosmology and a CMB Cold Spot
Energy Technology Data Exchange (ETDEWEB)
Adler, R.J.; /Stanford U., HEPL; Bjorken, J.D.; /SLAC; Overduin, J.M.; /Stanford U., HEPL
2006-03-20
The standard cosmological model posits a spatially flat universe of infinite extent. However, no observation, even in principle, could verify that the matter extends to infinity. In this work we model the universe as a finite spherical ball of dust and dark energy, and obtain a lower limit estimate of its mass and present size: the mass is at least 5 x 10{sup 23}M{sub {circle_dot}} and the present radius is at least 50 Gly. If we are not too far from the dust-ball edge we might expect to see a cold spot in the cosmic microwave background, and there might be suppression of the low multipoles in the angular power spectrum. Thus the model may be testable, at least in principle. We also obtain and discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter with a naked singularity, and provides an interesting picture of cosmogenesis. Finally we briefly sketch how radiation and inflation eras may be incorporated into the model.
Exact combinatorial approach to finite coagulating systems
Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr
2018-02-01
This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.
International Nuclear Information System (INIS)
Dina Al Akhrass; Bruchon, Julien; Drapier, Sylvain; Fayolle, Sebastien
2014-01-01
This paper deals with the treatment of incompressibility in solid mechanics in finite-strain elasto-plasticity. A finite-strain model proposed by Miehe, Apel and Lambrecht, which is based on a logarithmic strain measure and its work-conjugate stress tensor is chosen. Its main interest is that it allows for the adoption of standard constitutive models established in a small-strain framework. This model is extended to take into account the plastic incompressibility constraint intrinsically. In that purpose, an extension of this model to a three-field mixed finite element formulation is proposed, involving displacements, a strain variable and pressure as nodal variables with respect to standard finite element. Numerical examples of finite-strain problems are presented to assess the performance of the formulation. To conclude, an industrial case for which the classical under-integrated elements fail is considered. (authors)
Stellinga, B.; Mügge, D.
2014-01-01
The European and global regulation of accounting standards have witnessed remarkable changes over the past twenty years. In the early 1990s, EU accounting practices were fragmented along national lines and US accounting standards were the de facto global standards. Since 2005, all EU listed
2011-08-01
Specifications and Standards; Guide Specifications; CIDs; and NGSs . Learn. Perform. Succeed. STANDARDIZATION DOCUMENTS Federal Specifications Commercial...national or international standardization document developed by a private sector association, organization, or technical society that plans ...Maintain lessons learned • Examples: Guidance for application of a technology; Lists of options Learn. Perform. Succeed. DEFENSE HANDBOOK
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.
Three dimensional mathematical model of tooth for finite element analysis
Directory of Open Access Journals (Sweden)
Puškar Tatjana
2010-01-01
Full Text Available Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body into simple geometric bodies (cylinder, cone, pyramid,.... Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
Saranathan, Manojkumar; Rettmann, Dan W; Hargreaves, Brian A; Clarke, Sharon E; Vasanawala, Shreyas S
2012-06-01
To develop and evaluate a multiphasic contrast-enhanced MRI method called DIfferential Sub-sampling with Cartesian Ordering (DISCO) for abdominal imaging. A three-dimensional, variable density pseudo-random k-space segmentation scheme was developed and combined with a Dixon-based fat-water separation algorithm to generate high temporal resolution images with robust fat suppression and without compromise in spatial resolution or coverage. With institutional review board approval and informed consent, 11 consecutive patients referred for abdominal MRI at 3 Tesla (T) were imaged with both DISCO and a routine clinical three-dimensional SPGR-Dixon (LAVA FLEX) sequence. All images were graded by two radiologists using quality of fat suppression, severity of artifacts, and overall image quality as scoring criteria. For assessment of arterial phase capture efficiency, the number of temporal phases with angiographic phase and hepatic arterial phase was recorded. There were no significant differences in quality of fat suppression, artifact severity or overall image quality between DISCO and LAVA FLEX images (P > 0.05, Wilcoxon signed rank test). The angiographic and arterial phases were captured in all 11 patients scanned using the DISCO acquisition (mean number of phases were two and three, respectively). DISCO effectively captures the fast dynamics of abdominal pathology such as hyperenhancing hepatic lesions with a high spatio-temporal resolution. Typically, 1.1 × 1.5 × 3 mm spatial resolution over 60 slices was achieved with a temporal resolution of 4-5 s. Copyright © 2012 Wiley Periodicals, Inc.
Han, Fei; Zhou, Ziwu; Han, Eric; Gao, Yu; Nguyen, Kim-Lien; Finn, J Paul; Hu, Peng
2017-08-01
To develop and validate a cardiac-respiratory self-gating strategy for the recently proposed multiphase steady-state imaging with contrast enhancement (MUSIC) technique. The proposed SG strategy uses the ROtating Cartesian K-space (ROCK) sampling, which allows for retrospective k-space binning based on motion surrogates derived from k-space center line. The k-space bins are reconstructed using a compressed sensing algorithm. Ten pediatric patients underwent cardiac MRI for clinical reasons. The original MUSIC and 2D-CINE images were acquired as a part of the clinical protocol, followed by the ROCK-MUSIC acquisition, all under steady-state intravascular distribution of ferumoxytol. Subjective scores and image sharpness were used to compare the images of ROCK-MUSIC and original MUSIC. All scans were completed successfully without complications. The ROCK-MUSIC acquisition took 5 ± 1 min, compared to 8 ± 2 min for the original MUSIC. Image scores of ROCK-MUSIC were significantly better than original MUSIC at the ventricular outflow tracts (3.9 ± 0.3 vs. 3.3 ± 0.6, P ROCK-MUSIC in the other anatomic locations. ROCK-MUSIC provided images of equal or superior image quality compared to original MUSIC, and this was achievable with 40% savings in scan time and without the need for physiologic signal. Magn Reson Med 78:472-483, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Ichikawa, Shintaro; Motosugi, Utaroh; Oishi, Naoki; Shimizu, Tatsuya; Wakayama, Tetsuya; Enomoto, Nobuyuki; Matsuda, Masanori; Onishi, Hiroshi
2018-04-01
The aim of this study was to evaluate the efficacy of multiphasic hepatic arterial phase (HAP) imaging using DISCO (differential subsampling with Cartesian ordering) in increasing the confidence of diagnosis of hepatocellular carcinoma (HCC). This retrospective study was approved by the institutional review board, and the requirement for informed patient consent was waived. Consecutive patients (from 2 study periods) with malignant liver nodules were examined by gadoxetic acid-enhanced magnetic resonance imaging using either multiphasic (6 phases; n = 135) or single (n = 230) HAP imaging, which revealed 519 liver nodules other than benign ones (HCC, 497; cholangiocarcinoma, 11; metastases, 10; and malignant lymphoma, 1). All nodules were scored in accordance with the Liver Imaging Reporting and Data System (LI-RADS v2014), with or without consideration of ring-like enhancement in multiphasic HAP images as a major feature. In the multiphasic HAP group, 178 of 191 HCCs were scored as LR-3 to LR-5 (3 [1.69%], 85 [47.8%], and 90 [50.6%], respectively). Upon considering ring-like enhancement in multiphasic HAP images as a major feature, 5 more HCCs were scored as LR-5 (95 [53.4%]), which was a significantly more confident diagnosis than that with single HAP images (295 of 306 HCCs scored as LR-3 to LR-5: 13 [4.41%], 147 [49.8%], and 135 [45.8%], respectively; P = 0.0296). There was no significant difference in false-positive or false-negative diagnoses between the multiphasic and single HAP groups (P = 0.8400 and 0.1043, respectively). Multiphasic HAP imaging can improve the confidence of diagnosis of HCCs in gadoxetic acid-enhanced magnetic resonance imaging.
Küstner, Thomas; Würslin, Christian; Schwartz, Martin; Martirosian, Petros; Gatidis, Sergios; Brendle, Cornelia; Seith, Ferdinand; Schick, Fritz; Schwenzer, Nina F; Yang, Bin; Schmidt, Holger
2017-08-01
To enable fast and flexible high-resolution four-dimensional (4D) MRI of periodic thoracic/abdominal motion for motion visualization or motion-corrected imaging. We proposed a Cartesian three-dimensional k-space sampling scheme that acquires a random combination of k-space lines in the ky/kz plane. A partial Fourier-like constraint compacts the sampling space to one half of k-space. The central k-space line is periodically acquired to allow an extraction of a self-navigated respiration signal used to populate a k-space of multiple breathing positions. The randomness of the acquisition (induced by periodic breathing pattern) yields a subsampled k-space that is reconstructed using compressed sensing. Local image evaluations (coefficient of variation and slope steepness through organs) reveal information about motion resolvability. Image quality is inspected by a blinded reading. Sequence and reconstruction method are made publicly available. The method is able to capture and reconstruct 4D images with high image quality and motion resolution within a short scan time of less than 2 min. These findings are supported by restricted-isometry-property analysis, local image evaluation, and blinded reading. The proposed method provides a clinical feasible setup to capture periodic respiratory motion with a fast acquisition protocol and can be extended by further surrogate signals to capture additional periodic motions. Retrospective parametrization allows for flexible tuning toward the targeted applications. Magn Reson Med 78:632-644, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Interpretability degrees of finitely axiomatized sequential theories
Visser, Albert
In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory-like Elementary Arithmetic EA, IΣ1, or the Gödel-Bernays theory of sets and classes GB-have suprema. This partially answers a question posed
Interpretability Degrees of Finitely Axiomatized Sequential Theories
Visser, Albert
2012-01-01
In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory —like Elementary Arithmetic EA, IΣ1, or the Gödel-Bernays theory of sets and classes GB— have suprema. This partially answers a question
Finite Topological Spaces as a Pedagogical Tool
Helmstutler, Randall D.; Higginbottom, Ryan S.
2012-01-01
We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…
Lectures on zeta functions over finite fields
Wan, Daqing
2007-01-01
These are the notes from the summer school in G\\"ottingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over finite fields, focusing on moment zeta functions and zeta functions of affine toric hypersurfaces.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...
Finite p′-nilpotent groups. II
Directory of Open Access Journals (Sweden)
S. Srinivasan
1987-01-01
Full Text Available In this paper we continue the study of finite p′-nilpotent groups that was started in the first part of this paper. Here we give a complete characterization of all finite groups that are not p′-nilpotent but all of whose proper subgroups are p′-nilpotent.
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
Regularization of finite temperature string theories
International Nuclear Information System (INIS)
Leblanc, Y.; Knecht, M.; Wallet, J.C.
1990-01-01
The tachyonic divergences occurring in the free energy of various string theories at finite temperature are eliminated through the use of regularization schemes and analytic continuations. For closed strings, we obtain finite expressions which, however, develop an imaginary part above the Hagedorn temperature, whereas open string theories are still plagued with dilatonic divergences. (orig.)
∗-supplemented subgroups of finite groups
Indian Academy of Sciences (India)
A subgroup H of a group G is said to be M∗-supplemented in G if ... normal subgroups and determined the structure of finite groups by using some ...... [12] Monakhov V S and Shnyparkov A V, On the p-supersolubility of a finite group with a.
Properties of the distributional finite Fourier transform
Carmichael, Richard D.
2016-01-01
The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.
Dynamic pricing and learning with finite inventories
den Boer, A.V.; Zwart, Bert
2013-01-01
We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season, perishes. The goal of the seller is to determine a pricing strategy
Dynamic pricing and learning with finite inventories
den Boer, A.V.; Zwart, Bert
We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a pricing strategy
Dynamic Pricing and Learning with Finite Inventories
A.P. Zwart (Bert); A.V. den Boer (Arnoud)
2015-01-01
htmlabstractWe study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a
Dynamic pricing and learning with finite inventories
Boer, den A.V.; Zwart, B.
2015-01-01
We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a pricing strategy
A Finite Model Property for Intersection Types
Directory of Open Access Journals (Sweden)
Rick Statman
2015-03-01
Full Text Available We show that the relational theory of intersection types known as BCD has the finite model property; that is, BCD is complete for its finite models. Our proof uses rewriting techniques which have as an immediate by-product the polynomial time decidability of the preorder <= (although this also follows from the so called beta soundness of BCD.
Why do probabilistic finite element analysis ?
Thacker, Ben H
2008-01-01
The intention of this book is to provide an introduction to performing probabilistic finite element analysis. As a short guideline, the objective is to inform the reader of the use, benefits and issues associated with performing probabilistic finite element analysis without excessive theory or mathematical detail.
Finite-Element Software for Conceptual Design
DEFF Research Database (Denmark)
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...
The finite-dimensional Freeman thesis.
Rudolph, Lee
2008-06-01
I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.
Factoring polynomials over arbitrary finite fields
Lange, T.; Winterhof, A.
2000-01-01
We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the existence of a deterministic algorithm which completely factors all monic polynomials of
Stochastic delocalization of finite populations
International Nuclear Information System (INIS)
Geyrhofer, Lukas; Hallatschek, Oskar
2013-01-01
The localization of populations of replicating bacteria, viruses or autocatalytic chemicals arises in various contexts, such as ecology, evolution, medicine or chemistry. Several deterministic mathematical models have been used to characterize the conditions under which localized states can form, and how they break down due to convective driving forces. It has been repeatedly found that populations remain localized unless the bias exceeds a critical threshold value, and that close to the transition the population is characterized by a diverging length scale. These results, however, have been obtained upon ignoring number fluctuations (‘genetic drift’), which are inevitable given the discreteness of the replicating entities. Here, we study the localization/delocalization of a finite population in the presence of genetic drift. The population is modeled by a linear chain of subpopulations, or demes, which exchange migrants at a constant rate. Individuals in one particular deme, called ‘oasis’, receive a growth rate benefit, and the total population is regulated to have constant size N. In this ecological setting, we find that any finite population delocalizes on sufficiently long time scales. Depending on parameters, however, populations may remain localized for a very long time. The typical waiting time to delocalization increases exponentially with both population size and distance to the critical wind speed of the deterministic approximation. We augment these simulation results by a mathematical analysis that treats the reproduction and migration of individuals as branching random walks subject to global constraints. For a particular constraint, different from a fixed population size constraint, this model yields a solvable first moment equation. We find that this solvable model approximates very well the fixed population size model for large populations, but starts to deviate as population sizes are small. Nevertheless, the qualitative behavior of the
An introduction to finite tight frames
Waldron, Shayne F D
2018-01-01
This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing. Key features and topics: * First book entirely devoted to finite frames * Extensive exercises and MATLAB examples for classroom use * Important examples, such as harmonic and Heisenberg frames, are presented in preliminary chapters, encouraging readers to explore and develop an intuitive feeling for tight frames * Later chapters delve into general theory details and recent research results * Many illustrations showing the special aspects of the geometry of finite frames * Provides an overview of the field of finite tight frames * Discusses future research directions in the field Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook ...
Finite density aspects of leptogenesis
International Nuclear Information System (INIS)
Hohenegger, Andreas
2010-01-01
Leptogenesis takes place in the early universe at high temperatures and densities and a deviation from equilibrium in the decay of heavy Majorana neutrinos is a fundamental requirement for the generation of the asymmetry. The equations, commonly used for its description, are largely based on classical Boltzmann equations (BEs) while the source of CP-violation is a quantum interference phenomenon. In view of this clash, it is desirable to study such processes in terms of non-equilibrium quantum field theory. On the other hand, it is simpler to solve BEs rather than the corresponding quantum field theoretical ones. Therefore, we derive modified BEs from first principles in the Kadanoff-Baym (KB) formalism. The results, found for a simple toy model, can be applied to popular phenomenological scenarios by analogy. This approach uncovers structural differences of the corrected equations and leads to different results for the form of the finite density contributions to the CP-violating parameter. In the case of degenerate heavy neutrino masses, corresponding to the popular scenario of resonant leptogenesis, it allows to explicitly distinguish between regimes where BEs are applicable or inapplicable.
Finite element coiled cochlea model
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
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
What is finiteness? (Abhishek Banerjee) (Indian Institute of Science)
Indian Academy of Sciences (India)
Do finites get enough respect? • Finiteness is easy, no? • Just count whether 1, 2, 3,... • But then we miss out on the true richness of the concept of finitness. • There's more finiteness around. In fact, finiteness is what helps us really understand things. 5 ...
Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method
Miyazaki, Yutaka; Tsuchiya, Takao
2012-07-01
The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.
Stokes, A V
1986-01-01
Communications Standards deals with the standardization of computer communication networks. This book examines the types of local area networks (LANs) that have been developed and looks at some of the relevant protocols in more detail. The work of Project 802 is briefly discussed, along with a protocol which has developed from one of the LAN standards and is now a de facto standard in one particular area, namely the Manufacturing Automation Protocol (MAP). Factors that affect the usage of networks, such as network management and security, are also considered. This book is divided into three se
Finite element modeling of electrically rectified piezoelectric energy harvesters
International Nuclear Information System (INIS)
Wu, P H; Shu, Y C
2015-01-01
Finite element models are developed for designing electrically rectified piezoelectric energy harvesters. They account for the consideration of common interface circuits such as the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits, as well as complicated structural configurations such as arrays of piezoelectric oscillators. The idea is to replace the energy harvesting circuit by the proposed equivalent load impedance together with the capacitance of negative value. As a result, the proposed framework is capable of being implemented into conventional finite element solvers for direct system-level design without resorting to circuit simulators. The validation based on COMSOL simulations carried out for various interface circuits by the comparison with the standard modal analysis model. The framework is then applied to the investigation on how harvested power is reduced due to fabrication deviations in geometric and material properties of oscillators in an array system. Remarkably, it is found that for a standard array system with strong electromechanical coupling, the drop in peak power turns out to be insignificant if the optimal load is carefully chosen. The second application is to design broadband energy harvesting by developing array systems with suitable interface circuits. The result shows that significant broadband is observed for the parallel (series) connection of oscillators endowed with the parallel-SSHI (series-SSHI) circuit technique. (paper)
Finite element modeling of electrically rectified piezoelectric energy harvesters
Wu, P. H.; Shu, Y. C.
2015-09-01
Finite element models are developed for designing electrically rectified piezoelectric energy harvesters. They account for the consideration of common interface circuits such as the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits, as well as complicated structural configurations such as arrays of piezoelectric oscillators. The idea is to replace the energy harvesting circuit by the proposed equivalent load impedance together with the capacitance of negative value. As a result, the proposed framework is capable of being implemented into conventional finite element solvers for direct system-level design without resorting to circuit simulators. The validation based on COMSOL simulations carried out for various interface circuits by the comparison with the standard modal analysis model. The framework is then applied to the investigation on how harvested power is reduced due to fabrication deviations in geometric and material properties of oscillators in an array system. Remarkably, it is found that for a standard array system with strong electromechanical coupling, the drop in peak power turns out to be insignificant if the optimal load is carefully chosen. The second application is to design broadband energy harvesting by developing array systems with suitable interface circuits. The result shows that significant broadband is observed for the parallel (series) connection of oscillators endowed with the parallel-SSHI (series-SSHI) circuit technique.
A General Finite Element Scheme for Limit State Analysis and Optimization
DEFF Research Database (Denmark)
Damkilde, Lars
1999-01-01
Limit State analysis which is based on a perfect material behaviour is used in many different applications primarily within Structural Engineering and Geotechnics. The calculation methods have not reached the same level of automation such as Finite Element Analysis for elastic structures....... The computer based systems are more ad hoc based and are typically not well-integrated with pre- and postprocessors well-known from commercial Finite Element codes.A finite element based formulation of limit state analysis is presented which allows an easy integration with standard Finite Element codes...... for elastic analysis. In this way the user is able to perform a limit state analysis on the same model used for elastic analysis only adding data for the yield surface.The method is based on the lower-bound theorem and uses stress-based elements with a linearized yield surface. The mathematical problem...
The Wigner distribution function for the su(2) finite oscillator and Dyck paths
International Nuclear Information System (INIS)
Oste, Roy; Jeugt, Joris Van der
2014-01-01
Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum, was developed. This distribution function is defined on discrete phase-space (a finite square grid), and can thus be referred to as the Wigner matrix. In the current paper, we compute this Wigner matrix (or rather, the pre-Wigner matrix, which is related to the Wigner matrix by a simple matrix multiplication) for the case of the su(2) finite oscillator. The first expression for the matrix elements involves sums over squares of Krawtchouk polynomials, and follows from standard techniques. We also manage to present a second solution, where the matrix elements are evaluations of Dyck polynomials. These Dyck polynomials are defined in terms of the well-known Dyck paths. This combinatorial expression of the pre-Wigner matrix elements turns out to be particularly simple. (paper)
Clifford algebra in finite quantum field theories
International Nuclear Information System (INIS)
Moser, M.
1997-12-01
We consider the most general power counting renormalizable and gauge invariant Lagrangean density L invariant with respect to some non-Abelian, compact, and semisimple gauge group G. The particle content of this quantum field theory consists of gauge vector bosons, real scalar bosons, fermions, and ghost fields. We assume that the ultimate grand unified theory needs no cutoff. This yields so-called finiteness conditions, resulting from the demand for finite physical quantities calculated by the bare Lagrangean. In lower loop order, necessary conditions for finiteness are thus vanishing beta functions for dimensionless couplings. The complexity of the finiteness conditions for a general quantum field theory makes the discussion of non-supersymmetric theories rather cumbersome. Recently, the F = 1 class of finite quantum field theories has been proposed embracing all supersymmetric theories. A special type of F = 1 theories proposed turns out to have Yukawa couplings which are equivalent to generators of a Clifford algebra representation. These algebraic structures are remarkable all the more than in the context of a well-known conjecture which states that finiteness is maybe related to global symmetries (such as supersymmetry) of the Lagrangean density. We can prove that supersymmetric theories can never be of this Clifford-type. It turns out that these Clifford algebra representations found recently are a consequence of certain invariances of the finiteness conditions resulting from a vanishing of the renormalization group β-function for the Yukawa couplings. We are able to exclude almost all such Clifford-like theories. (author)
A Novel Polygonal Finite Element Method: Virtual Node Method
Tang, X. H.; Zheng, C.; Zhang, J. H.
2010-05-01
Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.
COMPREHENSIVE GYROKINETIC SIMULATION OF TOKAMAK TURBULENCE AT FINITE RELATIVE GYRORADIUS
International Nuclear Information System (INIS)
WALTZ, R.E.; CANDY, J.; ROSENBLUTH, M.N.
2002-01-01
OAK B202 COMPREHENSIVE GYROKINETIC SIMULATION OF TOKAMAK TURBULENCE AT FINITE RELATIVE GYRORADIUS. A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate turbulent transport in actual experimental profiles and allow direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite beta, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius (ρ*) so as to treat the profile shear stabilization effects which break gyroBohm scaling. The code operates in a cyclic flux tube limit which allows only gyroBohm scaling and a noncyclic radial annulus with physical profile variation. The later requires an adaptive source to maintain equilibrium profiles. Simple ITG simulations demonstrate the broken gyroBohm scaling depends on the actual rotational velocity shear rates competing with mode growth rates, direct comprehensive simulations of the DIII-D ρ*-scaled L-mode experiments are presented as a quantitative test of gyrokinetics and the paradigm
Finite Element Simulation of Diametral Strength Test of Hydroxyapatite
International Nuclear Information System (INIS)
Ozturk, Fahrettin; Toros, Serkan; Evis, Zafer
2011-01-01
In this study, the diametral strength test of sintered hydroxyapatite was simulated by the finite element software, ABAQUS/Standard. Stress distributions on diametral test sample were determined. The effect of sintering temperature on stress distribution of hydroxyapatite was studied. It was concluded that high sintering temperatures did not reduce the stress on hydroxyapatite. It had a negative effect on stress distribution of hydroxyapatite after 1300 deg. C. In addition to the porosity, other factors (sintering temperature, presence of phases and the degree of crystallinity) affect the diametral strength of the hydroxyapatite.
Finite difference evolution equations and quantum dynamical semigroups
International Nuclear Information System (INIS)
Ghirardi, G.C.; Weber, T.
1983-12-01
We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)
Non-perturbative Debye mass in finite-T QCD
Kajantie, Keijo; Peisa, J; Rajantie, A; Rummukainen, K; Shaposhnikov, Mikhail E
1997-01-01
Employing a non-perturbative gauge invariant definition of the Debye screening mass m_D in the effective field theory approach to finite T QCD, we use 3d lattice simulations to determine the leading O(g^2) and to estimate the next-to-leading O(g^3) corrections to m_D in the high temperature region. The O(g^2) correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD.
Critical acceleration of finite temperature SU(2) gauge simulations
International Nuclear Information System (INIS)
Ben-Av, R.; Marcu, M.; Hamburg Univ.; Solomon, S.
1991-04-01
We present a cluster algorithm that strongly reduces critical slowing down for the SU(2) gauge theory on one time slice. The idea that underlies the new algorithm is to perform efficient flips for the signs of Polyakov loops. Ergodicity is ensured by combining it with a standard local algorithm. We show how to quantify critical slowing down for such a mixed algorithm. At the finite temperature transition, the dynamical critical exponent z is ≅0.5, whereas for the purely local algoirthm z ≅ 2. (orig.)
The theory of finitely generated commutative semigroups
Rédei, L; Stark, M; Gravett, K A H
1966-01-01
The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single """"fundamental theorem"""" and exhibits resemblance in many respects to the algebraic theory of numbers. The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. This volume is comprised of five chapters and begins with preliminaries on finitely generated commutative semigroups before
Finite Markov processes and their applications
Iosifescu, Marius
2007-01-01
A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch
An introduction to finite projective planes
Albert, Abraham Adrian
2015-01-01
Geared toward both beginning and advanced undergraduate and graduate students, this self-contained treatment offers an elementary approach to finite projective planes. Following a review of the basics of projective geometry, the text examines finite planes, field planes, and coordinates in an arbitrary plane. Additional topics include central collineations and the little Desargues' property, the fundamental theorem, and examples of finite non-Desarguesian planes.Virtually no knowledge or sophistication on the part of the student is assumed, and every algebraic system that arises is defined and
Polyelectrolyte Bundles: Finite size at thermodynamic equilibrium?
Sayar, Mehmet
2005-03-01
Experimental observation of finite size aggregates formed by polyelectrolytes such as DNA and F-actin, as well as synthetic polymers like poly(p-phenylene), has created a lot of attention in recent years. Here, bundle formation in rigid rod-like polyelectrolytes is studied via computer simulations. For the case of hydrophobically modified polyelectrolytes finite size bundles are observed even in the presence of only monovalent counterions. Furthermore, in the absence of a hydrophobic backbone, we have also observed formation of finite size aggregates via multivalent counterion condensation. The size distribution of such aggregates and the stability is analyzed in this study.
Books and monographs on finite element technology
Noor, A. K.
1985-01-01
The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.
Modelling robot's behaviour using finite automata
Janošek, Michal; Žáček, Jaroslav
2017-07-01
This paper proposes a model of a robot's behaviour described by finite automata. We split robot's knowledge into several knowledge bases which are used by the inference mechanism of the robot's expert system to make a logic deduction. Each knowledgebase is dedicated to the particular behaviour domain and the finite automaton helps us switching among these knowledge bases with the respect of actual situation. Our goal is to simplify and reduce complexity of one big knowledgebase splitting it into several pieces. The advantage of this model is that we can easily add new behaviour by adding new knowledgebase and add this behaviour into the finite automaton and define necessary states and transitions.
Electrical machine analysis using finite elements
Bianchi, Nicola
2005-01-01
OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I
Finite element analysis of piezoelectric materials
International Nuclear Information System (INIS)
Lowrie, F.; Stewart, M.; Cain, M.; Gee, M.
1999-01-01
This guide is intended to help people wanting to do finite element analysis of piezoelectric materials by answering some of the questions that are peculiar to piezoelectric materials. The document is not intended as a complete beginners guide for finite element analysis in general as this is better dealt with by the individual software producers. The guide is based around the commercial package ANSYS as this is a popular package amongst piezoelectric material users, however much of the information will still be useful to users of other finite element codes. (author)
International Nuclear Information System (INIS)
Agnihotri, Newal
2003-01-01
The article describes the benefits of and required process and recommendations for implementing the standardization of training in the nuclear power industry in the United States and abroad. Current Information and Communication Technologies (ICT) enable training standardization in the nuclear power industry. The delivery of training through the Internet, Intranet and video over IP will facilitate this standardization and bring multiple benefits to the nuclear power industry worldwide. As the amount of available qualified and experienced professionals decreases because of retirements and fewer nuclear engineering institutions, standardized training will help increase the number of available professionals in the industry. Technology will make it possible to use the experience of retired professionals who may be interested in working part-time from a remote location. Well-planned standardized training will prevent a fragmented approach among utilities, and it will save the industry considerable resources in the long run. It will also ensure cost-effective and safe nuclear power plant operation
Implicit and fully implicit exponential finite difference methods
Indian Academy of Sciences (India)
Burgers' equation; exponential finite difference method; implicit exponential finite difference method; ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. ... Current Issue
Rapoport, Diego L.
2011-01-01
In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown's primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard's gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation
Han, Fei; Zhou, Ziwu; Du, Dongsu; Gao, Yu; Rashid, Shams; Cao, Minsong; Shaverdian, Narek; Hegde, John V; Steinberg, Michael; Lee, Percy; Raldow, Ann; Low, Daniel A; Sheng, Ke; Yang, Yingli; Hu, Peng
2018-06-01
To optimize and evaluate the respiratory motion-resolved, self-gated 4D-MRI using Rotating Cartesian K-space (ROCK-4D-MRI) method in a 0.35 T MRI-guided radiotherapy (MRgRT) system. The study included seven patients with abdominal tumors treated on the MRgRT system. ROCK-4D-MRI and 2D-CINE, was performed immediately after one of the treatment fractions. Motion quantification based on 4D-MRI was compared with those based on 2D-CINE. The image quality of 4D-MRI was evaluated against 4D-CT. The gross tumor volumes (GTV) were defined based on individual respiratory phases of both 4D-MRI and 4D-CT and compared for their variability over the respiratory cycle. The motion measurements based on 4D-MRI matched well with 2D-CINE, with differences of 1.04 ± 0.52 mm in the superior-inferior and 0.54 ± 0.21 mm in the anterior-posterior directions. The image quality scores of 4D-MRI were significantly higher than 4D-CT, with better tumor contrast (3.29 ± 0.76 vs. 1.86 ± 0.90) and less motion artifacts (3.57 ± 0.53 vs. 2.29 ± 0.95). The GTVs were more consistent in 4D-MRI than in 4D-CT, with significantly smaller GTV variability (9.31 ± 4.58% vs. 34.27 ± 23.33%). Our study demonstrated the clinical feasibility of using the ROCK-4D-MRI to acquire high quality, respiratory motion-resolved 4D-MRI in a low-field MRgRT system. The 4D-MRI image could provide accurate dynamic information for radiotherapy treatment planning. Copyright © 2018 Elsevier B.V. All rights reserved.
Super-renormalizable or finite Lee–Wick quantum gravity
Directory of Open Access Journals (Sweden)
Leonardo Modesto
2016-08-01
Full Text Available We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole in k2=0 and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee–Wick and Cutkosky, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists of the graviton and short lived elementary unstable particles that we named “anti-gravitons” because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the conjugate complex of the micro black hole precursor can be interpreted as a white hole precursor consistently with the 't Hooft complementarity principle. It is proved that the quantum theory is super-renormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularity-free Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new super-renormalizable or finite Lee–Wick standard model of particle physics.
Energy Technology Data Exchange (ETDEWEB)
Geisler, G C [Pennsylvania State University (United States)
1974-07-01
At the conference there was a considerable interest in research reactor standards and effluent standards in particular. On the program, this is demonstrated by the panel discussion on effluents, the paper on argon 41 measured by Sims, and the summary paper by Ringle, et al. on the activities of ANS research reactor standards committee (ANS-15). As a result, a meeting was organized to discuss the proposed ANS standard on research reactor effluents (15.9). This was held on Tuesday evening, was attended by members of the ANS-15 committee who were present at the conference, participants in the panel discussion on the subject, and others interested. Out of this meeting came a number of excellent suggestions for changes which will increase the utility of the standard, and a strong recommendation that the effluent standard (15.9) be combined with the effluent monitoring standard. It is expected that these suggestions and recommendations will be incorporated and a revised draft issued for comment early this summer. (author)
International Nuclear Information System (INIS)
Fichtner, N.; Becker, K.; Bashir, M.
1981-01-01
This compilation of all nuclear standards available to the authors by mid 1980 represents the third, carefully revised edition of a catalogue which was first published in 1975 as EUR 5362. In this third edition several changes have been made. The title has been condensed. The information has again been carefully up-dated, covering all changes regarding status, withdrawal of old standards, new projects, amendments, revisions, splitting of standards into several parts, combination of several standards into one, etc., as available to the authors by mid 1980. The speed with which information travels varies and requires in many cases rather tedious and cumbersome inquiries. Also, the classification scheme has been revised with the goal of better adjustment to changing situations and priorities. Whenever it turned out to be difficult to attribute a standard to a single subject category, multiple listings in all relevant categories have been made. As in previous editions, within the subcategories the standards are arranged by organization (in Categorie 2.1 by country) alphabetically and in ascending numerical order. It covers all relevant areas of power reactors, the fuel cycle, radiation protection, etc., from the basic laws and governmental regulations, regulatory guides, etc., all the way to voluntary industrial standards and codes of pratice. (orig./HP)
HEATING-7, Multidimensional Finite-Difference Heat Conduction Analysis
International Nuclear Information System (INIS)
2000-01-01
1 - Description of program or function: HEATING 7.2i and 7.3 are the most recent developments in a series of heat-transfer codes and obsolete all previous versions distributed by RSICC as SCA-1/HEATING5 and PSR-199/HEATING 6. Note that Unix and PC versions of HEATING7 are available in the CCC-545/SCALE 4.4 package. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat- generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- and position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a run-time memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. In June 1997 HEATING 7.3 was added to the HEATING 7.2i packages, and the Unix and PC versions of both 7.2i and 7.3 were merged into one package. HEATING 7.3 is being released as a beta-test version; therefore, it does not entirely replace HEATING 7.2i. There is no published documentation for HEATING 7.3; but a listing of input specifications, which reflects changes for 7.3, is included in the PSR-199 documentation. For 3-D
Polynomials in finite geometries and combinatorics
Blokhuis, A.; Walker, K.
1993-01-01
It is illustrated how elementary properties of polynomials can be used to attack extremal problems in finite and euclidean geometry, and in combinatorics. Also a new result, related to the problem of neighbourly cylinders is presented.
Finite Volumes for Complex Applications VII
Ohlberger, Mario; Rohde, Christian
2014-01-01
The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative propert...
The finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
Quantiles for Finite Mixtures of Normal Distributions
Rahman, Mezbahur; Rahman, Rumanur; Pearson, Larry M.
2006-01-01
Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)
Jauch-Piron logics with finiteness conditions
Rogalewicz, Vladimír
1991-04-01
We show that there are no non-Boolean block-finite orthomodular posets possessing a unital set of Jauch-Piron states. Thus, an orthomodular poset representing a quantum physical system must have infinitely many blocks.
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Finite boson mappings of fermion systems
International Nuclear Information System (INIS)
Johnson, C.W.; Ginocchio, J.N.
1994-01-01
We discuss a general mapping of fermion pairs to bosons that preserves Hermitian conjugation, with an eye towards producing finite and usable boson Hamiltonians that approximate well the low-energy dynamics of a fermion Hamiltonian
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
A note on powers in finite fields
Aabrandt, Andreas; Lundsgaard Hansen, Vagn
2016-08-01
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.
Finite N=1 SUSY gauge field theories
International Nuclear Information System (INIS)
Kazakov, D.I.
1986-01-01
The authors give a detailed description of the method to construct finite N=1 SUSY gauge field theories in the framework of N=1 superfields within dimensional regularization. The finiteness of all Green functions is based on supersymmetry and gauge invariance and is achieved by a proper choice of matter content of the theory and Yukawa couplings in the form Y i =f i (ε)g, where g is the gauge coupling, and the function f i (ε) is regular at ε=0 and is calculated in perturbation theory. Necessary and sufficient conditions for finiteness are determined already in the one-loop approximation. The correspondence with an earlier proposed approach to construct finite theories based on aigenvalue solutions of renormalization-group equations is established
ANSYS mechanical APDL for finite element analysis
Thompson, Mary Kathryn
2017-01-01
ANSYS Mechanical APDL for Finite Element Analysis provides a hands-on introduction to engineering analysis using one of the most powerful commercial general purposes finite element programs on the market. Students will find a practical and integrated approach that combines finite element theory with best practices for developing, verifying, validating and interpreting the results of finite element models, while engineering professionals will appreciate the deep insight presented on the program's structure and behavior. Additional topics covered include an introduction to commands, input files, batch processing, and other advanced features in ANSYS. The book is written in a lecture/lab style, and each topic is supported by examples, exercises and suggestions for additional readings in the program documentation. Exercises gradually increase in difficulty and complexity, helping readers quickly gain confidence to independently use the program. This provides a solid foundation on which to build, preparing readers...
Collaborative Systems – Finite State Machines
Directory of Open Access Journals (Sweden)
Ion IVAN
2011-01-01
Full Text Available In this paper the finite state machines are defined and formalized. There are presented the collaborative banking systems and their correspondence is done with finite state machines. It highlights the role of finite state machines in the complexity analysis and performs operations on very large virtual databases as finite state machines. It builds the state diagram and presents the commands and documents transition between the collaborative systems states. The paper analyzes the data sets from Collaborative Multicash Servicedesk application and performs a combined analysis in order to determine certain statistics. Indicators are obtained, such as the number of requests by category and the load degree of an agent in the collaborative system.
Chiral crossover transition in a finite volume
Shi, Chao; Jia, Wenbao; Sun, An; Zhang, Liping; Zong, Hongshi
2018-02-01
Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo-transition temperature {T}{{c}} of the crossover, showing a significant decrease in {T}{{c}} as L decreases below 3 fm. Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 51405027), the Fundamental Research Funds for the Central Universities (020414380074), China Postdoctoral Science Foundation (2016M591808) and Open Research Foundation of State Key Lab. of Digital Manufacturing Equipment & Technology in Huazhong University of Science & Technology (DMETKF2015015)
A Finite Axiomatization of G-Dependence
Paolini, Gianluca
2015-01-01
We show that a form of dependence known as G-dependence (originally introduced by Grelling) admits a very natural finite axiomatization, as well as Armstrong relations. We also give an explicit translation between functional dependence and G-dependence.
Review on Finite Element Method * ERHUNMWUN, ID ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and ... residual procedures, are examples of the direct approach ... The paper centred on the "stiffness and deflection of ...
Finite element bending behaviour of discretely delaminated ...
African Journals Online (AJOL)
user
due to their light weight, high specific strength and stiffness properties. ... cylindrical shell roofs respectively using finite element method with centrally located .... where { }ε and { }γ are the direct and shear strains in midplane and { }κ denotes ...
A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension
Energy Technology Data Exchange (ETDEWEB)
Garrick, Daniel P. [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States); Owkes, Mark [Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT (United States); Regele, Jonathan D., E-mail: jregele@iastate.edu [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States)
2017-06-15
Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.
Three-dimensional body-wave model of Nepal using finite difference tomography
Ho, T. M.; Priestley, K.; Roecker, S. W.
2017-12-01
The processes occurring during continent-continent collision are still poorly understood. Ascertaining the seismic properties of the crust and uppermost mantle in such settings provides insight into continental rheology and geodynamics. The most active present-day continent-continent collision is that of India with Eurasia which has created the Himalayas and the Tibetan Plateau. Nepal provides an ideal laboratory for imaging the crustal processes resulting from the Indo-Eurasia collision. We build body wave models using local body wave arrivals picked at stations in Nepal deployed by the Department of Mining and Geology of Nepal. We use the tomographic inversion method of Roecker et al. [2006], the key feature of which is that the travel times are generated using a finite difference solution to the eikonal equation. The advantage of this technique is increased accuracy in the highly heterogeneous medium expected for the Himalayas. Travel times are calculated on a 3D Cartesian grid with a grid spacing of 6 km and intragrid times are estimated by trilinear interpolation. The gridded area spans a region of 80-90o longitude and 25-30o latitude. For a starting velocity model, we use IASP91. Inversion is performed using the LSQR algorithm. Since the damping parameter can have a significant effect on the final solution, we tested a range of damping parameters to fully explore its effect. Much of the seismicity is clustered to the West of Kathmandu at depths Small areas of strong fast wavespeeds exist in the centre of the region in the upper 30 km of the crust. At depths of 40-50 km, large areas of slow wavespeeds are present which track along the plate boundary.
High Resolution DNS of Turbulent Flows using an Adaptive, Finite Volume Method
Trebotich, David
2014-11-01
We present a new computational capability for high resolution simulation of incompressible viscous flows. Our approach is based on cut cell methods where an irregular geometry such as a bluff body is intersected with a rectangular Cartesian grid resulting in cut cells near the boundary. In the cut cells we use a conservative discretization based on a discrete form of the divergence theorem to approximate fluxes for elliptic and hyperbolic terms in the Navier-Stokes equations. Away from the boundary the method reduces to a finite difference method. The algorithm is implemented in the Chombo software framework which supports adaptive mesh refinement and massively parallel computations. The code is scalable to 200,000 + processor cores on DOE supercomputers, resulting in DNS studies at unprecedented scale and resolution. For flow past a cylinder in transition (Re = 300) we observe a number of secondary structures in the far wake in 2D where the wake is over 120 cylinder diameters in length. These are compared with the more regularized wake structures in 3D at the same scale. For flow past a sphere (Re = 600) we resolve an arrowhead structure in the velocity in the near wake. The effectiveness of AMR is further highlighted in a simulation of turbulent flow (Re = 6000) in the contraction of an oil well blowout preventer. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Contract Number DE-AC02-05-CH11231.
Dynamic Pricing and Learning with Finite Inventories
Zwart, Bert; Boer, Arnoud
2015-01-01
We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season, perishes. The goal of the seller is to determine a pricing strategy that maximizes the expected revenue. Inference on the unknown parameters is made by maximum likelihood estimation. We propose a pricing strategy for this problem, and show that the Regret - which i...
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.
Finite W-algebras and intermediate statistics
International Nuclear Information System (INIS)
Barbarin, F.; Ragoucy, E.; Sorba, P.
1995-01-01
New realizations of finite W-algebras are constructed by relaxing the usual constraint conditions. Then finite W-algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well adapted for a possible generalization of the anyon statistics. ((orig.))
Finite Optimal Stopping Problems: The Seller's Perspective
Hemmati, Mehdi; Smith, J. Cole
2011-01-01
We consider a version of an optimal stopping problem, in which a customer is presented with a finite set of items, one by one. The customer is aware of the number of items in the finite set and the minimum and maximum possible value of each item, and must purchase exactly one item. When an item is presented to the customer, she or he observes its…
Directory of Open Access Journals (Sweden)
S. Srinivasan
1987-01-01
Full Text Available In this paper we consider finite p′-nilpotent groups which is a generalization of finite p-nilpotent groups. This generalization leads us to consider the various special subgroups such as the Frattini subgroup, Fitting subgroup, and the hypercenter in this generalized setting. The paper also considers the conditions under which product of p′-nilpotent groups will be a p′-nilpotent group.
Entangling transformations in composite finite quantum systems
International Nuclear Information System (INIS)
Vourdas, A
2003-01-01
Phase space methods are applied in the context of finite quantum systems. 'Galois quantum systems' (with a dimension which is a power of a prime number) are considered, and symplectic Sp(2,Z(d)) transformations are studied. Composite systems comprising two finite quantum systems are also considered. Symplectic Sp(4,Z(d)) transformations are classified into local and entangling ones and the necessary matrices which perform such transformations are calculated numerically
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Probabilistic finite elements for fracture mechanics
Besterfield, Glen
1988-01-01
The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.
Group foliation of finite difference equations
Thompson, Robert; Valiquette, Francis
2018-06-01
Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.
Anomalies in curved spacetime at finite temperature
International Nuclear Information System (INIS)
Boschi-Filho, H.; Natividade, C.P.
1993-01-01
We discuss the problem of the breakdown of conformal and gauge symmetries at finite temperature in curved spacetime background, when the changes in the background are gradual. We obtain the expressions for the Seeley's coefficients and the heat kernel expansion in this regime. As applications, we consider the self-interacting lambda phi''4 and chiral Schwinger models in curved backgrounds at finite temperature. (Author) 9 refs
Collision Probabilities for Finite Cylinders and Cuboids
Energy Technology Data Exchange (ETDEWEB)
Carlvik, I
1967-05-15
Analytical formulae have been derived for the collision probabilities of homogeneous finite cylinders and cuboids. The formula for the finite cylinder contains double integrals, and the formula for the cuboid only single integrals. Collision probabilities have been calculated by means of the formulae and compared with values obtained by other authors. It was found that the calculations using the analytical formulae are much quicker and give higher accuracy than Monte Carlo calculations.
Rough Finite State Automata and Rough Languages
Arulprakasam, R.; Perumal, R.; Radhakrishnan, M.; Dare, V. R.
2018-04-01
Sumita Basu [1, 2] recently introduced the concept of a rough finite state (semi)automaton, rough grammar and rough languages. Motivated by the work of [1, 2], in this paper, we investigate some closure properties of rough regular languages and establish the equivalence between the classes of rough languages generated by rough grammar and the classes of rough regular languages accepted by rough finite automaton.
Yamamoto, Naoki; Kanazawa, Takuya
2009-01-01
We study the properties of QCD at high baryon density in a finite volume where color superconductivity occurs. We derive exact sum rules for complex eigenvalues of the Dirac operator at finite chemical potential, and show that the Dirac spectrum is directly related to the color superconducting gap $\\Delta$. Also, we find a characteristic signature of color superconductivity: an X-shaped spectrum of partition function zeros in the complex quark mass plane near the origin, reflecting the $Z(2)_...
Surgery simulation using fast finite elements
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1996-01-01
This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism......This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism...
Generators for finite depth subfactor planar algebras
Indian Academy of Sciences (India)
The main result of Kodiyalam and Tupurani [3] shows that a subfactor planar algebra of finite depth is singly generated with a finite presentation. If P is a subfactor planar algebra of depth k, it is shown there that a single 2k-box generates P. It is natural to ask what the smallest s is such that a single s-box generates P. While ...
Thomas Fermi model of finite nuclei
International Nuclear Information System (INIS)
Boguta, J.; Rafelski, J.
1977-01-01
A relativistic Thomas-Fermi model of finite-nuclei is considered. The effective nuclear interaction is mediated by exchanges of isoscalar scalar and vector mesons. The authors include also a self-interaction of the scalar meson field and the Coulomb repulsion of the protons. The parameters of the model are constrained by the average nuclear properties. The Thomas-Fermi equations are solved numerically for finite, stable nuclei. The particular case of 208 82 Pb is considered in more detail. (Auth.)
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
International Nuclear Information System (INIS)
Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.
2006-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)
Farmer, R. E.
1982-11-01
The MATE (Modular Automatic Test Equipment) program was developed to combat the proliferation of unique, expensive ATE within the Air Force. MATE incorporates a standard management approach and a standard architecture designed to implement a cradle-to-grave approach to the acquisition of ATE and to significantly reduce the life cycle cost of weapons systems support. These standards are detailed in the MATE Guides. The MATE Guides assist both the Air Force and Industry in implementing the MATE concept, and provide the necessary tools and guidance required for successful acquisition of ATE. The guides also provide the necessary specifications for industry to build MATE-qualifiable equipment. The MATE architecture provides standards for all key interfaces of an ATE system. The MATE approach to the acquisition and management of ATE has been jointly endorsed by the commanders of Air Force Systems Command and Air Force Logistics Command as the way of doing business in the future.
A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids
Energy Technology Data Exchange (ETDEWEB)
McCorquodale, Peter; Colella, Phillip
2011-01-28
We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.
Zhu, D.; Zhu, H.; Luo, Y.; Chen, X.
2008-12-01
We use a new finite difference method (FDM) and the slip-weakening law to model the rupture dynamics of a non-planar fault embedded in a 3-D elastic media with free surface. The new FDM, based on boundary- conforming grid, sets up the mapping equations between the curvilinear coordinate and the Cartesian coordinate and transforms irregular physical space to regular computational space; it also employs a higher- order non-staggered DRP/opt MacCormack scheme which is of low dispersion and low dissipation so that the high accuracy and stability of our rupture modeling are guaranteed. Compared with the previous methods, not only we can compute the spontaneous rupture of an arbitrarily shaped fault, but also can model the influence of the surface topography on the rupture process of earthquake. In order to verify the feasibility of this method, we compared our results and other previous results, and found out they matched perfectly. Thanks to the boundary-conforming FDM, problems such as dynamic rupture with arbitrary dip, strike and rake over an arbitrary curved plane can be handled; and supershear or subshear rupture can be simulated with different parameters such as the initial stresses and the critical slip displacement Dc. Besides, our rupture modeling is economical to be implemented owing to its high efficiency and does not suffer from displacement leakage. With the help of inversion data of rupture by field observations, this method is convenient to model rupture processes and seismograms of natural earthquakes.
International Nuclear Information System (INIS)
Farhanieh, B.; Amanifard, N.; Ghorbanian, K.
2002-01-01
An unsteady two-dimensional numerical investigation was performed on the viscous flow passing through a multi-blade cascade. A Cartesian finite-volume approach was linked to Van-Leer's and Roe's flux splitting schemes to evaluate inviscid flux terms. To prevent the oscillatory behavior of numerical results and to increase the accuracy, Mon tonic Upstream Scheme for Conservation Laws was added to flux splitting schemes. The Baldwin-Lo max (B L) turbulence model was implemented to solve the turbulent case studies. Implicit solution was also provided using Lower and Upper (L U) decomposition technique to compare with explicit solutions. To validate the numerical procedure, two test cases are prepared and flow over a Na Ca 0012 airfoil was investigated and the pressure coefficients were compared to the reference data. The numerical solver was implemented to study the flow passing over a compressor cascade. The results of various combinations of splitting schemes and the Mon tonic Upstream Scheme for Conventional Laws limiter were compared with each other to find the suitable methods in cascade problems. Finally the convergence histories of implemented schemes were compared to each other to show the behavior of the solver in using various methods before implementation of them in flow instability studies
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
International Nuclear Information System (INIS)
Lee, Young Jung; Lee, Sang Jin; Choun, Young Sun; Seo, Jeong Moon
2003-05-01
The objective of this research is to assess the performance of lower order solid finite elements which will be ultimately applied into the safety analysis of nuclear containment building. For the safety analysis of large structures such as nuclear containment building, efficient lower order finite element is necessarily required to calculate the structural response of containment building with low computational cost. In this study, the state of the art formulations of lower order solid finite element are throughly reviewed and the best possible solid finite element is adopted into the development of nuclear containment analysis system. Three 8-node solid finite elements based on standard strain-displacement relationship, B-bar method and EAS method are implemented as computer modules and completely tested with various plate and shell structures. The present results can be directly applied into the analysis code development for general reinforced concrete structures
Stimulus-Response Theory of Finite Automata, Technical Report No. 133.
Suppes, Patrick
The central aim of this paper and its projected successors is to prove in detail that stimulus-response theory, or at least a mathematically precise version, can give an account of the learning of many phrase-structure grammars. Section 2 is concerned with standard notions of finite and probabilistic automata. An automaton is defined as a device…
Modelling optimization involving different types of elements in finite element analysis
International Nuclear Information System (INIS)
Wai, C M; Rivai, Ahmad; Bapokutty, Omar
2013-01-01
Finite elements are used to express the mechanical behaviour of a structure in finite element analysis. Therefore, the selection of the elements determines the quality of the analysis. The aim of this paper is to compare and contrast 1D element, 2D element, and 3D element used in finite element analysis. A simple case study was carried out on a standard W460x74 I-beam. The I-beam was modelled and analyzed statically with 1D elements, 2D elements and 3D elements. The results for the three separate finite element models were compared in terms of stresses, deformation and displacement of the I-beam. All three finite element models yield satisfactory results with acceptable errors. The advantages and limitations of these elements are discussed. 1D elements offer simplicity although lacking in their ability to model complicated geometry. 2D elements and 3D elements provide more detail yet sophisticated results which require more time and computer memory in the modelling process. It is also found that the choice of element in finite element analysis is influence by a few factors such as the geometry of the structure, desired analysis results, and the capability of the computer
Riehle, Fritz
2006-01-01
Of all measurement units, frequency is the one that may be determined with the highest degree of accuracy. It equally allows precise measurements of other physical and technical quantities, whenever they can be measured in terms of frequency.This volume covers the central methods and techniques relevant for frequency standards developed in physics, electronics, quantum electronics, and statistics. After a review of the basic principles, the book looks at the realisation of commonly used components. It then continues with the description and characterisation of important frequency standards
XML Diagnostics Description Standard
International Nuclear Information System (INIS)
Neto, A.; Fernandes, H.; Varandas, C.; Lister, J.; Yonekawa, I.
2006-01-01
A standard for the self-description of fusion plasma diagnostics will be presented, based on the Extensible Markup Language (XML). The motivation is to maintain and organise the information on all the components of a laboratory experiment, from the hardware to the access security, to save time and money when problems arises. Since there is no existing standard to organise this kind of information, every Association stores and organises each experiment in different ways. This can lead to severe problems when the organisation schema is poorly documented or written in national languages. The exchange of scientists, researchers and engineers between laboratories is a common practice nowadays. Sometimes they have to install new diagnostics or to update existing ones and frequently they lose a great deal of time trying to understand the currently installed system. The most common problems are: no documentation available; the person who understands it has left; documentation written in the national language. Standardisation is the key to solving all the problems mentioned. From the commercial information on the diagnostic (component supplier; component price) to the hardware description (component specifications; drawings) to the operation of the equipment (finite state machines) through change control (who changed what and when) and internationalisation (information at least in the native language and in English), a common XML schema will be proposed. This paper will also discuss an extension of these ideas to the self-description of ITER plant systems, since the problems will be identical. (author)
Indian Academy of Sciences (India)
.86: Ethernet over LAPS. Standard in China and India. G.7041: Generic Framing Procedure (GFP). Supports Ethernet as well as other data formats (e.g., Fibre Channel); Protocol of ... IEEE 802.3x for flow control of incoming Ethernet data ...
DEFF Research Database (Denmark)
Henningsson, Stefan
2014-01-01
International e-Customs is going through a standardization process. Driven by the need to increase control in the trade process to address security challenges stemming from threats of terrorists, diseases, and counterfeit products, and to lower the administrative burdens on traders to stay...
DEFF Research Database (Denmark)
Henningsson, Stefan
2016-01-01
International e-Customs is going through a standardization process. Driven by the need to increase control in the trade process to address security challenges stemming from threats of terrorists, diseases, and counterfeit products, and to lower the administrative burdens on traders to stay...
International Nuclear Information System (INIS)
Marshall, N.H.
1981-01-01
Because of its vast software investment in Fortran programs, the nuclear community has an inherent interest in the evolution of Fortran. This paper reviews the impact of the new Fortran 77 standard and discusses the projected changes which can be expected in the future
Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method
Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N.
2016-01-01
We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385-404]. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely det...
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.
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2012-07-01
Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...