Directory of Open Access Journals (Sweden)
O. A. Domínguez-Ramírez
2006-01-01
Full Text Available Perception and interaction with virtual surfaces, through kinaesthetic sensation and visual stimuli, is the basic issue of a haptic interface. When the virtual or real object is in a remote location, and guidance is required to perceive kinaesthetic feedback, a haptic guidance scheme is required. In this document, with purpose of haptic-guided exploration, a new scheme for simultaneous control of force and cartesian position is proposed without using inverse kinematics, and without using the dynamic model of PHANToM, though a strict stability analysis includes the dynamic model of PHANToM. We rely on our previously proposed results to propose a new haptic cartesian controller to reduce the burden of computing cartesian forces in PHANToM. Furthermore, a time base generator for finite-time tracking is also proposed to achieve very fast tracking and high precision, which translated into high fidelity kinaesthetic feedback.
Directory of Open Access Journals (Sweden)
Fanxi LYU
2017-06-01
Full Text Available To meet the requirements of fast and automatic computation of subsonic and transonic aerodynamics in aircraft conceptual design, a novel finite volume solver for full potential flows on adaptive Cartesian grids is developed in this paper. Cartesian grids with geometric adaptation are firstly generated automatically with boundary cells processed by cell-cutting and cell-merging algorithms. The nonlinear full potential equation is discretized by a finite volume scheme on these Cartesian grids and iteratively solved in an implicit fashion with a generalized minimum residual (GMRES algorithm. During computation, solution-based mesh adaptation is also applied so as to capture flow features more accurately. An improved ghost-cell method is proposed to implement the non-penetration wall boundary condition where the velocity-potential of a ghost cell is modified by an analytic method instead. According to the characteristics of the Cartesian grids, the Kutta condition is applied by specially computing the gradients on Kutta-faces without directly assigning the potential jump to cells adjacent wake faces, which can significantly improve the solution converging speed. The feasibility and accuracy of the proposed method are validated by several typical cases of sub/transonic flows around an ONERA M6 wing, a DLR-F4 wing-body, and an unconventional figuration of a blended wing body (BWB. The validation cases demonstrate a fast convergence with fully automatic grid treatment and computation, and the results suggest its capacity in application for aircraft conceptual design.
ON FINITE DIFFERENCE SCHEMES FOR THE 3-D WAVE EQUATION USING NON-CARTESIAN GRIDS
B. Hamilton; S. Bilbao
2013-01-01
In this paper, we investigate ﬁnite difference schemes forthe 3-D wave equation using 27-point stencils on the cubiclattice, a 13-point stencil on the face-centered cubic (FCC)lattice, and a 9-point stencil on the body-centered cubic(BCC) lattice. The tiling of the wavenumber space for nonCartesian grids is considered in order to analyse numericaldispersion. Schemes are compared for computational efﬁ-ciency in terms of minimising numerical wave speed error.It is shown that the 13-point scheme...
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.
Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.
2018-01-01
We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.
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).
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.
Analysis of a non-standard mixed finite element method with applications to superconvergence
Brandts, J.H.
2009-01-01
We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite element method is superconvergent.
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
Energy Technology Data Exchange (ETDEWEB)
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.
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.
Discourse Structure and Cartesian Scepticism. | Ryan | South ...
African Journals Online (AJOL)
I provide a new account of the nature of Cartesian scepticism, in which I show that if we draw on the notion of discourse structure we can show exactly how Cartesian scepticism is induced and that it is, in principle, impossible to dispel. The account proceeds by showing that, given the nature of discourse structure, there is no ...
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.
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.
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
The Cartesian Heritage of Bloom's Taxonomy
Bertucio, Brett
2017-01-01
This essay seeks to contribute to the critical reception of "Bloom's Taxonomy of Educational Objectives" by tracing the Taxonomy's underlying philosophical assumptions. Identifying Bloom's work as consistent with the legacy of Cartesian thought, I argue that its hierarchy of behavioral objectives provides a framework for certainty and…
Conversion of contours to cartesian grids
DEFF Research Database (Denmark)
Mann, Jakob; Broe, Brian Riget
A robust and efficient method of calculating a cartesian grid of heights or roughnesses from contour line maps is developed. The purpose of the grids is to serve as input for atmospheric flow solvers such as WAsP Engineering or EllipSys3D. The method builds on Delaunay triangulation constrained t...
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
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.
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.)
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.
Material translations in the Cartesian brain.
Bassiri, Nima
2012-03-01
This article reexamines the controversial doctrine of the pineal gland in Cartesian psychophysiology. It argues initially that Descartes' combined metaphysics and natural philosophy yield a distinctly human subject who is rational, willful, but also a living and embodied being in the world, formed in the union and through the dynamics of the interaction between the soul and the body. However, Descartes only identified one site at which this union was staged: the brain, and more precisely, the pineal gland, the small bulb of nervous tissue at the brain's center. The pineal gland was charged with the incredible task of ensuring the interactive mutuality between the soul and body, while also maintaining the necessary ontological incommensurability between them. This article reconsiders the theoretical obligations placed on the pineal gland as the site of the soul-body union, and looks at how the gland was consequently forced to adopt a very precarious ontological status. The article ultimately questions how successfully the Cartesian human could be localized in the pineal gland, while briefly considering the broader historical consequences of the ensuing equivalence of the self and brain. Copyright © 2011 Elsevier Ltd. All rights reserved.
GOD AND THE DEMON IN CARTESIAN AND AKAN PHILOSOPHIES
African Journals Online (AJOL)
HP
examine whether, and how, the human being who is deemed to know right and wrong is in some way portrayed in Cartesian and Akan philosophies as morally responsible for his or her actions, despite the potencies and influences of God and the demon. Knowledge and Activities of God and the Demon in Cartesian.
God and the demon in Cartesian and Akan philosophies: a ...
African Journals Online (AJOL)
I analyse presentations of God and the demon in Cartesian philosophy (as specifically found in his Meditations) and how they compare with the conceptions of God and the demon in indigenous Akan philosophy. Using the qualitative method, I also examine some implications of both the Cartesian and Akan notions of God ...
Revisiting the Cartesian model of pain.
Goldberg, Joel S
2008-01-01
In modern medicine, the Cartesian or nociceptive concept of chronic pain has been replaced with the biopsychosocial model in both theory and practice. This paper presents an argument along with observations in favor of chronic pain as a pure nociceptive experience separate from suffering and outlines theoretical and practical solutions to improve the diagnosis and treatment of patients who experience chronic pain. Theoretical solutions include increasing inhibitory descending neurotransmitters using monoamine oxidase inhibitors of subtype A in combination with dextroamphetamine, increasing beta endorphin through enzymology and/or ultrasound stimulation of the periaqueductal gray, developing long duration opioid analgesics using spin label probes of morphine and morphine analogs and destructive interference of nociceptive action potentials by eddy currents generated by a variable magnetic field. Practical solutions include prolonging local anesthetic blockade of small pain fibers with patient administered local anesthetic storage devices and abandonment of the multidisciplinary pain clinic.
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.
Recurrence relations for the Cartesian derivatives of the Zernike polynomials.
Stephenson, Philip C L
2014-04-01
A recurrence relation for the first-order Cartesian derivatives of the Zernike polynomials is derived. This relation is used with the Clenshaw method to determine an efficient method for calculating the derivatives of any linear series of Zernike polynomials.
Spectral properties and stability of perturbed Cartesian product
Indian Academy of Sciences (India)
Prakash A Dabhi
This Banach algebra will be denoted by A ×T B. When T = 0, A ×T B is the Cartesian product space. Thus A ×T B can be regarded as a perturbation of the Cartesian product. When A is unital with identity e and θ : B → C is a multiplicative linear functional, then T : B → A defined by T(x) = θ(x)e (x ∈ B) is an algebra ...
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.
Estimation of Cartesian Space Robot Trajectories Using Unit Quaternion Space
Directory of Open Access Journals (Sweden)
Alesš Ude
2014-08-01
Full Text Available The ability to estimate Cartesian space trajectories that include orientation is of great importance for many practical applications. While it is becoming easier to acquire trajectory data by computer vision methods, data measured by general-purpose vision or depth sensors are often rather noisy. Appropriate smoothing methods are thus needed in order to reconstruct smooth Cartesian space trajectories given noisy measurements. In this paper, we propose an optimality criterion for the problem of the smooth estimation of Cartesian space trajectories that include the end-effector orientation. Based on this criterion, we develop an optimization method for trajectory estimation which takes into account the special properties of the orientation space, which we represent by unit quaternions. The efficiency of the developed approach is discussed and experimental results are presented.
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.
Virtual Prototyping through Co-simulation of a Cartesian Plotter
Groothuis, M.A.; Damstra, A.S.; Broenink, Johannes F.
This paper shows a model-based design trajectory for the development of real-time embedded control software using virtual prototyping. As a test case, a Cartesian plotter is designed. Functional correctness of the plotter software has been ensured by means of co-simulation using a virtual prototype
Power domination of the cartesian product of graphs
Directory of Open Access Journals (Sweden)
K.M. Koh
2016-04-01
Full Text Available In this paper, we first give a brief survey on the power domination of the Cartesian product of graphs. Then we conjecture a Vizing-like inequality for the power domination problem, and prove that the inequality holds when at least one of the two graphs is a tree.
Geometry of good sets in n-fold Cartesian product
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Geometry of good sets in n-fold Cartesian product. A KŁOPOTOWSKI1, M G NADKARNI2,3 and. K P S BHASKARA RAO4. 1Université Paris XIII, Institut Galilée, 93430 Villetaneuse Cedex, France. 2Institute of Mathematical Sciences, C.I.T. Campus, Chennai 600 113, India. 3Chennai Mathematical Institute, Chennai 600 ...
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
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)
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.
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.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
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 ...
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.
A weakly-compressible Cartesian grid approach for hydrodynamic flows
Bigay, P.; Oger, G.; Guilcher, P.-M.; Le Touzé, D.
2017-11-01
The present article aims at proposing an original strategy to solve hydrodynamic flows. In introduction, the motivations for this strategy are developed. It aims at modeling viscous and turbulent flows including complex moving geometries, while avoiding meshing constraints. The proposed approach relies on a weakly-compressible formulation of the Navier-Stokes equations. Unlike most hydrodynamic CFD (Computational Fluid Dynamics) solvers usually based on implicit incompressible formulations, a fully-explicit temporal scheme is used. A purely Cartesian grid is adopted for numerical accuracy and algorithmic simplicity purposes. This characteristic allows an easy use of Adaptive Mesh Refinement (AMR) methods embedded within a massively parallel framework. Geometries are automatically immersed within the Cartesian grid with an AMR compatible treatment. The method proposed uses an Immersed Boundary Method (IBM) adapted to the weakly-compressible formalism and imposed smoothly through a regularization function, which stands as another originality of this work. All these features have been implemented within an in-house solver based on this WCCH (Weakly-Compressible Cartesian Hydrodynamic) method which meets the above requirements whilst allowing the use of high-order (> 3) spatial schemes rarely used in existing hydrodynamic solvers. The details of this WCCH method are presented and validated in this article.
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.
ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach
Directory of Open Access Journals (Sweden)
M. Jähn
2015-02-01
Full Text Available In this work, the fully compressible, three-dimensional, nonhydrostatic atmospheric model called All Scale Atmospheric Model (ASAM is presented. A cut cell approach is used to include obstacles and orography into the Cartesian grid. Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied. Necessary shifting and interpolation techniques are outlined. The method can be generalized to any other orthogonal grids, e.g., a lat–long grid. A linear implicit Rosenbrock time integration scheme ensures numerical stability in the presence of fast sound waves and around small cells. Analyses of five two-dimensional benchmark test cases from the literature are carried out to show that the described method produces meaningful results with respect to conservation properties and model accuracy. The test cases are partly modified in a way that the flow field or scalars interact with cut cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid-scale model, a two-moment bulk microphysics scheme, and precipitation and surface fluxes using a sophisticated multi-layer soil model are implemented and described. Results of an idealized three-dimensional simulation are shown, where the flow field around an idealized mountain with subsequent gravity wave generation, latent heat release, orographic clouds and precipitation are modeled.
Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)
2002-01-01
Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.
Cartesian moral philosophy and control over human beings
Solano Villareal, Diana
2016-01-01
This paper presents a deeper analysis of the Cartesian moral philosophy in the Discours de la méthode, Les passions de l’âme, and the Principia Philosophiae, also in search of arguments to make clear a relation of connection control of some human beings on other, and the mechanism by which this control hypothetical relationship between humans could manifest. Este artículo presenta un análisis más profundo de la filosofía moral cartesiana en el Discours de la méthode, Les passions de l’âme...
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.
Automatic off-body overset adaptive Cartesian mesh method based on an octree approach
International Nuclear Information System (INIS)
Péron, Stéphanie; Benoit, Christophe
2013-01-01
This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.
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.
International Nuclear Information System (INIS)
Abreu, Marcos P. de; Alves Filho, Hermes; Barros, Ricardo C.
2001-01-01
We describe hybrid spectral nodal methods for discrete ordinates (SN) eigenvalue problems in Cartesian geometry. These coarse-mesh methods are based on three ingredients: the use of the standard discretized spatial balance SN equations; the use of the non-standard spectral diamond (SD) auxiliary equations in the multiplying regions of the domain, e.g. fuel assemblies; and 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. We show numerical results to typical model problems to illustrate the accuracy of spectral nodal methods for coarse-mesh SN criticality calculations. (author)
Directory of Open Access Journals (Sweden)
Allahyar Geramy
2018-02-01
Full Text Available Objectives: This study aimed to analyze functional stresses around short and long implant-supported prostheses with different crown heights.Materials and Methods: Four three-dimensional (3D models were designed with SolidWorks 2015. In models 1 (control and 2, three dental implants (second premolar 4.1x8 mm, molars: 4.8x8 mm were placed. In models 3 and 4, three dental implants (second premolar 4.1x4 mm, molars: 4.8x4 were placed. Residual bone height was 10 mm in groups 1 and 2 (grafted bone models and 6 mm in groups 3 and 4. The crown heights were modeled at 11.5 mm for groups 1 to 3, and 15 mm for group 4. The applied oblique force was 220 N to simulate chewing movements. The maximum von Mises and principal stresses on the implants and the supporting tissues were compared using the 3D finite element method.Results: In all models, the highest stress value was seen within the most coronal part of bone (crestal bone, which was cortical or grafted bone. The highest stress values in the bone supporting the implant neck were seen in the premolar region of each model, especially in model 4 (291.16 MPa. The lowest stress values were demonstrated in the molar region of model 3 (48.066 MPa. The model 2 implants showed the highest von Mises stress concentrated at their neck (424.44 MPa.Conclusions: In atrophic posterior mandible with increased crown height space, short implants with wider diameter seem to be a more feasible approach compared to grafting methods.
Static Aeroelastic Analysis with an Inviscid Cartesian Method
Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.
2014-01-01
An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.
Solus Secedo and Sapere Aude: Cartesian Meditation as Kantian Enlightenment
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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.
A System for Acoustic Field Measurement Employing Cartesian Robot
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Szczodrak Maciej
2016-09-01
Full Text Available A system setup for measurements of acoustic field, together with the results of 3D visualisations of acoustic energy flow are presented in the paper. Spatial sampling of the field is performed by a Cartesian robot. Automatization of the measurement process is achieved with the use of a specialized control system. The method is based on measuring the sound pressure (scalar and particle velocity(vector quantities. The aim of the system is to collect data with a high precision and repeatability. The system is employed for measurements of acoustic energy flow in the proximity of an artificial head in an anechoic chamber. In the measurement setup an algorithm for generation of the probe movement path is included. The algorithm finds the optimum path of the robot movement, taking into account a given 3D object shape present in the measurement space. The results are presented for two cases, first without any obstacle and the other - with an artificial head in the sound field.
Energy Technology Data Exchange (ETDEWEB)
Lee, Hong-Pyo; Choun, Young-Sun; Seo, Jeong-Moon
2005-02-01
The objective of this research is to investigate the elasto-plastic solid element model for the safety assessment of the nuclear containment buildings and finally to implement into the computer module. For this purpose, 8-node solid element has been formulated with elasto-plastic reinforced concrete material model based on the Drucker-Prager failure criteria. The material model has employed standard plasticity theories, isotropic hardening model, associated plastic flow rule, 3-dimensional cracking criteria, concrete tensile softening model, shear transfer model due to aggregate interaction and compressive strength reduction factor. The stress-strain curves for reinforcement steel are generally used bi-linear hardening model in tension and compression. Several benchmark tests have been employed to validate developed elasto-plastic material model. The research result throughout this study can be directly used as basis information for the development of numerical analysis system for the nuclear containment buildings and general reinforced concrete structures.
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.
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
Directory of Open Access Journals (Sweden)
Zimmerman Peter A
2010-06-01
Full Text Available Abstract Background Diagnosis of infectious diseases now benefits from advancing technology to perform multiplex analysis of a growing number of variables. These advances enable simultaneous surveillance of markers characterizing species and strain complexity, mutations associated with drug susceptibility, and antigen-based polymorphisms in relation to evaluation of vaccine effectiveness. We have recently developed assays detecting single nucleotide polymorphisms (SNPs in the P. falciparum genome that take advantage of post-PCR ligation detection reaction and fluorescent microsphere labeling strategies. Data from these assays produce a spectrum of outcomes showing that infections result from single to multiple strains. Traditional methods for distinguishing true positive signal from background can cause false positive diagnoses leading to incorrect interpretation of outcomes associated with disease treatment. Results Following analysis of Plasmodium falciparum dihydrofolate reductase SNPs associated with resistance to a commonly used antimalarial drug, Fansidar (Sulfadoxine/pyrimethamine, and presumably neutral SNPs for parasite strain differentiation, we first evaluated our data after setting a background signal based on the mean plus three standard deviations for known negative control samples. Our analysis of single allelic controls suggested that background for the absent allele increased as the concentration of the target allele increased. To address this problem, we introduced a simple change of variables from customary (X,Y (Cartesian coordinates to planar polar coordinates (X = rcos(θ, Y = rsin(θ. Classification of multidimensional fluorescence signals based on histograms of angular and radial data distributions proved more effective than classification based on Cartesian thresholds. Comparison with known diallelic dilution controls suggests that histogram-based classification is effective for major:minor allele concentration ratios as
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)
Lugauer, Felix; Wetzl, Jens; Forman, Christoph; Schneider, Manuel; Kiefer, Berthold; Hornegger, Joachim; Nickel, Dominik; Maier, Andreas
2018-01-25
Our aim was to develop and validate a 3D Cartesian Look-Locker [Formula: see text] mapping technique that achieves high accuracy and whole-liver coverage within a single breath-hold. The proposed method combines sparse Cartesian sampling based on a spatiotemporally incoherent Poisson pattern and k-space segmentation, dedicated for high-temporal-resolution imaging. This combination allows capturing tissue with short relaxation times with volumetric coverage. A joint reconstruction of the 3D + inversion time (TI) data via compressed sensing exploits the spatiotemporal sparsity and ensures consistent quality for the subsequent multistep [Formula: see text] mapping. Data from the National Institute of Standards and Technology (NIST) phantom and 11 volunteers, along with reference 2D Look-Locker acquisitions, are used for validation. 2D and 3D methods are compared based on [Formula: see text] values in different abdominal tissues at 1.5 and 3 T. [Formula: see text] maps obtained from the proposed 3D method compare favorably with those from the 2D reference and additionally allow for reformatting or volumetric analysis. Excellent agreement is shown in phantom [bias[Formula: see text] see text] see text] mapping with high accuracy and precision is feasible in one breath-hold using spatiotemporally incoherent, sparse 3D Cartesian sampling.
LES of Internal Combustion Engine Flows Using Cartesian Overset Grids
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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
Problems of Cartesian Product Solved by Elementary School Students Sandra Maria Pinto MaginaI
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Sandra Maria Pinto Magina
2018-03-01
Full Text Available The study investigated the solution of direct (which requires multiplication for its resolution and inverse (which requires division for its resolution Cartesian product problems by elementary education students, examining the level of problem complexity and the children procedures according to the type of problem. A total of 269 8 and 10 year-old students attending from 3rd to 5th grade, were asked 8 and 10 years to solve direct and inverse Cartesian product problems. As expected, the inverse problem was the most difficult one. The strategies showed that levels of combinatorial reasoning vary according to the type of problem. It was also found a progression in the solution of direct Cartesian product problems, but not in relation to the solution of inverse problems.
Werner, F.; Gdaniec, N.; Knopp, T.
2017-05-01
Magnetic particle imaging (MPI) is a quantitative imaging modality that allows us to determine the distribution of superparamagnetic nanoparticles. Sampling is achieved by moving a field-free point (FFP) along a specific trajectory through the volume of interest. The magnetic material that lies along the path or in the close vicinity of the FFP changes its magnetization and induces a voltage in the surrounding receiver coils. Various trajectories for the FFP are conceivable, but most experimental MPI scanners either use a Cartesian or a Lissajous sampling trajectory. For the first time, this study compares both sampling methods experimentally using an MPI scanner that allows us to implement both sampling patterns. By default, the scanner is capable of scanning 2D and 3D field of views using a Lissajous trajectory. But since it also has a 1D mode, it is possible to perform Cartesian measurements by shifting the 1D scan line in a perpendicular direction to the FFP movement using the focus field. These line scans are jointly reconstructed to obtain a 2D image. In a further step, the unidirectional Cartesian trajectory is improved by interchanging the excitation and the focus-field direction leading to a bidirectional Cartesian trajectory. Our findings reveal similar results for the bidirectional Cartesian and Lissajous trajectory concerning the overall image quality and sensitivity. In a more detailed view, the bidirectional Cartesian trajectory achieves a slightly higher spatial center resolution, whereas the Lissajous trajectory is more efficient regarding the temporal resolution since less acquisition time is needed to reach an adequate image quality.
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
Developing seamless method to calculate heat convection and conduction on cartesian grid
International Nuclear Information System (INIS)
Tanno, I.; Morinishi, K.; Matsuno, K.; Nishida, H.
2005-01-01
In these days, studying and developing algorithms which calculate fluid flows which have interfaces or bodies on cartesian grid become trend of computational fluid dynamics area. In this paper, we propose Virtual Flux Method (VFM) which calculates heat and fluid flow around interfaces or bodies on cartesian grid. This method enables to seamlessly calculate heat convection on the surface of the bodies and fluid and heat conduction inside bodies. In three dimensional calculations of shell and tube type heat exchangers, there is a possibility that fluid inside and outside tubes and heat flow between these fluid and tube bodies are calculated without any kind of extra algorithms but VFM. (author)
The First Orchestrated Attack on Spinoza: Johannes Melchioris and the Cartesian Network in Utrecht.
Gootjes, Albert
2018-01-01
This article examines the immediate Dutch reception of the Tractatus theologico-politicus. Using newfound archival sources it demonstrates that the anti-Spinoza activity of the Cartesians in Utrecht extends far beyond the well-known writings of Lambertus van Velthuysen and Regnerus van Mansveld. Their Cartesian network not only produced the very first public refutation to appear, but also formed a center for coordinating much of the Dutch response to Spinoza. This engagement, it is argued in closing, must be accounted for in Spinoza reception history, and forms the background to the mysterious visit Spinoza paid to Utrecht in the summer of 1673.
Expanding from discrete Cartesian to permutation Gene-pool Optimal Mixing Evolutionary Algorithms
P.A.N. Bosman (Peter); N.H. Luong (Ngoc Hoang); D. Thierens (Dirk)
2016-01-01
textabstractThe recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) family, which includes the Linkage Tree Genetic Algorithm (LTGA), has been shown to scale excellently on a variety of discrete, Cartesian-space, optimization problems. This paper shows that GOMEA can quite
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…
Rapid Non-Cartesian Parallel Imaging Reconstruction on Commodity Graphics Hardware
DEFF Research Database (Denmark)
Sørensen, Thomas Sangild; Atkinson, David; Boubertakh, Redha
2008-01-01
This presentation describes an implementation of non-Cartesian SENSE and kt-SENSE accelerated on commodity graphics hardware. This inexpensive hardware platform is now fully programmable and very suited for solving reconstruction problems. We show that for both SENSE and kt-SENSE the reconstruction...
Indian Academy of Sciences (India)
com. Email: singh_shivaraj@rediffmail.com. In this article we provide a solution to a problem in the famous analysis book [1] by Rudin. It does not use trans- finite induction, and readers may find it more transpar- ent than the treatment in [2]. Here is ...
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.
Smith, C U
2001-08-01
J. C. Eccles (1903-1997) had a highly distinguished career in neurophysiology, being awarded the Nobel Prize for Medicine or Physiology in 1963. This paper sets him within the Cartesian tradition of British neurophysiology initiated by Thomas Henry Huxley in the mid-19th century. It shows how the mind-brain problematique of the Cartesian tradition troubled him throughout his career, leading him finally to a solution in terms of quantum microphysics and microphysiology. This position, which has subsequently become fashionable, is discussed and shown (at least in the form Eccles espoused) to provide no solution to the problem posed by Descartes in the early 17th century. Copyright 2001 Academic Press.
Robust Adaptive Control of a Free-Floating Space Robot System in Cartesian Space
Directory of Open Access Journals (Sweden)
Fuhai Zhang
2015-11-01
Full Text Available This paper presents a novel, robust, adaptive trajectory-tracking control scheme for the free-floating space robot system in Cartesian space. The dynamic equation of the free-floating space robot system in Cartesian space is derived from the augmented variable method. The proposed basic robust adaptive controller is able to deal with parametric and non-parametric uncertainties simultaneously. Another advantage of the control scheme is that the known and unknown external disturbance bounds can be considered using a modification of the parameter-estimation law. In addition, three cases are certified to achieve robustness for both parametric uncertainties and external disturbances. The simulation results show that the control scheme can ensure stable tracking of the desired trajectory of the end-effector.
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)
Continuous Genetic Algorithms for Collision-Free Cartesian Path Planning of Robot Manipulators
Directory of Open Access Journals (Sweden)
Za'er S. Abo-Hammour
2011-12-01
Full Text Available A novel continuous genetic algorithm (CGA along with distance algorithm for solving collisions‐free path planning problem for robot manipulators is presented in this paper. Given the desired Cartesian path to be followed by the manipulator, the robot configuration as described by the D‐H parameters, and the available stationary obstacles in the workspace of the manipulator, the proposed approach will autonomously select a collision free path for the manipulator that minimizes the deviation between the generated and the desired Cartesian path, satisfy the joints limits of the manipulator, and maximize the minimum distance between the manipulator links and the obstacles. One of the main features of the algorithm is that it avoids the manipulator kinematic singularities due to the inclusion of forward kinematics model in the calculations instead of the inverse kinematics. The new robot path planning approach has been applied to two different robot configurations; 2R and PUMA 560, as non‐ redundant manipulators. Simulation results show that the proposed CGA will always select the safest path avoiding obstacles within the manipulator workspace regardless of whether there is a unique feasible solution, in terms of joint limits, or there are multiple feasible solutions. In addition to that, the generated path in Cartesian space will be of very minimal deviation from the desired one.
Continuous Genetic Algorithms for Collision-Free Cartesian Path Planning of Robot Manipulators
Directory of Open Access Journals (Sweden)
Za'er S. Abo-Hammour
2011-12-01
Full Text Available A novel continuous genetic algorithm (CGA along with distance algorithm for solving collisions-free path planning problem for robot manipulators is presented in this paper. Given the desired Cartesian path to be followed by the manipulator, the robot configuration as described by the D-H parameters, and the available stationary obstacles in the workspace of the manipulator, the proposed approach will autonomously select a collision free path for the manipulator that minimizes the deviation between the generated and the desired Cartesian path, satisfy the joints limits of the manipulator, and maximize the minimum distance between the manipulator links and the obstacles. One of the main features of the algorithm is that it avoids the manipulator kinematic singularities due to the inclusion of forward kinematics model in the calculations instead of the inverse kinematics. The new robot path planning approach has been applied to two different robot configurations; 2R and PUMA 560, as non-redundant manipulators. Simulation results show that the proposed CGA will always select the safest path avoiding obstacles within the manipulator workspace regardless of whether there is a unique feasible solution, in terms of joint limits, or there are multiple feasible solutions. In addition to that, the generated path in Cartesian space will be of very minimal deviation from the desired one.
Cyclones and Vortices: Alejo Carpentier's Reasons of State as Cartesian Discourse
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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.
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
International Nuclear Information System (INIS)
Honarvar, M; Rohling, R; Lobo, J; Mohareri, O; Salcudean, S E
2015-01-01
To produce images of tissue elasticity, the vibro-elastography technique involves applying a steady-state multi-frequency vibration to tissue, estimating displacements from ultrasound echo data, and using the estimated displacements in an inverse elasticity problem with the shear modulus spatial distribution as the unknown. In order to fully solve the inverse problem, all three displacement components are required. However, using ultrasound, the axial component of the displacement is measured much more accurately than the other directions. Therefore, simplifying assumptions must be used in this case. Usually, the equations of motion are transformed into a Helmholtz equation by assuming tissue incompressibility and local homogeneity. The local homogeneity assumption causes significant imaging artifacts in areas of varying elasticity. In this paper, we remove the local homogeneity assumption. In particular we introduce a new finite element based direct inversion technique in which only the coupling terms in the equation of motion are ignored, so it can be used with only one component of the displacement. Both Cartesian and cylindrical coordinate systems are considered. The use of multi-frequency excitation also allows us to obtain multiple measurements and reduce artifacts in areas where the displacement of one frequency is close to zero. The proposed method was tested in simulations and experiments against a conventional approach in which the local homogeneity is used. The results show significant improvements in elasticity imaging with the new method compared to previous methods that assumes local homogeneity. For example in simulations, the contrast to noise ratio (CNR) for the region with spherical inclusion increases from an average value of 1.5–17 after using the proposed method instead of the local inversion with homogeneity assumption, and similarly in the prostate phantom experiment, the CNR improved from an average value of 1.6 to about 20. (paper)
Santucci, Domiziana; Lee, Sheila S.; Hartman, Heidi; Walgampaya, Shyama; AlObaidy, Mamdoh; Ramalho, Miguel; Dale, Brian M.; Semelka, Richard C.
2017-01-01
Abstract Objective: The purpose of this study was to compare two short-tau inversion recovery (STIR) sequences, Cartesian and radial (BLADE) acquisitions, for breast magnetic resonance imaging (MRI) examinations. Materials and Methods: Ninety-six women underwent 1.5 T breast MRI exam (48 Cartesian and 48 BLADE). Qualitative analysis including image artifacts, image quality, fat-suppression, chest-wall depiction, lesion detection, lymph node depiction and overall impression were evaluated by...
Coirier, William John
1994-01-01
A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a
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
Fara, Patricia
2008-12-01
Few original portraits exist of René Descartes, yet his theories of vision were central to Enlightenment thought. French philosophers combined his emphasis on sight with the English approach of insisting that ideas are not innate, but must be built up from experience. In particular, Denis Diderot criticised Descartes's views by describing how Nicholas Saunderson--a blind physics professor at Cambridge--relied on touch. Diderot also made Saunderson the mouthpiece for some heretical arguments against the existence of God.
Motion correction for functional MRI with three-dimensional hybrid radial-Cartesian EPI.
Graedel, Nadine N; McNab, Jennifer A; Chiew, Mark; Miller, Karla L
2017-08-01
Subject motion is a major source of image degradation for functional MRI (fMRI), especially when using multishot sequences like three-dimensional (3D EPI). We present a hybrid radial-Cartesian 3D EPI trajectory enabling motion correction in k-space for functional MRI. The EPI "blades" of the 3D hybrid radial-Cartesian EPI sequence, called TURBINE, are rotated about the phase-encoding axis to fill out a cylinder in 3D k-space. Angular blades are acquired over time using a golden-angle rotation increment, allowing reconstruction at flexible temporal resolution. The self-navigating properties of the sequence are used to determine motion parameters from a high temporal-resolution navigator time series. The motion is corrected in k-space as part of the image reconstruction, and evaluated for experiments with both cued and natural motion. We demonstrate that the motion correction works robustly and that we can achieve substantial artifact reduction as well as improvement in temporal signal-to-noise ratio and fMRI activation in the presence of both severe and subtle motion. We show the potential for hybrid radial-Cartesian 3D EPI to substantially reduce artifacts for application in fMRI, especially for subject groups with significant head motion. The motion correction approach does not prolong the scan, and no extra hardware is required. Magn Reson Med 78:527-540, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.
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.
Energy Technology Data Exchange (ETDEWEB)
Biondo, Elliott D., E-mail: biondo@wisc.edu; Davis, Andrew, E-mail: davisa@engr.wisc.edu; Wilson, Paul P.H., E-mail: wilsonp@engr.wisc.edu
2016-05-15
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{sup 5} for problems using the FNG geometry.
Rapid compressed sensing reconstruction of 3D non-Cartesian MRI.
Baron, Corey A; Dwork, Nicholas; Pauly, John M; Nishimura, Dwight G
2018-05-01
Conventional non-Cartesian compressed sensing requires multiple nonuniform Fourier transforms every iteration, which is computationally expensive. Accordingly, time-consuming reconstructions have slowed the adoption of undersampled 3D non-Cartesian acquisitions into clinical protocols. In this work we investigate several approaches to minimize reconstruction times without sacrificing accuracy. The reconstruction problem can be reformatted to exploit the Toeplitz structure of matrices that are evaluated every iteration, but it requires larger oversampling than what is strictly required by nonuniform Fourier transforms. Accordingly, we investigate relative speeds of the two approaches for various nonuniform Fourier transform kernel sizes and oversampling for both GPU and CPU implementations. Second, we introduce a method to minimize matrix sizes by estimating the image support. Finally, density compensation weights have been used as a preconditioning matrix to improve convergence, but this increases noise. We propose a more general approach to preconditioning that allows a trade-off between accuracy and convergence speed. When using a GPU, the Toeplitz approach was faster for all practical parameters. Second, it was found that properly accounting for image support can prevent aliasing errors with minimal impact on reconstruction time. Third, the proposed preconditioning scheme improved convergence rates by an order of magnitude with negligible impact on noise. With the proposed methods, 3D non-Cartesian compressed sensing with clinically relevant reconstruction times (<2 min) is feasible using practical computer resources. Magn Reson Med 79:2685-2692, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
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.
DEFF Research Database (Denmark)
Häyrynen, Teppo; Østerkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz
2017-01-01
Recently, an open geometry Fourier modal method based on a new combination ofan open boundary condition and a non-uniform $k$-space discretization wasintroduced for rotationally symmetric structures providing a more efficientapproach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am....... A33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)Cartesian coordinates allowing for the modeling of rectangular geometries inopen space. The open boundary condition is a consequence of having an infinitecomputational domain described using basis functions that expand...... moreaccurate and efficient modeling of open 3D nanophotonic structures....
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
Rosenzweig, Sebastian; Holme, Hans Christian Martin; Wilke, Robin N; Voit, Dirk; Frahm, Jens; Uecker, Martin
2018-04-01
The development of a calibrationless parallel imaging method for accelerated simultaneous multi-slice (SMS) MRI based on Regularized Nonlinear Inversion (NLINV), evaluated using Cartesian and radial fast low-angle shot (FLASH). NLINV is a parallel imaging method that jointly estimates image content and coil sensitivities using a Newton-type method with regularization. Here, NLINV is extended to SMS-NLINV for reconstruction and separation of all simultaneously acquired slices. The performance of the extended method is evaluated for different sampling schemes using phantom and in vivo experiments based on Cartesian and radial SMS-FLASH sequences. The basic algorithm was validated in Cartesian experiments by comparison with ESPIRiT. For Cartesian and radial sampling, improved results are demonstrated compared to single-slice experiments, and it is further shown that sampling schemes using complementary samples outperform schemes with the same samples in each partition. The extension of the NLINV algorithm for SMS data was implemented and successfully demonstrated in combination with a Cartesian and radial SMS-FLASH sequence. Magn Reson Med 79:2057-2066, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
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.
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.
High resource of azimuthal entanglement in terms of Cartesian variables of noncollinear biphotons
Fedorov, M. V.
2018-01-01
Single-particle and coincidence distributions of photons are analyzed for the noncollinear frequency-degenerate type-I regime of spontaneous parametric down-conversion. Noncollinearity itself is shown to provide a new mechanism of strong broadening of the single-particle distributions in Cartesian components of the photon's transverse wave vectors. Related to this, the degree of entanglement appears to be very high in agreement with the earlier performed analysis in the formalism of spherical angles characterizing photon's wave vectors [Phys. Rev. A 93, 033830 (2016), 10.1103/PhysRevA.93.033830]. In Cartesian variables, very broad curves of single-particle distributions are found to have a rather unusual and peculiar shape. In theory, the key reason for these effects is the reduction of the total wave function of two photons over one of two orthogonal degrees of freedom. In the suggested and discussed experimental schemes this means that all photons of the emission cone have to be taken into account rather than only photons propagating in one given plane which is a common practice in many experiments.
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.
Directory of Open Access Journals (Sweden)
Domiziana Santucci
Full Text Available Abstract Objective: The purpose of this study was to compare two short-tau inversion recovery (STIR sequences, Cartesian and radial (BLADE acquisitions, for breast magnetic resonance imaging (MRI examinations. Materials and Methods: Ninety-six women underwent 1.5 T breast MRI exam (48 Cartesian and 48 BLADE. Qualitative analysis including image artifacts, image quality, fat-suppression, chest-wall depiction, lesion detection, lymph node depiction and overall impression were evaluated by three blinded readers. Signal to noise ratios (SNRs were calculated. Cronbach's alpha test was used to assess inter-observer agreement. Subanalyses of image quality, chest-wall depiction and overall impression in 15 patients with implants and image quality in 31 patients with clips were correlated using Pearson test. Wilcoxon rank sum test and t-test were performed. Results: Motion artifacts were present in 100% and in 0% of the Cartesian and the BLADE exams, respectively. Chemical-shift artifacts were present in 8% of the Cartesian exams. Flow artifacts were more frequent on BLADE. BLADE sequence was statistically superior to Cartesian for all qualitative features (p < 0.05 except for fat-suppression (p = 0.054. In the subanalysis, BLADE was superior for implants and clips (p < 0.05. SNR was statistically greater for BLADE (48.35 vs. 16.17. Cronbach ranged from 0.502 to 0.813. Conclusion: BLADE appears to be superior to Cartesian acquisition of STIR imaging as measured by improved image quality, fewer artifacts, and improved chest wall and lymph node depiction.
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.
High-order finite difference methods for earthquake rupture dynamics in complex geometries
O'Reilly, O.; Kozdon, J. E.; Dunham, E. M.; Nordström, J.
2010-12-01
In this work we continue our development of high-order summation-by-parts (SBP) finite difference methods for earthquake rupture dynamics. SBP methods use centered spatial differences in the interior and one-sided differences near the boundary. The transition to one-sided differences is done in a particular manner that permits one to provably maintain stability and accuracy. In many methods the boundary conditions are strongly enforced by modifying the difference operator at the boundary so that the solution there exactly satisfies the boundary condition. Though conceptually straightforward, this approach can introduce instabilities. In contrast, when boundary conditions are enforced weakly by adding a penalty term to the spatial discretization, it is possible to prove that the method is strictly stable, dissipating energy slightly faster than the continuous problem (with the additional dissipation vanishing under grid refinement). Another benefit of SBP operators is their built-in inner product which, if correctly constructed, can be interpreted as a quadrature operator. Thus, important integrated quantities such as the total mechanical energy in the system, the energy dissipation rate along faults, and the radiated energy flux through exterior boundaries can be rigorously calculated. These numerically integrated quantities converge to their true values with the same order of accuracy as the difference approximation. Though standard SBP methods are based on uniform Cartesian grids, it is possible to use the methods for problems with nonplanar faults, free surface topography, and branching faults through the use of coordinate transforms. Recently, it has also been shown how second-order SBP methods can be extended to unstructured grids. Due to the SBP character of both the finite difference and node-centered finite volume method they can be used together in a stable and accurate way. Inclusion of these techniques will be important for problems that have regions
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.
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.
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
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)
Li, Shuo; Zhu, Yanchun; Xie, Yaoqin; Gao, Song
2018-01-01
Dynamic magnetic resonance imaging (DMRI) is used to noninvasively trace the movements of organs and the process of drug delivery. The results can provide quantitative or semiquantitative pathology-related parameters, thus giving DMRI great potential for clinical applications. However, conventional DMRI techniques suffer from low temporal resolution and long scan time owing to the limitations of the k-space sampling scheme and image reconstruction algorithm. In this paper, we propose a novel DMRI sampling scheme based on a golden-ratio Cartesian trajectory in combination with a compressed sensing reconstruction algorithm. The results of two simulation experiments, designed according to the two major DMRI techniques, showed that the proposed method can improve the temporal resolution and shorten the scan time and provide high-quality reconstructed images.
Directory of Open Access Journals (Sweden)
Shuo Li
Full Text Available Dynamic magnetic resonance imaging (DMRI is used to noninvasively trace the movements of organs and the process of drug delivery. The results can provide quantitative or semiquantitative pathology-related parameters, thus giving DMRI great potential for clinical applications. However, conventional DMRI techniques suffer from low temporal resolution and long scan time owing to the limitations of the k-space sampling scheme and image reconstruction algorithm. In this paper, we propose a novel DMRI sampling scheme based on a golden-ratio Cartesian trajectory in combination with a compressed sensing reconstruction algorithm. The results of two simulation experiments, designed according to the two major DMRI techniques, showed that the proposed method can improve the temporal resolution and shorten the scan time and provide high-quality reconstructed images.
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.
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.
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.
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.
Nonlinear, finite deformation, finite element analysis
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated
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.
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.
2018-03-07
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.
Indian Academy of Sciences (India)
IAS Admin
plitude waves and finite amplitude waves. This article provides a brief introduction to finite amplitude wave theories. Some of the general characteristics of waves as well as the importance of finite amplitude wave theories are touched upon. 2. Small Amplitude Waves. The topmost and the lowest levels of the waves are re-.
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.
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.
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.
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
López-Muñoz, Francisco; Rubio, Gabriel; Molina, Juan D; Alamo, Cecilio
2011-04-25
The relationship between the "passions" (emotions or feelings) and psychopathology has been a constant throughout the history of medicine. In this context, melancholy was considered a perversion of the soul (corruption of the passions). One of the most influential authors on this subject was René Descartes, who discussed it in his work The Treatise on the Passions of the Soul (1649). Descartes believed that "passions" were sensitive movements that the soul experienced due to its union with the body (res extensa). According to this theory, the soul was located in the pineal gland, where it was actively involved in overseeing the functions of the "human machine" and kept its dysfunctions under control, by circulating animal spirits. Descartes described sadness as one of "the six primitive passions of the soul", which leads to melancholy if not remedied. Cartesian theories had a great deal of influence on the way that mental pathologies were considered throughout the entire 17th century (Spinoza, Willis, Pitcairn) and during much of the 18th century (Le Cat, Tissot). From the 19th century onwards, emotional symptomatology finally began to be used in diagnostic criteria for mood disorders. Copyright © 2011 Elsevier Inc. All rights reserved.
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.
Directory of Open Access Journals (Sweden)
Mochamad Diki Muliyawan
2017-12-01
Full Text Available Abstrak -- Dengan munculnya teknologi manufaktur aditif pada pertengahan 1980-an, teknologi pencetakan tiga dimensi (3D yang mencetak benda dengan mengandalkan ekstrusi termoplastik untuk pembuatan prototipe/pemodelan. Bahan termoplastik yang digunakan adalah Asam Polylatic (PLA dan Acrylonitrile Butadiene Styrene (ABS yang dicetak dengan cara dicairkan mengunakan nozzel yang dialirkan secara berlapis lapis sehingga membentuk sebuah benda. Rancang bangun konstruksi rangka mesin 3D printer tipe cartesian berbasis FDM dengan penggerak menggunakan 3 sumbu utama yaitu sumbu X dengan panjang area cetak 380 mm ,sumbu Y dengan panjang area cetak 400 mm,dan sumbu Z dengan panjang area cetak 380 mm, dan material yang digunakan yaitu baja JIS G3103 1995 SS400, dan Alumunium Al1100. Penelitian ini bertujuan untuk memperoleh kekuatan rangka batang sumbu Z, dan sumbu X dengan, menganalisa kekuatan pada leadscrew sumbu Y dan sumbu Z, menganalisa kekuatan sabuk timing, memperoleh nilai kekuatan pada kampuh las pada rangka Y,Z. Hasil analisa pada rangka sumbu X nilai tegangan tegangan ijin 18 MPa maka dianggap aman, analisa gaya buckling pada rangka sumbu Z adalah sebesar pembebanan 15,147 Kg maka dianggap aman, tegangan geser= 0,38 MPa tegangan geser maksimum = 0,42 MPa maka dianggap aman untuk lead screw sumbu Y, tegangan geser
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.
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.
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.
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.
Başar, Erol; Güntekin, Bahar
2007-04-01
The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications of Newtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causality principle became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept of cloudy wave packets. The approach to the brain-body-mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis of the brain-body-mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiple causalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulences in the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g. chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physical processes in the body. The brain shows deterministic chaos with a correlation dimension of approx. D(2)=6, the smooth muscles approx. D(2)=3. According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze the processes in the brain-body-mind system. If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this "New Cartesian System" is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite this chain of reasoning we can still provide predictions on brain-body-mind incorporations. We tentatively assume that the processes or mechanisms of the brain-body-mind system can be analyzed and predicted similar to the
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.
Panou, G.; Korakitis, R.
2017-02-01
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.
A finite volume code for meridional circulation in stars
Talon, S; Michaud, G; Richer, J
2003-01-01
To understand the driving of both meridional circulation and differential rotation in radiative envelopes of stars, one has to solve for 3D mass, momentum, and energy conservation equations for a compressible gas in a central gravity field. In this study, we propose a novel finite volume technique that uses Cartesian geometry thus reducing greatly the complexity of spherical operators. The boundary conditions are efficiently imposed at the surface of the star using the fictitious points technique. We use the anelastic approximation and the Poisson equation for pressure is solved by the Jacobi method which preserves natural symmetries. We present analytical test cases of the fictitious domain technique, and show our results of asymptotic circulation in a model with little stratification and a large viscosity.
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.
Folio, Les R; Fischer, Tatjana; Shogan, Paul; Frew, Michael; Dwyer, Andrew; Provenzale, James M
2011-08-01
The purpose of this study is to determine the agreement with which radiologists identify wound paths in vivo on MDCT and calculate missile trajectories on the basis of Cartesian coordinates using a Cartesian positioning system (CPS). Three radiologists retrospectively identified 25 trajectories on MDCT in 19 casualties who sustained penetrating trauma in Iraq. Trajectories were described qualitatively in terms of directional path descriptors and quantitatively as trajectory vectors. Directional descriptors, trajectory angles, and angles between trajectories were calculated based on Cartesian coordinates of entrance and terminus or exit recorded in x, y image and table space (z) using a Trajectory Calculator created using spreadsheet software. The consistency of qualitative descriptor determinations was assessed in terms of frequency of observer agreement and multirater kappa statistics. Consistency of trajectory vectors was evaluated in terms of distribution of magnitude of the angles between vectors and the differences between their paraaxial and parasagittal angles. In 68% of trajectories, the observers' visual assessment of qualitative descriptors was congruent. Calculated descriptors agreed across observers in 60% of the trajectories. Estimated kappa also showed good agreement (0.65-0.79, p trajectory vectors were within 20° across observers. Results show agreement of visually assessed and calculated qualitative descriptors and trajectory angles among observers. The Trajectory Calculator describes trajectories qualitatively similar to radiologists' visual assessment, showing the potential feasibility of automated trajectory analysis.
Schunck, N.; Dobaczewski, J.; Satuła, W.; Bączyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.
2017-07-01
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.
Peng, Bo; Blackman, Eric
2018-01-01
Closely interacting binary stars can incur Common Envelope Evolution (CEE) when at least one of the stars enters a giant phase. The extent to which CEE leads to envelope ejection and how tight the binaries become after CEE as a function of the mass and type of the companion stars has a broad range of phenomenological implications for both low mass and high mass binary stellar systems. Global simulations of CEE are emerging, but to understand the underlying physics of CEE and make connections with analytic formalisms, it helpful to employ reduced numerical models. Here we present results and analyses from simulations of gravitational drag using a Cartesian approach. Using AstroBEAR, a parallelized hydrodynamic/MHD simulation code, we simulate a system in which a 0.1 MSun main sequence secondary star is embedded in gas characteristic of the Envelope of a 3 MSun AGB star. The relative motion of the secondary star against the stationary envelope is represented by a supersonic wind that immerses a point particle, which is initially at rest, yet gradually dragged by the wind. Our approach differs from previous related wind-tunnel work by MacLeod et al. (2015,2017) in that we allow the particle to be displaced, offering a direct measurement of the drag force from its motion. We verify the validity of our method, extract the accretion rate of material in the wake via numerical integration, and compare the results between our method and previous work. We also use the results to help constrain the efficiency parameter in widely used analytic parameterizations of CEE.
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.
The effect of object-centered instructions in Cartesian and polar coordinates on saccade vector
Edelman, Jay A.; Mieses, Alexa M.; Konnova, Kira; Shiu, David
2017-01-01
Express saccades (ES) are the most reflexive saccadic eye movements, with very short reaction times of 70–110 ms. It is likely that ES have the shortest saccade reaction times (SRTs) possible given the known physiological and anatomical delays present in sensory and motor systems. Nevertheless, it has been demonstrated that a vector displacement of ES to spatially extended stimuli can be influenced by spatial cognition. Edelman, Kristjansson, and Nakayama (2007) found that when two horizontally separated visual stimuli appear at a random location, the spatial vector, but not the reaction time, of human ES is strongly influenced by an instruction to make a saccade to one side (either left or right) of a visual stimulus array. Presently, we attempt to extend these findings of cognitive effects on saccades in three ways: (a) determining whether ES could be affected by other types of spatial instructions: vertical, polar amplitude, and polar direction; (b) determining whether these spatial effects increased with practice; and (c) determining how these effects depended on SRTs. The results demonstrate that both types of Cartesian as well as polar amplitude instructions strongly affect ES vector, but only modestly affect SRTs. Polar direction instructions had sizable effects only on nonreflexive saccades where the visual stimuli could be viewed for several hundred milliseconds prior to saccade execution. Short- (trial order within a block) and long-term (experience across several sessions) practice had little effect, though the effect of instruction increased with SRT. Such findings suggest a generalized, innate ability of cognition to affect the most reflexive saccadic eye movements. PMID:28265650
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.
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)
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)
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.
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.
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
Branduardi, Davide; Faraldo-Gómez, José D.
2014-01-01
The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string. PMID
High-Reynolds Number Viscous Flow Simulations on Embedded-Boundary Cartesian Grids
2016-05-05
viscosity ; at convergence when viscosity is back to being positive the equations are the same). Many researchers use a first order finite volume scheme...0052 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Marsha Berger 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION...PROGRAM ELEMENT NUMBER. Enter all program element numbers as they appear in the report, e.g. 61101A. 5d. PROJECT NUMBER. Enter all project
A finite element solution of transonic flow
Tatum, K. E.
1978-01-01
The use of finite elements is explored in a field in which its use has previously not been deemed very feasible, that of transonic flow. The specific problem chosen is that of steady small-disturbance transonic flow. The nonlinear equations are formulated with an artificial viscosity term added to yield the proper domain of dependence and directional bias in supersonic regions and across imbedded shock waves. Justification is given for the problem and means of solution chosen, and the potential advantages of the finite element procedure over standard finite difference procedures are discussed. Several possible improvements on the method as presently derived are stated. Computational mesh requirements and certain mesh variations are described. Some results equivalent to finite difference calculations are given as a sample solution.
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
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)
Finite Higgs mass without Supersymmetry
Antoniadis, Ignatios; Quirós, Mariano
2001-01-01
We identify a class of chiral models where the one-loop effective potential for Higgs scalar fields is finite without any requirement of supersymmetry. It corresponds to the case where the Higgs fields are identified with the components of a gauge field along compactified extra dimensions. We present a six dimensional model with gauge group U(3)xU(3) and quarks and leptons accomodated in fundamental and bi-fundamental representations. The model can be embedded in a D-brane configuration of type I string theory and, upon compactification on a T^2/Z_2 orbifold, it gives rise to the standard model with two Higgs doublets.
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.
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
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...
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.
Inflation with finite temperature
International Nuclear Information System (INIS)
Bellini, M.; Michoacan, Univ. Michoacana de S.Nicola de Hidalgo
1998-01-01
In this work the inflationary scenario of the Universe with finite temperature is studied. In this context, thermal equilibrium is closely maintained at the end of inflation. The example of the de Sitter expansion is developed
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.)
Flexoelectric effect in finite samples
Tagantsev, Alexander K.; Yurkov, Alexander S.
2012-08-01
Static flexoelectric effect in a finite sample of a solid is addressed in terms of phenomenological theory for the case of a thin plate subjected to bending. It has been shown that despite an explicit asymmetry inherent to the bulk constitutive electromechanical equations which take into account the flexoelectric coupling, there exists a situation where electromechanical response for a finite sample is "symmetric." "Symmetric" means that if a sensor and an actuator are made of a flexoelectric element, performance of such devices can be characterized by the same effective piezoelectric coefficient. This behavior is consistent with the thermodynamic arguments offered earlier, being in conflict with the current point of view on the matter in literature. This result was obtained using standard mechanical boundary conditions valid for the case where the polarization vanishes at the surface. It was shown that, for the case where the polarization at the surface is not zero, the aforementioned symmetry of electromechanical response may be violated if standard mechanical boundary conditions are used, leading to a conflict with the thermodynamic arguments. It is suggested that this conflict may be resolved when using modified mechanical boundary conditions. It is also shown that the contribution of surface piezoelectricity to the flexoelectric response of a finite sample is expected to be comparable to that of the static bulk contribution (including materials with high values of the dielectric constant) and to scale as the bulk value of the dielectric constant (similar to the bulk contribution). This finding implies that if the experimentally measured flexoelectric coefficient scales as the dielectric constant of the material, this does not imply that the measured flexoelectric response is controlled by the static bulk contribution to the flexoelectric effect.
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)
Reliable finite element methods for self-adjoint singular perturbation ...
African Journals Online (AJOL)
It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...
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…
Suryanto, A.; van Groesen, Embrecht W.C.; Hammer, Manfred; Hoekstra, Hugo
We present a simple numerical scheme based on the finite element method (FEM) using transparent-influx boundary conditions to study the nonlinear optical response of a finite one-dimensional grating with Kerr medium. Restricting first to the linear case, we improve the standard FEM to get a fourth
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
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......, discrete Gabor coefficients. Reconstruction of a signal from its Gabor coefficients is done by the use of a so-called dual window. This thesis presents a number of iterative algorithms to compute dual and self-dual windows. The Linear Time Frequency Toolbox is a Matlab/Octave/C toolbox for doing basic...... discrete time/frequency and Gabor analysis. It is intended to be both an educational and a computational tool. The toolbox was developed as part of this Ph.D. project to provide a solid foundation for the field of computational Gabor analysis....
Ballester-Bolinches, Adolfo; Asaad, Mohamed
2010-01-01
The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups.
Forman, Christoph; Grimm, Robert; Hutter, Jana Maria; Maier, Andreas; Hornegger, Joachim; Zenge, Michael O
2013-01-01
Respiratory motion remains a major challenge for whole-heart coronary magnetic resonance angiography (CMRA). Recently, iterative reconstruction has been augmented with non-rigid motion compensation to correct for the effects of respiratory motion. The major challenge of this approach is the estimation of dense deformation fields. In this work, the application of such a motion-compensated reconstruction is proposed for accelerated 3D Cartesian whole-heart CMRA. Without the need for extra calibration data or user interaction, the nonrigid deformations due to respiratory motion are directly estimated on the acquired image data. In-vivo experiments on 14 healthy volunteers were performed to compare the proposed method with the result of a navigator-gated reference scan. While reducing the acquisition time by one third, the reconstructed images resulted in equivalent vessel sharpness of 0.44 +/- 0.06 mm(-1) and 0.45 +/- 0.05 mm(-1), respectively.
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.
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
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.
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.
Undecidability and finite automata
Endrullis, Jörg; Shallit, Jeffrey; Smith, Tim
2017-01-01
Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to prove the undecidability of a related problem about
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.
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
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.
Solution of Fokker–Planck equation by finite element and finite ...
Indian Academy of Sciences (India)
hindered by the problem of dimensionality. In this paper numerical solution of the stationary and transient form of the Fokker–Planck (FP) equation corresponding to two state nonlinear systems is obtained by standard sequential finite element method. (FEM) using C0 shape function and Crank–Nicholson time integration ...
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.
Yong, Daeseong; Kim, Jaeup U.
2017-12-01
For the purpose of checking material conservation of various numerical algorithms used in the self-consistent-field theory (SCFT) of polymeric systems, we develop an algebraic method using matrix and bra-ket notation, which traces the Hermiticity of the product of the volume and evolution matrices. Algebraic tests for material conservation reveal that the popular pseudospectral method in the Cartesian grid conserves material perfectly, while the finite-volume method (FVM) is the proper tool when real-space SCFT with the Crank-Nicolson method is adopted in orthogonal coordinate systems. We also find that alternating direction implicit methods combined with the FVM exhibit small mass errors in the SCFT calculation. By introducing fractional cells in the FVM formulation, accurate SCFT calculations are performed for systems with irregular geometries and the results are consistent with previous experimental and theoretical works.
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)
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.
Liégeois, Vincent; Champagne, Benoît; Lazzeretti, Paolo
2008-06-28
Two molecular properties, the nuclear electromagnetic hypershielding (psi(gamma,alphabeta) ('I)) and the gradient of the electric dipole-magnetic dipole polarizability (nabla(Igamma)G(alphabeta) (')), have been calculated using the time-dependent Hartree-Fock method. Provided the Hellmann-Feynman theorem is satisfied, these quantities are equivalent and are related through the nabla(Igamma)G(alphabeta) (')=eZ(I)psi(gamma,alphabeta) ('I) relation, where Z(I) is the atomic number of atom I and e the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of G(alphabeta) (') of requiring only the knowledge of nine mixed second-order derivatives of the density matrix with respect to both electric and magnetic fields (D(alpha,beta)(-omega,omega)) instead of the 3N (N is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates (D(Igamma)). It is shown here for the H(2)O(2) molecule that very large basis sets such as the aug-cc-pVQZ or the R12 basis are required to satisfy the Hellmann-Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of G(alphabeta) (') has then been theoretically described and verified for the H(2)O(2) molecule.
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.
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.
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
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.
Structural Topology Optimization Based on the Smoothed Finite Element Method
Directory of Open Access Journals (Sweden)
Vahid Shobeiri
Full Text Available Abstract In this paper, the smoothed finite element method, incorporated with the level set method, is employed to carry out the topology optimization of continuum structures. The structural compliance is minimized subject to a constraint on the weight of material used. The cell-based smoothed finite element method is employed to improve the accuracy and stability of the standard finite element method. Several numerical examples are presented to prove the validity and utility of the proposed method. The obtained results are compared with those obtained by several standard finite element-based examples in order to access the applicability and effectiveness of the proposed method. The common numerical instabilities of the structural topology optimization problems such as checkerboard pattern and mesh dependency are studied in the examples.
Emílio Borges; João Pedro Braga; Jadson Cláudio Belchior
2007-01-01
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 ...
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.
Inoue, Yuuji; Yoneyama, Masami; Nakamura, Masanobu; Takemura, Atsushi
2018-03-07
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.
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.
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
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
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
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
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
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.)
Statistical finite element analysis.
Khalaji, Iman; Rahemifar, Kaamran; Samani, Abbas
2008-01-01
A novel technique is introduced for tissue deformation and stress analysis. Compared to the conventional Finite Element method, this technique is orders of magnitude faster and yet still very accurate. The proposed technique uses preprocessed data obtained from FE analyses of a number of similar objects in a Statistical Shape Model framework as described below. This technique takes advantage of the fact that the body organs have limited variability, especially in terms of their geometry. As such, it is well suited for calculating tissue displacements of body organs. The proposed technique can be applied in many biomedical applications such as image guided surgery, or virtual reality environment development where tissue behavior is simulated for training purposes.
Sunvisson, Helena; Habermann, Barbara; Weiss, Sara; Benner, Patricia
2009-10-01
Using three paradigm cases of persons living with Parkinson's Disease (PD) the authors make a case for augmenting and enriching a Cartesian medical account of the pathophysiology of PD with an enriched understanding of the lived body experience of PD, the lived implications of PD for a particular person's concerns and coping with the illness. Linking and adding a thick description of the lived experience of PD can enrich caregiving imagination and attunement to the patient's possibilities, concerns and constraints. The work of Merleau-Ponty is used to articulate the middle terms of the lived experience of dwelling in a lifeworld. Examining lived experience of embodied intentionality, skilled bodily capacities as highlighted in Merleau-Ponty's non-mechanistic physiology opens new therapeutic, coping and caregiving possibilities. Matching temporal rhythms can decrease the stress of being assisted with activities of daily living. For example, caregivers and patients alike can be taught strategies for extending their lived bodily capacities by altering rhythms, by shifting hyperactivity to different parts of the body and other strategies that change the perceptual experience associated with walking in different environment. A medical account of the pathophysiology of PD is nessessary and useful, but not sufficient for designing caregiving in ways that enrich and extend the existential skills of dwelling of persons with PD. The dominance of mechanistic physiology makes caregivers assume that it is the 'real discourse' about the disease, causing researchers and caregivers alike to overlook the equally real lived experience of the patient which requires different descriptive discourses and different sources of understanding. Lack of dialogue between the two discourses is tragic for patients because caregivers need both in order to provide attuned, effective caregiving.
Levine, Evan; Daniel, Bruce; Vasanawala, Shreyas; Hargreaves, Brian; Saranathan, Manojkumar
2017-05-01
To enable robust, high spatio-temporal-resolution three-dimensional Cartesian MRI using a scheme incorporating a novel variable density random k-space sampling trajectory allowing flexible and retrospective selection of the temporal footprint with compressed sensing (CS). A complementary Poisson-disc k-space sampling trajectory was designed to allow view sharing and varying combinations of reduced view sharing with CS from the same prospective acquisition. These schemes were used for two-point Dixon-based dynamic contrast-enhanced MRI (DCE-MRI) of the breast and abdomen. Results were validated in vivo with a novel approach using variable-flip-angle data, which was retrospectively accelerated using the same methods but offered a ground truth. In breast DCE-MRI, the temporal footprint could be reduced 2.3-fold retrospectively without introducing noticeable artifacts, improving depiction of rapidly enhancing lesions. Further, experiments with variable-flip-angle data showed that reducing view sharing improved accuracy in reconstruction and T 1 mapping. In abdominal MRI, 2.3-fold and 3.6-fold reductions in temporal footprint allowed reduced motion artifacts. The complementary-Poisson-disc k-space sampling trajectory allowed a retrospective spatiotemporal resolution tradeoff using CS and view sharing, imparting robustness to motion and contrast enhancement. The technique was also validated using a novel approach of fully acquired variable-flip-angle acquisition. Magn Reson Med 77:1774-1785, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
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)
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...... features that justify the development of specialized solution algorithms....
Finite strain discrete dislocation plasticity
Deshpande, VS; Needleman, A; Van der Giessen, E
2003-01-01
A framework for carrying out finite deformation discrete dislocation plasticity calculations is presented. The discrete dislocations are presumed to be adequately represented by the singular linear elastic fields so that the large deformations near dislocation cores are not modeled. The finite
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.
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
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
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.)
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
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
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)
Anderson, D.V.; Breazeal, J.; Finan, C.H.; Johnston, B.M.
1976-09-14
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.
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.
A curved finite element for general thin shell structures
International Nuclear Information System (INIS)
Jones, R.F. Jr.
1978-01-01
This work describes the development of a curved quadrilateral shell finite element which demonstrates very good convergence properties. A general description is used in deriving the element so that it may be applied to any thin shell problem. The element is shown to be very efficient. It has a total of 36 degrees-of-freedom with 9 at each of the corners of the element. There are several distinct advantages that the element offers for practical applications. Most of the shell elements that have been presented in the past are limited to problems in which the coordinates on the shell surface are orthogonal. The element that is described in the paper is derived using a general description so that it may be applied to any thin shell problem including those in which the shell coordinates are not orthogonal. The degree-of-freedom at each of the four nodes are the three Cartesian displacements and their first derivatives with respect to the two surface coordinates. The imposition of boundary conditions is simplified since each of the degrees-of-freedom can be can be associated with a quantity which has a simple physical meaning. During the course of the derivation of the element, the strain displacement relationships are derived in a very simple manner consistent with Love's first approximation for thin shells. The derivation in the paper starts from basic principles and should help to shed some light on the proper form for the bending strain. Two primary contributions are presented in this work. The first is the presentation of a procedure for the development of a general quadrilateral shell element. The second is the simple derivation of the bending strain for the thin shells which apparently has not been presented previously. (Auth.)
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
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
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
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 in...
A species sampling model with finitely many types
Gnedin, A.V.|info:eu-repo/dai/nl/189792809
2010-01-01
A two-parameter family of exchangeable partitions with a simple updating rule is introduced. The partition is identified with a randomized version of a standard symmetric Dirichlet speciessampling model with finitely many types. A power-like distribution for the number of types is derived.
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.
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)
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.
Accurate finite difference beam propagation method for complex integrated optical structures
DEFF Research Database (Denmark)
Rasmussen, Thomas; Povlsen, Jørn Hedegaard; Bjarklev, Anders Overgaard
1993-01-01
A simple and effective finite-difference beam propagation method in a z-varying nonuniform mesh is developed. The accuracy and computation time for this method are compared with a standard finite-difference method for both the 3-D and 2-D versions...
Solid finite elements through three decades
Venkatesh, DN; Shrinivasa, U
1994-01-01
conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in tune with our perceptions on developing finite elements, without taking recourse to any extra variational techniques, we discuss a few of the techniques which have been applied to solid finite elements. Finally we critically examine our own work on formulating solid finite elemen...
Quantum mechanics on spaces with finite fundamental group
International Nuclear Information System (INIS)
Giulini, D.
1995-01-01
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that arise from the non-simply connectedness of the classical configuration space. We define the quantum theory on the universal cover but restrict the algebra of observables O to the commutant of the algebra generated by deck-transformations. We apply standard superselection principles and construct the corresponding sectors. We emphasize the relevance of all sectors and not just the abelian ones. (orig.)
AEROTAXI ground static test and finite element model validation
Directory of Open Access Journals (Sweden)
Radu BISCA
2011-06-01
Full Text Available In this presentation, we will concentrate on typical Ground Static Test (GST and Finite Element (FE software comparisons. It is necessary to note, that standard GST are obligatory for any new aircraft configuration. We can mention here the investigations of the AeroTAXITM, a small aircraft configuration, using PRODERA® equipment. A Finite Element Model (FEM of the AeroTAXITM has been developed in PATRAN/NASTRAN®, partly from a previous ANSYS® model. FEM can be used to investigate potential structural modifications or changes with realistic component corrections. Model validation should be part of every modern engineering analysis and quality assurance procedure.
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 ...
Finite element methods for engineers
Fenner, Roger T
2013-01-01
This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...
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).
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...... in the radiation formula directly, and no pre-windowing is needed. Examples are given for the radiation efficiency, and the results are compared with results found in the literature....
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
Finite connectivity attractor neural networks
Wemmenhove, B.; Coolen, A. C. C.
2003-09-01
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.
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 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.
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.)
On the definition and measurement of fitness in finite populations.
Hansen, Thomas F
2017-04-21
I argue that some standard accounts of fitness in finite populations are both inaccurate and conceptually misleading. I show that the usual population-genetics conceptualization of fitness as the ratio between amounts of a type after selection and before selection works just as well in finite as in infinite populations. Fitness then becomes a random variable, and selection can be conceptualized as any difference in the distribution of this variable while genetic drift can be conceptualized through realized variation in the variable. I derive exact equations for and novel approximations to the mean and variance of relative fitness, approximations for selection gradients in finite populations, and an expression for the variance effective population size in the presence of selection. Copyright © 2017 Elsevier Ltd. All rights reserved.
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.
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
Lattice QCD at finite temperature
International Nuclear Information System (INIS)
DeTar, C.
1988-01-01
Recent progress in the numerical simulation of QCD at finite temperature is reviewed. Eight topics are treated briefly: (1) T c scaling, (2) Equation of state, (3) Baryon susceptibility, (4) The QCD Phase Diagram, (5) J/Ψ Binding in the Plasma, (6) The Screening Spectrum of the Plasma, (7) Gauge Symmetry Breaking at High T, (8) Progress in Computing Power. (author)
Linguistics, Logic, and Finite Trees
Blackburn, P.; Meyer-Viol, W.
1993-01-01
A modal logic is developed to deal with finite ordered binary trees as they are used in (computational) linguistics. A modal language is introduced with operators for the 'mother of', 'first daughter of' and 'second daughter of' relations together with their transitive reflexive closures.
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
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 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
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)
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)
Extension of TOUGH-FLAC to the finite strain framework
Blanco-Martín, Laura; Rutqvist, Jonny; Birkholzer, Jens T.
2017-11-01
The TOUGH-FLAC simulator for coupled thermal-hydraulic-mechanical processes modeling has been extended to the finite strain framework. In the approach selected, this extension has required modifications to the flow simulator (TOUGH2) and to the coupling scheme between the geomechanics and the flow sub-problems. In TOUGH2, the mass and energy balance equations have been extended to account for volume changes. Additionally, as large deformations are computed by FLAC3D, the geometry is updated in the flow sub-problem. The Voronoi partition needed in TOUGH2 is computed using an external open source library (Voro++) that uses the centroids of the deformed geomechanics mesh as generators of the Voronoi diagram. TOUGH-FLAC in infinitesimal and finite strain frameworks is verified against analytical solutions and other approaches to couple flow and geomechanics. Within the finite strain framework, TOUGH-FLAC is also successfully applied to a large-scale case. The extension of TOUGH-FLAC to the finite strain framework has little impact to the user as only one additional executable is needed (for Voro++), and the input files and the workflow of a simulation are the same as in standard TOUGH-FLAC. With this new provision for finite strains, TOUGH-FLAC can be used in the analysis of a wider range of engineering problems, and the areas of application of this simulator are therefore broadened.
Quality management of finite element analysis
Barlow, John
1991-09-01
A quality management system covering the use of finite element analysis is described. The main topics are as follows: acquisition, development and verification of software (including the software suppliers software quality control system), support, documentation, error control, internal software, software acceptance and release; development and qualification of analysis methods, including software evaluation, analysis procedure qualification and documentation, procedure quality checks, control of analysis procedure errors; product design and integrity analysis, including project quality assurance and analysis planning, task specification and allocation, analysis, execution, results checking and analysis records. Other issues include the commercial and business advantages of quality systems, project and technical management and the training and experience of personnel. The items are correlated with the requirements of International Standard Organization 9001.
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
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
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...
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.
Factorization properties of finite spaces
Energy Technology Data Exchange (ETDEWEB)
Simkhovich, B; Mann, A; Zak, J, E-mail: boriskas@tx.technion.ac.i, E-mail: ady@physics.technion.ac.i, E-mail: zak@physics.technion.ac.i [Department of Physics, Technion-Israel Institute of Technology, Haifa 32000 (Israel)
2010-01-29
In 1960 Schwinger (J Schwinger 1960 Proc. Natl Acad. Sci. 46 570-9) proposed the algorithm for factorization of unitary operators in the finite M-dimensional Hilbert space according to a coprime decomposition of M. Using a special permutation operator A we generalize the Schwinger factorization to every decomposition of M. We obtain the factorized pairs of unitary operators and show that they obey the same commutation relations as Schwinger's. We apply the new factorization to two problems. First, we show how to generate two kq-like mutually unbiased bases for any composite dimension. Then, using a Harper-like Hamiltonian model in the finite dimension M = M{sub 1}M{sub 2}, we show how to design a physical system with M{sub 1} energy levels, each having degeneracy M{sub 2}.
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 ...
Finite Metric Spaces of Strictly Negative Type
DEFF Research Database (Denmark)
Hjorth, Poul; Lisonek, P.; Markvorsen, Steen
1998-01-01
We prove that, if a finite metric space is of strictly negative type, then its transfinite diameter is uniquely realized by the infinite extender (load vector). Finite metric spaces that have this property include all spaces on two, three, or four points, all trees, and all finite subspaces of Eu...
The construction of finite solvable groups revisited
Eick, Bettina; Horn, Max
2013-01-01
We describe a new approach towards the systematic construction of finite groups up to isomorphism. This approach yields a practical algorithm for the construction of finite solvable groups up to isomorphism. We report on a GAP implementation of this method for finite solvable groups and exhibit some sample applications.
Proving Finite Satisfiability of Deductive Databases
Bry, François; Manthey, Rainer
1987-01-01
It is shown how certain refutation methods can be extended into semi-decision procedures that are complete for both unsatisfiability and finite satisfiability. The proposed extension is justified by a new characterization of finite satisfiability. This research was motivated by a database design problem: Deduction rules and integrity constraints in definite databases have to be finitely satisfiable
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
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
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)
Strange matter at finite temperatures
International Nuclear Information System (INIS)
Reinhardt, H.; Dang, B.V.
1987-12-01
The properties of strange quark matter at finite temperatures and in equilibrium with respect to weak interaction are explored on the basis of the MIT bag model picture of QCD. Furthermore, to determine the stability of strange quark matter analogous investigations are also performed for nuclear matter within Walecka's model field theory. It is found that strange quark matter can be stable at zero external pressure only for temperatures below 20 MeV. (orig.)
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.
Propagator for finite range potentials
International Nuclear Information System (INIS)
Cacciari, Ilaria; Moretti, Paolo
2006-01-01
The Schroedinger equation in integral form is applied to the one-dimensional scattering problem in the case of a general finite range, nonsingular potential. A simple expression for the Laplace transform of the transmission propagator is obtained in terms of the associated Fredholm determinant, by means of matrix methods; the particular form of the kernel and the peculiar aspects of the transmission problem play an important role. The application to an array of delta potentials is shown
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
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
Extension of p-local finite groups
Broto, Carles; Castellana, Natalia; Grodal, Jesper; Levi, Ran; Oliver, Bob
2005-01-01
A p-local finite group consists of a finite p-group S, together with a pair of categories which encode ``conjugacy'' relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as p-completed classifying spaces of finite groups. In this paper, we study and classify extensions of p-local finite groups, and also compute the fundamental group of the...
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...... matrix of a finite metric space is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points....
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.
An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries
International Nuclear Information System (INIS)
Kim, Jung Woo; Choi, Hae Cheon
2004-01-01
An immersed boundary method for solving the Navier-Stokes and thermal energy equations is developed to compute the heat transfer over or inside the complex geometries in the cartesian or cylindrical coordinates by introducing the momentum forcing, mass source/sink, and heat source/sink. The present method is based on the finite volume approach on a staggered mesh together with a fractional step method. The method of applying the momentum forcing and mass source/sink to satisfy the no-slip condition on the body surface is explained in detail in Kim, Kim and Choi (2001, Journal of Computational Physics). In this paper, the heat source/sink is introduced on the body surface or inside the body to satisfy the iso-thermal or iso-heat-flux condition on the immersed boundary. The present method is applied to three different problems : forced convection around a circular cylinder, mixed convection around a pair of circular cylinders, and forced convection around a main cylinder with a secondary small cylinder. The results show good agreements with those obtained by previous experiments and numerical simulations, verifying the accuracy of the present method
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.
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.
Directory of Open Access Journals (Sweden)
Chiorescu Dan
2017-01-01
Full Text Available In this present paper, because of the complexity of the system soil – agricultural machine, we will use an analytical model which respects the geometry of the active element, realising a prediction of the forces which result at the dislocation of the soil. This study analyses the behavior of the working tool, part of the soil processing machine, using the Finite Element Method (FEM in three different stages. In the pre-processing stage, the objective was to design a three dimensional model in CATIA V5, in keeping with the geometry of the active element, represented by the Cartesian coordinates, together with a portion of the soil rendered as a parallelepiped shape. The second stage followed the introduction of conditions both for the working part, through the fastening of the plowshare frame, the moving direction and velocity, and for the soil, through the action of the cohesion and internal friction forces. In the third stage, called the processing stage, there is the simulation of the process of soil displacement done in real conditions, for various degrees of refinement of the discretization network in finite elements.
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
Myllyla, R.; Ahola, R.; Kopola, H.; Kostamovaara, J.; Voho, P.
1986-07-01
The determination of position and orientation errors made by large-scale cartesian coordinate robots using latest 3D-measurement methods has proved to be difficult in practise. A method has been developed to determine the mechanical inaccuracies of linear motions, perpendiculars, deflections, rotations and bends of a robot, relative to the common reference coordinates of the robot and the work area. The measurement method is based on the use of a laser diode and a position sensitive detector (PSD). A PSD is an optoelectronic sensor capable of providing position data about a light spot incident on its surface. The dual-axis, non-discrete PSD provides continuous analog X- and Y-axis information as the light spot transverses its active area. It senses the centroid of the light spot so that the position daa is indpendent of the focus of the spot. The PSD typically has an active area of - 1 cm - 20 cm , a resolution of 1/5000, nonlinearity of + 1% - + 15% and a fast response enabling accurate detection even of a rapidly moving light spot. The system developed consists of a laser diode transmitter, two beam splitters, a retro-reflective mirror, a PSD based receiver and a microcomputer unit for controlling the system and analysing the measured information. The divergence of the laser diode transmitter is - 0.1 mrad, it is small in size and lightweight (about 100 g), the direction of the laser beam of a fastened transmitter can easily be adjusted and it can be modulated electronically. The direction of the laser beam is not so sensitive to temperature variations as is for example an He-Ne-laser. The effective size of the PSD is enlarged with the aid of optics to have a diameter of 10 cm. Using a modulated laser beam the background light can be compensated. The position data from the PSD receiver to the memory of the microcomputer is gathered continuously and information is produced by a graphic printer in the form of graphs or numbers. This enables the measurement of the
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
Entropy conservative finite element schemes
Tadmor, E.
1986-01-01
The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.
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
DEFF Research Database (Denmark)
Liu, Yuanrong; Chen, Weimin; Zhong, Jing
2017-01-01
The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard ...
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.
Lamarche, L.; Degrez, G.; Prince, A.
A method is described that combines the geometric flexibility of finite element methodology with recent developments of high-resolution finite difference schemes for hyperbolic systems of equations. It is proposed to use the standard weighted residual approach to set up the discrete equations. Upwinding is then achieved via a modified quadrature rule. The Gaussian point is chosen to match the finite difference discretization on a model scalar equation. The extension to systems of equations is then obtained following the flux-splitting approach suggested by Steger and Warming (1981) and Van Leer (1982).
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.
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.)
Finite Unification: Theory and Predictions
Heinemeyer, S; Zoupanos, G
2010-01-01
All-loop Finite Unified Theories (FUTs) are very interesting N=1 supersymmetric Grand Unified Theories (GUTs) which not only realise an old field theoretic dream but also have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensionless couplings that guarantee the vanishing of all beta-functions in certain N=1 GUTs even to all orders. Furthermore developments in the soft supersymmetry breaking sector of N=1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory too. Based on the above theoretical framework phenomenologically consistent FUTS have been constructed. Here we present FUT models based on the SU(5) and SU(3)^3 gauge groups and their predictions. Of particular intere...
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.
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...
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.
Bending analysis of laminated composite plates using finite element ...
African Journals Online (AJOL)
user
Laminated composite plate structures find numerous applications in aerospace, military and automotive industries. The role of transverse shear .... node i about vector {b}. Note that the nodal translations are in global Cartesian space, and the nodal rotations are based on the element (s-t) space. 2.2. Stress-strain relationship.
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
ANSYS duplicate finite-element checker routine
Ortega, R.
1995-01-01
An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.
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
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.)
['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
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)
Reduction of parameters in Finite Unified Theories and the MSSM
Directory of Open Access Journals (Sweden)
Sven Heinemeyer
2018-02-01
Full Text Available 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 model of magnetoconvection of a ferrofluid
International Nuclear Information System (INIS)
Snyder, S.M.; Cader, Tahir; Finlayson, B.A.
2003-01-01
Combined natural and magnetic convective heat transfer through a ferrofluid in a cubic enclosure is simulated numerically. The momentum equation includes a magnetic term that arises when a magnetic fluid is in the presence of a magnetic field gradient and a temperature gradient. In order to validate the theory, the wall temperature isotherms and Nusselt numbers are compared to experimental work of Sawada et al. (Int. J. Appl. Electromagn. Mater. 4 (1994) 329). Results are obtained using standard computational fluid dynamics codes, with modifications to account for the Langevin factor when needed. The CFD code FIDAP uses the finite element method, sometimes with a user-defined subroutine. The CFD code FEMLAB uses the finite element method with a user-supplied body force
Relaxation and correlations in time in a finite volume
International Nuclear Information System (INIS)
Zinn-Justin, J.
1986-01-01
To describe relaxation towards equilibrium and correlating in time in stochastic numerical simulations, it is necessary to examine dynamical stochastic evolution equations from the renormalization group (R.G.) point of view, and then finite volume effects since all numerical simulations take place of course in a finite volume. The stochastic evolution equation which describes in the continuum space and time limit the time behavior of numerical simulations is the Langevin equation and in a first part we shall discuss briefly its algebraic properties. We shall show how it is possible to associate with the Langevin equation a conventional effective action in such a way that its renomalization and R.G. properties can be discussed in the language of standard field theory. However in this discussion it is essential to recognize that this effective action has a B.R.S. type symmetry of the form encountered in the quantization of gauge theories
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.
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.
Axisymmetric finite deformation membrane problems
Energy Technology Data Exchange (ETDEWEB)
Feng, W.W.
1980-12-12
Many biomechanic problems involve the analysis of finite deformation axisymmetric membranes. This paper presents the general formulation for solving a class of axisymmetric membrane problems. The material nonlinearity, as well as the geometric nonlinearity, is considered. Two methods are presented to solve these problems. The first method is solving a set of differential equilibrium equations. The governing equations are reduced to three first-order ordinary-differential equations with explicit derivatives. The second method is the Ritz method where a general potential energy functional valid for all axisymmetric deformed positions is presented. The geometric admissible functions that govern the deformed configuration are written in terms of a series with unknown coefficients. These unknown coefficients are determined by the minimum potential energy principle that of all geometric admissible deformed configurations, the equilibrium configuration minimizes the potential energy. Some examples are presented. A comparison between these two methods is mentioned.
Finite volume schemes for Vlasov
Directory of Open Access Journals (Sweden)
Crouseilles Nicolas
2013-01-01
Full Text Available We present finite volume schemes for the numerical approximation of the one-dimensional Vlasov-Poisson equation (FOV CEMRACS 2011 project. Stability analysis is performed for the linear advection and links with semi-Lagrangian schemes are made. Finally, numerical results enable to compare the different methods using classical plasma test cases. Des schémas de type volumes finis sont étudiés ici pour l’approximation de l’équation de Vlasov-Poisson (projet FOV, CEMRACS 2011. Une analyse de stabilité est effectuée dans le cas de l’advection linéaire et plusieurs liens sont faits entre les méthodes volumes finis et semi-Lagrangiennes. Enfin, les méthodes sont comparées sur des cas tests académiques de la physique des plasmas.
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)
Nuclear deformation at finite temperature.
Alhassid, Y; Gilbreth, C N; Bertsch, G F
2014-12-31
Deformation, a key concept in our understanding of heavy nuclei, is based on a mean-field description that breaks the rotational invariance of the nuclear many-body Hamiltonian. We present a method to analyze nuclear deformations at finite temperature in a framework that preserves rotational invariance. The auxiliary-field Monte Carlo method is used to generate a statistical ensemble and calculate the probability distribution associated with the quadrupole operator. Applying the technique to nuclei in the rare-earth region, we identify model-independent signatures of deformation and find that deformation effects persist to temperatures higher than the spherical-to-deformed shape phase-transition temperature of mean-field theory.
Nuclear Deformation at Finite Temperature
Alhassid, Y.; Gilbreth, C. N.; Bertsch, G. F.
2014-12-01
Deformation, a key concept in our understanding of heavy nuclei, is based on a mean-field description that breaks the rotational invariance of the nuclear many-body Hamiltonian. We present a method to analyze nuclear deformations at finite temperature in a framework that preserves rotational invariance. The auxiliary-field Monte Carlo method is used to generate a statistical ensemble and calculate the probability distribution associated with the quadrupole operator. Applying the technique to nuclei in the rare-earth region, we identify model-independent signatures of deformation and find that deformation effects persist to temperatures higher than the spherical-to-deformed shape phase-transition temperature of mean-field theory.
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.
[Three dimensional mathematical model of tooth for finite element analysis].
Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka
2010-01-01
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. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing 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. 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. 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.
Finite element based inversion for time-harmonic electromagnetic problems
Schwarzbach, Christoph; Haber, Eldad
2013-05-01
In this paper we address the inverse problem and present some recent advances in numerical methods to recover the subsurface electrical conductivity from time-harmonic electromagnetic data. We rigorously formulate and discretize both the forward and the inverse problem in the finite element framework. To solve the forward problem, we derive a finite element discretization of the first-order system of Maxwell's equations in terms of the electric field and the magnetic induction. We show that our approach is equivalent to the standard discretization of the vector Helmholtz equation in terms of the electric field and that the discretization of magnetic induction of the same approximation order is hidden in the standard discretization. We implement the forward solver on unstructured tetrahedral meshes using edge elements. Unstructured meshes are not only capable of representing complex geometry. They can also reduce the overall problem size and, thus, the size of the system of linear equations arising from the forward problem such that direct methods for its solution using a sparse matrix factorization become feasible. The inverse problem is formulated as a regularized output least squares problem. We consider two regularization functions. First, we derive a smoothness regularizer using a primal-dual mixed finite element formulation which generalizes the standard Laplacian operator for a piecewise constant conductivity model on unstructured meshes. Secondly, we derive a total variation regularizer for the same class of models. For the choice of the regularization parameter we revisit the so-called dynamic regularization and compare it to a standard regularization scheme with fixed regularization parameter. The optimization problem is solved by the Gauss-Newton method which can be efficiently implemented using sparse matrix-vector operations and exploiting the sparse matrix factorization of the forward problem system matrix. A synthetic data example from marine
Exact Fit of Simple Finite Mixture Models
Directory of Open Access Journals (Sweden)
Dirk Tasche
2014-11-01
Full Text Available How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year’s portfolio-wide default rate. We point out that the maximum-likelihood (ML approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fixed. From this observation we can conclude that the standard default rate forecast based on last year’s conditional default rates will always be located between last year’s portfolio-wide default rate and the ML forecast for next year. As an application example, cost quantification is then discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.
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.
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.
Bause, Markus; Radu, Florin A; Köcher, Uwe
2017-01-01
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods in space for simulating transport processes have been demonstrated in a wide class of works. We consider a family of continuous Galerkin-Petrov time discretization schemes that is combined with a mixed finite element approximation of the spatial variables. The existence and uniqueness of the semidiscrete approximation and of the fully discrete solution are established. For this, the Banach-Nečas-Babuška theorem is applied in a non-standard way. Error estimates with explicit rates of convergence are proved for the scalar and vector-valued variable. An optimal order estimate in space and time is proved by duality techniques for the scalar variable. The convergence rates are analyzed and illustrated by numerical experiments, also on stochastically perturbed meshes.
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
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.
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...
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...
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...
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…
On p-supersolvability of finite groups
Indian Academy of Sciences (India)
[2] Ballester-Bolinches A, Ezquerro L M and Skiba A N, On second maximal subgroups of. Sylow subgroups of finite groups, J. Pure Appl. Algebra 215 (2011) 705–714. [3] Ballester-Bolinches A and Pedraza-Aguilera M C, On minimal subgroups of finite groups,. Acta Math. Hungar. 73 (1996) 335–342. [4] Chen X and Guo W ...
Extracting excited mesons from the finite volume
Energy Technology Data Exchange (ETDEWEB)
Doring, Michael [George Washington Univ., Washington, DC (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2014-12-01
As quark masses come closer to their physical values in lattice simulations, finite volume effects dominate the level spectrum. Methods to extract excited mesons from the finite volume are discussed, like moving frames in the presence of coupled channels. Effective field theory can be used to stabilize the determination of the resonance spectrum.
On the orders of finite semisimple groups
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 115; Issue 4 ... The aim of this paper is to investigate the order coincidences among the finite semisimple groups and to give a reasoning of such order coincidences through the transitive ... We investigate the situation for finite semisimple groups of Lie type.
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
On Finite $J$-Hermitian Quantum Mechanics
Lee, Sungwook
2014-01-01
In his recent paper arXiv:1312.7738, the author discussed $J$-Hermitian quantum mechanics and showed that $PT$-symmetric quantum mechanics is essentially $J$-Hermitian quantum mechanics. In this paper, the author discusses finite $J$-Hermitian quantum mechanics which is derived naturally from its continuum one and its relationship with finite $PT$-symmetric quantum mechanics.
Least-squares finite element methods
Bochev, Pavel
2009-01-01
Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. This book presents the theory and practice of least-square finite element methods, their strengths and weaknesses, successes, and open problems
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.
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.
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.
Topology optimization using the finite volume method
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole
2005-01-01
Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, s......: the Finite Volume Method. London: Longman Scientific Technical......Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, see......, e.g. [2]) in order to develop methods for topology design for applications where conservation laws are critical such that element--wise conservation in the discretized models has a high priority. This encompasses problems involving for example mass and heat transport. The work described...
Averaging theorems in finite deformation plasticity
Nemat-Nasser, S C
1999-01-01
The transition from micro- to macro-variables of a representative volume element (RVE) of a finitely deformed aggregate (e.g., a composite or a polycrystal) is explored. A number of exact fundamental results on averaging techniques, $9 valid at finite deformations and rotations of any arbitrary heterogeneous continuum, are obtained. These results depend on the choice of suitable kinematic and dynamic variables. For finite deformations, the deformation gradient and $9 its rate, and the nominal stress and its rate, are optimally suited for the averaging purposes. A set of exact identities is presented in terms of these variables. An exact method for homogenization of an ellipsoidal inclusion in an $9 unbounded finitely deformed homogeneous solid is presented, generalizing Eshelby's method for application to finite deformation problems. In terms of the nominal stress rate and the rate of change of the deformation gradient, $9 measured relative to any arbitrary state, a general phase-transformation problem is con...
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 ...
Optimization of finite-size errors in finite-temperature calculations of unordered phases.
Iyer, Deepak; Srednicki, Mark; Rigol, Marcos
2015-06-01
It is common knowledge that the microcanonical, canonical, and grand-canonical ensembles are equivalent in thermodynamically large systems. Here, we study finite-size effects in the latter two ensembles. We show that contrary to naive expectations, finite-size errors are exponentially small in grand canonical ensemble calculations of translationally invariant systems in unordered phases at finite temperature. Open boundary conditions and canonical ensemble calculations suffer from finite-size errors that are only polynomially small in the system size. We further show that finite-size effects are generally smallest in numerical linked cluster expansions. Our conclusions are supported by analytical and numerical analyses of classical and quantum systems.
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
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 ...
International Nuclear Information System (INIS)
Young, T. D.; Armiento, R.
2010-01-01
A Schroedinger eigenvalue problem is solved for the 2D quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, (i) an application of the Kelly error estimator, and (ii) a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver. (general)
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.
Design of Finite Word Length Linear-Phase FIR Filters in the Logarithmic Number System Domain
Directory of Open Access Journals (Sweden)
Syed Asad Alam
2014-01-01
Full Text Available Logarithmic number system (LNS is an attractive alternative to realize finite-length impulse response filters because of multiplication in the linear domain being only addition in the logarithmic domain. In the literature, linear coefficients are directly replaced by the logarithmic equivalent. In this paper, an approach to directly optimize the finite word length coefficients in the LNS domain is proposed. This branch and bound algorithm is implemented based on LNS integers and several different branching strategies are proposed and evaluated. Optimal coefficients in the minimax sense are obtained and compared with the traditional finite word length representation in the linear domain as well as using rounding. Results show that the proposed method naturally provides smaller approximation error compared to rounding. Furthermore, they provide insights into finite word length properties of FIR filters coefficients in the LNS domain and show that LNS FIR filters typically provide a better approximation error compared to a standard FIR filter.
A finite element method for analysis of vibration induced by maglev trains
Ju, S. H.; Ho, Y. S.; Leong, C. C.
2012-07-01
This paper developed a finite element method to perform the maglev train-bridge-soil interaction analysis with rail irregularities. An efficient proportional integral (PI) scheme with only a simple equation is used to control the force of the maglev wheel, which is modeled as a contact node moving along a number of target nodes. The moving maglev vehicles are modeled as a combination of spring-damper elements, lumped mass and rigid links. The Newmark method with the Newton-Raphson method is then used to solve the nonlinear dynamic equation. The major advantage is that all the proposed procedures are standard in the finite element method. The analytic solution of maglev vehicles passing a Timoshenko beam was used to validate the current finite element method with good agreements. Moreover, a very large-scale finite element analysis using the proposed scheme was also tested in this paper.
Social exclusion in finite populations
Li, Kun; Cong, Rui; Wu, Te; Wang, Long
2015-04-01
Social exclusion, keeping free riders from benefit sharing, plays an important role in sustaining cooperation in our world. Here we propose two different exclusion regimes, namely, peer exclusion and pool exclusion, to investigate the evolution of social exclusion in finite populations. In the peer exclusion regime, each excluder expels all the defectors independently, and thus bears the total cost on his own, while in the pool exclusion regime, excluders spontaneously form an institution to carry out rejection of the free riders, and each excluder shares the cost equally. In a public goods game containing only excluders and defectors, it is found that peer excluders outperform pool excluders if the exclusion costs are small, and the situation is converse once the exclusion costs exceed some critical points, which holds true for all the selection intensities and different update rules. Moreover, excluders can dominate the whole population under a suitable parameters range in the presence of second-order free riders (cooperators), showing that exclusion has prominent advantages over common costly punishment. More importantly, our finding indicates that the group exclusion mechanism helps the cooperative union to survive under unfavorable conditions. Our results may give some insights into better understanding the prevalence of such a strategy in the real world and its significance in sustaining cooperation.
FEBio: finite elements for biomechanics.
Maas, Steve A; Ellis, Benjamin J; Ateshian, Gerard A; Weiss, Jeffrey A
2012-01-01
In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://mrl.sci.utah.edu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics.
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 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.
Finite Element Framework for Computational Fluid Dynamics in FEBio.
Ateshian, Gerard A; Shim, Jay J; Maas, Steve A; Weiss, Jeffrey A
2018-02-01
The mechanics of biological fluids is an important topic in biomechanics, often requiring the use of computational tools to analyze problems with realistic geometries and material properties. This study describes the formulation and implementation of a finite element framework for computational fluid dynamics (CFD) in FEBio, a free software designed to meet the computational needs of the biomechanics and biophysics communities. This formulation models nearly incompressible flow with a compressible isothermal formulation that uses a physically realistic value for the fluid bulk modulus. It employs fluid velocity and dilatation as essential variables: The virtual work integral enforces the balance of linear momentum and the kinematic constraint between fluid velocity and dilatation, while fluid density varies with dilatation as prescribed by the axiom of mass balance. Using this approach, equal-order interpolations may be used for both essential variables over each element, contrary to traditional mixed formulations that must explicitly satisfy the inf-sup condition. The formulation accommodates Newtonian and non-Newtonian viscous responses as well as inviscid fluids. The efficiency of numerical solutions is enhanced using Broyden's quasi-Newton method. The results of finite element simulations were verified using well-documented benchmark problems as well as comparisons with other free and commercial codes. These analyses demonstrated that the novel formulation introduced in FEBio could successfully reproduce the results of other codes. The analogy between this CFD formulation and standard finite element formulations for solid mechanics makes it suitable for future extension to fluid-structure interactions (FSIs).
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
The Iris biometric feature segmentation using finite element method
Directory of Open Access Journals (Sweden)
David Ibitayo LANLEGE
2015-05-01
Full Text Available This manuscript presents a method for segmentation of iris images based on a deformable contour (active contour paradigm. The deformable contour is a novel approach in image segmentation. A type of active contour is the Snake. Snake is a parametric curve defined within the domain of the image. Snake properties are specified through a function called energy functional. This means they consist of packets of energy which expressed as partial Differential Equations. The partial Differential Equation is the controlling engine of the active contour since this project, the Finite Element Method (Standard Galerkin Method implementation for deformable model is presented.
Breakdown of thermalization in finite one-dimensional systems.
Rigol, Marcos
2009-09-04
We use quantum quenches to study the dynamics and thermalization of hard core bosons in finite one-dimensional lattices. We perform exact diagonalizations and find that, far away from integrability, few-body observables thermalize. We then study the breakdown of thermalization as one approaches an integrable point. This is found to be a smooth process in which the predictions of standard statistical mechanics continuously worsen as the system moves toward integrability. We establish a direct connection between the presence or absence of thermalization and the validity or failure of the eigenstate thermalization hypothesis, respectively.
Stabilized Finite Elements in FUN3D
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
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)
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
Finite-dimensional division algebras over fields
Jacobson, Nathan
2009-01-01
Finite-Dimensional Division Algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the so-called 'multiplication algebras of Riemann matrices'. The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of parti
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)
A Note on Powers in Finite Fields
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2016-01-01
, 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 which 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....
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
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
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
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.
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.
Finite element form of FDV for widely varying flowfields
Richardson, G. A.; Cassibry, J. T.; Chung, T. J.; Wu, S. T.
2010-01-01
We present the Flowfield Dependent Variation (FDV) method for physical applications that have widely varying spatial and temporal scales. Our motivation is to develop a versatile numerical method that is accurate and stable in simulations with complex geometries and with wide variations in space and time scales. The use of a finite element formulation adds capabilities such as flexible grid geometries and exact enforcement of Neumann boundary conditions. While finite element schemes are used extensively by researchers solving computational fluid dynamics in many engineering fields, their use in space physics, astrophysical fluids and laboratory magnetohydrodynamic simulations with shocks has been predominantly overlooked. The FDV method is unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in these regimes. The first part of this paper concentrates on the presentation of our numerical method formulation for Newtonian and relativistic hydrodynamics. In the second part we present several standard simulation examples that test the method's limitations and verify the FDV method. We show that our finite element formulation is stable and accurate for a range of both Mach numbers and Lorentz factors in one-dimensional test problems. We also present the converging/diverging nozzle which contains both incompressible and compressible flow in the flowfield over a range of subsonic and supersonic regions. We demonstrate the stability of our method and the accuracy by comparison with the results of other methods including the finite difference Total Variation Diminishing method. We explore the use of FDV for both non-relativistic and relativistic fluids (hydrodynamics) with strong shocks in order to establish the effectiveness in future applications of this method in astrophysical and laboratory plasma environments.
DEFF Research Database (Denmark)
Henningsson, Stefan
2016-01-01
competitive, national customs and regional economic organizations are seeking to establish a standardized solution for digital reporting of customs data. However, standardization has proven hard to achieve in the socio-technical e-Customs solution. In this chapter, the authors identify and describe what has......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...... to be harmonized in order for a global company to perceive e-Customs as standardized. In doing so, they contribute an explanation of the challenges associated with using a standardization mechanism for harmonizing socio-technical information systems....
DEFF Research Database (Denmark)
Henningsson, Stefan
2014-01-01
competitive, national customs and regional economic organizations are seeking to establish a standardized solution for digital reporting of customs data. However, standardization has proven hard to achieve in the socio-technical e-Customs solution. In this chapter, the authors identify and describe what has......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...... to be harmonized in order for a global company to perceive e-Customs as standardized. In doing so, they contribute an explanation of the challenges associated with using a standardization mechanism for harmonizing socio-technical information systems....
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
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
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.
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.
Multigrid methods for mortar finite elements
Wohlmuth, Barbara
2000-01-01
Multigrid methods for mortar finite elements / R. Krause ; B. Wohlmuth. - In: Multigrid methods VI / Erik Dick ... (ed.). - Berlin u.a. : Springer, 2000. - S. 136-142 (Lecture notes in computational science and engineering ; 14)
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 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...
Deterministic equation solving over finite fields
Woestijne, Christiaan Evert van de
2006-01-01
It is shown how to solve diagonal forms in many variables over finite fields by means of a deterministic efficient algorithm. Applications to norm equations, quadratic forms, and elliptic curves are given.
Gravity-induced stresses in finite slopes
Savage, W.Z.
1994-01-01
An exact solution for gravity-induced stresses in finite elastic slopes is presented. This solution, which is applied for gravity-induced stresses in 15, 30, 45 and 90?? finite slopes, has application in pit-slope design, compares favorably with published finite element results for this problem and satisfies the conditions that shear and normal stresses vanish on the ground surface. The solution predicts that horizontal stresses are compressive along the top of the slopes (zero in the case of the 90?? slope) and tensile away from the bottom of the slopes, effects which are caused by downward movement and near-surface horizontal extension in front of the slope in response to gravity loading caused by the additional material associated with the finite slope. ?? 1994.
Super-renormalizable and finite gravitational theories
Directory of Open Access Journals (Sweden)
Leonardo Modesto
2014-12-01
Full Text Available We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV completion of Einstein general relativity. These theories are unitary (ghost free and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta functions vanish even at one-loop. These results can be easily extended in extra dimensions and it is likely that the higher dimensional theory can be made finite, too. Therefore we have the possibility for “finite quantum gravity” in any dimension.
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...
African Journals Online (AJOL)
direction (σx) had a maximum value of 375MPa (tensile) and minimum value of ... These results shows that the residual stresses obtained by prediction from the finite element method are in fair agreement with the experimental results.
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)
Discrete mechanics Based on Finite Element Methods
Chen, Jing-bo; Guo, Han-Ying; Wu, Ke
2002-01-01
Discrete Mechanics based on finite element methods is presented in this paper. We also explore the relationship between this discrete mechanics and Veselov discrete mechanics. High order discretizations are constructed in terms of high order interpolations.
Critical-Point Structure in Finite Nuclei
International Nuclear Information System (INIS)
Leviatan, A.
2006-01-01
Properties of quantum shape-phase transitions in finite nuclei are considered in the framework of the interacting boson model. Special emphasis is paid to the dynamics at the critical-point of a general first-order phase transition
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.)
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...
Mean field canonical treatments at finite temperature
International Nuclear Information System (INIS)
Rossignoli, R.
1990-01-01
A method is proposed to make mean field and higher order canonical treatments at finite temperature. Definite improvements are made over the usual Hartree-Fock thermal (great canonical) treatment. (Author). 10 refs., 3 figs
Finite elements in CAD and ADINA
International Nuclear Information System (INIS)
Bathe, K.J.
1986-01-01
The use of finite element methods in computer-aided-design - CAD - is discussed. Some current capabilities are presented and important future developments are outlined. The discussion focusses on the use of the ADINA program in CAD applications. (orig.)
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.
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.
Gray, F.; Cen, J.; Boek, E. S.
2016-10-01
We present a pore-scale dissolution model for the simulation of reactive transport in complex porous media such as those encountered in carbon-storage injection processes. We couple a lattice Boltzmann model for flow calculation with a finite-volume method for solving chemical transport equations, and allow the computational grid to change as mineral surfaces are dissolved according to first-order reaction kinetics. We appraise this scheme for use with high Péclet number flows in three-dimensional geometries and show how the popular first-order convection scheme is affected by severe numerical diffusion when grid Péclet numbers exceed unity, and confirm that this can be overcome relatively easily by using a second-order method in conjunction with a flux-limiter function. We then propose a surface rescaling method which uses parabolic elements to counteract errors in surface area exposed by the Cartesian grid and avoid the use of more complex embedded surface methods when surface reaction kinetics are incorporated. Finally, we compute dissolution in an image of a real porous limestone rock sample injected with HCl for different Péclet numbers and obtain dissolution patterns in concordance with theory and experimental observation. A low injection flow rate was shown to lead to erosion of the pore space concentrated at the face of the rock, whereas a high flow rate leads to wormhole formation.
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)
Finite element approximation of the Isaacs equation
Salgado, Abner J.; Zhang, Wujun
2015-01-01
We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size $h$ whereas the coarse scale $\\varepsilon$ is dictated by an integro-differential approximation of the partial differential equation. We show that the method satisfies the discrete maximum principle provided that the mesh is weakly acute. This, in conjunction with weak operator consistency of the finite element method, allows us to establish convergence of the numerical s...
Finite Element Model of Gear Induction Hardening
Hodek, J; Zemko, M; Shykula, P
2015-01-01
International audience; This paper presents a finite element model of a gear induction hardening process. The gear was surface-heated by an induction coil and quickly cooled by spraying water. The finite element model was developed as a three-dimensional model. The electromagnetic field, temperature field, stress distribution and microstructure distribution were examined. Temperature and microstructural characteristics were measured and used. The gear material data was obtained in part by mea...
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 ...
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
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…
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...
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.)
On finitely strained magnetoelastic solids
Kankanala, Sundeep Venkat
Magnetorheological elastomers (MREs) are a class of magnetoelastic solids whose mechanical properties can be altered by the application of magnetic fields. MREs, which are particle filled elastomers, have been developed and proposed as unique solutions for a number of engineering applications, such as tunable engine and chassis mounts in automobiles. In this dissertation we present a study of the magnetoelastic coupling in finitely deformable MREs. Two different continuum formulations for these solids are presented: an Eulerian based direct approach using the second law of thermodynamics plus the conservation laws of mechanics and a new, Lagrangian type formulation based on the unconstrained minimization of a potential energy functional. It is shown that both approaches yield the same governing equations and boundary conditions. Following a discussion of general properties of the free energy function of MREs, a particular such function is used to illustrate the magnetoelastic coupling phenomena in a cylinder subjected to traction or torsion under the presence of external magnetic fields. Motivated by the classical magnetoelastic buckling problem, the general theory is then applied to the solution of the stability of a rectangular block subjected to a uniform magnetic field perpendicular to its longitudinal axis. The variational approach employed utilizes an unconstrained energy minimization. The analytical solution for the critical buckling fields for both the anti-symmetric and symmetric modes are obtained for three different constitutive laws. The corresponding result for beams is extracted asymptotically for a special material and the solution is compared to previously published results. The last part of this work delves into the constitutive modeling of MBEs. Uniaxial experiments are conducted to study the effect of particle chain orientation on the magnetostriction and magnetization responses of an MRE for different levels of compressive and tensile
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
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.
Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation
Nechaev, O.V.; Shurina, E.P.; Bochev, Mikhail A.
2008-01-01
In the edge vector finite element solution of the frequency domain Maxwell equations, the presence of a large kernel of the discrete rotor operator is known to ruin convergence of standard iterative solvers. We extend the approach of [R. Hiptmair, Multigrid method for Maxwell’s equations, SIAM J.
Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation
Nechaev, O.V.; Shurina, E.P.; Bochev, Mikhail A.
In the edge vector finite element solution of the frequency domain Maxwell equations, the presence of a large kernel of the discrete rotor operator is known to ruin convergence of standard iterative solvers. We extend the approach of [1] and, using domain decomposition ideas, construct a multilevel
In vitro debonding of orthodontic retainers analyzed with finite element analysis
Milheiro, A.; de Jager, N.; Feilzer, A.J.; Kleverlaan, C.J.
2015-01-01
Objective: The aim of this in vitro study was to determine the load and deflection at failure of different lingual retainers bonded with composite to enamel in a standardized three-point bending test. The results were rationalized with finite element analysis (FEA) models. Materials and methods:
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…
Williams, M. H.
1982-01-01
A new approach is presented to diffraction problems involving plane strip barriers or slit apertures. These are problems that display the effects of multiple interacting edges. The approach taken here provides exact, compact solutions. The theory is introduced through a series of examples that are, in fact, the 'standard' problems of the subject, diffraction of a plane oblique wave by a slit, for example. In each case, the solutions are found to depend explicitly on a single 'special' function and its Fourier transform. These fundamental functions are described, with the emphasis placed on practical computational methods. The example problems are all couched in the language of acoustics.
International Nuclear Information System (INIS)
Prihantoro, Rudy; Sutarno, Doddy; Nurhasan
2016-01-01
In this work, we seek numerical solution of 3-D Magnetotelluric (MT) using edge- based finite element method. This approach is a variant of standard finite element method and commonly referred as vector finite-element (VFE) method. Nonphysical solutions usually occurred when the solution is sought using standard finite element which is a node based element. Vector finite element attempt to overcome those nonphysical solutions by using the edges of the element as vector basis. The proposed approach on solving second order Maxwell differential equation of 3-D MT is using direct solver rather than iterative method. Therefore, divergence correction to accelerate the rate of convergence for its iterative solution is no longer needed. The utilization of direct solver has been verified previously for correctness by comparing the resulting solution to those given by analytical solution, as well as the solution come from the other numerical methods, for earth layered model, 2-D models and COMMEMI 3D-2 model. In this work, further verification resulted from recent comparison model of Dublin Test Model 1 (DTM1) is presented. (paper)
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)
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...
Energy Technology Data Exchange (ETDEWEB)
Majima, K.; Miyazaki, T.; Oishi, K. [Nagaoka Univ. of Technology., Niigata (Japan)
1997-10-20
This paper proposes a new dynamic gait control method of biped robot based on robust joint servo control. The method consists of two subjects. The first subject is the approximation of biped robot to the inverted pendulum for sagittal plane and lateral plane. The second subject is the constitution of dynamic gait control based on robust joint servo control and kinematics. The motion description in Cartesian space is determined from the motion of the inverted pendulum for sagittal plane and lateral plane. Suitability of the biped motion reference is confirmed by distribution of ZMP (Zero Moment Point). Using the inverse kinematics of biped robot, the biped motion references in Cartesian space is transformed to the position references in joint space. In joint space, the robust position control system consists of two-degrees-of-freedom control system based on coprime factorization and disturbance observer. Since the robust joint servo control system compensates the inertia variation and disturbance torque on dynamic gait control, this control system is suitable for the dynamic gait control of biped robot. The validity of the proposed method is confirmed by the experimental results. 15 refs., 11 figs., 2 tabs.
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
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex
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
2015-01-01
Full Text Available A fully-coupled partitioned finite volume–finite volume and hybrid finite volume–finite element fluid-structure interaction scheme is presented. The fluid domain is modelled as a viscous incompressible isothermal region governed by the Navier...
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 ...
The Galerkin finite element method for a multi-term time-fractional diffusion equation
Jin, Bangti
2015-01-01
© 2014 The Authors. 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 difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... of bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...... Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...
Centralizers in simple locally finite groups
Directory of Open Access Journals (Sweden)
Mahmut Kuzucuoğlu
2013-03-01
Full Text Available This is a survey article on centralizers of finitesubgroups in locally finite, simple groups or LFS-groups as wewill call them. We mention some of the open problems aboutcentralizers of subgroups in LFS-groups and applications of theknown information about the centralizers of subgroups to thestructure of the locally finite group. We also prove thefollowing: Let $G$ be a countably infinite non-linear LFS-groupwith a Kegel sequence $mathcal{K}={(G_i,N_i | iinmathbf{N} }$. If there exists an upper bound for ${ |N_i| |iin mathbf{N} }$, then for any finite semisimplesubgroup $F$ in $G$ the subgroup $C_G(F$ has elements oforder $p_i$ for infinitely many distinct prime $p_i$. Inparticular $C_G(F$ is an infinite group. This answers Hartley'squestion provided that there exists a bound on ${ |N_i| | iin mathbf{N}$.
Geometrically unfitted finite element methods and applications
Burman, Erik; Larson, Mats; Olshanskii, Maxim
2017-01-01
This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and aug...
Essentially finitely indecomposable QTAG-Modules
Directory of Open Access Journals (Sweden)
Alveera Mehdi
2016-01-01
Full Text Available A right module $M$ over an associative ring with unity is a $QTAG$-module if every finitely generated submodule of any homomorphic image of $M$ is a direct sum of uniserial modules. There are many fascinating results related to these modules and essentially indecomposable modules are extensively researched. Motivated by these modules we generalize them as essentially finitely indecomposable modules whose every direct decomposition $M=\\bigoplus\\limits_{k\\in I} M_k$ implies that there exists a positive integer $n$ such that $H_n(M_i=0$ for all $M_i$'s except for a finite number of $M_i$'s. Here we investigate these modules and their relationship with $HT$-modules. The cases when the modules are not $HT$-modules are especially highlighted.
Shear sum rules at finite chemical potential
David, Justin R.; Jain, Sachin; Thakur, Somyadip
2012-03-01
We derive sum rules which constrain the spectral density corresponding to the retarded propagator of the T xy component of the stress tensor for three gravitational duals. The shear sum rule is obtained for the gravitational dual of the mathcal{N} = {4} Yang-Mills, theory of the M2-branes and M5-branes all at finite chemical potential. We show that at finite chemical potential there are additional terms in the sum rule which involve the chemical potential. These modifications are shown to be due to the presence of scalars in the operator product expansion of the stress tensor which have non-trivial vacuum expectation values at finite chemical potential.
Visualizing higher order finite elements. Final report
Energy Technology Data Exchange (ETDEWEB)
Thompson, David C; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
Electron–phonon coupling from finite differences
Monserrat, Bartomeu
2018-02-01
The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron–phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron–phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron–phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron–phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron–phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron–phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron–phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron–phonon interaction.
DEFF Research Database (Denmark)
Palleti, Hara Naga Krishna Teja; Santiuste, Carlos; Thomsen, Ole Thybo
2010-01-01
Thermo-mechanical interaction effects including thermal material degradation in polymer foam cored sandwich structures is investigated using the commercial Finite Element Analysis (FEA) package ABAQUS/Standard. Sandwich panels with different boundary conditions in the form of simply supported...
Energy Technology Data Exchange (ETDEWEB)
Lykken, Joseph D.; /Fermilab
2010-05-01
'BSM physics' is a phrase used in several ways. It can refer to physical phenomena established experimentally but not accommodated by the Standard Model, in particular dark matter and neutrino oscillations (technically also anything that has to do with gravity, since gravity is not part of the Standard Model). 'Beyond the Standard Model' can also refer to possible deeper explanations of phenomena that are accommodated by the Standard Model but only with ad hoc parameterizations, such as Yukawa couplings and the strong CP angle. More generally, BSM can be taken to refer to any possible extension of the Standard Model, whether or not the extension solves any particular set of puzzles left unresolved in the SM. In this general sense one sees reference to the BSM 'theory space' of all possible SM extensions, this being a parameter space of coupling constants for new interactions, new charges or other quantum numbers, and parameters describing possible new degrees of freedom or new symmetries. Despite decades of model-building it seems unlikely that we have mapped out most of, or even the most interesting parts of, this theory space. Indeed we do not even know what is the dimensionality of this parameter space, or what fraction of it is already ruled out by experiment. Since Nature is only implementing at most one point in this BSM theory space (at least in our neighborhood of space and time), it might seem an impossible task to map back from a finite number of experimental discoveries and measurements to a unique BSM explanation. Fortunately for theorists the inevitable limitations of experiments themselves, in terms of resolutions, rates, and energy scales, means that in practice there are only a finite number of BSM model 'equivalence classes' competing at any given time to explain any given set of results. BSM phenomenology is a two-way street: not only do experimental results test or constrain BSM models, they also suggest
Finite continuum quasi distributions from lattice QCD
Monahan, Christopher; Orginos, Kostas
2018-03-01
We present a new approach to extracting continuum quasi distributions from lattice QCD. Quasi distributions are defined by matrix elements of a Wilson-line operator extended in a spatial direction, evaluated between nucleon states at finite momentum. We propose smearing this extended operator with the gradient flow to render the corresponding matrix elements finite in the continuum limit. This procedure provides a nonperturbative method to remove the power-divergence associated with the Wilson line and the resulting matrix elements can be directly matched to light-front distributions via perturbation theory.
Virtual photon spectra for finite nuclei
International Nuclear Information System (INIS)
Wolynec, E.; Martins, M.N.
1988-01-01
The experimental results of an isochromat of the virtual photon spectrum, obtained by measuring the number of ground-state protons emitted by the 16.28 MeV isobaric analogue state in 90 Zr as a function of electron incident energy in the range 17-105 MeV, are compared with the values predicted by a calculation of the E1 DWBA virtual photon spectra for finite nuclei. It is found that the calculations are in excellent agreement with the experimental results. The DWBA virtual photon spectra for finite nuclei for E2 and M1 multipoles are also assessed. (author) [pt
Finite elements for analysis and design
Akin, J E; Davenport, J H
1994-01-01
The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee
Finite W-algebras and intermediate statistics
International Nuclear Information System (INIS)
Barbarin, F.; Ragoucy, E.; Sorba, P.
1994-09-01
New realizations of finite W-algebras are constructed by relaxing the usual 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. (author). 13 refs
Quadrature representation of finite element variational forms
DEFF Research Database (Denmark)
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations. An alter......This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations...
Variational integrators for the dynamics of thermo-elastic solids with finite speed thermal waves
Energy Technology Data Exchange (ETDEWEB)
Mata, Pablo [Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4040 (United States); Centro de Investigación en Ecosistemas de la Patagonia (CIEP), Conicyt Regional/CIEP R10C1003, Universidad Austral de Chile, Ignacio Serrrano 509, Coyhaique (Chile); Lew, Adrian J., E-mail: lewa@stanford.edu [Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4040 (United States)
2014-01-15
This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the fact that the Green–Naghdi theory of type II for thermo-elastic solids has a Hamiltonian structure. Thus, standard techniques to construct variational integrators can be applied to finite element discretizations of the problem. The resulting discrete-in-time trajectories are then consistent with the laws of thermodynamics for these systems: for an isolated system, they exactly conserve the total entropy, and nearly exactly conserve the total energy over exponentially long periods of time. Moreover, linear and angular momenta are also exactly conserved whenever the exact system does. For definiteness, we construct an explicit second-order accurate algorithm for affine tetrahedral elements in two and three dimensions, and demonstrate its performance with numerical examples.
An Implementation in C of an Algorithm for Construction of Finitely Presented Lie Superalgebras
Directory of Open Access Journals (Sweden)
V. Gerdt
1996-12-01
Full Text Available The purpose of this paper is to describe a C program FPLSA for investigating finitely presented Lie algebras and superalgebras. The program takes as input data a finite set of generators and relations for these elements. The relations have the form of Lie polynomials with coefficients being either integers or polynomials over integers in a given finite set of parameters. The program is based on an algorithm of constructing complete set of relations called also standard basis or Grobner basis of ideal of free Lie (superalgebra generated by the input set of relations. The output data of the program are the Grobner basis, the explicit form of basis elements for the quotient algebra of the free (superalgebra with respect to given ideal and also the table of their commutators.
Finite-element solution of the Schroedinger equation for the helium ground state
International Nuclear Information System (INIS)
Levin, F.S.; Shertzer, J.
1985-01-01
The finite-element method has been used to obtain numerical solutions to the Schroedinger equation for the ground state of the helium atom. In contrast to the globally defined trial functions of the standard variational approach, the finite-element algorithm employs locally defined interpolation functions to approximate the unknown wave function. The calculation reported herein used a three-dimensional grid containing nine nodal points along the radial coordinates of the two electrons and four nodal points along the direction corresponding to the cosine of the interelectronic angle. This produced an energy of -2.9032 a.u., which lies 0.017% above the Frankowski-Pekeris value. The values of , for n = -2,-1, 1, and 2, are closer to those of Frankowski and Pekeris than from all of the variational calculations with the exception of the calculation performed by Weiss, whose energy and values are comparable to those of the finite-element computation
Application of the control volume mixed finite element method to a triangular discretization
Naff, R.L.
2012-01-01
A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.
Variational integrators for the dynamics of thermo-elastic solids with finite speed thermal waves
International Nuclear Information System (INIS)
Mata, Pablo; Lew, Adrian J.
2014-01-01
This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the fact that the Green–Naghdi theory of type II for thermo-elastic solids has a Hamiltonian structure. Thus, standard techniques to construct variational integrators can be applied to finite element discretizations of the problem. The resulting discrete-in-time trajectories are then consistent with the laws of thermodynamics for these systems: for an isolated system, they exactly conserve the total entropy, and nearly exactly conserve the total energy over exponentially long periods of time. Moreover, linear and angular momenta are also exactly conserved whenever the exact system does. For definiteness, we construct an explicit second-order accurate algorithm for affine tetrahedral elements in two and three dimensions, and demonstrate its performance with numerical examples
Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering.
Perrey-Debain, E; Laghrouche, O; Bettess, P; Trevelyan, J
2004-03-15
Classical finite-element and boundary-element formulations for the Helmholtz equation are presented, and their limitations with respect to the number of variables needed to model a wavelength are explained. A new type of approximation for the potential is described in which the usual finite-element and boundary-element shape functions are modified by the inclusion of a set of plane waves, propagating in a range of directions evenly distributed on the unit sphere. Compared with standard piecewise polynomial approximation, the plane-wave basis is shown to give considerable reduction in computational complexity. In practical terms, it is concluded that the frequency for which accurate results can be obtained, using these new techniques, can be up to 60 times higher than that of the conventional finite-element method, and 10 to 15 times higher than that of the conventional boundary-element method.
Fringe—A Java-based finite fringe analysis package
McIntyre, Timothy J.; Bishop, Alexis I.
2012-09-01
A package for analysing two-dimensional finite fringe interferograms is described. Through a combination of automatic and interactive routines, an interferogram can be processed to extract the phase shift imparted on the recording light by a transparent object. The package consists of routines to condition and pad the original image for Fourier transform analysis, to filter the image and obtain the phase, to unwrap the phase, and to remove the background phase ramp. A sample image recorded using holographic interferometry is successfully analysed. Program summary Program title: FRINGE Catalogue identifier: AEMM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 134006 No. of bytes in distributed program, including test data, etc.: 4029801 Distribution format: tar.gz Programming language: Java. Computer: Personal Computers. Operating system: Mac OS X, Windows XP, Linux and any other system that can run Java Jar files. RAM: 1GB recommended Classification: 18. Nature of problem: A standalone multi-platform program to perform analysis of finite fringe interferograms. Solution method: Fourier filtering approach with phase unwrapping and background subtraction. Restrictions: Designed to analyse square images. Running time: Interactive processing takes several minutes. Minimal cpu time.
A Finite Layer Formulation for Groundwater Flow to Horizontal Wells.
Xu, Jin; Wang, Xudong
2016-09-01
A finite layer approach for the general problem of three-dimensional (3D) flow to horizontal wells in multilayered aquifer systems is presented, in which the unconfined flow can be taken into account. The flow is approximated by an integration of the standard finite element method in vertical direction and the analytical techniques in the other spatial directions. Because only the vertical discretization is involved, the horizontal wells can be completely contained in one specific nodal plane without discretization. Moreover, due to the analytical eigenfunctions introduced in the formulation, the weighted residual equations can be decoupled, and the formulas for the global matrices and flow vector corresponding to horizontal wells can be obtained explicitly. Consequently, the bandwidth of the global matrices and computational cost rising from 3D analysis can be significantly reduced. Two comparisons to the existing solutions are made to verify the validity of the formulation, including transient flow to horizontal wells in confined and unconfined aquifers. Furthermore, an additional numerical application to horizontal wells in three-layered systems is presented to demonstrate the applicability of the present method in modeling flow in more complex aquifer systems. © 2016, National Ground Water Association.
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
Strength Analysis on Ship Ladder Using Finite Element Method
Budianto; Wahyudi, M. T.; Dinata, U.; Ruddianto; Eko P., M. M.
2018-01-01
In designing the ship’s structure, it should refer to the rules in accordance with applicable classification standards. In this case, designing Ladder (Staircase) on a Ferry Ship which is set up, it must be reviewed based on the loads during ship operations, either during sailing or at port operations. The classification rules in ship design refer to the calculation of the structure components described in Classification calculation method and can be analysed using the Finite Element Method. Classification Regulations used in the design of Ferry Ships used BKI (Bureau of Classification Indonesia). So the rules for the provision of material composition in the mechanical properties of the material should refer to the classification of the used vessel. The analysis in this structure used program structure packages based on Finite Element Method. By using structural analysis on Ladder (Ladder), it obtained strength and simulation structure that can withstand load 140 kg both in static condition, dynamic, and impact. Therefore, the result of the analysis included values of safety factors in the ship is to keep the structure safe but the strength of the structure is not excessive.
FINITE VOLUME METHOD FOR DETERMINING THE NATURAL CHARACTERISTICS OF STRUCTURES
Directory of Open Access Journals (Sweden)
N. FALLAH
2013-02-01
Full Text Available In this paper a finite volume based formulation is developed to calculate the structural natural characteristics including the natural frequencies and the critical buckling loads of slender beam/beam-columns in which the shear effects are taken into account. For natural frequency calculations, both shear effects and rotational inertia effects are considered. In this finite volume based approach, the equilibrium equations of control volumes are expressed and used with the boundary conditions to obtain the eigenvalue equation in the standard format. Then, the natural characteristics of beam/beam-columns are obtained by solving the eigenvalue equations. The formulation is tested on a number of benchmark problems. Accordingly, the proposed formulation has been found to accurately predict the natural frequencies and the critical buckling loads of the test problems. Also, the formulation is tested for the very thin and thick beams. It is found that the formulation is also able to analyze the thin beams in which no shear locks is observed.
On p-supersolvability of finite groups
Indian Academy of Sciences (India)
Supersolvability; p-nilpotency; weakly τ-embedded subgroups. 2010 Mathematics Subject Classification. 20D10, 20D20. 1. Introduction. Throughout the paper, all groups are finite. Recall that a subgroup H of a group G is said to permute with a subgroup ...
Finite difference order doubling in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Killingbeck, John P [Mathematics Centre, University of Hull, Hull HU6 7RX (United Kingdom); Jolicard, Georges [Universite de Franche-Comte, Institut Utinam (UMR CNRS 6213), Observatoire de Besancon, 41 bis Avenue de l' Observatoire, BP1615, 25010 Besancon cedex (France)
2008-03-28
An order doubling process previously used to obtain eighth-order eigenvalues from the fourth-order Numerov method is applied to the perturbed oscillator in two dimensions. A simple method of obtaining high order finite difference operators is reported and an odd parity boundary condition is found to be effective in facilitating the smooth operation of the order doubling process.
Flexural vibrations of finite composite poroelastic cylinders
Indian Academy of Sciences (India)
infinite hollow poroelastic cylinders. Axially symmetric vibrations of finite composite poroe- lastic cylinders that are bonded end to end are investigated by Shah & Tajuddin (2009). The analysis of the flexural vibrations in cylindrical structures has wide applications in the field of acoustics structural design and Biomechanics, ...
Finite Algorithms for Robust Linear Regression
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun
1990-01-01
The Huber M-estimator for robust linear regression is analyzed. Newton type methods for solution of the problem are defined and analyzed, and finite convergence is proved. Numerical experiments with a large number of test problems demonstrate efficiency and indicate that this kind of approach may...
∗-supplemented subgroups of finite groups
Indian Academy of Sciences (India)
complemented in G. In 1998, Ballester-Bolinches and Pedraza-Aguilera [2] introduced. S-quasinormally embedded ... concept of M-supplemented subgroups and characterized the structure of finite groups by ... A subgroup H of a group G is said to be M∗-supplemented in G if there exists a subgroup. K of G such that G = HK ...
A Note on Powers in Finite Fields
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2016-01-01
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…
The Finite Lamplighter Groups: A Guided Tour
Siehler, Jacob A.
2012-01-01
In this article, we present a family of finite groups, which provide excellent examples of the basic concepts of group theory. To work out the center, conjuagacy classes, and commutators of these groups, all that's required is a bit of linear algebra.
Finite element analysis of photonic crystal fibers
Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.
2005-01-01
A finite-element-based vectorial optical mode solver, furnished with Bayliss-Gunzburger-Turkel-like transparent boundary conditions, is used to rigorously analyze photonic crystal fibers (PCFs). Both the real and imaginary part of the modal indices can be computed in a relatively small computational
Finite element simulation of asphalt fatigue testing
DEFF Research Database (Denmark)
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...
Legendre Elliptic Curves over Finite Fields
Auer, Roland; Top, Jakob
2002-01-01
We show that every elliptic curve over a finite field of odd characteristic whose number of rational points is divisible by 4 is isogenous to an elliptic curve in Legendre form, with the sole exception of a minimal respectively maximal elliptic curve. We also collect some results concerning the
On partially saturated formations of finite groups
International Nuclear Information System (INIS)
Ballester-Bolinches, Adolfo; Calvo, Clara; Shemetkov, L A
2007-01-01
Various types of partially saturated formations and connections between them are considered. It is shown that partially saturated formations can be characterized as classes of finite groups with generalized central series. A theorem on the decomposition of an FG-module into a sum of two submodules with special properties is proved. Bibliography: 26 titles.
Thermoelectric properties of finite graphene antidot lattices
DEFF Research Database (Denmark)
Gunst, Tue; Markussen, Troels; Jauho, Antti-Pekka
2011-01-01
We present calculations of the electronic and thermal transport properties of graphene antidot lattices with a finite length along the transport direction. The calculations are based on the π-tight-binding model and the Brenner potential. We show that both electronic and thermal transport...
The geometry of finite equilibrium sets
DEFF Research Database (Denmark)
Balasko, Yves; Tvede, Mich
2009-01-01
We investigate the geometry of finite datasets defined by equilibrium prices, income distributions, and total resources. We show that the equilibrium condition imposes no restrictions if total resources are collinear, a property that is robust to small perturbations. We also show that the set...
Finite element modelling of solidification phenomena
Indian Academy of Sciences (India)
The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation is ...
Finite-size effects from giant magnons
Energy Technology Data Exchange (ETDEWEB)
Arutyunov, Gleb [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)]. E-mail: g.arutyunov@phys.uu.nl; Frolov, Sergey [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany)]. E-mail: frolovs@aei.mpg.de; Zamaklar, Marija [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany)]. E-mail: marzam@aei.mpg.de
2007-08-27
In order to analyze finite-size effects for the gauge-fixed string sigma model on AdS{sub 5}xS{sup 5}, we construct one-soliton solutions carrying finite angular momentum J. In the infinite J limit the solutions reduce to the recently constructed one-magnon configuration of Hofman and Maldacena. The solutions do not satisfy the level-matching condition and hence exhibit a dependence on the gauge choice, which however disappears as the size J is taken to infinity. Interestingly, the solutions do not conserve all the global charges of the psu(2,2-vertical bar4) algebra of the sigma model, implying that the symmetry algebra of the gauge-fixed string sigma model is different from psu(2,2-vertical bar4) for finite J, once one gives up the level-matching condition. The magnon dispersion relation exhibits exponential corrections with respect to the infinite J solution. We also find a generalisation of our one-magnon configuration to a solution carrying two charges on the sphere. We comment on the possible implications of our findings for the existence of the Bethe ansatz describing the spectrum of strings carrying finite charges.
The Finite Embeddability Property for Residuated Groupoids
Czech Academy of Sciences Publication Activity Database
Haniková, Zuzana; Horčík, Rostislav
2014-01-01
Roč. 72, č. 1 (2014), s. 1-13 ISSN 0002-5240 R&D Projects: GA ČR GAP202/11/1632 Institutional support: RVO:67985807 Keywords : residuated groupoid * distributive lattice * finite embeddability property Subject RIV: BA - General Mathematics Impact factor: 0.442, year: 2014
Adsorption of Lithium on Finite Graphitic Clusters
DEFF Research Database (Denmark)
Martinez, Jose Ignacio; Cabria, I.; Lopez, M.J.
2009-01-01
The apparent discrepancies between density functional (DFT) and Moller-Plesset (MP2) calculations for the interaction of lithium with graphene recently pointed out by Ferre-Vilaplana (J. Phys. Chem. C 2008, 112, 3998) are discussed. In his calculations, this author used a finite coronene cluster, C...
Fast finite elements for surgery simulation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix...
Finite Feedback Cycling in Structural Equation Models
Hayduk, Leslie A.
2009-01-01
In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few…
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
these methods. Keywords. hp-Finite element method; continuous Galerkin methods; wave solutions; Gibbs' phenomenon. 1. Introduction. Galerkin methods belong to the class of solution methods for PDEs where the solution residue is minimized giving rise to the well-known weak formulation of problems. In this approach,.
Equivalent drawbead model in finite element simulations
Carleer, Bart D.; Carleer, B.D.; Meinders, Vincent T.; Huetink, Han; Lee, J.K.; Kinzel, G.L.; Wagoner, R.
1996-01-01
In 3D simulations of the deep drawing process the drawbead geometries are seldom included. Therefore equivalent drawbeads are used. In order to investigate the drawbead behaviour a 2D plane strain finite element model was used. For verification of this model experiments were performed. The analyses
Effective permittivity of finite inhomogeneous objects
Raghunathan, S.B.; Budko, N.V.
2010-01-01
A generalization of the S-parameter retrieval method for finite three-dimensional inhomogeneous objects under arbitrary illumination and observation conditions is presented. The effective permittivity of such objects may be rigorously defined as a solution of a nonlinear inverse scattering problem.
On higher order pyramidal finite elements
Czech Academy of Sciences Publication Activity Database
Liu, L.; Davies, K.B.; Křížek, Michal; Guan, L.
2011-01-01
Roč. 3, č. 2 (2011), s. 131-140 ISSN 2070-0733 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : pyramidal polynomial basis functions * finite element method * composite elements * three-dimensional mortar elements Subject RIV: BA - General Mathematics Impact factor: 0.750, year: 2011
The circle equation over finite fields
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2017-01-01
Interesting patterns in the geometry of a plane algebraic curve C can be observed when the defining polynomial equation is solved over the family of finite fields. In this paper, we examine the case of C the classical unit circle defined by the circle equation x2 + y2 = 1. As a main result, we es...
Restricted Schur polynomials and finite N counting
International Nuclear Information System (INIS)
Collins, Storm
2009-01-01
Restricted Schur polynomials have been posited as orthonormal operators for the change of basis from N=4 SYM to type IIB string theory. In this paper we briefly expound the relationship between the restricted Schur polynomials and the operators forwarded by Brown, Heslop, and Ramgoolam. We then briefly examine the finite N counting of the restricted Schur polynomials.
A Ring Construction Using Finite Directed Graphs
Bardzell, Michael
2012-01-01
In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…
Finite Cycle Gibbs Measures on Permutations of
Armendáriz, Inés; Ferrari, Pablo A.; Groisman, Pablo; Leonardi, Florencia
2015-03-01
We consider Gibbs distributions on the set of permutations of associated to the Hamiltonian , where is a permutation and is a strictly convex potential. Call finite-cycle those permutations composed by finite cycles only. We give conditions on ensuring that for large enough temperature there exists a unique infinite volume ergodic Gibbs measure concentrating mass on finite-cycle permutations; this measure is equal to the thermodynamic limit of the specifications with identity boundary conditions. We construct as the unique invariant measure of a Markov process on the set of finite-cycle permutations that can be seen as a loss-network, a continuous-time birth and death process of cycles interacting by exclusion, an approach proposed by Fernández, Ferrari and Garcia. Define as the shift permutation . In the Gaussian case , we show that for each , given by is an ergodic Gibbs measure equal to the thermodynamic limit of the specifications with boundary conditions. For a general potential , we prove the existence of Gibbs measures when is bigger than some -dependent value.
Finiteness of PST self-dual models
International Nuclear Information System (INIS)
Del Cima, Oswaldo M.; Piguet, Olivier; Sarandy, Marcelo S.
2000-12-01
The Pasti-Sorokin-Tonin model for describing chiral forms is considered at the quantum level. We study the ultraviolet and infrared behaviour of the model in two, four and six dimensions in the framework of algebraic renormalization. The absence of anomalies, as well as the finiteness, up to non-physical renormalizations, are shown in all dimensions analyzed. (author)
Simplicial Finite Elements in Higher Dimensions
Czech Academy of Sciences Publication Activity Database
Brandts, J.; Korotov, S.; Křížek, Michal
2007-01-01
Roč. 52, č. 3 (2007), s. 251-265 ISSN 0862-7940 R&D Projects: GA ČR GA201/04/1503 Institutional research plan: CEZ:AV0Z10190503 Keywords : n-simplex * finite element method * superconvergence Subject RIV: BA - General Mathematics
Counting Subspaces of a Finite Vector Space
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 11. Counting Subspaces of a Finite Vector Space – 1. Amritanshu Prasad. General Article Volume 15 Issue 11 November 2010 pp 977-987. Fulltext. Click here to view fulltext PDF. Permanent link:
Chiral symmetry breaking in finite quantum electrodynamics
International Nuclear Information System (INIS)
Montero, J.C.; Pleitez, V.
1987-01-01
The dynamical breakdown of chiral symmetry in a finite Abelian gauge theory using a variational approach for the effective potential for composite operators is discussed. It is shown that, at least in a variational approach, the fermion either remains massless or gets a dynamical mass for every non-zero coupling constant. (Author) [pt
Regular Event Structures and Finite Petri Nets
DEFF Research Database (Denmark)
Nielsen, M.; Thiagarajan, P.S.
2002-01-01
We present the notion of regular event structures and conjecture that they correspond exactly to finite 1-safe Petri nets. We show that the conjecture holds for the conflict-free case. Even in this restricted setting, the proof is non-trivial and involves a natural subclass of regular event...
Directory of Open Access Journals (Sweden)
P.B. Silva
2013-01-01
Full Text Available Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the waveguide. As an illustrating example, spectral elements are derived for straight uniform rods and beams and used to calculate the forced response in the longitudinal and transverse directions. Results obtained with the spectral element formulation are shown to agree well with results obtained with a finite element model of the whole beam. The proposed approach can be used to generate spectral elements of waveguides of arbitrary cross section and, potentially, of arbitrary order.
Transient finite element modeling of functional electrical stimulation.
Filipovic, Nenad D; Peulic, Aleksandar S; Zdravkovic, Nebojsa D; Grbovic-Markovic, Vesna M; Jurisic-Skevin, Aleksandra J
2011-03-01
Transcutaneous functional electrical stimulation is commonly used for strengthening muscle. However, transient effects during stimulation are not yet well explored. The effect of an amplitude change of the stimulation can be described by static model, but there is no differency for different pulse duration. The aim of this study is to present the finite element (FE) model of a transient electrical stimulation on the forearm. Discrete FE equations were derived by using a standard Galerkin procedure. Different tissue conductive and dielectric properties are fitted using least square method and trial and error analysis from experimental measurement. This study showed that FE modeling of electrical stimulation can give the spatial-temporal distribution of applied current in the forearm. Three different cases were modeled with the same geometry but with different input of the current pulse, in order to fit the tissue properties by using transient FE analysis. All three cases were compared with experimental measurements of intramuscular voltage on one volunteer.
Finite element analysis of elasto-plastic tee joints
International Nuclear Information System (INIS)
Powell, G.H.
1974-09-01
The theory and computational procedures used in the computer program B169TJ/EP for the analysis of elasto-plastic tee joints are described, and detailed user's guide is presented. The program is particularly applicable to joints conforming to the ANSI B16.9 Manufacturing Standard, but can also be applied to other joint geometries. The joint may be loaded by internal pressure and by arbitrary combinations of applied forces and moments at the ends of the branch and run pipes, and the loading sequence may be arbitrary. The joint material is assumed to yield according to the von Mises criterion, and to exhibit either linear kinematic hardening or nonlinear isotropic hardening after yield. The program makes use of the finite element and mesh generation procedures previously applied in the elastic stress analysis program B16.9TJ/ SA, with minor modifications. (U.S.)
Transition to collective oscillations in finite Kuramoto ensembles
Peter, Franziska; Pikovsky, Arkady
2018-03-01
We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this purpose, the minimal value of the amplitude of the complex Kuramoto order parameter appears as a proper indicator. The dependence of this minimum on coupling strength varies due to sampling variations and correlates with the sample kurtosis of the natural frequency distribution. The skewness of the frequency sample determines the frequency of the resulting collective mode. The effects of kurtosis and skewness hold in the thermodynamic limit of infinite ensembles. We prove this by integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively.
Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime
International Nuclear Information System (INIS)
Zumbusch, G
2009-01-01
Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second-order symmetric hyperbolic. It is discretized in four-dimensional spacetime by finite differences, finite elements and interior penalty discontinuous Galerkin methods, the latter being related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and nonlinear test problems of the Apples-with-Apples collection.
International Nuclear Information System (INIS)
Al-Akhrass, Dina
2014-01-01
Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)
Energy Technology Data Exchange (ETDEWEB)
Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F
2010-07-01
Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.
International Nuclear Information System (INIS)
Heinemann, D.; Rosen, A.; Fricke, B.
1990-01-01
The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N 2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the opne dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method. (orig.)
Comparison study of finite element and basis set methods for finite size scaling
International Nuclear Information System (INIS)
Antillon, Edwin; Moy, Winton; Wei Qi; Kais, Sabre
2009-01-01
We compare two methods of obtaining critical parameters for a quantum Hamiltonian using a finite size scaling approach. A finite element and basis set method were used in conjunction with the finite size scaling to obtain the critical parameters for the Hulthen potential. The critical parameters obtained analytically were the coupling constant λ c =(1/2), the critical exponents for the energy α=2 and for the 'correlation length 'ν=1. The extrapolated results for finite size scaling with the basis set method are λ c =0.499 99, α=1.9960, and ν=0.999 10. The results for the finite element solutions are λ c =0.501 84, α=1.999 93, and ν=1.000 79 for the linear interpolation and λ c =0.500 00, α=2.000 11, and ν=1.000 32 for the Hermite interpolation. The results for each method compare very well with the analytical results obtained for the Hulthen potential. However, the finite element method is easier to implement and may be combined with ab initio and density functional theory to obtain quantum critical parameters for more complex systems.
Finite element modeling for materials engineers using Matlab
Oluwole, Oluleke
2014-01-01
Finite Element Modeling for Materials Engineers Using MATLAB® combines the finite element method with MATLAB to offer materials engineers a fast and code-free way of modeling for many materials processes.
Finite Element Based Design and Optimization for Piezoelectric Accelerometers
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.; Yao, Q.
1998-01-01
A systematic Finite Element design and optimisation procedure is implemented for the development of piezoelectric accelerometers. Most of the specifications of accelerometers can be obtained using the Finite Element simulations. The deviations between the simulated and calibrated sensitivities...
Branched standard spines of 3-manifolds
Benedetti, Riccardo
1997-01-01
This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the notion of branched standard spine, introduced in the book as a combination of the notion of branched surface with that of standard spine. The book is intended for readers interested in low-dimensional topology, and some familiarity with the basics is assumed. A list of questions, some of which concerning relations with the theory of quantum invariants, is enclosed.
Two inquiries about finite groups and well-behaved quotients
Blum-Smith, Ben
2018-01-01
This thesis addresses questions in representation and invariant theory of finite groups. The first concerns singularities of quotient spaces under actions of finite groups. We introduce a class of finite groups such that the quotients have at worst abelian quotient singularities. We prove that supersolvable groups belong to this class and show that nonabelian finite simple groups do not belong to it. The second question concerns the Cohen-Macaulayness of the invariant ring $\\mathbb{Z}[x_1,\\do...