Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Fodor, Z; Katz, S D; Lellouch, L; Portelli, A; Szabo, K K; Toth, B C
2015-01-01
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Energy Technology Data Exchange (ETDEWEB)
Fodor, Z. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich (Germany); Institute for Theoretical Physics, Eötvös University, H-1117 Budapest (Hungary); Hoelbling, C. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Katz, S.D. [Institute for Theoretical Physics, Eötvös University, H-1117 Budapest (Hungary); MTA-ELTE Lendület Lattice Gauge Theory Research Group, H-1117 Budapest (Hungary); Lellouch, L., E-mail: lellouch@cpt.univ-mrs.fr [CNRS, Aix-Marseille U., U. de Toulon, CPT, UMR 7332, F-13288, Marseille (France); Portelli, A. [School of Physics & Astronomy, University of Southampton, SO17 1BJ (United Kingdom); Szabo, K.K. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich (Germany); Toth, B.C. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany)
2016-04-10
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Directory of Open Access Journals (Sweden)
Z. Fodor
2016-04-01
Full Text Available Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
De Soto, F
2006-01-01
The numerical solutions of the non-relativistic Yukawa model on a 3-dimensional size lattice with periodic boundary conditions are obtained. The possibility to extract the corresponding -- infinite space -- low energy parameters and bound state binding energies from eigensates computed at finite lattice size is discussed.
Light Fermion Finite Mass Effects in Non-relativistic Bound States
Eiras, D; Eiras, Dolors; Soto, Joan
2000-01-01
We present analytic expressions for the vacuum polarization effects due to a light fermion with finite mass in the binding energy and in the wave function at the origin of QED and (weak coupling) QCD non-relativistic bound states. Applications to exotic atoms, \\Upsilon (1s) and t\\bar{t} production near threshold are briefly discussed.
A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
Nicolis, Alberto
2012-01-01
We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theories at finite charge density. It is customary to treat systems at finite density via non-relativistic Hamiltonians. Here we highlight the importance of the underlying relativistic dynamics. This leads to seemingly new results whenever the charge in question is spontaneously broken and does not commute with other broken charges. These would normally be associated with gapless Goldstone excitations. We find that, in fact, their currents interpolate gapped excitations. We derive exact non-perturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called high energy substantially differ between non-relativistic and relativistic cases.
Energy Technology Data Exchange (ETDEWEB)
Soto, F. de [Laboratoire Physique Subatomique et Cosmologie, 53 av. des Martyrs, 38026 Grenoble (France)]|[Dpto. Sistemas Fisicos, Quimicos y Naturales, U. Pablo de Olavide, 41013 Sevilla (Spain); Carbonell, J. [Laboratoire Physique Subatomique et Cosmologie, 53 av. des Martyrs, 38026 Grenoble (France)
2007-04-15
The numerical solutions of the non-relativistic Yukawa model on a 3-dimensional size lattice with periodic boundary conditions are obtained. The possibility to extract the corresponding - infinite space - low energy parameters and bound state binding energies from eigenstates computed at finite lattice size is discussed. The results have been obtained with a non relativistic model, which is justified by the small energies involved in the calculations. Despite its simplicity, the model considered contains an essential ingredient of the hadron-hadron interaction - its finite range - which plays a relevant role in view of extracting the low energy parameters from the finite volume spectra. It offers a wieldy and physically sound tool to test the validity of the different approaches discussed in the literature to study the low energy scattering of baryon-baryon or meson-baryon systems from a lattice simulations in QCD. The results presented in this work have been essentially limited to the ground state of central attractive interactions, depending only on one parameter. The method can be easily applied to more involved interactions, like hard core repulsive terms or non central potentials leading to coupled channel equations. (authors)
Finite-dimensional (*)-serial algebras
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties of (*)-serial algebras, and we obtain suficient and necessary conditions for an associative algebra to be (*)-serial.
Radon Transform in Finite Dimensional Hilbert Space
Revzen, M.
2012-01-01
Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators are underpinned with finite geometry which provide intuitive perspective to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite dimensional quantum mechani...
Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
Hartong, Jelle; Obers, Niels A
2016-01-01
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a...
Stepanov, Nikolay S.; Zelekson, Lev A.
2017-03-01
The exact stationary solution of one-dimensional non-relativistic Vlasov equation is obtained in the article. It is shown that in the energy exchange with the self-consistent longitudinal electric field, both wave trapped charged particles and the passing ones take part. It is proved that the trapped electron distribution is fundamentally different from distribution functions described by other authors, which used the Bernstein, Greene, and Kruskal method. So, the correct distribution function is characterized by its sudden change at the equality of wave and electrons' velocity but not on the edges of the potential well. This jump occurs for any arbitrary small value of wave potential. It was also found that the energy density of fast electrons trapped by the wave is less than the energy density of slow trapped electrons. This leads to the fact that the energy of the self-consistent electric field may both increase and decrease due to the nonlinear Landau damping. The conditions under which a similar effect can be observed are defined. Also for the first time, it is shown that the self-generated strong electric field always produces antitropic electron beams.
Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity
Hartong, Jelle; Lei, Yang; Obers, Niels A.
2016-09-01
We show that certain three-dimensional Hořava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various nonrelativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schrödinger algebras each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Hořava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Hořava-Lifshitz gravity with a local U (1 ) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schrödinger algebra containing three extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of nonprojectable conformal Hořava-Lifshitz gravity that we refer to as Chern-Simons Schrödinger gravity. This theory has a z =2 Lifshitz geometry as a vacuum solution and thus provides a new framework to study Lifshitz holography.
Geometrical Underpinning of Finite Dimensional Hilbert space
Revzen, M
2011-01-01
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of Hilbert space operators that form mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among them revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.
Geometrical Underpinning of Finite Dimensional Hilbert space
Revzen, M.
2011-01-01
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among operators in Hilbert space, revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.
Infinite matter properties and zero-range limit of nonrelativistic finite-range interactions
Davesne, D; Pastore, A; Navarro, J
2016-01-01
We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin-orbit terms from the spin-isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin-orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range N3LO Skyrme interaction and we emphasize from this analogy the benefits of N3LO.
Infinite matter properties and zero-range limit of non-relativistic finite-range interactions
Davesne, D.; Becker, P.; Pastore, A.; Navarro, J.
2016-12-01
We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin-orbit terms from the spin-isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin-orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.
Infinite matter properties and zero-range limit of non-relativistic finite-range interactions
Energy Technology Data Exchange (ETDEWEB)
Davesne, D. [Université de Lyon, Université Lyon 1, CNRS/IN2P3, Institut de Physique Nucléaire de Lyon, UMR 5822, F-69622 Villeurbanne cedex (France); Becker, P., E-mail: pbecker@ipnl.in2p3.fr [Université de Lyon, Université Lyon 1, CNRS/IN2P3, Institut de Physique Nucléaire de Lyon, UMR 5822, F-69622 Villeurbanne cedex (France); Pastore, A. [Department of Physics, University of York, Heslington, York, Y010 5DD (United Kingdom); Navarro, J. [IFIC (CSIC-Universidad de Valencia), Apartado Postal 22085, E-46.071-Valencia (Spain)
2016-12-15
We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin–orbit terms from the spin–isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin–orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.
Quantum mechanics in finite dimensional Hilbert space
de la Torre, A C
2002-01-01
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.
Exotic Non-relativistic String
Casalbuoni, Roberto; Longhi, Giorgio
2007-01-01
We construct a classical non-relativistic string model in 3+1 dimensions. The model contains a spurion tensor field that is responsible for the non-commutative structure of the model. Under double dimensional reduction the model reduces to the exotic non-relativistic particle in 2+1 dimensions.
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
Radon Transform for Finite Dimensional Hilbert Space
Revzen, M
2012-01-01
Finite dimensional, d, Hilbert space operators are underpinned with ?nite geometry. The analysis emphasizes a central role for mutual unbiased bases (MUB) states projectors. Interrelation among the Hilbert space operators revealed via their (?nite) dual a?ne plane geometry (DAPG) underpin- ning is studied and utilized in formulating a ?nite dimensional Radon transformation. The ?nite geometry required for our study is outlines.
Finite Dimensional KP \\tau-functions I. Finite Grassmannians
Balogh, F; Harnad, J
2014-01-01
We study \\tau-functions of the KP hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Pl\\"ucker coordinates appearing as coefficients in the Schur function expansion of the \\tau-function.
Finite-dimensional collisionless kinetic theory
Burby, J W
2016-01-01
A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.
Finite dimensional quadratic Lie superalgebras
Jarvis, Peter; Yates, Luke
2010-01-01
We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Hypercontractivity in finite-dimensional matrix algebras
Energy Technology Data Exchange (ETDEWEB)
Junge, Marius, E-mail: junge@math.uiuc.edu [Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, Illinois 61891 (United States); Palazuelos, Carlos, E-mail: carlospalazuelos@ucm.es [Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Plaza de Ciencias s/n, 28040 Madrid (Spain); Parcet, Javier, E-mail: javier.parcet@icmat.es; Perrin, Mathilde, E-mail: mathilde.perrin@icmat.es [Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera 13-15, 28049 Madrid (Spain)
2015-02-15
We obtain hypercontractivity estimates for a large class of semigroups defined on finite-dimensional matrix algebras M{sub n}. These semigroups arise from Poisson-like length functions ψ on ℤ{sub n} × ℤ{sub n} and provide new hypercontractive families of quantum channels when ψ is conditionally negative. We also study the optimality of our estimates.
Abdelmadjid Maireche
2016-01-01
A novel theoretical study for the exact solvability of nonrelativistic quantum spectrum systems for potential containing coulomb and quadratic terms is discussed used both Boopp’s shift method and standard perturbation theory in both noncommutativity two dimensional real space and phase (NC-2D: RSP), it has been observed that the exact corrections for the ground states spectrum of studied potential was depended on two infinitesimals parameters and which plays an opposite rolls, and we ha...
Lamb Shift in Nonrelativistic Quantum Electrodynamics.
Grotch, Howard
1981-01-01
The bound electron self-energy or Lamb shift is calculated in nonrelativistic quantum electrodynamics. Retardation is retained and also an interaction previously dropped in other nonrelativistic approaches is kept. Results are finite without introducing a cutoff and lead to a Lamb shift in hydrogen of 1030.9 MHz. (Author/JN)
The finite-dimensional Witsenhausen counterexample
Grover, Pulkit; Sahai, Anant
2010-01-01
Recently, a vector version of Witsenhausen's counterexample was considered and it was shown that in that limit of infinite vector length, certain quantization-based control strategies are provably within a constant factor of the optimal cost for all possible problem parameters. In this paper, finite vector lengths are considered with the dimension being viewed as an additional problem parameter. By applying a large-deviation "sphere-packing" philosophy, a lower bound to the optimal cost for the finite dimensional case is derived that uses appropriate shadows of the infinite-length bound. Using the new lower bound, we show that good lattice-based control strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters, including the vector length. For Witsenhausen's original problem -- the scalar case -- the gap between regular lattice-based strategies and the lower bound is numerically never more than a factor of 8.
Finite dimensional quotients of commutative operator algebras
Meyer, R
1997-01-01
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital operator algebras. This allows to define invariant distances on the spectrum of commutative operator algebras analogous to the Caratheodory distance for complex manifolds. Moreover, unitizations of two-dimensional operator algebras with zero multiplication provide a rich class of counterexamples. Especially, several badly behaved quotients of function algebras are exhibited. Recently, Arveson has developed a model theory for d-contractions. Quotients of the operator algebra of the d-shift are much more well-behaved than quotients of function algebras. Completely isometric representations of these quotients are obtained explicitly. This provides a generalization of Nevanlinna-Pick theory. An important property of quotients of the d-shift algebra is that their quotients of finit...
Entanglement and mutual information in 2d nonrelativistic field theories
Hosseini, Seyed Morteza
2015-01-01
We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of (1+1)-dimensional Lifshitz field theories --- this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.
Nonrelativistic Geodesic Motion
Mangiarotti, L
1999-01-01
We show that any second order dynamic equation on a configuration space $X\\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. We compare relativistic and nonrelativistic geodesic equations, and study the Jacobi vector fields along nonrelativistic geodesics.
Computations in finite-dimensional Lie algebras
Directory of Open Access Journals (Sweden)
A. M. Cohen
1997-12-01
Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.
The finite-dimensional Freeman thesis.
Rudolph, Lee
2008-06-01
I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.
Wavefunction controllability for finite-dimensional bilinear quantum systems
Energy Technology Data Exchange (ETDEWEB)
Turinici, Gabriel [INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France); Rabitz, Herschel [Department of Chemistry, Princeton University, Princeton, NJ 08544-1009 (United States)
2003-03-14
We present controllability results for quantum systems interacting with lasers. Exact controllability for the wavefunction in these bilinear systems is proved in the finite-dimensional case under very natural hypotheses.
-Boundedness and -Compactness in Finite Dimensional Probabilistic Normed Spaces
Indian Academy of Sciences (India)
Reza Saadati; Massoud Amini
2005-11-01
In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of -compactness and -boundedness in probabilistic normed spaces.
Operator spaces and residually finite-dimensional $C^{*}$-algebras
Pestov, V G
1993-01-01
For every operator space $X$ the $C^\\ast$-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In particular, the free $C^\\ast$-algebra on any normed space so is. This is an extension of an earlier result by Goodearl and Menal, and our short proof is based on a criterion due to Exel and Loring.
Finite-dimensional Hilbert space and frame quantization
Energy Technology Data Exchange (ETDEWEB)
Cotfas, Nicolae [Faculty of Physics, University of Bucharest, PO Box 76-54, Post Office 76, Bucharest (Romania); Gazeau, Jean Pierre [Laboratoire APC, Universite Paris Diderot, 10, rue A Domon et L Duquet, 75205 Paris Cedex 13 (France); Vourdas, Apostol, E-mail: ncotfas@yahoo.com, E-mail: gazeau@apc.univ-paris7.fr, E-mail: A.Vourdas@bradford.ac.uk [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)
2011-04-29
The quantum observables used in the case of quantum systems with finite-dimensional Hilbert space are defined either algebraically in terms of an orthonormal basis and discrete Fourier transformation or by using a continuous system of coherent states. We present an alternative approach to these important quantum systems based on the finite frame quantization. Finite systems of coherent states, usually called finite tight frames, can be defined in a natural way in the case of finite quantum systems. Novel examples of such tight frames are presented. The quantum observables used in our approach are obtained by starting from certain classical observables described by functions defined on the discrete phase space corresponding to the system. They are obtained by using a finite frame and a Klauder-Berezin-Toeplitz-type quantization. Semi-classical aspects of tight frames are studied through lower symbols of basic classical observables.
Detecting dimensional crossover and finite Hilbert space through entanglement entropies
Garagiola, Mariano; Cuestas, Eloisa; Pont, Federico M.; Serra, Pablo; Osenda, Omar
2016-01-01
The information content of the two-particle one- and two-dimensional Calogero model is studied using the von Neumann and R\\'enyi entropies. The one-dimensional model is shown to have non-monotonic entropies with finite values in the large interaction strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confine...
Finite dimensional quotients of commutative operator algebras
Meyer, Ralf
1997-01-01
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital operator algebras. This allows to define invariant distances on the spectrum of commutative operator algebras analogous to the Caratheodory distance for complex manifolds. Moreover, unitizations of two-dimensional operator algebras with zero multiplication pro...
A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras
Koç, Ayten; Güloğlu, Ismail; Kanuni, Müge; Koc, Ayten; Esin, Songul; Guloglu, Ismail; Kanuni, Muge
2012-01-01
Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are exactly the field K. All such finite dimensional semisimple algebras arise as a finite dimensional Leavitt path algebra. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely detemined specific graph - which we name as a truncated tree associated with A - whose Leavitt path algebra is isomorphic to A. We define an algebraic invariant {\\kappa}(A) for A and count the number of isomorphism classes of Leavitt path algebras with {\\kappa}(A)=n. Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras of possible trees with a given number of vertices and determine the number of distinct Leavitt path algebras of a line graph with a given number of vertices.
The Socle and Finite Dimensionality of some Banach Algebras
Indian Academy of Sciences (India)
Ali Ghaffari; Ali Reza Medghalchi
2005-08-01
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group , is compact if there exists a measure in $\\mathrm{Soc} (L^1(G))$ such that () ≠ 0. We also prove that is finite if $\\mathrm{Soc}(M(G))$ is closed and every nonzero left ideal in () contains a minimal left ideal.
Finite-Dimensional Representations for Controlled Diffusions with Delay
Energy Technology Data Exchange (ETDEWEB)
Federico, Salvatore, E-mail: salvatore.federico@unimi.it [Università di Milano, Dipartimento di Economia, Management e Metodi Quantitativi (Italy); Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr [Université Paris Diderot, Laboratoire de Probabilités et Modèles Aléatoires (France)
2015-02-15
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.
Finite-dimensional representations of twisted hyper loop algebras
Bianchi, Angelo
2012-01-01
We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the classification of the irreducible modules, the definition of the universal highest-weight modules, called the Weyl modules, and, under a certain mild restriction on the characteristic of the ground field, a proof that the simple modules and the Weyl modules for the twisted hyper loop algebras are isomorphic to appropriate simple and Weyl modules for the non-twisted hyper loop algebras, respectively, via restriction of the action.
Orthogonal apartments in Hilbert Grassmannians. Finite-dimensional case
Pankov, Mark
2015-01-01
Let $H$ be a complex Hilbert space of finite dimension $n\\ge 3$. Denote by ${\\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces of $H$. Every orthogonal apartment of ${\\mathcal G}_{k}(H)$ is defined by a certain orthogonal base of $H$ and consists of all $k$-dimensional subspaces spanned by subsets of this base. For $n\
Confined two-dimensional fermions at finite density
De Francia, M; Loewe, M; Santangelo, E M; De Francia, M; Falomir, H; Loewe, M; Santangelo, E M
1995-01-01
We introduce the chemical potential in a system of two-dimensional massless fermions, confined to a finite region, by imposing twisted boundary conditions in the Euclidean time direction. We explore in this simple model the application of functional techniques which could be used in more complicated situations.
Finite dimensional thermo-mechanical systems and second order constraints
Cendra, Hernán; Amaya, Maximiliano Palacios
2016-01-01
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples. The evolution equations of the involved observables are obtained in each example by using, essentially, the Newton's law and the First Law of Thermodynamics only. We show that such equations are similar to those defining certain mechanical systems with higher order constraints. Moreover, we show that all of the given examples can be described in a variational formalism in terms of second order constrained systems.
Spin & Statistics in Nonrelativistic Quantum Mechanics, II
Kuckert, B; Kuckert, Bernd; Mund, Jens
2004-01-01
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.
Azam, Saeid; Yousofzadeh, Malihe
2011-01-01
We classify finite-dimensional irreducible highest weight modules of generalized quantum groups whose positive part is infinite dimensional and has a Kharchenko's PBW basis with an irreducible finite positive root system.
Finite dimensional semigroup quadratic algebras with minimal number of relations
Iyudu, Natalia
2011-01-01
A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. We prove that a quadratic semigroup algebra given by $n$ generators and $d\\leq \\frac{n^2+n}{4}$ relations is always infinite dimensional. This strengthens the Golod--Shafarevich estimate for the above class of algebras. Our main result however is that for every $n$, there is a finite dimensional quadratic semigroup algebra with $n$ generators and $\\delta_n$ generators, where $\\delta_n$ is the first integer greater than $\\frac{n^2+n}{4}$. This shows that the above Golod-Shafarevich type estimate for semigroup algebras is sharp.
Wigner distributions for finite dimensional quantum systems: An algebraic approach
Indian Academy of Sciences (India)
S Chaturvedi; E Ercolessi; G Marmo; G Morandi; N Mukunbda; R Simon
2005-12-01
We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space' and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail.
Symmetry and Covariance of Non-relativistic Quantum Mechanics
Omote, Minoru; kamefuchi, Susumu
2000-01-01
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum mechanics.
Renormalization group for non-relativistic fermions.
Shankar, R
2011-07-13
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.
Surprises with Nonrelativistic Naturalness
Horava, Petr
2016-01-01
We explore the landscape of technical naturalness for nonrelativistic systems, finding surprises which challenge and enrich our relativistic intuition already in the simplest case of a single scalar field. While the immediate applications are expected in condensed matter and perhaps in cosmology, the study is motivated by the leading puzzles of fundamental physics involving gravity: The cosmological constant problem and the Higgs mass hierarchy problem.
Finite-dimensional attractors for the Kirchhoff models
Zhijian, Yang
2010-09-01
The paper studies the existence of the finite-dimensional global attractor and exponential attractor for the dynamical system associated with the Kirchhoff models arising in elasto-plastic flow utt-div{|∇u|m -1∇u}-Δut+Δ2u+h(ut)+g(u)=f(x). By using the method of ℓ-trajectories and the operator technique, it proves that under subcritical case, 1≤m
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Gomis, Joaquim; Not, Daniel
2017-02-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Not, Daniel
2016-01-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Finite de Finetti theorem for infinite-dimensional systems.
D'Cruz, Christian; Osborne, Tobias J; Schack, Rüdiger
2007-04-20
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state |Psi/Psi| chosen from a family of subsets {Cn} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family {Cn}.
A Finite de Finetti Theorem for Infinite-Dimensional Systems
D'Cruz, C; Schack, R; Cruz, Christian D'; Osborne, Tobias J.; Schack, Ruediger
2006-01-01
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state from a family of subspaces {S_n} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give two simple equivalent characterizations of the family {S_n}.
Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems
Institute of Scientific and Technical Information of China (English)
严承华; 王赤忠; 程尔升
2001-01-01
A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domainsecond order theory of water waves. Liquid sloshing in a rectangular container subjected to a horizontal excitation is sim-ulated by the finite element method. Comparisons between the two theories are made based on their numerical results. Itis found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur forlarge amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features ofnonlinear wave and can be used instead of the fully nonlinear theory.
Three-dimensional finite element analysis of platform switched implant
2017-01-01
PURPOSE The purpose of this study was to analyze the influence of the platform switching concept on an implant system and peri-implant bone using three-dimensional finite element analysis. MATERIALS AND METHODS Two three-dimensional finite element models for wide platform and platform switching were created. In the wide platform model, a wide platform abutment was connected to a wide platform implant. In the platform switching model, the wide platform abutment of the wide platform model was replaced by a regular platform abutment. A contact condition was set between the implant components. A vertical load of 300 N was applied to the crown. The maximum von Mises stress values and displacements of the two models were compared to analyze the biomechanical behavior of the models. RESULTS In the two models, the stress was mainly concentrated at the bottom of the abutment and the top surface of the implant in both models. However, the von Mises stress values were much higher in the platform switching model in most of the components, except for the bone. The highest von Mises values and stress distribution pattern of the bone were similar in the two models. The components of the platform switching model showed greater displacement than those of the wide platform model. CONCLUSION Due to the stress concentration generated in the implant and the prosthodontic components of the platform switched implant, the mechanical complications might occur when platform switching concept is used. PMID:28243389
Supersymmetric solutions for non-relativistic holography
Energy Technology Data Exchange (ETDEWEB)
Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Blackett Laboratory, Imperial College, London (United Kingdom)]|[Institute for Mathematical Sciences, Imperial College, London (United Kingdom)
2009-01-15
We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic conformal algebra for various values of dynamical exponent z{>=}4 and z{>=}3, respectively. The solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds and generalise the known solutions with dynamical exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively. (orig.)
Song, Huimin
In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and
Frehner, Marcel; Schmalholz, Stefan M.; Saenger, Erik H.; Steeb, Holger
2008-01-01
Two-dimensional scattering of elastic waves in a medium containing a circular heterogeneity is investigated with an analytical solution and numerical wave propagation simulations. Different combinations of finite difference methods (FDM) and finite element methods (FEM) are used to numerically solve
Frehner, Marcel; Schmalholz, Stefan M.; Saenger, Erik H.; Steeb, Holger Karl
2008-01-01
Two-dimensional scattering of elastic waves in a medium containing a circular heterogeneity is investigated with an analytical solution and numerical wave propagation simulations. Different combinations of finite difference methods (FDM) and finite element methods (FEM) are used to numerically solve
More On Nonrelativistic Diffeomorphism Invariance
Andreev, Oleg
2014-01-01
Certain aspects of nonrelativistic diffeomorphisms in 2+1 dimensions are investigated. These include a nonrelativistic limit of some relativistic actions in 3 dimensions, the Seiberg-Witten map, a modification of the viscosity tensor in particular due to a non-uniform magnetic field, a redefinition of background fields, and 1/R terms on Riemann surfaces of constant curvature.
Discrete coherent states and probability distributions in finite-dimensional spaces
Energy Technology Data Exchange (ETDEWEB)
Galetti, D.; Marchiolli, M.A.
1995-06-01
Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well know results. (author). 20 refs, 2 figs.
Finite Dimensional Integrable Systems Related to Generalized Schr(o)dinger Equations
Institute of Scientific and Technical Information of China (English)
施齐焉
2003-01-01
The binary nonlinearization method is applied to a 4×4 matrix eigenvalue problem. The typical system of the corresponding soliton hierarchy associated with this eigenvalue problem is the multi-component generalization of the nonlinear Schrodinger equation. With this method, Lax pairs and adjoint Lax pairs of the soliton hierarchy are reduced to two classes of finite dimensional Hamiltonian systems: a spatial finite dimensional Hamiltonian system and a hierarchy of temporal finite dimensional Hamiltonian systems. These finite dimensional Hamiltonian systems are commutative and Liouville integrable.
Quantum key distribution for composite dimensional finite systems
Shalaby, Mohamed; Kamal, Yasser
2017-06-01
The application of quantum mechanics contributes to the field of cryptography with very important advantage as it offers a mechanism for detecting the eavesdropper. The pioneering work of quantum key distribution uses mutually unbiased bases (MUBs) to prepare and measure qubits (or qudits). Weak mutually unbiased bases (WMUBs) have weaker properties than MUBs properties, however, unlike MUBs, a complete set of WMUBs can be constructed for systems with composite dimensions. In this paper, we study the use of weak mutually unbiased bases (WMUBs) in quantum key distribution for composite dimensional finite systems. We prove that the security analysis of using a complete set of WMUBs to prepare and measure the quantum states in the generalized BB84 protocol, gives better results than using the maximum number of MUBs that can be constructed, when they are analyzed against the intercept and resend attack.
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2012-01-01
A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.
Finite-Temperature Properties of Three-Dimensional Chiral Helimagnets
Shinozaki, Misako; Hoshino, Shintaro; Masaki, Yusuke; Kishine, Jun-ichiro; Kato, Yusuke
2016-07-01
We study a three-dimensional (3d) classical chiral helimagnet at finite temperatures through analysis of a spin Hamiltonian, which is defined on a simple cubic lattice and consists of the Heisenberg exchange, monoaxial Dzyaloshinskii-Moriya interactions, and the Zeeman energy due to a magnetic field applied in the plane perpendicular to the helical axis. We take account of the quasi-two-dimensionality of the known monoaxial chiral helimagnet CrNb3S6 and we adopt three methods: (i) a conventional mean-field (MF) analysis, which we call the 3dMF method, (ii) a hybrid method called the 2dMC-1dMF method, which is composed of a classical Monte Carlo (MC) simulation and a MF approximation applied respectively to the intra- and interlayer interactions, and (iii) a simple-MC simulation (3dMC) at zero field. The temperature dependence of the magnetization calculated by the 3dMF method shows a cusp-like structure similar to that observed in experiments. In the absence of a magnetic field, both 2dMC-1dMF and 3dMC yield similar values of the transition temperature. The 2dMC-1dMF method provides a quantitative description of the thermodynamic properties, even under an external field, at an accessible numerical cost.
K1 Group of Finite Dimensional Path Algebra
Institute of Scientific and Technical Information of China (English)
Xue Jun GUO; Li Bin LI
2001-01-01
In this paper, by calculating the commutator subgroup of the unit group of finite pathalgebra κ/△ and the unit group abelianized, we explicitly characterize the K1 group of finite dimensionalpath algebra over an arbitrary field.
QED multi-dimensional vacuum polarization finite-difference solver
Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo
2015-11-01
The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph
Non-Relativistic Anti-Snyder Model and Some Applications
Ching, Chee Leong; Ng, Wei Khim
2016-01-01
We examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the non-relativistic anti-Snyder model which is relevant to deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigen solutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states due to the orthogonality of the polynomials and the maximum energy is truncated at the maximum n. Similar to the minimal length case, the degeneracy of the Dirac-Landau levels in anti- Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit. By taking zero mass limit, we explore the motion of effective zero mass charged Fermions in Graphene like material and obtained a maximum bound of deformed parameter. Furthermore, we consider the modified energy dispersion relations and its...
Nonrelativistic anti-Snyder model and some applications
Ching, C. L.; Yeo, C. X.; Ng, W. K.
2017-01-01
In this paper, we examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the nonrelativistic anti-Snyder model which is relevant to doubly/deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigensolutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states nmax due to the orthogonality of the polynomials and the maximum energy is truncated at nmax. Similar to the minimal length case, the degeneracy of the Dirac-Landau levels in anti-Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit β → 0. By taking m → 0, we explore the motion of effective massless charged fermions in graphene-like material and obtained a maximum bound of deformed parameter βmax. Furthermore, we consider the modified energy dispersion relations and its application in describing the behavior of neutrinos oscillation under modified commutation relations.
Energy Technology Data Exchange (ETDEWEB)
Giunta, G.; Belouettar, S. [Centre de Recherche Public Henri Tudor, 29, av. John F. Kennedy, L-1855, Luxembourg-Kirchberg, Luxembourg (Belgium)
2015-03-10
In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigations show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.
Experimental and three-dimensional finite element investigation of fatigue
Bomidi, John A. R.
Materials often fail at cyclic loads that are lower than their ultimate strength or even their yield strength due to progressive internal material degradation; commonly known as fatigue. Moreover, there is a wide scatter in observed fatigue lives of mechanical components operating under identical loading conditions. The randomness of fatigue failure is considered to be linked to basic microstructural effects such as random microstructure topology and the initiation/growth of cracks along inter/transgranular planes. Several modeling approaches have been previously presented ranging from 2D discrete element to 3D Finite Element methods with explicit representation of microstructure topology and continuum damage mechanics to capture dispersion in rolling contact fatigue life and fatigue spalling. There is, however, a need to compare the modeling approach with experimental fatigue test conditions in order to verify and as required enhance the modeling approach to capture observed fatigue failure. This dissertation presents experimental test results and three-dimensional modeling approach that capture fatigue failure. The three-dimensional modeling approach is enhanced according to the experimental observations to consider inter/trans granular failure, different modes of fatigue initiation and propagation and finally for considering effect of plasticity in fatigue of rolling contacts. The following phenomena have been investigated: (1) Fatigue of microbeams: (a )Results of fatigue life and failure from 3D modeling of intergranular fatigue in microbeams are compared with experimental observations reported in literature (2) Tensile fatigue of thin sheets: (a) A test rig with a new grip and alignment system is developed to address the challenges associated with thin sheet testing and conduct fatigue experiments. (b) The 3D fatigue model is enhanced to capture the dominant transgranular fatigue observed in the experiments. The observed and modeled fatigue life and failure
Institute of Scientific and Technical Information of China (English)
Meng Xiang-Guo; Wang Ji-Suo; Liu Tang-Kun
2008-01-01
In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states(EONLPCSs),which can be realized via operating the superposed evolution operators D±(τ)on the state |q,0),is constructed,then their orthonormalized property,completeness relations and some nonclassical properties are discussed.It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations.Moreover,the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q,η and ξ.
Non-Relativistic Limit of the Dirac Equation
Ajaib, Muhammad Adeel
2016-01-01
We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.
On the finite-dimensional PUA representations of the Shubnikov space groups
Broek, van den P.M.
1977-01-01
The finite-dimensional PUA epresentations of the Shubnikov space groups are discussed using the method of generalised induction given by Shaw and Lever. In particular we derive expressions for the calculation of the little groups.
Contraction of the Finite One-Dimensional Oscillator
Atakishiyev, Natig M.; Pogosyan, George S.; Wolf, Kurt Bernardo
The finite oscillator model of 2j + 1 points has the dynamical algebra u(2), consisting of position, momentum and mode number. It is a paradigm of finite quantum mechanics where a sequence of finite unitary models contract to the well-known continuum theory. We examine its contraction as the number and density of points increase. This is done on the level of the dynamical algebra, of the Schrödinger difference equation, the (Kravchuk) wave functions, and the Fourier-Kravchuk transformation between position and momentum representations.
Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
Lukácová-Medvid'ová, Maria; Saibertova, Jitka
2004-01-01
In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bich...
Multisymplectic Structure-Preserving in Simple Finite Element Method in High Dimensional Case
Institute of Scientific and Technical Information of China (English)
BAI Yong-Qiang; LIU Zhen; PEI Ming; ZHENG Zhu-Jun
2003-01-01
In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems inhigh-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method cankeep a preserved multisymplectic structure.
Elementary Nonrelativistic Quantum Mechanics
Rosu, H C
2000-01-01
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different countries. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Ransom, Jonathan B.
2002-01-01
A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
ON LOCKING-FREE FINITE ELEMENT SCHEMES FOR THREE-DIMENSIONAL ELASTICITY
Institute of Scientific and Technical Information of China (English)
He Qi; Lie-heng Wang; Wei-ying Zheng
2005-01-01
In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lame constant λ→∞. Three kinds of finite elements are proposed and analyzed to approximate the three-dimensional elasticity with pure displacement boundary condition. Optimal order error estimates which are uniform with respect to λ∈ (0, +∞) are obtained for three schemes. Furthermore, numerical results are presented to show that, our schemes are locking-free and and the trilinear conforming finite element scheme is locking.
Two-dimensional finite-element temperature variance analysis
Heuser, J. S.
1972-01-01
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Liu, Chang; Zhu, Xian-chun; Zhang, Xing; Tai, Yin-xia; Yan, Sen
2011-02-01
To build the physical model of four suturae which are related to the growth of maxilla in the three-dimensional finite-element model of maxillofacial bones. A 16 years old volunteer with individual normal occlusion, good periodontium health condition and without diseases of temporomandibular joint was chosen to be the material of modeling. The three-dimensional finite-element model of the volunteer's maxillofacial bones was built using the CT scan and the finite-element modeling method. Finally we built the physical model of four suturae which were related to the growth of maxilla in the model of maxillofacial bones. The model of maxillofacial bones with 86,575 nodes and 485,915 elements was generated. This model contained four suturae including sutura frontomaxillaris, sutura zygomaticomaxillaris, sutura temporozygomatica and sutura pterygopalatine. A three-dimensional finite-element model of maxillofacial bones with good biological similarity was developed.
Finite-temperature correlations in the Lieb-Liniger one-dimensional Bose gas
Panfil, M.; Caux, J.-S.
2014-01-01
We address the problem of calculating finite-temperature response functions of an experimentally relevant low-dimensional, strongly correlated system: the integrable one-dimensional Bose gas with a repulsive δ-function interaction (the Lieb-Liniger model). Focusing on the dynamical density-density f
Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra
Camacho, Luisa M.; Ladra, Manuel; Karimjanov, Iqboljon A.; Omirov, Bakhrom A.
2016-03-01
In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra 𝕯 and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un 1, Un 2 or Wn 1 or Wn 2.
Transport through a Finite One-Dimensional Crystal
Kouwenhoven, L.P.; Hekking, F.W.J.; Wees, B.J. van; Harmans, C.J.P.M.; Timmering, C.E.; Foxon, C.T.
1990-01-01
We have studied the magnetotransport properties of an artificial one-dimensional crystal. The crystal consists of a sequence of fifteen quantum dots, defined in the two-dimensional electron gas of a GaAs/AlGaAs heterostructure by means of a split-gate technique. At a fixed magnetic field of 2 T, two
Finite-key analysis of a practical decoy-state high-dimensional quantum key distribution
Bao, Haize; Bao, Wansu; Wang, Yang; Zhou, Chun; Chen, Ruike
2016-05-01
Compared with two-level quantum key distribution (QKD), high-dimensional QKD enables two distant parties to share a secret key at a higher rate. We provide a finite-key security analysis for the recently proposed practical high-dimensional decoy-state QKD protocol based on time-energy entanglement. We employ two methods to estimate the statistical fluctuation of the postselection probability and give a tighter bound on the secure-key capacity. By numerical evaluation, we show the finite-key effect on the secure-key capacity in different conditions. Moreover, our approach could be used to optimize parameters in practical implementations of high-dimensional QKD.
Regularization independence of finite states in four dimensional quantized gravity
Ita, Eyo
2009-01-01
This is one of a series of works designed to address a major criticism concerning the mathematical rigor of the generalized Kodama states. The present paper analyzes the criterion for finiteness due to cancellation of the ultraviolet divergences stemming from the quantum Hamiltonian constraint, in the full theory. We argue that any reliable state must be independent of the regulating functions and parameters utilized to extract finite results. Using point-splitting regularization, we show that the results, typically regarded either as being purely formal or meaningless, are indeed mathematically rigorous and consistent with the axioms of field theory and regulator independence. Our analysis is carried out at the level of the quantum constraint solutions, and does not consider the algebra of constraints.
A construction of full qed using finite dimensional Hilbert space
Francis, Charles
2006-01-01
While causal perturbation theory and lattice regularisation allow treatment of the ultraviolet divergences in qed, they do not resolve the issues of constructive field theory, or show the validity of qed except as a perturbation theory. I present a rigorous construction of quantum and classical electrodynamics from fundamental principles of quantum theory. Hilbert space of dimension N is justified from statements about measurements with finite range and resolution. Using linear combinations o...
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 volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2004-01-01
The subject of the paper is the derivation of finite volume evolution Galerkin schemes for three-dimensional wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The idea is to evolve the initial function using the characteristic cone and then to project onto a finite element space. Numerical experiments are presented to demonstrate the accuracy and the multidimensional behaviour of the solutio...
Three-dimensional finite element analysis of critical pre-twist strain angle for torsional axis
Institute of Scientific and Technical Information of China (English)
ZHOU Guo-feng; LI Xiao-yan; SHI Yao-wu; XU Bin-shi
2005-01-01
A three-dimensional elasto-plastic finite element analysis of pre-twist process for a torsional axis made of 45GrNiMoVA steel, was carried out using a commercial finite element analysis code, MSC MARC 2001. The results show that the critical pre-twist strain angle is 0. 027 rad and the maximum elastic shear stress after pre-twist is 1 694 MPa for the torsional axis.
Invariants of 3-Manifolds derived from finite dimensional hopf algebras
Kauffman, L H; Louis H Kauffman; David E Radford
1994-01-01
Abstract: This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the class of Witten-Reshetikhin-Turaev invariants.
Finite-dimensional attractors for the Kirchhoff models with critical exponents
Zhijian, Yang
2012-03-01
The paper studies the existence of the finite-dimensional global attractor and exponential attractor for the dynamical system associated with the Kirchhoff models utt - ∇ . {|∇u|m - 1∇u} - Δut + Δ2u + h(ut) + g(u) = f(x). It proves that for the subcritical and critical cases: 1
Examples of bosonic de Finetti states over finite dimensional Hilbert spaces
Gottlieb, A D
2005-01-01
According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose-Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle states with Bose-Einstein symmetry that arise as limits of Gibbs ensembles on finite dimensional spaces, and displays their de Finetti representations. We consider Gibbs ensembles for systems of bosons in a finite dimensional setting and discover limits as the number of particles tends to infinity, provided the temperature is scaled in proportion to particle number.
A finite-dimensional reduction method for slightly supercritical elliptic problems
Directory of Open Access Journals (Sweden)
Riccardo Molle
2004-01-01
Full Text Available We describe a finite-dimensional reduction method to find solutions for a class of slightly supercritical elliptic problems. A suitable truncation argument allows us to work in the usual Sobolev space even in the presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite-dimensional reduction can be obtained applying the methods already developed in the subcritical case; finally, we show that, if the truncation is realized at a sufficiently large level, then the solutions of the approximating problems, given by these methods, also solve the supercritical problems when the parameter is small enough.
A finite area scheme for shallow granular flows on three-dimensional surfaces
Rauter, Matthias
2017-04-01
Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.
Conformal Data from Finite Entanglement Scaling
Stojevic, Vid; McCulloch, I P; Tagliacozzo, L; Verstraete, Frank
2014-01-01
In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to $(1+1)$ dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. The assumption that the scaling hypothesis holds for this kind of perturbation is known in the literature as finite entanglement scaling. We provide further evidence for the validity of finite entanglement scaling and based on this formulate a scaling algorithm to estimate the central charge and critical exponents of the conformally invariant field theories describing the critical models under investigation. The algorithm is applied to three exemplary models; the cMPS version to the non-relativistic Lieb-Liniger model and the relativistic massless boson, and MPS version to the one-dimensional quantum Ising model at the critical point. Another new aspect to our approach is that we directly...
Matveev, A. D.
2016-11-01
To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.
Non-Relativistic Spacetimes with Cosmological Constant
Aldrovandi, R.; Barbosa, A. L.; Crispino, L.C.B.; Pereira, J. G.
1998-01-01
Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible ...
Relativistic and non-relativistic geodesic equations
Energy Technology Data Exchange (ETDEWEB)
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Finite amplitude waves in two-dimensional lined ducts
Nayfeh, A. H.; Tsai, M.-S.
1974-01-01
A second-order uniform expansion is obtained for nonlinear wave propagation in a two-dimensional duct lined with a point-reacting acoustic material consisting of a porous sheet followed by honeycomb cavities and backed by the impervious wall of the duct. The waves in the duct are coupled with those in the porous sheet and the cavities. An analytical expression is obtained for the absorption coefficient in terms of the sound frequency, the physical properties of the porous sheet, and the geometrical parameters of the flow configuration. The results show that the nonlinearity flattens and broadens the absorption vs. frequency curve, irrespective of the geometrical dimensions or the porous material acoustic properties, in agreement with experimental observations.
Lorimer, W. L.; Lieu, D. K.; Hull, J. R.; Mulcahy, T. M.; Rossing, T. D.
A permanent magnet quadrupole spinning over an aluminum disk was constructed, and drag torque was measured for various speeds and gap sizes. The experiment was modeled using a three-dimensional finite element program. Experimental and analytical results were compared, and the effect of magnet polarity was determined.
Large parallel volumes of finite and compact sets in d-dimensional Euclidean space
DEFF Research Database (Denmark)
Kampf, Jürgen; Kiderlen, Markus
The r-parallel volume V (Cr) of a compact subset C in d-dimensional Euclidean space is the volume of the set Cr of all points of Euclidean distance at most r > 0 from C. According to Steiner’s formula, V (Cr) is a polynomial in r when C is convex. For finite sets C satisfying a certain geometric ...
Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System
Jing Yu; Jingwei Han
2014-01-01
Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation and $r$ -matrix are also given in this paper.
Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System
Directory of Open Access Journals (Sweden)
Jing Yu
2014-01-01
Full Text Available Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation and r-matrix are also given in this paper.
Generalized results on the role of new-time transformations in finite-dimensional Poisson systems
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2010-01-25
The problem of characterizing all new-time transformations preserving the Poisson structure of a finite-dimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given.
Energy Technology Data Exchange (ETDEWEB)
Marek-Crnjac, L. [Institute of Mathematics and Physics, University of Maribor (Slovenia)], E-mail: Leila.marek@guest.arnes.si; Iovane, G. [DIIMA - Universita di Salerno, Via Ponte don Melillo, 84084 Fisciano (Saudi Arabia) (Italy)], E-mail: iovane@diima.unisa.it; Nada, S.I. [Department of Mathematics, Faculty of Science, Qatar University (Qatar)], E-mail: snada@qu.edu.qa; Zhong, Ting [Department of Mathematics, Jishou University, 427000 Zhangjiajie, Hunan (China)], E-mail: zhongting_2005@126.com
2009-11-30
The present work gives first a review of the mathematical theory of finite and infinite dimensional topological spaces. Subsequently we connect the discussion with E-infinity theory and the theory of partially ordered sets. Finally, we contemplate the relevance of abstract results for quantum gravity.
The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
Balog, Janos(Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, MTA Lendület Holographic QFT Group, 1525, Budapest 114, P.O.B. 49, Hungary); Hegedus, Arpad
2009-01-01
Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model in a periodic box. Numerical results for the energy eigenvalues are compared to the rotator spectrum and perturbation theory for small volumes and with the recently proposed generalized Luscher formulas at large volumes.
Coherent States for generalized oscillator with finite-dimensional Hilbert space
Borzov, Vadim V.; Damaskinsky, Eugene V.
2006-01-01
The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As example we consider the generalized oscillator connected with Krawtchouk polynomials.
A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Bagchi, B. [Calcutta Univ. (India). Dept. of Applied Mathematics; Roy, P.K. [Department of Physics, Haldia Government College, Haldia 721 657, West Bengal (India)
1995-05-08
In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.)).
A three-dimensional finite element model of the polymerization process in dental restorations.
Barink, M.; Mark, P.C. van der; Fennis, W.M.M.; Kuys, R.H.; Kreulen, C.M.; Verdonschot, N.J.J.
2003-01-01
Restoration of dental restorations with resin composite is hampered by shrinkage of the material during the polymerization process. In this study, we simulated the polymerization process in a detailed three-dimensional finite element model of a human upper premolar with a cusp-replacing restoration.
Three-dimensional finite element simulation of intermingled-fiber hybrid composite behavior
Mital, Subodh K.; Chamis, Christos C.
1992-01-01
Three-dimensional finite element methods and the intraply hybrid micromechanics equations are used to predict composite properties for a unidirectional graphite-epoxy primary composite with S-glass fibers used as hybridizing fibers. The micromechanics equations are embedded in a computer code ICAN (Integrated Composites Analyzer). The three-dimensional finite element model consists of three-by-three unit cell array, with a total fiber volume ratio of 0.54. There is a good agreement between the composite properties and microstresses obtained from both methods. The results indicate that the finite element methods and micromechanics equations can be used to obtain the properties of intermingled hybrid composites needed for analysis/design of hybrid composite structures.
Three dimensional finite temperature SU(3) gauge theory near the phase transition
Bialas, Piotr; Morel, Andre; Petersson, Bengt
2012-01-01
We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent \
Venkataraman, Divya
2016-01-01
Solutions to finite-dimensional (all spatial Fourier modes set to zero beyond a finite wavenumber $K_G$), inviscid equations of hydrodynamics at long times are known to be at variance with those obtained for the original infinite dimensional partial differential equations or their viscous counterparts. Surprisingly, the solution to such Galerkin-truncated equations develop sharp localised structures, called {\\it tygers} [Ray, et al., Phys. Rev. E {\\bf 84}, 016301 (2011)], which eventually lead to completely thermalised states associated with an equipartition energy spectrum. We now obtain precise estimates, theoretically and via direct numerical simulations, the time $\\tau_c$ at which thermalisation is triggered and show that $\\tau_c \\sim K_G^\\xi$, with $\\xi = -4/9$. Our results have several implications including for the analyticity strip method to numerically obtain evidence for or against blow-ups of the three-dimensional incompressible Euler equations.
Finite-size scaling study of the three-dimensional classical Heisenberg model
Holm, C; Holm, Christian; Janke, Wolfhard
1993-01-01
We use the single-cluster Monte Carlo update algorithm to simulate the three-dimensional classical Heisenberg model in the critical region on simple cubic lattices of size $L^3$ with $L=12, 16, 20, 24, 32, 40$, and $48$. By means of finite-size scaling analyses we compute high-precision estimates of the critical temperature and the critical exponents, using extensively histogram reweighting and optimization techniques. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.
Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations
Institute of Scientific and Technical Information of China (English)
Tongke
2010-01-01
This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Vineet K., E-mail: vineetsriiitm@gmail.com [ISRO Telemetry, Tracking and Command Network (ISTRAC), Bangalore-560058 (India); Awasthi, Mukesh K. [Department of Mathematics, University of Petroleum and Energy Studies, Dehradun-248007 (India); Singh, Sarita [Department of Mathematics, WIT- Uttarakhand Technical University, Dehradun-248007 (India)
2013-12-15
This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
Directory of Open Access Journals (Sweden)
Vineet K. Srivastava
2013-12-01
Full Text Available This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM, for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
Phase transitions in a one-dimensional multibarrier potential of finite range
Bar, D
2002-01-01
We have previously studied properties of a one-dimensional potential with $N$ equally spaced identical barries in a (fixed) finite interval for both finite and infinite $N$. It was observed that scattering and spectral properties depend sensitively on the ratio $c$ of spacing to width of the barriers (even in the limit $N \\to \\infty$). We compute here the specific heat of an ensemble of such systems and show that there is critical dependence on this parameter, as well as on the temperature, strongly suggestive of phase transitions.
Holographic thermalization from nonrelativistic branes
Roychowdhury, Dibakar
2016-05-01
In this paper, based on the fundamental principles of gauge/gravity duality and considering a global quench, we probe the physics of thermalization for certain special classes of strongly coupled nonrelativistic quantum field theories that are dual to an asymptotically Schrödinger D p brane space time. In our analysis, we note that during the prelocal stages of the thermal equilibrium the entanglement entropy has a faster growth in time compared to its relativistic cousin. However, it shows a linear growth during the postlocal stages of thermal equilibrium where the so-called tsunami velocity associated with the linear growth of the entanglement entropy saturates to that of its value corresponding to the relativistic scenario. Finally, we explore the saturation region and it turns out that one must constraint certain parameters of the theory in a specific way in order to have discontinuous transitions at the point of saturation.
Finite Dimensional Compensators for Infinite Dimensional Systems with Unbounded Control Action.
1984-05-01
from infinite dimensional linear systems theory that A + GC . V(A) + X generates an exponentially stable semigroup on X (see (5) or [161). It is also...Matheatica Aplicada e Computacional, 2 (1983). 15] R.F. CURTAIN/A.J. PRITCHARD Infinite Dimensional Linear Systems Theory LNCIS 8, Springer-Verlag
Symmetries and couplings of non-relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Festuccia, Guido [Department of Physics and Astronomy, Uppsala University,Lägerhyddsvägen 1, Uppsala (Sweden); Hansen, Dennis [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark); Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes,Université Libre de Bruxelles, C.P. 231, Brussels, 1050 (Belgium); Obers, Niels A. [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark)
2016-11-08
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell’s equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a U(1) current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galilei algebra plus two dilatations remain. Hence one can scale time and space independently, allowing Lifshitz scale symmetries for any value of the critical exponent z.
Symmetries and Couplings of Non-Relativistic Electrodynamics
Festuccia, Guido; Hartong, Jelle; Obers, Niels A
2016-01-01
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a $U(1)$ current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galile...
A finite-dimensional representation of the quantum angular momentum operator
Campos, R G; Campos, Rafael G.
2000-01-01
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into polynomial subspaces of finite dimension and it can be interpreted as a generator of discrete rotations associated to the z-component of the projection of the angular momentum operator in such subspaces, inheriting thus some properties of the continuum operator. The group associated to these discrete rotations is the cyclic group of order N. Since the square of the quantum angular momentum L^2 is associated to a partial differential boundary value problem in the angular variables $\\theta$ and $\\phi$ whose solution is given in terms of the spherical harmonics, we can project such a differential equation to obtain an eigenvalue matrix problem of finite dimension by extending to several variables a projection technique for solving numerically two point boundary value problems and usi...
Finite element method for one-dimensional rill erosion simulation on a curved slope
Directory of Open Access Journals (Sweden)
Lijuan Yan
2015-03-01
Full Text Available Rill erosion models are important to hillslope soil erosion prediction and to land use planning. The development of rill erosion models and their use has become increasingly of great concern. The purpose of this research was to develop mathematic models with computer simulation procedures to simulate and predict rill erosion. The finite element method is known as an efficient tool in many other applications than in rill soil erosion. In this study, the hydrodynamic and sediment continuity model equations for a rill erosion system were solved by the Galerkin finite element method and Visual C++ procedures. The simulated results are compared with the data for spatially and temporally measured processes for rill erosion under different conditions. The results indicate that the one-dimensional linear finite element method produced excellent predictions of rill erosion processes. Therefore, this study supplies a tool for further development of a dynamic soil erosion prediction model.
Theory of finite-entanglement scaling at one-dimensional quantum critical points.
Pollmann, Frank; Mukerjee, Subroto; Turner, Ari M; Moore, Joel E
2009-06-26
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for one-dimensional systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality. Finite-entanglement scaling in one-dimensional systems is governed not by the scaling dimension of an operator but by the "central charge" of the critical point. An important ingredient is the universal distribution of density-matrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)10.1103/PhysRevA.78.032329]. The parameter-free theory is checked against numerical scaling at several quantum critical points.
A complementarity-based approach to phase in finite-dimensional quantum systems
Energy Technology Data Exchange (ETDEWEB)
Klimov, A B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico); Sanchez-Soto, L L [Departamento de Optica, Facultad de Fisica, Universidad Complutense, 28040 Madrid (Spain); Guise, H de [Department of Physics, Lakehead University, Thunder Bay, ON, P7B 5E1 (Canada)
2005-09-01
We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased bases, which exist for dimensions that are powers of a prime. For a d-dimensional system (qudit) we explicitly construct d+1 classes of maximally commuting operators, each one consisting of d-1 operators. One of these classes consists of diagonal operators that represent amplitudes (or inversions). By finite Fourier transformation, it is mapped onto ladder operators that can be appropriately interpreted as phase variables. We discuss examples of qubits and qutrits, and show how these results generalize previous approaches.
Dimensionality and Finite Number Effect on BCS Transition of Atomic Fermi Gas
Institute of Scientific and Technical Information of China (English)
CUI Hai-Tao; WANG Lin-Cheng; YI Xue-Xi
2005-01-01
The effect of finite number and dimensionality has been discussed in this paper. The finite number effect has a negative correction to final temperature for 2D or 3D atomic Fermi gases. The changing of final temperature obtained by scanning from BEC region to BCS region are 10% or so with N ≤ 103 and can be negligible when N ＞ 103.However, in 1D atomic Fermi gas, the effect gives a positive correction which greatly changes the final temperature in Fermi gas. This behavior is completely opposed to the 2D and 3D cases and a proper explanation is still to be found.Dimensionality also has a positive correction, in which the more tightly trapping, the higher final temperature one gets with the same particle number. A discussion is also presented.
Finite-size effects in quasi-one-dimensional conductors with a charge-density wave
Energy Technology Data Exchange (ETDEWEB)
Zaitsev-Zotov, Sergei V [Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow (Russian Federation)
2004-06-30
Recent studies of finite-size effects in charge-density wave conductors are reviewed. Various manifestations of finite-size effects, including the transverse-size dependence of the nonlinear-conduction threshold field, the Peierls transition temperature, high-frequency conduction, and the relaxation rates of metastable states, are discussed. Resistivity jumps in thin samples, the smeared threshold field for nonlinear conduction, and threshold conduction above the Peierls transition temperature are considered, as are mesoscopic oscillations of the threshold field, one-dimensional conduction in thin crystals, absolute negative conductivity of quasi-one-dimensional conductors, the length dependence of the phase-slip voltage, and the Aharonov-Bohm oscillations in sliding CDWs. Problems yet to be solved are discussed. (reviews of topical problems)
Directory of Open Access Journals (Sweden)
Carlos Salinas
2011-05-01
Full Text Available The work was aimed at simulating two-dimensional wood drying stress using the control-volume finite element method (CVFEM. Stress/strain was modeled by moisture content gradients regarding shrinkage and mechanical sorption in a cross-section of wood. CVFEM was implemented with triangular finite elements and lineal interpolation of the independent variable which were programmed in Fortran 90 language. The model was validated by contrasting results with similar ones available in the specialised literature. The present model’s results came from isothermal (20ºC drying of quaking aspen (Populus tremuloides: two-dimensional distribution of stress/strain and water content, 40, 80, 130, 190 and 260 hour drying time and evolution of normal stress (2.5 <σ͓ ͓ < 1.2, MPa, from the interior to the exterior of wood.
Finite Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite
Li, Xuetao; Binienda, Wieslaw K.; Goldberg, Robert K.
2010-01-01
A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.
Effects of finite laser pulse width on two-dimensional electronic spectroscopy
Leng, Xuan; Yue, Shuai; Weng, Yu-Xiang; Song, Kai; Shi, Qiang
2017-01-01
We combine the hierarchical equations of motion method and the equation-of-motion phase-matching approach to calculate two-dimensional electronic spectra of model systems. When the laser pulse is short enough, the current method reproduces the results based on third-order response function calculations in the impulsive limit. Finite laser pulse width is found to affect both the peak positions and shapes, as well as the time evolution of diagonal and cross peaks. Simulations of the two-color two-dimensional electronic spectra also show that, to observe quantum beats in the diagonal and cross peaks, it is necessary to excite the related excitonic states simultaneously.
Three-dimensional finite element modeling of a magnet array spinning above a conductor
Lorimer, W. L.; Lieu, D. K.; Hull, J. R.; Mulcahy, T. M.; Rossing, T. D.
Drag forces due to eddy currents induced by the relative motion of a conductor and a magnetic field occur in many practical devices: motors, brakes, magnetic bearings, and magnetically levitated vehicles. Recently, finite element codes have included solvers for three dimensional eddy current geometries and have the potential to be very useful in the design and analysis of these devices. In this paper, numerical results from three dimensional modeling of a magnet array spinning above a conductor are compared to experimental results in order to assess the capabilities of these codes.
Natale, Andrea
2016-01-01
We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative discretisation introduced in Natale and Cotter (2016a) and the SUPG discretisation of the vorticity advection equation. Such discretisations provide control on enstrophy by modelling different types of scale interactions. We quantify the performance of the schemes in reproducing the non-local energy backscatter that characterises two-dimensional turbulent flows.
Non-relativistic Bondi–Metzner–Sachs algebra
Batlle, Carles; Delmastro, Diego; Gomis, Joaquim
2017-09-01
We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein–Gordon field.
Elastic fields of stationary and moving dislocations in three dimensional finite samples
1997-01-01
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for the stress field, thus satisfying the expectation that stresses should depend on the location of the dislocation loop, but not on the location of surfaces bounded by such loops that are devoid of physical significance. In the stationary case the line integral...
Frequency bands of negative refraction in finite one-dimensional photonic crystals
Institute of Scientific and Technical Information of China (English)
Chen Yuan-Yuan; Huang Zhao-Ming; Shi Jie-Long; Li Chun-Fang; Wang Qi
2007-01-01
We have discussed theoretically the negative refraction in finite one-dimensional (1D) photonic crystals (PCs)composed of alternative layers with high index contrast. The frequency bands of negative refraction are obtained with the help of the photonic band structure, the group velocity and the power transmittance, which are all obtained in analytical expression. There shows negative transverse position shift at the endface when negative refraction occurs,which is analysed in detail.
CONVERGENCE OF AN EXPLICIT UPWIND FINITE ELEMENT METHOD TO MULTI-DIMENSIONAL CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Jin-chao Xu; Lung-an Ying
2001-01-01
An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality.To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the Lp strong convergence of this scheme is proved.
Banks, H. T.; Smith, Ralph C.; Wang, Yun
1994-01-01
Based on a distributed parameter model for vibrations, an approximate finite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the effectiveness of this design.
Ultraviolet finiteness of Chiral Perturbation Theory for two-dimensional Quantum Electrodynamics
Paston, S A; Franke, V A
2003-01-01
We consider the perturbation theory in the fermion mass (chiral perturbation theory) for the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction is exponential and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass.
Fast-forward scaling in a finite-dimensional Hilbert space
TAKAHASHI, Kazutaka
2014-01-01
Time evolution of quantum systems is accelerated by the fast-forward scaling. We reformulate the method to study systems in a finite-dimensional Hilbert space. For several simple systems, we explicitly construct the acceleration potential. We also use our formulation to accelerate the adiabatic dynamics. Applying the method to the transitionless quantum driving, we find that the fast-forward potential can be understood as a counterdiabatic term.
Dynamics of a harmonic oscillator in a finite-dimensional Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Kuang Leman (CCAST (World Lab.), Beijing, BJ (China) Dept. of Physics and Inst. of Physics, Hunan Normal Univ. (China)); Wang Fabo (Dept. of Physics, Hunan Normal Univ. (China)); Zhou Yanguo (Dept. of Physics, Hunan Normal Univ. (China))
1993-11-29
Some dynamical properties of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are studied. The time evolution of the position and momentum operators and the second-order quadrature squeezing are investigated in detail. It is shown that the coherent states of the FDHSHO are not the minimum uncertainty states of the position and momentum operators of the FDHSHO. It is found that the second-order squeezing of the quadrature operators vanishes and reappears periodically in the time evolution. (orig.)
Linear Commuting Maps on Parab olic Subalgebras of Finite-dimensional Simple Lie Algebras
Institute of Scientific and Technical Information of China (English)
CHEN Zheng-xin; WANG Bing
2014-01-01
A map ϕ on a Lie algebra g is called to be commuting if [ϕ(x), x] = 0 for all x∈g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapϕon P is commuting if and only ifϕis a scalar multiplication map on P .
Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2003-01-01
The subject of the paper is the derivation and analysis of third order finite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the first order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation from the piecewise constants, to feed into the calculation of the fluxes. We estimate the truncation error and give numerical examples to demonstrate the higher order...
Analysis of 3-dimensional finite element after reconstruction of impaired ankle deltoid ligament
Ji, Yunhan; Tang, Xianzhong; Li, Yifan; Xu, Wei; Qiu, Wenjun
2016-01-01
We compared four repair techniques for impaired ankle ligament deltoideum, namely Wiltberger, Deland, Kitaoka and Hintermann using a 3-dimensional finite element. We built an ankle ligament deltoideum model, including six pieces of bone structures, gristles and main ligaments around the ankle. After testing the model, we built an impaired ligament deltoideum model plus four reconstruction models. Subsequently, different levels of force on ankles with different flexion were imposed and ankle b...
Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems.
Wu, Huai-Ning; Li, Han-Xiong
2007-10-01
This correspondence studies the problem of finite-dimensional constrained fuzzy control for a class of systems described by nonlinear parabolic partial differential equations (PDEs). Initially, Galerkin's method is applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, a systematic modeling procedure is given to construct exactly a Takagi-Sugeno (T-S) fuzzy model for the finite-dimensional ODE system under state constraints. Then, based on the T-S fuzzy model, a sufficient condition for the existence of a stabilizing fuzzy controller is derived, which guarantees that the state constraints are satisfied and provides an upper bound on the quadratic performance function for the finite-dimensional slow system. The resulting fuzzy controllers can also guarantee the exponential stability of the closed-loop PDE system. Moreover, a local optimization algorithm based on the linear matrix inequalities is proposed to compute the feedback gain matrices of a suboptimal fuzzy controller in the sense of minimizing the quadratic performance bound. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.
Quantum-optical states in finite-dimensional Hilbert space; 1, General formalism
Miranowicz, A; Imoto, N; Miranowicz, Adam; Leonski, Wieslaw; Imoto, Nobuyuki
2001-01-01
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation and measurement techniques, in particular, by the development of the discrete quantum-state tomography. In the first part of our review we present two essentially different approaches to define harmonic oscillator states in the finite-dimensional Hilbert spaces. One of them is related to the truncation scheme of Pegg, Phillips and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The second method corresponds to the truncation scheme of Leo\\'nski and Tana\\'s [Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states related to these truncation schemes and find their explicit forms in the Fock representation. We discuss finite-dimensional generalizations of coherent states, phase coherent states, displaced number states, Schr\\"odinger cats, and squeezed vacuum. We show some i...
Do non-relativistic neutrinos oscillate?
Akhmedov, Evgeny
2017-07-01
We study the question of whether oscillations between non-relativistic neutrinos or between relativistic and non-relativistic neutrinos are possible. The issues of neutrino production and propagation coherence and their impact on the above question are discussed in detail. It is demonstrated that no neutrino oscillations can occur when neutrinos that are non-relativistic in the laboratory frame are involved, except in a strongly mass-degenerate case. We also discuss how this analysis depends on the choice of the Lorentz frame. Our results are for the most part in agreement with Hinchliffe's rule.
The Three-Dimensional Finite-Volume Non-Hydrostatic Icosahedral Model (NIM)
Lee, J. L.; MacDonald, A. E.
2014-12-01
A multi-scales Non-hydrostatic Icosahedral Model (NIM) has been developed at Earth System Research Laboratory (ESRL) to meet NOAA's future prediction mission ranging from mesoscale short-range, high-impact weather forecasts to longer-term intra-seasonal climate prediction. NIM formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM is designed to utilize the state-of-art computing architecture such as Graphic Processing Units (GPU) processors to run globally at kilometer scale resolution to explicitly resolve convective storms and complex terrains. The novel features of NIM numerical design include: 1.1. A local coordinate system upon which finite-volume integrations are undertaken. The use of a local Cartesian coordinate greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. 1.2. A general indirect addressing scheme developed for modeling on irregular grid. It arranges the icosahedral grid with a one-dimensional vector loop structure, table specified memory order, and an indirect addressing scheme that yields very compact code despite the complexities of this grid. 1.3. Use of three-dimensional finite-volume integration over control volumes constructed on the height coordinates. Three-dimensional finite-volume integration accurately represents the Newton Third Law over terrain and improves pressure gradient force over complex terrain. 1.4. Use of the Runge-Kutta 4th order conservative and positive-definite transport scheme 1.5. NIM dynamical solver has been implemented on CPU as well as GPU. As one of the potential candidates for NWS next generation models, NIM dynamical core has been successfully verified with various benchmark test cases including those proposed by DCMIP
Entropy current for non-relativistic fluid
Banerjee, Nabamita; Jain, Akash; Roychowdhury, Dibakar
2014-01-01
We study transport properties of a parity-odd, non-relativistic charged fluid in presence of background electric and magnetic fields. To obtain stress tensor and charged current for the non-relativistic system we start with the most generic relativistic fluid, living in one higher dimension and reduce the constituent equations along the light-cone direction. We also reduce the equation satisfied by the entropy current of the relativistic theory and obtain a consistent entropy current for the non-relativistic system (we call it "canonical form" of the entropy current). Demanding that the non-relativistic fluid satisfies the second law of thermodynamics we impose constraints on various first order transport coefficients. For parity even fluid, this is straight forward; it tells us positive definiteness of different transport coefficients like viscosity, thermal conductivity, electric conductivity etc. However for parity-odd fluid, canonical form of the entropy current fails to confirm the second law of thermody...
One-parameter nonrelativistic supersymmetry for microtubules
Rosu, H C
2003-01-01
The simple supersymmetric model of Caticha [PRA 51, 4264 (1995)], as used by Rosu [PRE 55, 2038 (1997)] for microtubules, is generalized to the case of Mielnik's one-parameter nonrelativistic susy [JMP 25, 3387 (1984)
Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz
1996-01-01
Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.
Three-dimensional supersonic flow around double compression ramp with finite span
Lee, H. S.; Lee, J. H.; Park, G.; Park, S. H.; Byun, Y. H.
2017-01-01
Three-dimensional flows of Mach number 3 around a double-compression ramp with finite span have been investigated numerically. Shadowgraph visualisation images obtained in a supersonic wind tunnel are used for comparison. A three-dimensional Reynolds-averaged Navier-Stokes solver was used to obtain steady numerical solutions. Two-dimensional numerical results are also compared. Four different cases were studied: two different second ramp angles of 30° and 45° in configurations with and without sidewalls, respectively. Results showed that there is a leakage of mass and momentum fluxes heading outwards in the spanwise direction for three-dimensional cases without sidewalls. The leakage changed the flow characteristics of the shock-induced boundary layer and resulted in the discrepancy between the experimental data and two-dimensional numerical results. It is found that suppressing the flow leakage by attaching the sidewalls enhances the two-dimensionality of the experimental data for the double-compression ramp flow.
Three-dimensional finite element analysis of the human temporomandibular joint disc.
Beek, M; Koolstra, J H; van Ruijven, L J; van Eijden, T M
2000-03-01
A three-dimensional finite element model of the articular disc of the human temporomandibular joint has been developed. The geometry of the articular cartilage and articular disc surfaces in the joint was measured using a magnetic tracking device. First, polynomial functions were fitted through the coordinates of these scattered measurements. Next, the polynomial description was transformed into a triangulated description to allow application of an automatic mesher. Finally, a finite element mesh of the articular disc was created by filling the geometry with tetrahedral elements. The articulating surfaces of the mandible and skull were modeled by quadrilateral patches. The finite element mesh and the patches were combined to create a three-dimensional model in which unrestricted sliding of the disc between the articulating surfaces was allowed. Simulation of statical joint loading at the closed jaw position predicted that the stress and strain distributions were located primarily in the intermediate zone of the articular disc with the highest values in the lateral part. Furthermore, it was predicted that considerable deformations occurred for relatively small joint loads and that relatively large variations in the direction of joint loading had little influence on the distribution of the deformations.
Alessandri, Angelo; Gaggero, Mauro; Zoppoli, Riccardo
2012-06-01
Optimal control for systems described by partial differential equations is investigated by proposing a methodology to design feedback controllers in approximate form. The approximation stems from constraining the control law to take on a fixed structure, where a finite number of free parameters can be suitably chosen. The original infinite-dimensional optimization problem is then reduced to a mathematical programming one of finite dimension that consists in optimizing the parameters. The solution of such a problem is performed by using sequential quadratic programming. Linear combinations of fixed and parameterized basis functions are used as the structure for the control law, thus giving rise to two different finite-dimensional approximation schemes. The proposed paradigm is general since it allows one to treat problems with distributed and boundary controls within the same approximation framework. It can be applied to systems described by either linear or nonlinear elliptic, parabolic, and hyperbolic equations in arbitrary multidimensional domains. Simulation results obtained in two case studies show the potentials of the proposed approach as compared with dynamic programming.
Finite Element Analysis of Electromagnetic Waves in Two-Dimensional Transformed Bianisotropic Media
Liu, Yan; Guenneau, Sebastien
2015-01-01
We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations (PDEs) for longitudinal electric and magnetic field components. Perfectly Matched Layers (PMLs) are discussed to model such unbounded media. We implement these PDEs and PMLs in a finite element software. We apply transformation optics in order to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. We propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magneto-electric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that well-known metamaterials can be transposed to bianisotropic media.
Institute of Scientific and Technical Information of China (English)
张德悦; 马富明
2004-01-01
In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.
A Remark on the Unitary Group of a Tensor Product of Finite-Dimensional Hilbert Spaces
Indian Academy of Sciences (India)
K R Parthasarathy
2003-02-01
Let $H_i, 1 ≤ i ≤ n$ be complex finite-dimensional Hilbert spaces of dimension $d_i, 1 ≤ i ≤ n$ respectively with $d_i ≥ 2$ for every . By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on the tensor product $H = H_1 \\otimes H_2 \\otimes\\ldots \\otimes H_n$ can be expressed as a composition of a finite number of unitary operators living on pair products $H_i \\otimes H_j, 1 ≤ i, j ≤ n$. An estimate of the number of operators appearing in such a composition is obtained.
Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density
Fujii, Hirotsugu; Kikukawa, Yoshio
2015-01-01
We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling $\\beta$ and/or large lattice size $L$, while they are in good agreement at the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit keeping the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model's thimble structure. And these results imply...
Finite element simulation of three-dimensional temperature field in underwater welding
Institute of Scientific and Technical Information of China (English)
Liu Xiwen; Wang Guorong; Shi Yonghua; Zhong Jiguang
2007-01-01
Mathematical models of three-dimensional temperature fields in underwater welding with moving heat sources are built. Double ellipsoid Gauss model is proposed as heat sources models. Several factors which affect the temperature fields of underwater welding are analyzed. Water has little influence on thermal efficiency. Water convection coefficient varies with the temperature difference between the water and the workpiece, and water convection makes molten pool freeze quickly. With the increase of water depth, the dimensions of heat sources model should be reduced as arc shrinks. Finite element technology is used to solve mathematical models. ANSYS software is used as finite element tool, and ANSYS Parametric Design Language is used to develop subprograms for loading the moving heat sources and the various convection coefficients. Experiment results show that computational results by using double ellipsoid Gauss heat sources model accord well with the experimental results.
INTERVAL FINITE VOLUME METHOD FOR UNCERTAINTY SIMULATION OF TWO-DIMENSIONAL RIVER WATER QUALITY
Institute of Scientific and Technical Information of China (English)
HE Li; ZENG Guang-ming; HUANG Guo-he; LU Hong-wei
2004-01-01
Under the interval uncertainties, by incorporating the discretization form of finite volume method and interval algebra theory, an Interval Finite Volume Method (IFVM) was developed to solve water quality simulation issues for two-dimensional river when lacking effective data of flow velocity and flow quantity. The IFVM was practically applied to a segment of the Xiangjiang River because the Project of Hunan Inland Waterway Multipurpose must be started working after the environmental impact assessment for it. The simulation results suggest that there exist rather apparent pollution zones of BOD5 downstream the Dongqiaogang discharger and that of COD downstream Xiaoxiangjie discharger, but the pollution sources have no impact on the safety of the three water plants located in this river segment. Although the developed IFVM is to be perfected, it is still a powerful tool under interval uncertainties for water environmental impact assessment, risk analysis, and water quality planning, etc. besides water quality simulation studied in this paper.
Equilibrium charge distribution on a finite straight one-dimensional wire
Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Alkhambashi, Majid; Farouk, Ahmed
2017-09-01
The electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges.
A 3-dimensional finite-difference method for calculating the dynamic coefficients of seals
Dietzen, F. J.; Nordmann, R.
1989-01-01
A method to calculate the dynamic coefficients of seals with arbitrary geometry is presented. The Navier-Stokes equations are used in conjunction with the k-e turbulence model to describe the turbulent flow. These equations are solved by a full 3-dimensional finite-difference procedure instead of the normally used perturbation analysis. The time dependence of the equations is introduced by working with a coordinate system rotating with the precession frequency of the shaft. The results of this theory are compared with coefficients calculated by a perturbation analysis and with experimental results.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
Bessel-Modal Method for Finite-Height Two-Dimensional Photonic Crystal
Institute of Scientific and Technical Information of China (English)
SHI Jun-Feng; HUANG Sheng-Ye; WANG Dong-Sheng
2005-01-01
@@ By applying the dyadic Green function, the dispersion relation of two-dimensional photonic crystal can be ex pressed as the cylindrical wave expansions of eigenmodes. With the aid of Green's theorem, the plane-wavecoefficients of eigenmodes are reconstructed and employed to formulate the scattering matrix of finite-height twodimensional photonic crystal. These operations make the convergence rate very rapid, and reduce the dimension of the scattering matrix. As a demonstration, we present the transmission and electromagnetic field distributions for an InGaAsIn photonic crystal, and investigate their convergence.
Energy Technology Data Exchange (ETDEWEB)
Castellani, Marco; Giuli, Massimiliano, E-mail: massimiliano.giuli@univaq.it [University of L’Aquila, Department of Information Engineering, Computer Science and Mathematics (Italy)
2016-02-15
We study pseudomonotone and quasimonotone quasivariational inequalities in a finite dimensional space. In particular we focus our attention on the closedness of some solution maps associated to a parametric quasivariational inequality. From this study we derive two results on the existence of solutions of the quasivariational inequality. On the one hand, assuming the pseudomonotonicity of the operator, we get the nonemptiness of the set of the classical solutions. On the other hand, we show that the quasimonoticity of the operator implies the nonemptiness of the set of nonzero solutions. An application to traffic network is also considered.
Directory of Open Access Journals (Sweden)
Santhosh George
2004-01-01
Full Text Available Simplified regularization using finite-dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill-posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the noise level are shown to be of optimal order with respect to certain natural assumptions on the ill posedness of the equation. The results are shown to be applicable to a wide class of spline approximations in the setting of Sobolev scales.
Encounter distribution of two random walkers on a finite one-dimensional interval
Energy Technology Data Exchange (ETDEWEB)
Tejedor, Vincent; Schad, Michaela; Metzler, Ralf [Physics Department, Technical University of Munich, James Franck Strasse, 85747 Garching (Germany); Benichou, Olivier; Voituriez, Raphael, E-mail: metz@ph.tum.de [Laboratoire de Physique Theorique de la Matiere Condensee (UMR 7600), Universite Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex (France)
2011-09-30
We analyse the first-passage properties of two random walkers confined to a finite one-dimensional domain. For the case of absorbing boundaries at the endpoints of the interval, we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries. For the case of reflecting boundaries, we obtain the mean first encounter time of the two particles. Our approach leads to closed-form expressions that are more easily tractable than a previously derived solution in terms of the Weierstrass' elliptic function. (paper)
How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism
Gwilliam, Owen
2012-01-01
The Batalin-Vilkovisky formalism in quantum field theory was originally invented to avoid the difficult problem of finding diagrammatic descriptions of oscillating integrals with degenerate critical points. But since then, BV algebras have become interesting objects of study in their own right, and mathematicians sometimes have good understanding of the homological aspects of the story without any access to the diagrammatics. In this note we reverse the usual direction of argument: we begin by asking for an explicit calculation of the homology of a BV algebra, and from it derive Wick's Theorem and the other Feynman rules for finite-dimensional integrals.
A History of the Description of the Three-Dimensional Finite Rotation
Fraiture, Luc
2009-01-01
A history of the description of a three-dimensional finite rotation is given starting with Cardano in the middle of the sixteenth century and ending with Bryan in the beginning of the past century. Description means both a textual description and/or a mathematical representation. To appreciate the historical context of the milestones reached over the centuries, the background and personality of the main players in this history are given. At the end, a short critical discussion is added, reviewing the present names of rotation parameters in use related to the scientists which have been considered here.
Finite-time barriers to front propagation in two-dimensional fluid flows
Mahoney, John R
2015-01-01
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear", introduced by Farazmand, Blazevski, and Haller [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our techniqu...
Energy Technology Data Exchange (ETDEWEB)
Song, Youlin [Zhengzhou University, China; Zhao, Ke [ORNL; Jia, Yu [Zhengzhou University, China; Hu, Xing [Zhengzhou University, China; Zhang, Zhenyu [ORNL
2008-01-01
Finite size effects on the optical properties of one-dimensional 1D and two-dimensional 2D nanoshell dimer arrays are investigated using generalized Mie theory and coupled dipole approximation within the context of surface-enhanced Raman spectroscopy SERS. It is shown that the huge enhancement in the electromagnetic EM field at the center of a given dimer oscillates with the length of the 1D array. For an array of fixed length, the EM enhancement also oscillates along the array, but with a different period. Both types of oscillations can be attributed to the interference of the dynamic dipole fields from different dimers in the array. When generalized to 2D arrays, EM enhancement higher than that of the 1D arrays can be gained with a constant magnitude, a salient feature advantageous to experimental realization of single-molecule SERS. 2008 American Institute of Physics. DOI: 10.1063/1.3009293
Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
Charbonneau, Patrick; Kurchan, Jorge; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2017-03-01
Despite decades of work, gaining a first-principles understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution of a microscopic glass-forming model in the mean-field limit of infinite spatial dimension. Numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner, and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the theory and uncover its more sensitive features. We conclude with a brief overview of ongoing research.
Latif, A. Afiff; Ibrahim, M. Rasidi; Rahim, E. A.; Cheng, K.
2017-04-01
The conventional milling has many difficulties in the processing of hard and brittle material. Hence, ultrasonic vibration assisted milling (UVAM) was proposed to overcome this problem. The objective of this research is to study the behavior of compliance mechanism (CM) as the critical part affect the performance of the UVAM. The design of the CM was investigated and focuses on 1-Dimensional. Experimental result was obtained from a portable laser digital vibrometer. While the 1-Dimensional value such as safety factor, deformation of hinges and stress analysis are obtained from finite elements simulation. Finally, the findings help to find the best design judging from the most travelled distance of the piezoelectric actuators. In addition, this paper would provide a clear picture the behavior of the CM embedded in the UVAM, which can provide good data and to improve the machining on reducing tool wear, and lower cutting force on the workpiece surface roughness.
Development and application of a three-dimensional finite element vapor intrusion model.
Pennell, Kelly G; Bozkurt, Ozgur; Suuberg, Eric M
2009-04-01
Details of a three-dimensional finite element model of soil vapor intrusion, including the overall modeling process and the stepwise approach, are provided. The model is a quantitative modeling tool that can help guide vapor intrusion characterization efforts. It solves the soil gas continuity equation coupled with the chemical transport equation, allowing for both advective and diffusive transport. Three-dimensional pressure, velocity, and chemical concentration fields are produced from the model. Results from simulations involving common site features, such as impervious surfaces, porous foundation sub-base material, and adjacent structures are summarized herein. The results suggest that site-specific features are important to consider when characterizing vapor intrusion risks. More importantly, the results suggest that soil gas or subslab gas samples taken without proper regard for particular site features may not be suitable for evaluating vapor intrusion risks; rather, careful attention needs to be given to the many factors that affect chemical transport into and around buildings.
Grishanin, B A; Grishanin, Boris A.; Zadkov, Victor N.
2005-01-01
A concept of the generalized quantum measurement is introduced as the transformation, which establishes a correspondence between the initial states of the object system and final states of the object--measuring device (meter) system with the help of a classical informational index, unambiguously linked to the classically compatible set of states of the object--meter system. It is shown that the generalized measurement covers all the key known quantum measurement concepts--standard projective, entangling, fuzzy and the generalized measurement with the partial or complete destruction of the initial information contained in the object. A special class of partially-destructive measurements that map the continual set of the states in finite-dimensional quantum systems to that one of the infinite-dimensional quantum systems is considered. Their informational essence and some information characteristics are discussed in detail.
Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich
2013-12-01
This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.
Directory of Open Access Journals (Sweden)
Jiang-Jun Zhou
2017-01-01
Full Text Available In this study, we developed and validated a refined three-dimensional finite element model of middle femoral comminuted fracture to compare the biomechanical stability after two kinds of plate fixation: a newly designed assembly locking compression plate (NALCP and a locking compression plate (LCP. CT data of a male volunteer was converted to middle femoral comminuted fracture finite element analysis model. The fracture was fixated by NALCP and LCP. Stress distributions were observed. Under slow walking load and torsion load, the stress distribution tendency of the two plates was roughly uniform. The anterolateral femur was the tension stress area, and the bone block shifted toward the anterolateral femur. Maximum stress was found on the lateral border of the number 5 countersink of the plate. Under a slow walking load, the NALCP maximum stress was 2.160e+03 MPa and the LCP was 8.561e+02 MPa. Under torsion load, the NALCP maximum stress was 2.260e+03 MPa and the LCP was 6.813e+02 MPa. Based on those results of finite element analysis, the NALCP can provide adequate mechanical stability for comminuted fractures, which would help fixate the bone block and promote bone healing.
Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander
2011-01-01
A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.
[Establishment of 3-dimensional finite element model of human knee joint and its biomechanics].
Yuan, Ping; Wang, Wanchun
2010-01-01
To establish a 3-dimensional (3-D) finite element knee model in healthy Chinese males, to verify the validity of the model, and to analyze the biomechanics of this model under axial load, flexion moment, varus/valgus torque, and internal/external axial torque. A set of consecutive transectional computerized tomography images of normal male knee joints in upright weight-bearing position was selected. With image processing and inversion technology, the 3-D finite element model of the normal knee joint was established through the software ABAQOUS/STANDARD Version-6.5.Biomechanical analysis of this model was processed under axial load, flexion moment, varus/valgus torque, and internal/external axial torque. A 3-D finite element model of healthy Chinese males was successfully established. The ranges of motion of varus and valgus were both small and the difference between them has no statistical significance (P>0.05). The motion of internal and external rotation of the knee took place only in flexion situation.The range of motion of external rotation was larger than that of internal rotation in the same knee (Pknee resembles the actual knee segments. It can imitate the knee response to different loads. This model could be used for further study on knee biomechanics.
Three Dimensional Viscous Finite Element Formulation For Acoustic Fluid Structure Interaction
Cheng, Lei; White, Robert D.; Grosh, Karl
2010-01-01
A three dimensional viscous finite element model is presented in this paper for the analysis of the acoustic fluid structure interaction systems including, but not limited to, the cochlear-based transducers. The model consists of a three dimensional viscous acoustic fluid medium interacting with a two dimensional flat structure domain. The fluid field is governed by the linearized Navier-Stokes equation with the fluid displacements and the pressure chosen as independent variables. The mixed displacement/pressure based formulation is used in the fluid field in order to alleviate the locking in the nearly incompressible fluid. The structure is modeled as a Mindlin plate with or without residual stress. The Hinton-Huang’s 9-noded Lagrangian plate element is chosen in order to be compatible with 27/4 u/p fluid elements. The results from the full 3d FEM model are in good agreement with experimental results and other FEM results including Beltman’s thin film viscoacoustic element [2] and two and half dimensional inviscid elements [21]. Although it is computationally expensive, it provides a benchmark solution for other numerical models or approximations to compare to besides experiments and it is capable of modeling any irregular geometries and material properties while other numerical models may not be applicable. PMID:20174602
Reductions in finite-dimensional integrable systems and special points of classical r-matrices
Skrypnyk, T.
2016-12-01
For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.
Finite-key analysis for time-energy high-dimensional quantum key distribution
Niu, Murphy Yuezhen; Xu, Feihu; Shapiro, Jeffrey H.; Furrer, Fabian
2016-11-01
Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.
Semi-automatic computer construction of three-dimensional shapes for the finite element method.
Aharon, S; Bercovier, M
1993-12-01
Precise estimation of spatio-temporal distribution of ions (or other constitutives) in three-dimensional geometrical configuration plays a major role in biology. Since a direct experimental information regarding the free intracellular Ca2+ spatio-temporal distribution is not available to date, mathematical models have been developed. Most of the existing models are based on the classical numerical method of finite-difference (FD). Using this method one is limited when dealing with complicated geometry, general boundary conditions and variable or non-linear material properties. These difficulties are easily solved when the finite-element-method (FEM) is employed. The first step in the implementation of the FEM procedure is the mesh generation which is the single most tedious, time consuming task and vulnerable to mistake. In order to overcome these limitations we developed a new interface called AUTOMESH. This tool is used as a preprocessor program which generates two- and three-dimensional meshes for some known and often-used shapes in neurobiology. AUTOMESH creates an appropriate mesh by using the mesh generator commercial tool of FIDAP.
Institute of Scientific and Technical Information of China (English)
LUO Zu-jiang; ZHANG Ying-ying; WU Yong-xia
2008-01-01
For deep foundation pit dewatering in the Yangtze River Delta, it is easy to make a dramatic decrease of the underground water level surrounding the dewatering area and cause land subsidence and geologic disasters. In this work, a three-dimensional finite element simulation method was applied in the forth subway of Dongjiadu tunnel repair foundation pit dewatering in Shanghai. In order to control the decrease of the underground water level around the foundation pit, the foundation pit dewatering method was used to design the optimization project of dewatering ,which was simulated under these conditions that the aquifers deposited layer by layer, the bottom of the aquifers went deep to 144.45 m, the retaining wall of foundation pit shield went deep to 65 m, the filters of the extraction wells were located between 44 m to 59 m, the water level in the deep foundation pit was decreased by 34 m, and the maximum decrease of water level outside the foundation pit was 3 m. It is shown that the optimization project and the practical case are consistent with each other. Accordingly, the three-dimensional finite element numerical simulation is the basic theory of optimization design of engineering structures of dewatering in deep foundation pit in such areas.
Three dimensional finite element analysis and optimal design of cast-iron bronze-inlaid gate
Tang, Liangbao; Fang, Yuefei
2005-12-01
The three-dimensional finite element model of the body of cast-iron bronze-inlaid gate is established to calculate its deformation and stress. By calculation, we obtain the law of deformation and stress under static water pressure. Then we optimize the structure of the body of cast-iron bronze-inlaid gate vie above calculation results. To validate the effect of proposed method, an engineering example of 1000mm×1500mm gate in a certain sewage process plant is introduced. The comparisons are made between the calculation results of the proposed method and those obtained by conventional design. The comparison results show that three dimensional finite element methods can obtain the actual stress and deformation of the gate body under static water pressure. In addition, we further optimize the structure and dimension of the cast-iron bronze-inlaid gate. The final optimization results show that the proposed method can reduce the weight of the gate by 20% compared those results by conventional design.
Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.
2016-05-01
Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator e-β H for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) β . Coarse graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension D . The coarse graining is performed by a tree tensor network of isometries. The isometries are optimized variationally, taking into account full tensor environment, to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase, the critical temperature is estimated at Tc=0.0606 (4 ) J , where J is the isotropic coupling constant between S =1/2 pseudospins.
Full-thickness tears of the supraspinatus tendon: A three-dimensional finite element analysis.
Quental, C; Folgado, J; Monteiro, J; Sarmento, M
2016-12-08
Knowledge regarding the likelihood of propagation of supraspinatus tears is important to allow an early identification of patients for whom a conservative treatment is more likely to fail, and consequently, to improve their clinical outcome. The aim of this study was to investigate the potential for propagation of posterior, central, and anterior full-thickness tears of different sizes using the finite element method. A three-dimensional finite element model of the supraspinatus tendon was generated from the Visible Human Project data. The mechanical behaviour of the tendon was fitted from experimental data using a transversely isotropic hyperelastic constitutive model. The full-thickness tears were simulated at the supraspinatus tendon insertion by decreasing the interface area. Tear sizes from 10% to 90%, in 10% increments, of the anteroposterior length of the supraspinatus footprint were considered in the posterior, central, and anterior regions of the tendon. For each tear, three finite element analyses were performed for a supraspinatus force of 100N, 200N, and 400N. Considering a correlation between tendon strain and the risk of tear propagation, the simulated tears were compared qualitatively and quantitatively by evaluating the volume of tendon for which a maximum strain criterion was not satisfied. The finite element analyses showed a significant impact of tear size and location not only on the magnitude, but also on the patterns of the maximum principal strains. The mechanical outcome of the anterior full-thickness tears was consistently, and significantly, more severe than that of the central or posterior full-thickness tears, which suggests that the anterior tears are at greater risk of propagating than the central or posterior tears.
Noninertial effects on nonrelativistic topological quantum scattering
Mota, H. F.; Bakke, K.
2017-08-01
We investigate noninertial effects on the scattering problem of a nonrelativistic particle in the cosmic string spacetime. By considering the nonrelativistic limit of the Dirac equation we are able to show, in the regime of small rotational frequencies, that the phase shift has two contribution: one related to the noninertial reference frame, and the other, due to the cosmic string conical topology. We also show that both the incident wave and the scattering amplitude are altered as a consequence of the noninertial reference frame and depend on the rotational frequency.
Two-dimensional thermal analysis of a fuel rod by finite volume method
Energy Technology Data Exchange (ETDEWEB)
Costa, Rhayanne Y.N.; Silva, Mario A.B. da; Lira, Carlos A.B. de O., E-mail: ryncosta@gmail.com, E-mail: mabs500@gmail.com, E-mail: cabol@ufpe.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Departamaento de Energia Nuclear
2015-07-01
In a nuclear reactor, the amount of power generation is limited by thermal and physic limitations rather than by nuclear parameters. The operation of a reactor core, considering the best heat removal system, must take into account the fact that the temperatures of fuel and cladding shall not exceed safety limits anywhere in the core. If such considerations are not considered, damages in the fuel element may release huge quantities of radioactive materials in the coolant or even core meltdown. Thermal analyses for fuel rods are often accomplished by considering one-dimensional heat diffusion equation. The aim of this study is to develop the first paper to verify the temperature distribution for a two-dimensional heat transfer problem in an advanced reactor. The methodology is based on the Finite Volume Method (FVM), which considers a balance for the property of interest. The validation for such methodology is made by comparing numerical and analytical solutions. For the two-dimensional analysis, the results indicate that the temperature profile agree with expected physical considerations, providing quantitative information for the development of advanced reactors. (author)
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
[Three-dimensional Finite Element Analysis to T-shaped Fracture of Pelvis in Sitting Position].
Fan, Yanping; Lei, Jianyin; Liu, Haibo; Li, Zhiqiang; Cai, Xianhua; Chen, Weiyi
2015-10-01
We developed a three-dimensional finite element model of the pelvis. According to Letournel methods, we established a pelvis model of T-shaped fracture with its three different fixation systems, i. e. double column reconstruction plates, anterior column plate combined with posterior column screws and anterior column plate combined with quadrilateral area screws. It was found that the pelvic model was effective and could be used to simulate the mechanical behavior of the pelvis. Three fixation systems had great therapeutic effect on the T-shaped fracture. All fixation systems could increase the stiffness of the model, decrease the stress concentration level and decrease the displacement difference along the fracture line. The quadrilateral area screws, which were drilled into cortical bone, could generate beneficial effect on the T-type fracture. Therefore, the third fixation system mentioned above (i. e. the anterior column plate combined with quadrilateral area screws) has the best biomechanical stability to the T-type fracture.
Directory of Open Access Journals (Sweden)
Kunal Pathak
2016-09-01
Full Text Available The calcium signaling plays a crucial role in expansion and contraction of cardiac myocytes. This calcium signaling is achieved by calcium diffusion, buffering mechanisms and influx in cardiac myocytes. The various calcium distribution patterns required for achieving calcium signaling in myocytes are still not well understood. In this paper an attempt has been made to develop a model of calcium distribution in myocytes incorporating diffusion of calcium, point source and excess buffer approximation. The model has been developed for a two dimensional unsteady state case. Appropriate boundary conditions and initial condition have been framed. The finite element method has been employed to obtain the solution. The numerical results have been used to study the effect of buffers and source amplitude on calcium distribution in myocytes.
Finite-Difference Time-Domain Simulation for Three-dimensional Polarized Light Imaging
Menzel, Miriam; De Raedt, Hans; Michielsen, Kristel
2016-01-01
Three-dimensional Polarized Light Imaging (3D-PLI) is a promising technique to reconstruct the nerve fiber architecture of human post-mortem brains from birefringence measurements of histological brain sections with micrometer resolution. To better understand how the reconstructed fiber orientations are related to the underlying fiber structure, numerical simulations are employed. Here, we present two complementary simulation approaches that reproduce the entire 3D-PLI analysis: First, we give a short review on a simulation approach that uses the Jones matrix calculus to model the birefringent myelin sheaths. Afterwards, we introduce a more sophisticated simulation tool: a 3D Maxwell solver based on a Finite-Difference Time-Domain algorithm that simulates the propagation of the electromagnetic light wave through the brain tissue. We demonstrate that the Maxwell solver is a valuable tool to better understand the interaction of polarized light with brain tissue and to enhance the accuracy of the fiber orientati...
Shu, Chi-Wang
1998-01-01
This project is about the development of high order, non-oscillatory type schemes for computational fluid dynamics. Algorithm analysis, implementation, and applications are performed. Collaborations with NASA scientists have been carried out to ensure that the research is relevant to NASA objectives. The combination of ENO finite difference method with spectral method in two space dimension is considered, jointly with Cai [3]. The resulting scheme behaves nicely for the two dimensional test problems with or without shocks. Jointly with Cai and Gottlieb, we have also considered one-sided filters for spectral approximations to discontinuous functions [2]. We proved theoretically the existence of filters to recover spectral accuracy up to the discontinuity. We also constructed such filters for practical calculations.
Song, Youlin; Zhao, Ke; Jia, Yu; Hu, Xing; Zhang, Zhenyu
2009-03-01
Finite size effects on the optical properties of one-dimensional (1D) and 2D nanoshell dimer arrays are investigated using generalized Mie theory and coupled dipole approximation within the context of surface-enhanced Raman spectroscopy (SERS). It is shown that the huge enhancement in the electromagnetic (EM) field at the center of a given dimer oscillates with the length of the 1D array. For an array of fixed length, the EM enhancement also oscillates along the array, but with a different period. Both types of oscillations can be attributed to the interference of the dynamic dipole fields from different dimers in the array. When generalized to 2D arrays, EM enhancement higher than that of the 1D arrays can be gained with a constant magnitude, a salient feature advantageous to experimental realization of single-molecule SERS. [K. Zhao et al, J. Chem. Phys. 125, 081102 (2005); Y. L. Song et al, accepted by J. Chem. Phys.
A FINITE DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL VARIATIONAL BOUSSINESQ EQUATIONS
Directory of Open Access Journals (Sweden)
A. Suryanto
2012-06-01
Full Text Available The variational Boussinesq equations derived by Klopman et. al. (2005 con-verse mass, momentum and positive-definite energy. Moreover, they were shown to have significantly improved frequency dispersion characteristics, making it suitable for wave simulation from relatively deep to shallow water. In this paper we develop a numerica lcode for the variational Boussinesq equations. This code uses a fourth-order predictor-corrector method for time derivatives and fourth-order finite difference method for the first-order spatial derivatives. The numerical method is validated against experimen-tal data for one-dimensional nonlinear wave transformation problems. Furthermore, the method is used to illustrate the dispersive effects on tsunami-type of wave propagation.
A solution of two-dimensional magnetohydrodynamic flow using the finite volume method
Directory of Open Access Journals (Sweden)
Naceur Sonia
2014-01-01
Full Text Available This paper presents the two dimensional numerical modeling of the coupling electromagnetic-hydrodynamic phenomena in a conduction MHD pump using the Finite volume Method. Magnetohydrodynamic problems are, thus, interdisciplinary and coupled, since the effect of the velocity field appears in the magnetic transport equations, and the interaction between the electric current and the magnetic field appears in the momentum transport equations. The resolution of the Maxwell's and Navier Stokes equations is obtained by introducing the magnetic vector potential A, the vorticity z and the stream function y. The flux density, the electromagnetic force, and the velocity are graphically presented. Also, the simulation results agree with those obtained by Ansys Workbench Fluent software.
Three-dimensional finite element modelling of the uniaxial tension test
DEFF Research Database (Denmark)
Østergaard, Lennart; Stang, Henrik
2002-01-01
Experimental determination of the stress-crack opening relationship (σ-w) for concrete as defined in the fictitious crack model has proven to be difficult. This is due to the problems that may arise from application of the inverse analysis method necessary for the derivation of the relationship....... One of the most direct methods for determination of the σ-w relationship is the uniaxial tension test, where a notched specimen is pulled apart while the tensile load and the crack opening displacement is observed. This method is appealing since the interpretation is straightforward. The method...... is examined in this paper through three dimensional finite element analyses. It is concluded that the interpretation of the uniaxial tension test is indeed straightforward, if the testing machine stiffness is sufficiently high....
Institute of Scientific and Technical Information of China (English)
Tatsuyuki NEZU
2006-01-01
The three-dimensional stress distributions in the area surrounding indentation pattern for three different materials,Al2O3,Si3N4 and SiC were analyzed by finite element method(FEM). Those theoretical results were also compared with the experimental ones by Rockwell hardness test. The effect of loading stress on the plastic deformation in specimens,surface was investigated on the assumption of shear strain energy theory by Huber-Mises when the materials were indented. The distributions of nomal stress,shear stress,and Mises stress were analysed with variations of loading conditions. It is clear that the analytical results for the stress distributions,the crack length and its density of probability are in good agreement with the experimental results.
Moretti, Valter
2016-01-01
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of so-called frame functions, introduced by A.M. Gleason to prove his celebrated theorem. In particular, the problem of associating quantum state with positive Liouville densities is tackled from an axiomatic point of view, proving a theorem classifying all possible correspondences. A similar result is established for classical observables representing quantum ones. These correspondences turn out to be encoded in a one-parameter class and, in both cases, the classical objects representing quantum ones result to be frame functions. The requirements of $U(n)$ covariance and (convex) linearity play a central r\\^ole in the proof of those theorems. A new characterization of classical observables describing quantum observables is presented, together with a geometric description of the ...
Three-dimensional finite-element simulation of a turbulent push-pull ventilation system.
Flynn, M R; Ahn, K; Miller, C T
1995-10-01
A finite-element formulation with penalty approach to enforce continuity is employed here to simulate the three-dimensional velocity field resulting from a simple push-pull ventilation configuration. An analytic expression for the length scale and a transport equation for turbulent kinetic energy are coupled with the momentum equations. A coaxial square hood and jet are arranged with cross-draught perpendicular to the common centreline. Numerical predictions of the velocity and turbulence kinetic energy fields are evaluated in the plane of symmetry with hot film anemometry, and smoke-wire flow visualizations. The agreement of the simulated jet trajectories with flow visualizations is reasonable, as are velocities. Predictions of turbulence kinetic energy are not as good, particularly near the hood face. Despite the limitations the numerical approach is useful in assessing the impact of cross-draughts on the push-pull arrangement.
Transmission and reflection properties of two-dimensional finite metal crystals
Roszkiewicz, Agata; Nasalski, Wojciech
2017-07-01
Optical characteristics of a finite two-dimensional silver stripe photonic crystal of a square lattice are numerically analysed with use of multilayer Rigorous Coupled Wave Analysis. Qualitative changes in optical response of the crystal originated from modifications of the thickness and filling factors of each layer and the polarization direction of the incident wave are shown. The crystal manifests its various characteristics in wideband or narrowband reflection and transmission, while absorption remains low. The behaviour of the crystal is determined by its structure geometry yielding excitation of localized plasmons and collective modes together with interactions between them. The optical response of the square lattice structure is also compared with the response of a triangular lattice crystal.
Dynamical effects of a one-dimensional multibarrier potential of finite range
Bar, D
2002-01-01
We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section $\\sigma$, and the resonances of $\\sigma$ depend sensitively upon the ratio of the total spacing to the total barrier width. We also show that a time dependent wave packet passing through the system of potential barriers rapidly spreads and deforms, a criterion suggested by Zaslavsky for chaotic behaviour. Computing the spectrum by imposing (large) periodic boundary conditions we find a Wigner type distribution. We investigate also the S-matrix poles; many resonances occur for certain values of the relative spacing between the barriers in the potential.
Chernov, A. V.
2013-12-01
Approximating finite-dimensional mathematical programming problems are studied that arise from piecewise constant discretization of controls in the optimization of distributed systems of a fairly broad class. The smoothness of the approximating problems is established. Gradient formulas are derived that make use of the analytical solution of the original control system and its adjoint, thus providing an opportunity for algorithmic separation of numerical optimization and the task of solving a controlled initial-boundary value problem. The approximating problems are proved to converge to the original optimization problem with respect to the functional as the discretization is refined. The application of the approach to optimization problems is illustrated by solving the semilinear wave equation controlled by applying an integral criterion. The results of numerical experiments are analyzed.
Finite difference method and analysis for three-dimensional semiconductor device of heat conduction
Institute of Scientific and Technical Information of China (English)
袁益让
1996-01-01
The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Characteristic finite difference schemes for two kinds of boundary value problems are put forward. By using the thick and thin grids to form a complete set and treating the product threefold-quadratic interpolation, variable time step method with the boundary condition, calculus of variations and the theory of prior estimates and techniques, the optimal error estimates in L2 norm are derived in the approximate solutions.
Institute of Scientific and Technical Information of China (English)
苏佳灿; 张春才; 禹宝庆; 许硕贵; 王家林; 纪方; 张雪松; 吴建国; 王保华; 薛召军; 丁祖泉
2003-01-01
Objective: To study the memory biomechanical character of anatomic distal radius Nitinol memory connector (DRMC) in treating distal radius fracture. Methods: Establishing three dimensional model and finite element analysis, we calculated the stress in and around the fracture faces when distal radius fracture was fixated with DRMC. Results: Axial holding stress produced by holding part of DRMC on distal radius was 14.66 MPa. The maximum stress of holding part was 40-70 MPa, the minimum stress was 3-7 MPa,and the stress of compression part was 20-40 MPa. Conclusion: The distribution of stress produced by DRMC around the fracture line is reasonable, and axial holding stress can help stabilize fracture during earlier period. The existence of longitudal compression and memory effect can transfer fixated disused section into developed section and enhance fracture healing.
Aerodynamic effects of simulated ice shapes on two-dimensional airfoils and a swept finite tail
Alansatan, Sait
An experimental study was conducted to investigate the effect of simulated glaze ice shapes on the aerodynamic performance characteristics of two-dimensional airfoils and a swept finite tail. The two dimensional tests involved two NACA 0011 airfoils with chords of 24 and 12 inches. Glaze ice shapes computed with the LEWICE code that were representative of 22.5-min and 45-min ice accretions were simulated with spoilers, which were sized to approximate the horn heights of the LEWICE ice shapes. Lift, drag, pitching moment, and surface pressure coefficients were obtained for a range of test conditions. Test variables included Reynolds number, geometric scaling, control deflection and the key glaze ice features, which were horn height, horn angle, and horn location. For the three-dimensional tests, a 25%-scale business jet empennage (BJE) with a T-tail configuration was used to study the effect of ice shapes on the aerodynamic performance of a swept horizontal tail. Simulated glaze ice shapes included the LEWICE and spoiler ice shapes to represent 9-min and 22.5-min ice accretions. Additional test variables included Reynolds number and elevator deflection. Lift, drag, hinge moment coefficients as well as boundary layer velocity profiles were obtained. The experimental results showed substantial degradation in aerodynamic performance of the airfoils and the swept horizontal tail due to the simulated ice shapes. For the two-dimensional airfoils, the largest aerodynamic penalties were obtained when the 3-in spoiler-ice, which was representative of 45-min glaze ice accretions, was set normal to the chord. Scale and Reynolds effects were not significant for lift and drag. However, pitching moments and pressure distributions showed great sensitivity to Reynolds number and geometric scaling. For the threedimensional study with the swept finite tail, the 22.5-min ice shapes resulted in greater aerodynamic performance degradation than the 9-min ice shapes. The addition of 24
Yang, Taiseung; Spilker, Robert L
2007-06-01
A three-dimensional (3D) contact finite element formulation has been developed for biological soft tissue-to-tissue contact analysis. The linear biphasic theory of Mow, Holmes, and Lai (1984, J. Biomech., 17(5), pp. 377-394) based on continuum mixture theory, is adopted to describe the hydrated soft tissue as a continuum of solid and fluid phases. Four contact continuity conditions derived for biphasic mixtures by Hou et al. (1989, ASME J. Biomech. Eng., 111(1), pp. 78-87) are introduced on the assumed contact surface, and a weighted residual method has been used to derive a mixed velocity-pressure finite element contact formulation. The Lagrange multiplier method is used to enforce two of the four contact continuity conditions, while the other two conditions are introduced directly into the weighted residual statement. Alternate formulations are possible, which differ in the choice of continuity conditions that are enforced with Lagrange multipliers. Primary attention is focused on a formulation that enforces the normal solid traction and relative fluid flow continuity conditions on the contact surface using Lagrange multipliers. An alternate approach, in which the multipliers enforce normal solid traction and pressure continuity conditions, is also discussed. The contact nonlinearity is treated with an iterative algorithm, where the assumed area is either extended or reduced based on the validity of the solution relative to contact conditions. The resulting first-order system of equations is solved in time using the generalized finite difference scheme. The formulation is validated by a series of increasingly complex canonical problems, including the confined and unconfined compression, the Hertz contact problem, and two biphasic indentation tests. As a clinical demonstration of the capability of the contact analysis, the gleno-humeral joint contact of human shoulders is analyzed using an idealized 3D geometry. In the joint, both glenoid and humeral head
Energy Technology Data Exchange (ETDEWEB)
Kim, D.W. [Yonsei Univ., Seoul (Korea, Republic of)
1994-09-01
In this study impedance changes due to aortic expansion, blood and lung resistivity changes during systole were calculated for various electrode configurations in impedance cardiography using a three-dimensional finite element thoracic model. For the aortic expansion the aorta between the potential electrodes in the model was expanded for the increase of blood volume, 30ml. The blood volume increase in aorta was calculated with the basal impedance(Z) and the impedance change({Delta}Z) found from the finite element code using the formula, vol={rho}(L/Z){sup 2}{Delta}Z relating impedance change and blood volume change. The aortic expansions were simulated for six electrode configurations including the conventional one and then the blood volumes were calculated using the formula above to investigate which one was closer to the actual blood velum increase of 30ml. It was calculated to be 24ml for the conventional configuration. For the other five ones, they were all closer to 30ml than the conventional one. From the results above it can be also concluded that the impedance change in impedance cardiography is approximately proportional to the blood volume change in large arteries. (author). 10 refs., 3 figs.
Calibration of dimensional change in finite element models using AGR moderator brick measurements
Energy Technology Data Exchange (ETDEWEB)
McNally, K., E-mail: kevin.mcnally@hsl.gsi.gov.uk [Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire SK17 9JN (United Kingdom); Hall, G. [NGRG, School of MACE, University of Manchester, Manchester M13 9PL (United Kingdom); Tan, E. [Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire SK17 9JN (United Kingdom); Marsden, B.J. [NGRG, School of MACE, University of Manchester, Manchester M13 9PL (United Kingdom); Warren, N. [Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire SK17 9JN (United Kingdom)
2014-08-01
Physically based models, resolved using the finite element (FE) method, are often used to model changes in geometry and the associated stress fields of graphite moderator bricks within a reactor. These models require inputs that describe the loading conditions (field variables), and coded relationships describing the behaviour of material properties. Historically, behaviour on material properties have been obtained from Materials Test Reactor (MTR) experiments, however data relating to samples trepanned from operating reactors are increasingly being used to improve models. Geometry measurements from operating reactors offer the potential for improving the coded relationship for dimensional change in FE models. A non-linear mixed-effect model is presented for calibrating the parameters of FE models that are sensitive to mid-brick diameter, using channel geometry measurements obtained from inspection campaigns. The work makes use of a novel technique: the development of a Bayesian emulator, which is a surrogate for the FE model. The use of an emulator allows the influence of the inputs to the finite element model to be evaluated, and delivers a substantial reduction in the computational burden of calibration.
Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach
Ou, Yangxin; Chen, Yuntian
2015-01-01
We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into a series of independent 2D problems (2.5D), which reduces the computational cost. Moreover, the reduced 2D problems can be extremely accurate, compared to its 3D counterpart. Our method can precisely quantify the total emission rates, as well as the fraction of emission rates into different modal channels for waveguides with arbitrary cross-sections. We compare our method with dyadic Green's function for the light emission in single mode metallic nanowire, which yields an excellent agreement. This method is applied in multi-mode waveguides, as well as multi-core waveguides. We further show that our method has the full capability of including dipole orientations, as illustrated via a rotating dipole, which leads to unidirectional excitation of guide modes. The 2.5D Finite El...
Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach.
Ou, Yangxin; Pardo, David; Chen, Yuntian
2015-11-16
We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into a series of independent 2D problems (2.5D), which reduces the computational cost. Moreover, the reduced 2D problems can be extremely accurate, compared to its 3D counterpart. Our method can precisely quantify the total emission rates, as well as the fraction of emission rates into different modal channels for waveguides with arbitrary cross-sections. We compare our method with dyadic Green's function for the light emission in single mode metallic nanowire, which yields an excellent agreement. This method is applied in multi-mode waveguides, as well as multi-core waveguides. We further show that our method has the full capability of including dipole orientations, as illustrated via a rotating dipole, which leads to unidirectional excitation of guide modes. The 2.5D Finite Element Method (FEM) approach proposed here can be applied for various waveguides, thus it is useful to interface single-photon single-emitter in nano-structures, as well as for other scenarios involving coupled waveguide-emitters.
Finite current stationary states of random walks on one-dimensional lattices with aperiodic disorder
Miki, Hiroshi
2016-11-01
Stationary states of random walks with finite induced drift velocity on one-dimensional lattices with aperiodic disorder are investigated by scaling analysis. Three aperiodic sequences, the Thue-Morse (TM), the paperfolding (PF), and the Rudin-Shapiro (RS) sequences, are used to construct the aperiodic disorder. These are binary sequences, composed of two symbols A and B, and the ratio of the number of As to that of Bs converges to unity in the infinite sequence length limit, but their effects on diffusional behavior are different. For the TM model, the stationary distribution is extended, as in the case without current, and the drift velocity is independent of the system size. For the PF model and the RS model, as the system size increases, the hierarchical and fractal structure and the localized structure, respectively, are broken by a finite current and changed to an extended distribution if the system size becomes larger than a certain threshold value. Correspondingly, the drift velocity is saturated in a large system while in a small system it decreases as the system size increases.
High Performance Computing of Three-Dimensional Finite Element Codes on a 64-bit Machine
Directory of Open Access Journals (Sweden)
M.P Raju
2012-01-01
Full Text Available Three dimensional Navier-Stokes finite element formulations require huge computational power in terms of memory and CPU time. Recent developments in sparse direct solvers have significantly reduced the memory and computational time of direct solution methods. The objective of this study is twofold. First is to evaluate the performance of various state-of-the-art sequential sparse direct solvers in the context of finite element formulation of fluid flow problems. Second is to examine the merit in upgrading from 32 bit machine to a 64 bit machine with larger RAM capacity in terms of its capacity to solve larger problems. The choice of a direct solver is dependent on its computational time and its in-core memory requirements. Here four different solvers, UMFPACK, MUMPS, HSL_MA78 and PARDISO are compared. The performances of these solvers with respect to the computational time and memory requirements on a 64-bit windows server machine with 16GB RAM is evaluated.
Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance
Liang, Zhichun; Crepeau, Richard H.; Freed, Jack H.
2005-12-01
Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.
A Reduced Three Dimensional Model for SAW Sensors Using Finite Element Analysis.
El Gowini, Mohamed M; Moussa, Walied A
2009-01-01
A major problem that often arises in modeling Micro Electro Mechanical Systems (MEMS) such as Surface Acoustic Wave (SAW) sensors using Finite Element Analysis (FEA) is the extensive computational capacity required. In this study a new approach is adopted to significantly reduce the computational capacity needed for analyzing the response of a SAW sensor using the finite element (FE) method. The approach is based on the plane wave solution where the properties of the wave vary in two dimensions and are uniform along the thickness of the device. The plane wave solution therefore allows the thickness of the SAW device model to be minimized; the model is referred to as a Reduced 3D Model (R3D). Various configurations of this novel R3D model are developed and compared with theoretical and experimental frequency data and the results show very good agreement. In addition, two-dimensional (2D) models with similar configurations to the R3D are developed for comparison since the 2D approach is widely adopted in the literature as a computationally inexpensive approach to model SAW sensors using the FE method. Results illustrate that the R3D model is capable of capturing the SAW response more accurately than the 2D model; this is demonstrated by comparison of centre frequency and insertion loss values. These results are very encouraging and indicate that the R3D model is capable of capturing the MEMS-based SAW sensor response without being computationally expensive.
A Reduced Three Dimensional Model for SAW Sensors Using Finite Element Analysis
Directory of Open Access Journals (Sweden)
Mohamed M. El Gowini
2009-12-01
Full Text Available A major problem that often arises in modeling Micro Electro Mechanical Systems (MEMS such as Surface Acoustic Wave (SAW sensors using Finite Element Analysis (FEA is the extensive computational capacity required. In this study a new approach is adopted to significantly reduce the computational capacity needed for analyzing the response of a SAW sensor using the finite element (FE method. The approach is based on the plane wave solution where the properties of the wave vary in two dimensions and are uniform along the thickness of the device. The plane wave solution therefore allows the thickness of the SAW device model to be minimized; the model is referred to as a Reduced 3D Model (R3D. Various configurations of this novel R3D model are developed and compared with theoretical and experimental frequency data and the results show very good agreement. In addition, two-dimensional (2D models with similar configurations to the R3D are developed for comparison since the 2D approach is widely adopted in the literature as a computationally inexpensive approach to model SAW sensors using the FE method. Results illustrate that the R3D model is capable of capturing the SAW response more accurately than the 2D model; this is demonstrated by comparison of centre frequency and insertion loss values. These results are very encouraging and indicate that the R3D model is capable of capturing the MEMS-based SAW sensor response without being computationally expensive.
A one-dimensional mixed porohyperelastic transport swelling finite element model with growth.
Harper, J L; Simon, B R; Vande Geest, J P
2014-01-01
A one-dimensional, large-strain, mixed porohyperelastic transport and swelling (MPHETS) finite element model was developed in MATLAB and incorporated with a well-known growth model for soft tissues to allow the model to grow (increase in length) or shrink (decrease in length) at constant material density. By using the finite element model to determine the deformation and stress state, it is possible to implement different growth laws in the program in the future to simulate how soft tissues grow and behave when exposed to various stimuli (e.g. mechanical, chemical, or electrical). The essential assumptions needed to use the MPHETS model with growth are clearly identified and explained in this paper. The primary assumption in this work, however, is that the stress upon which growth acts is the stress in the solid skeleton, i.e. the effective stress, S(eff). It is shown that significantly different amounts of growth are experienced for the same loading conditions when using a porohyperelastic model as compared to a purely solid model. In one particular example, approximately 51% less total growth occurred in the MPHETS model than in the solid model even though both problems were subjected to the same external loading. This work represents a first step in developing more sophisticated models capable of capturing the complex mechanical and biochemical environment in growing and remodeling tissues.
Institute of Scientific and Technical Information of China (English)
Jun Liu; Zheng Nan; Ping Yi
2012-01-01
In the last decade,three dimensional discontinuous deformation analyses (3D DDA) has attracted more and more attention of researchers and geotechnical engineers worldwide.The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation,which would cause block expansion under rigid body rotation and thus limit its capability to model block deformation.In this paper,3D DDA is coupled with tetrahedron finite elements to tackle these two problems.Tetrahedron is the simplest in the 3D domain and makes it easy to implement automatic discretization,even for complex topology shape.Furthermore,element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly.The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested.Validation is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes,i.e.,wedge failure.Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases.Finally,a complex rockslide example demonstrates the robustness and versatility of the coupled method.
Finite-time scaling via linear driving: application to the two-dimensional Potts model.
Huang, Xianzhi; Gong, Shurong; Zhong, Fan; Fan, Shuangli
2010-04-01
We apply finite-time scaling to the q-state Potts model with q=3 and 4 on two-dimensional lattices to determine its critical properties. This consists in applying to the model a linearly varying external field that couples to one of its q states to manipulate its dynamics in the vicinity of its criticality and that drives the system out of equilibrium and thus produces hysteresis and in defining an order parameter other than the usual one and a nonequilibrium susceptibility to extract coercive fields. From the finite-time scaling of the order parameter, the coercivity, and the hysteresis area and its derivative, we are able to determine systematically both static and dynamic critical exponents as well as the critical temperature. The static critical exponents obtained in general and the magnetic exponent delta in particular agree reasonably with the conjectured ones. The dynamic critical exponents obtained appear to confirm the proposed dynamic weak universality but unlikely to agree with recent short-time dynamic results for q=4. Our results also suggest an alternative way to characterize the weak universality.
Liu, Xi-Jing; Hu, Bing-Quan; Cho, Sam Young; Zhou, Huan-Qiang; Shi, Qian-Qian
2016-10-01
Recently, the finite-size corrections to the geometrical entanglement per lattice site in the spin-1/2 chain have been numerically shown to scale inversely with system size, and its prefactor b has been suggested to be possibly universal [Q-Q. Shi et al., New J. Phys. 12, 025008 (2010)]. As possible evidence of its universality, the numerical values of the prefactors have been confirmed analytically by using the Affleck-Ludwig boundary entropy with a Neumann boundary condition for a free compactified field [J-M. Stephan et al., Phys. Rev. B 82, 180406(R) (2010)]. However, the Affleck-Ludwig boundary entropy is not unique and does depend on conformally invariant boundary conditions. Here, we show that a unique Affleck-Ludwig boundary entropy corresponding to a finitesize correction to the geometrical entanglement per lattice site exists and show that the ratio of the prefactor b to the corresponding minimum groundstate degeneracy gmin for the Affleck- Ludwig boundary entropy is a constant for any critical region of the spin-1 XXZ system with the single-ion anisotropy, i.e., b/(2 log2 g min ) = -1. Previously studied spin-1/2 systems, including the quantum three-state Potts model, have verified the universal ratio. Hence, the inverse finite-size correction to the geometrical entanglement per lattice site and its prefactor b are universal for one-dimensional critical systems.
A three-dimensional finite element model for biomechanical analysis of the hip.
Chen, Guang-Xing; Yang, Liu; Li, Kai; He, Rui; Yang, Bin; Zhan, Yan; Wang, Zhi-Jun; Yu, Bing-Nin; Jian, Zhe
2013-11-01
The objective of this study was to construct a three-dimensional (3D) finite element model of the hip. The images of the hip were obtained from Chinese visible human dataset. The hip model includes acetabular bone, cartilage, labrum, and bone. The cartilage of femoral head was constructed using the AutoCAD and Solidworks software. The hip model was imported into ABAQUS analysis system. The contact surface of the hip joint was meshed. To verify the model, the single leg peak force was loaded, and contact area of the cartilage and labrum of the hip and pressure distribution in these structures were observed. The constructed 3D hip model reflected the real hip anatomy. Further, this model reflected biomechanical behavior similar to previous studies. In conclusion, this 3D finite element hip model avoids the disadvantages of other construction methods, such as imprecision of cartilage construction and the absence of labrum. Further, it provides basic data critical for accurately modeling normal and abnormal loads, and the effects of abnormal loads on the hip.
Spectral properties of quasi-one-dimensional conductors with a finite transverse band dispersion
Energy Technology Data Exchange (ETDEWEB)
Losic, Z Bonacic; Zupanovic, P [Department of Physics, Faculty of Natural Sciences, Mathematics and Kinesiology, University of Split, Teslina 12, 21000 Split (Croatia); Bjelis, A [Department of Physics, Faculty of Science, University of Zagreb, POB 162, 10001 Zagreb (Croatia)], E-mail: agicz@pmfst.hr, E-mail: bjelis@phy.hr
2008-08-13
We determine the one-particle spectral function and the corresponding derived quantities for the conducting chain lattice with finite inter-chain hopping t{sub perpendicular} and three-dimensional long-range Coulomb electron-electron interaction. The standard G{sub 0}W{sub 0} approximation is used. It is shown that, due to the optical character of the anisotropic plasmon dispersion caused by the finite t{sub perpendicular}, a low energy quasi-particle {delta}-peak appears in the spectral function in addition to the hump present at energies of the order of the plasmon energy. Particular attention is devoted to the continuous crossover from the non-Fermi liquid regime to the Fermi liquid regime with increasing t{sub perpendicular}. It is shown that the spectral weight of the hump transfers to the quasi-particle as the optical gap in the plasmon dispersion increases together with t{sub perpendicular}, with the quasi-particle residuum Z behaving like -ln t{sub perpendicular}){sup -1} in the limit t{sub perpendicular} {yields}0. Our approach is appropriate for the wide range of energy scales given by the plasmon energy and the width of the conduction band, and is complementary to the Luttinger liquid techniques that are limited to the low energy regime close to the Fermi surface.
Classical and quantum mechanics of the nonrelativistic Snyder model in curved space
Mignemi, S
2011-01-01
The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales beside the speed of light, and is invariant under the action of the de Sitter group. Here, we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS). We discuss the classical and the quantum mechanics of a free particle and of an oscillator in this framework. In analogy with the flat case, the properties of the SdS and aSdS model are rather different. In the SdS case, a lower bound on the localization in position and momentum space exists, which does not arise in the aSdS model. In both cases the energy of the harmonic oscillator acquires a dependence on the frequency, but the quantum mechanical aSdS oscillator admits only a finite numb...
Weidinger, Lukas; Bauer, Florian; von Delft, Jan
2017-01-01
We introduce an equilibrium formulation of the functional renormalization group (fRG) for inhomogeneous systems capable of dealing with spatially finite-ranged interactions. In the general third-order truncated form of fRG, the dependence of the two-particle vertex is described by O (N4) independent variables, where N is the dimension of the single-particle system. In a previous paper [Bauer et al., Phys. Rev. B 89, 045128 (2014), 10.1103/PhysRevB.89.045128], the so-called coupled-ladder approximation (CLA) was introduced and shown to admit a consistent treatment for models with a purely onsite interaction, reducing the vertex to O (N2) independent variables. In this work, we introduce an extended version of this scheme, called the extended coupled ladder approximation (eCLA), which includes a spatially extended feedback between the individual channels, measured by a feedback length L , using O (N2L2) independent variables for the vertex. We apply the eCLA in a static approximation and at zero temperature to three types of one-dimensional model systems, focusing on obtaining the linear response conductance. First, we study a model of a quantum point contact (QPC) with a parabolic barrier top and on-site interactions. In our setup, where the characteristic length lx of the QPC ranges between approximately 4-10 sites, eCLA achieves convergence once L becomes comparable to lx. It also turns out that the additional feedback stabilizes the fRG flow. This enables us, second, to study the geometric crossover between a QPC and a quantum dot, again for a one-dimensional model with on-site interactions. Third, the enlarged feedback also enables the treatment of a finite-ranged interaction extending over up to L sites. Using a simple estimate for the form of such a finite-ranged interaction in a QPC with a parabolic barrier top, we study its effects on the conductance and the density. We find that for low densities and sufficiently large interaction ranges the conductance
Noninteracting fermions at finite temperature in a d -dimensional trap: Universal correlations
Dean, David S.; Le Doussal, Pierre; Majumdar, Satya N.; Schehr, Grégory
2016-12-01
We study a system of N noninteracting spinless fermions trapped in a confining potential, in arbitrary dimensions d and arbitrary temperature T . The presence of the confining trap breaks the translational invariance and introduces an edge where the average density of fermions vanishes. Far from the edge, near the center of the trap (the so-called "bulk regime"), where the fermions do not feel the curvature of the trap, physical properties of the fermions have traditionally been understood using the local density (or Thomas-Fermi) approximation. However, these approximations drastically fail near the edge where the density vanishes and thermal and quantum fluctuations are thus enhanced. The main goal of this paper is to show that, even near the edge, novel universal properties emerge, independently of the details of the shape of the confining potential. We present a unified framework to investigate both the bulk and the edge properties of the fermions. We show that for large N , these fermions in a confining trap, in arbitrary dimensions and at finite temperature, form a determinantal point process. As a result, any n -point correlation function, including the average density profile, can be expressed as an n ×n determinant whose entry is called the kernel, a central object for such processes. Near the edge, we derive the large-N scaling form of the kernels, parametrized by d and T . In d =1 and T =0 , this reduces to the so-called Airy kernel, that appears in the Gaussian unitary ensemble (GUE) of random matrix theory. In d =1 and T >0 we show a remarkable connection between our kernel and the one appearing in the (1 +1 )-dimensional Kardar-Parisi-Zhang equation at finite time. Consequently, our result provides a finite-T generalization of the Tracy-Widom distribution, that describes the fluctuations of the position of the rightmost fermion at T =0 , or those of the largest single-fermion momentum. In d >1 and T ≥0 , while the connection to GUE no longer holds
Institute of Scientific and Technical Information of China (English)
SU Jia-can; ZHANG Ben; YU Bao-qing; ZHANG Chun-cai; CHEN Xue-qiang; WANG Bao-hua; DING Zu-quan
2005-01-01
Objective:To explore the mechanical behavior of acetabulum loaded by static stress and provide the mechanical basis for clinical analysis and judgement on acetabular mechanical distribution and effect of static stress. Methods:By means of computer simulation, acetabular three dimensional model was input into three dimensional finite element analysis software ANSYS7.0. The acetabular mechanical behavior was calculated and the main stress value, stress distribution and acetabular unit displacement in the direction of main stress were analyzed when anterior wall of acetabulum and acetabular crest were loaded by 1 000 N static stress. Results :When acetabular anterior wall loaded by X direction and Z direction composition force, the stress passed along 4 directions: (1)from acetabular anterior wall to pubic symphysis a long superior branch of pubis firstly, (2)from acetabular anterior wall to cacroiliac joint along pelvic ring,(3)in the acetabulum, (4)from the suffered point to ischium. When acetabular crest loaded by X direction and Y direction composition force, the stress transmitted to 4 directions: (1)from acetabular crest to ilium firstly, (2)from suffered point to cacroiliac joint along pelvic ring, (3) in the acetabulum , (4)along the pubic branch ,but no stress transmitted to the ischium branch. Conclusion:Analyzing the stress distribution of acetabulum and units displacement when static stress loaded can provide internal fixation point for acetabular fracture treatment and help understand the stress distribution of acetabulum.
Clinical significance of three dimensional finite element analysis on humerus fracture
Institute of Scientific and Technical Information of China (English)
SU Jia-can; WAN Min; FU Qing-ge; ZHANG Chun-cai; XU Shuo-gui; REN Ke; WANG Jia-lin; XUE Zhao-jun; WU Jian-guo; DING Zu-quan; GAO Tang-cheng
2002-01-01
Objective: To treat humerus fracture with three dimensional pattern and finite element analysis,providing mechanical basis for treating humerus fracture. Methods: Humerus pattern was established based on the CT images, and calculation was done by ANSYS5.6 software. Three dimensional ten-node tetrahedron unit was selected and were divided into 2 729 nodes, 49 041 units. Distribution and amount of axial compression of humerus were analyzed when clip angle was 30°, 45°, 90° between fracture face and axial line with fixed X, Y, Z directions. Results: The distribution of stress was greatly different between fracture face and non fracture face. Stress in fracture part was fairly concentrated with incomplete symmetric distribution around the center of fracture face; Greater stressdistributed in the regions 10 mm from fracture face, which was 2-3 times that of other stress regions. Conclusion: Required load must be estimated under various conditions as to select the suitable internal fixation implants during the treatment of humerus fracture, which can provide helpful stress environment for fracture healing.
Three-dimensional finite element analysis of a newly designed onplant miniplate anchorage system.
Liu, Lin; Qu, Yin-Ying; Jiang, Li-Jun; Zhou, Qian; Tang, Tian-Qi
2016-06-01
The purpose of this research was to evaluate the structural stress and deformation of a newly designed onplant miniplate anchorage system compared to a standard anchorage system. A bone block integrated with a novel miniplate and fixation screw system was simulated in a three-dimensional model and subjected to force at different directions. The stress distribution and deformation of the miniplate system and cortical bone were evaluated using the three-dimensional finite element method. The results showed that the stress on the plate system and bone was linearly proportional to the force magnitude and was higher when the force was in a vertical direction (Y-axis). Stress and deformation values of the two screws (screw 1 and 2) were asymmetric when the force was added along Y-axis and was greater in screw 1. The highest deformation value of the screws was 7.5148 μm, much smaller than the limit value. The load was decreased for each single miniscrew, and the ability of the new anchorage system to bear the load was also enhanced to some degree. It was suggested that the newly designed onplant miniplate anchorage system is effective, easily implanted and minimally invasive.
Numerical investigations on the finite time singularity in two-dimensional Boussinesq equations
Yin, Z
2006-01-01
To investigate the finite time singularity in three-dimensional (3D) Euler flows, the simplified model of 3D axisymmetric incompressible fluids (i.e., two-dimensional Boussinesq approximation equations) is studied numerically. The system describes a cap-like hot zone of fluid rising from the bottom, while the edges of the cap lag behind, forming eye-like vortices. The hot liquid is driven by the buoyancy and meanwhile attracted by the vortices, which leads to the singularity-forming mechanism in our simulation. In the previous 2D Boussinesq simulations, the symmetricial initial data is used. However, it is observed that the adoption of symmetry leads to coordinate singularity. Moreover, as demonstrated in this work that the locations of peak values for the vorticity and the temperature gradient becomes far apart as $t$ approaches the predicted blow-up time. This suggests that the symmetry assumption may be unreasonable for searching solution blow-ups. One of the main contributions of this work is to propose a...
Prévost, Jean H.; Sukumar, N.
2016-01-01
Faults are geological entities with thicknesses several orders of magnitude smaller than the grid blocks typically used to discretize reservoir and/or over-under-burden geological formations. Introducing faults in a complex reservoir and/or geomechanical mesh therefore poses significant meshing difficulties. In this paper, we consider the strong-coupling of solid displacement and fluid pressure in a three-dimensional poro-mechanical (reservoir-geomechanical) model. We introduce faults in the mesh without meshing them explicitly, by using the extended finite element method (X-FEM) in which the nodes whose basis function support intersects the fault are enriched within the framework of partition of unity. For the geomechanics, the fault is treated as an internal displacement discontinuity that allows slipping to occur using a Mohr-Coulomb type criterion. For the reservoir, the fault is either an internal fluid flow conduit that allows fluid flow in the fault as well as to enter/leave the fault or is a barrier to flow (sealing fault). For internal fluid flow conduits, the continuous fluid pressure approximation admits a discontinuity in its normal derivative across the fault, whereas for an impermeable fault, the pressure approximation is discontinuous across the fault. Equal-order displacement and pressure approximations are used. Two- and three-dimensional benchmark computations are presented to verify the accuracy of the approach, and simulations are presented that reveal the influence of the rate of loading on the activation of faults.
Wang, S. S.
1985-01-01
A three-dimensional hybrid-stress finite element analysis of composite laminates containing cutouts and cracks is presented. Fully three-dimensional, hexahedral isoparametric elements of the hybrid-stress model are formulated on the basis of the Hellinger-Reissner variational principle. Traction-free edges, cutouts, and crack surfaces are modeled by imposition of exact traction boundary conditions along element surfaces. Special boundary and surface elements are constructed by introducing proper constraints on assumed stress functions. The Lagrangian multiplier technique is used to enforce ply-interface continuity conditions in hybrid bimaterial composite elements for modeling the interface region in a composite laminate. Two examples are given to illustrate the capability of the present method of approach: (1) the well-known delamination problem in an angle-ply laminate, and (2) the important problem of a composite laminate containing a circular hole. Results are presented in detail for each case. Implications of interlaminar and intralaminar crack initiation, growth and fracture in composites containing cracks and cutouts are discussed.
Bialas, P; Morel, A; Petersson, B
2009-01-01
We determine the correlation between Polyakov loops in three dimensional SU(3) gauge theory in the confined region at finite temperature. For this purpose we perform lattice calculations for the number of steps in the temperature direction equal to six. This is expected to be in the scaling region of the lattice theory. We compare the results to the bosonic string model. The agreement is very good for temperatures T<0.7T_c, where T_c is the critical temperature. In the region 0.7T_c
Chu, T M; Reddy, N P; Padovan, J
1995-07-01
An asymmetric 3-dimensional finite element model (FEM) of the ankle-foot orthosis (AFO) together with the ankle-foot complex was developed using the computer aided design (CAD) program PATRAN. Static analysis of normal and pathological motions of the ankle-foot complex such as the "drop-foot" problem were conducted using the FEM program ADINA. A total of 313 three dimensional solid elements and 10 truss elements were used. Heel strike and toe-off condition were simulated. Results revealed that the peak compressive stress (1.6 MPa) in the AFO model occurred in the heel regions of the AFO and the maximum tensile stress (0.8 MPa) occurred in the neck region of the AFO during toe-off. Parametric analyses revealed that the model was sensitive to the elastic moduli of the AFO and of the soft tissue, but was relatively insensitive to the ligament stiffness. The results confirmed the hypothesis that peak stresses in the orthosis occur in the heal and neck regions of the orthosis.
A three-dimensional finite element model for the mechanics of cell-cell interactions.
Viens, Denis; Brodland, G Wayne
2007-10-01
Technical challenges, including significant ones associated with cell rearrangement, have hampered the development of three-dimensional finite element models for the mechanics of embryonic cells. These challenges have been overcome by a new formulation in which the contents of each cell, assumed to have a viscosity mu, are modeled using a system of orthogonal dashpots. This approach overcomes a stiffening artifact that affects more traditional models, in which space-filling viscous elements are used to model the cytoplasm. Cells are assumed to be polyhedral in geometry, and each n-sided polygonal face is subdivided into n triangles with a common node at the face center so that it needs not remain flat. A constant tension gamma is assumed to act along each cell-cell interface, and cell rearrangements occur through one of two complementary topological transformations. The formulation predicts mechanical interactions between pairs of similar or dissimilar cells that are consistent with experiments, two-dimensional simulations, contact angle theory, and intracellular pressure calculations. Simulations of the partial engulfment of one tissue type by another show that the formulation is able to model aggregates of several hundred cells without difficulty. Simulations carried out using this formulation suggest new experimental approaches for measuring cell surface tensions and interfacial tensions. The formulation holds promise as a tool for gaining insight into the mechanics of isolated or aggregated embryonic cells and for the design and interpretation of experiments that involve them.
Non-relativistic quantum mechanics
Puri, Ravinder R.
2017-01-01
This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...
Chen, Si; Xu, Tian-min; Lou, Hang-di; Rong, Qi-guo
2012-12-01
To get individualized facial three-dimensional finite element (FE) model from transformation of a generic one to assist orthodontic analysis and prediction of treatment-related morphological change of facial soft tissue. A generic three-dimensional FE model of craniofacial soft and hard tissue was constructed based on a volunteer's spiral CT data. Seven pairs of main peri-oral muscles were constructed based on a combination of CT image and anatomical method. Individualized model could be obtained through transformation of the generic model based on selection of corresponding anatomical landmarks and radial basis functions (RBF) method. Validation was analyzed through superimposition of the transformed model and cone-beam CT (CBCT) reconstruction data. Pre- and post-treatment CBCT data of two patients were collected, which were superimposed to gain the amount of anterior teeth retraction and anterior alveolar surface remodeling that could be used as boundary condition. Different values of Poisson ratio ν and Young's modulus E were tested during simulation. Average deviation was 0.47 mm and 0.75 mm in the soft and hard tissue respectively. It could be decreased to a range of +0.29 mm and -0.21 mm after a second transformation at the lip-mouth region. The best correspondence between simulation and post-treatment result was found with elastic properties of soft tissues defined as follows. Poisson ratio ν for skin, muscle and fat being set as 0.45 while Young's modulus being set as 90.0 kPa, 6.2 kPa and 2.0 kPa respectively. Individualized three-dimensional facial FE model could be obtained through mathematical model transformation. With boundary condition defined according to treatment plan such FE model could be used to analyze the effect of orthodontic treatment on facial soft tissue.
Keulemans, F.; Shinya, A.; Lassila, L.V.J.; Vallittu, P.K.; Kleverlaan, C.J.; Feilzer, A.J.; De Moor, R.J.G.
2015-01-01
The aim of this study was to evaluate the influence of different framework materials on biomechanical behaviour of anterior two-unit cantilever resin-bonded fixed dental prostheses (RBFDPs). A three-dimensional finite element model of a two-unit cantilever RBFDP replacing a maxillary lateral incisor
Energy Technology Data Exchange (ETDEWEB)
Weitzman, Morley
1992-07-15
A three-dimensional finite-element code was developed and used to simulate the flow of groundwater towards an excavation in a saturated porous medium, allowing for seepage faces. An iterative procedure was used to predict the movement of the water table and the seepage flux. The numerical solution agreed well with experimental results from a sandbox experiment. (auth)
Finite-size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model
Colomé-Tatché, M.; Matveenko, S.I.; Shlyapnikov, G.V.
2010-01-01
We study finite-size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two types of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due
Keulemans, F.; Shinya, A.; Lassila, L.V.J.; Vallittu, P.K.; Kleverlaan, C.J.; Feilzer, A.J.; De Moor, R.J.G.
2015-01-01
The aim of this study was to evaluate the influence of different framework materials on biomechanical behaviour of anterior two-unit cantilever resin-bonded fixed dental prostheses (RBFDPs). A three-dimensional finite element model of a two-unit cantilever RBFDP replacing a maxillary lateral incisor
Perlov, Leo
2016-01-01
In this paper we find all possible finite dimensional representations and corresponding values of the Barbero-Immirzi parameter contained in the two solutions of the simplicity constraints. It turns out that for each non-zero pure imaginary with rational modulus value of the Barbero-Immirzi parameter $\\gamma = i \\frac{p}{q}, p, q \\in Z, p, q \
Finite-size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model
Colomé-Tatché, M.; Matveenko, S.I.; Shlyapnikov, G.V.
2010-01-01
We study finite-size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two types of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due
Bouchoule, I.; Szigeti, S. S.; Davis, M. J.; Kheruntsyan, K. V.
2016-11-01
We develop a finite-temperature hydrodynamic approach for a harmonically trapped one-dimensional quasicondensate and apply it to describe the phenomenon of frequency doubling in the breathing-mode oscillations of the quasicondensate momentum distribution. The doubling here refers to the oscillation frequency relative to the oscillations of the real-space density distribution, invoked by a sudden confinement quench. By constructing a nonequilibrium phase diagram that characterizes the regime of frequency doubling and its gradual disappearance, we find that this crossover is governed by the quench strength and the initial temperature rather than by the equilibrium-state crossover from the quasicondensate to the ideal Bose gas regime. The hydrodynamic predictions are supported by the results of numerical simulations based on a finite-temperature c -field approach and extend the utility of the hydrodynamic theory for low-dimensional quantum gases to the description of finite-temperature systems and their dynamics in momentum space.
Nonrelativistic quantum X-ray physics
Hau-Riege, Stefan P
2015-01-01
Providing a solid theoretical background in photon-matter interaction, Nonrelativistic Quantum X-Ray Physics enables readers to understand experiments performed at XFEL-facilities and x-ray synchrotrons. As a result, after reading this book, scientists and students will be able to outline and perform calculations of some important x-ray-matter interaction processes. Key features of the contents are that the scope reaches beyond the dipole approximation when necessary and that it includes short-pulse interactions. To aid the reader in this transition, some relevant examples are discussed in detail, while non-relativistic quantum electrodynamics help readers to obtain an in-depth understanding of the formalisms and processes. The text presupposes a basic (undergraduate-level) understanding of mechanics, electrodynamics, and quantum mechanics. However, more specialized concepts in these fields are introduced and the reader is directed to appropriate references. While primarily benefiting users of x-ray light-sou...
Institute of Scientific and Technical Information of China (English)
Ran SHEN; Yu Cai SU
2007-01-01
We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenberg-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series).
Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions
Energy Technology Data Exchange (ETDEWEB)
Carpenter, D.C.
1997-04-01
Recent advances have been made in the use of p-type finite element method (FEM) for structural and fluid dynamics problems that hold promise for reactor physics problems. These advances include using hierarchic shape functions, element-by-element iterative solvers and more powerful mapping techniques. Use of the hierarchic shape functions allows greater flexibility and efficiency in implementing energy-dependent flux expansions and incorporating localized refinement of the solution space. The irregular matrices generated by the p-type FEM can be solved efficiently using element-by-element conjugate gradient iterative solvers. These solvers do not require storage of either the global or local stiffness matrices and can be highly vectorized. Mapping techniques based on blending function interpolation allow exact representation of curved boundaries using coarse element grids. These features were implemented in a developmental two-dimensional neutron diffusion program based on the use of hierarchic shape functions (FEM2DH). Several aspects in the effective use of p-type analysis were explored. Two choices of elemental preconditioning were examined--the proper selection of the polynomial shape functions and the proper number of functions to use. Of the five shape function polynomials tested, the integral Legendre functions were the most effective. The serendipity set of functions is preferable over the full tensor product set. Two global preconditioners were also examined--simple diagonal and incomplete Cholesky. The full effectiveness of the finite element methodology was demonstrated on a two-region, two-group cylindrical problem but solved in the x-y coordinate space, using a non-structured element grid. The exact, analytic eigenvalue solution was achieved with FEM2DH using various combinations of element grids and flux expansions.
Esmail, Enas; Hassan, Noha; Kadah, Yasser
2010-02-01
In this study, three-dimensional (3D) finite element analysis was used to model the effect of the peri-implant bone geometry and thickness on the biomechanical behavior of a dental implant/supporting bone system. The 3D finite element model of the jaw bone, cancellous and cortical, was developed based on computerized tomography (CT) scan technology while the dental implant model was created based on a commercially available implant design. Two models, cylindrical and threaded, representing the peri-implant bone region were simulated. In addition, various thicknesses (0.1 mm, 0.3 mm, 0.5 mm) of the peri-implant bone region were modeled to account for the misalingnment during the drilling process. Different biomechanical properties of the peri-implant bone region were used to simulate the progression of the osseointegration process with time. Four stages of osseointegration were modeled to mimic different phases of tissue healing of the peri- implant region starting with soft connective tissue and ending with complete bone maturation. For the realistic threaded model of the peri-implant bone region, the maximum von Mises stress and displacement in the dental implant and jaw bone were higher than those computed for the simple cylindrical peri-implant bone region model. The average von Mises stress and displacement in the dental implant and the jaw bone decreased as the oseeointegration progressed with time for all thicknesses of the peri-implant bone region. On the other hand, the maximum absolute vertical displacement of the dental implant increased as the drilled thickness of the peri-implant bone region increased.
Directory of Open Access Journals (Sweden)
Rajkiran Chitumalla
2012-01-01
Full Text Available Aims: The aim of the study was to evaluate the stress distribution patterns in teeth and supporting structures of fixed prosthesis and design modifications in a fixed prosthesis with either normal or reduced bone support of an additional abutment. Study was also undertaken to disprove Ante′s law. Materials and Methods: Main models and variations of main models (modification 1, 2, 3, 4, 5, 6, 7, 8 were subjected to 200 N at angulations of 90° and 15° on functional cusps. Results for each loading were obtained as stress distribution color images and numerical values were recorded. A three-dimensional finite element analysis study of variations of normal models was performed using two finite element softwares, namely PRO-Engineer wildfire version 1.0 manufacturer: Parametric technology corporation, Needham, MA 02494 U.S.A. Results: When periodontal compromised abutment teeth was splinted with an additional abutment an increase of stress was observed in periodontally compromised abutments so an additional abutment is not required. Eventhough the pericemental area of compromised abutments with an additional abutment (canine was more than the combined pericemental area of pontics to be replaced, stress generated was more on abutments. This disproves Ante′s law. Hence, it may be a reference, but should not be the ultimate criterion in determining the number of multiple abutments. Conclusions: When periodontal compromised abutment teeth was splinted with an additional abutment an increase of stress was observed in periodontally compromised abutments so an additional abutment is not required. Even though the pericemental area of compromised abutments with an additional abutment (canine was more than combined pericemental area of pontics to be replaced, stress generated was more on abutments. This disproves Ante′s law. Hence, it may be a reference, but should not be the ultimate criterion in determining the number of multiple abutments.
A Three-Dimensional Finite Element Analysis of Displaced Intra-Articular Calcaneal Fractures.
Xu, Can; Liu, Hua; Li, Mingqing; Wang, Chenggong; Li, Kanghua
A better understanding of displaced intra-articular calcaneal fractures, their effect on joint mechanics, and the relationship between altered mechanics and osteoarthritis could aid in the development or refinement of treatment methods. Finite element modeling is accepted as the reference standard for evaluating joint contact stresses. The objective of the present study was to analyze the in vivo joint mechanical data from finite element modeling for normal and injured subtalar joints. A 3-dimensional model of the ankle-hindfoot was developed and validated. Both height loss and width increases in the calcaneus were simulated. Next, they were used to investigate the relationship between calcaneal height or width and the contact mechanics of the posterior facet of the subtalar joint. The contact area/joint area ratio increased in the subtalar joint with injury when the calcaneal width increased. Moreover, the peak contact pressure and the proportion of the area under high contact pressure (>6 MPa) increased. The contact area/joint area ratio decreased with reduced calcaneal height, but the peak contact pressure remained almost constant. The width increases of the calcaneus somewhat limited the subtalar joint motion, especially for eversion; however, the height loss mostly resulted in subtalar rotatory instability. The height loss diminished the subtalar joint's stability in eversion, internal rotation, and external rotation. The results of the present study support the advisability of surgery for these complex injuries. Reestablishing the calcaneal height and width could restore the normal kinematics and contact stress distribution in the subtalar joint, improve the tibiotalar position, and diminish long-term degeneration in the ankle.
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Stress analysis in platform-switching implants: a 3-dimensional finite element study.
Pellizzer, Eduardo Piza; Verri, Fellippo Ramos; Falcón-Antenucci, Rosse Mary; Júnior, Joel Ferreira Santiago; de Carvalho, Paulo Sérgio Perri; de Moraes, Sandra Lúcia Dantas; Noritomi, Pedro Yoshito
2012-10-01
The aim of this study was to evaluate the influence of the platform-switching technique on stress distribution in implant, abutment, and peri-implant tissues, through a 3-dimensional finite element study. Three 3-dimensional mandibular models were fabricated using the SolidWorks 2006 and InVesalius software. Each model was composed of a bone block with one implant 10 mm long and of different diameters (3.75 and 5.00 mm). The UCLA abutments also ranged in diameter from 5.00 mm to 4.1 mm. After obtaining the geometries, the models were transferred to the software FEMAP 10.0 for pre- and postprocessing of finite elements to generate the mesh, loading, and boundary conditions. A total load of 200 N was applied in axial (0°), oblique (45°), and lateral (90°) directions. The models were solved by the software NeiNastran 9.0 and transferred to the software FEMAP 10.0 to obtain the results that were visualized through von Mises and maximum principal stress maps. Model A (implants with 3.75 mm/abutment with 4.1 mm) exhibited the highest area of stress concentration with all loadings (axial, oblique, and lateral) for the implant and the abutment. All models presented the stress areas at the abutment level and at the implant/abutment interface. Models B (implant with 5.0 mm/abutment with 5.0 mm) and C (implant with 5.0 mm/abutment with 4.1 mm) presented minor areas of stress concentration and similar distribution pattern. For the cortical bone, low stress concentration was observed in the peri-implant region for models B and C in comparison to model A. The trabecular bone exhibited low stress that was well distributed in models B and C. Model A presented the highest stress concentration. Model B exhibited better stress distribution. There was no significant difference between the large-diameter implants (models B and C).
Sheer, F J; Swarts, J D; Ghadiali, S N
2012-06-01
A primary etiological factor underlying chronic middle ear disease is an inability to open the collapsible Eustachian tube (ET). However, the structure-function relationships responsible for ET dysfunction in patient populations at risk for developing otitis media (OM) are not known. In this study, three-dimensional (3D) finite element (FE) modeling techniques were used to investigate how changes in biomechanical and anatomical properties influence opening phenomena in three populations: normal adults, young children and infants with cleft palate. Histological data was used to create anatomically accurate models and FE techniques were used to simulate tissue deformation and ET opening. Lumen dilation was quantified using a computational fluid dynamic (CFD) technique and a sensitivity analysis was performed to ascertain the relative importance of the different anatomical and tissue mechanical properties. Results for adults suggest that ET function is highly sensitive to tensor veli palatini muscle (TVPM) forces and to periluminal mucosal tissue (PMT) elasticity. Young children and cleft palate subjects exhibited reduced sensitivity to TVPM forces while changes in PMT stiffness continued to have a significant impact on ET function. These results suggest that reducing PMT stiffness might be an effective way to restore ET function in these populations. Varying TVPM force vector relationships via changes in hamulus location had no effect on ET opening in young children and cleft palate subjects but did alter force transmission to the ET lumen during conditions of elevated adhesion. These models have therefore provided important new insights into the biomechanical mechanisms responsible for ET dysfunction.
Two-dimensional finite elements model for boron management in agroforestry sites.
Tayfur, Gokmen; Tanji, Kenneth K; Baba, Alper
2010-01-01
Agroforesty systems, which are recommended as a management option to lower the shallow groundwater level and to reuse saline subsurface drainage waters from the tile-drained croplands in the drainage-impacted areas of Jan Joaquin Valley of California, have resulted in excessive boron buildup in the soil root zone. To assess the efficacy of the long-term impacts of soil boron buildup in agroforesty systems, a mathematical model was developed to simulate non-conservative boron transport. The developed dynamic two-dimensional finite element model simulates water flow and boron transport in saturated-unsaturated soil system, including boron sorption and boron uptake by root-water extraction processes. The simulation of two different observed field data sets by the developed model is satisfactory, with mean absolute error of 1.5 mg/L and relative error of 6.5%. Application of the model to three different soils shows that boron adsorption is higher in silt loam soil than that in sandy loam and clay loam soils. This result agrees with the laboratory experimental observations. The results of the sensitivity analysis indicate that boron uptake by root-water extraction process influences the boron concentration distribution along the root zone. Also, absorption coefficient and maximum adsorptive capacity of a soil for boron are found to be sensitive parameters.
Tooth displacement due to occlusal contacts: a three-dimensional finite element study.
Gomes de Oliveira, S; Seraidarian, P I; Landre, J; Oliveira, D D; Cavalcanti, B N
2006-12-01
The use of the Finite Element Method (FE) is an appropriate way to study occlusal forces and tooth movement. The purpose of this study was to evaluate the effects of different occlusal contact patterns on tooth displacement in an adult dentition using a three-dimensional FE model of a human maxilla and mandible. Initially, images of a computerized tomography scan were redrawn in a computer program (CATIA) followed by the FE mesh construction. The MSC/Patran software was used to develop the FE mesh comprising 520,445 elements and 106,633 nodes. The MSC/Nastran program was utilized as pre and post-processor for all mathematical calculations necessary to evaluate dental and mandibular biomechanics. Four occlusal patterns were tested: FEM 1 - standard occlusal contacts; FEM 2 - removal of mesial marginal and mesial tripoidism contacts; FEM 3 - removal of distal marginal and distal tripoidism contacts; FEM 4 - similar to FEM 3 with added contacts between upper and lower incisors. Small changes in the standard distribution of occlusal contacts resulted in an imbalance of occlusal forces and changes in dental positioning. All simulations tested showed mesial displacement of posterior teeth. The most significant changes were registered in the model presenting unstable occlusal contacts when the anterior teeth were in occlusion (FEM 4). These findings may explain mandibular incisors crowding and maxillary incisors flaring as a result of small variations in dental contacts.
Humphries, Stanley; Johnson, Kristin; Rick, Kyle; Liu, Zheng-jun; Goldberg, S. Nahum
2005-04-01
ETherm3 is a finite-element software suite for simulations of electrosurgery and RF thermal ablation processes. Program components cover the complete calculation process from mesh generation to solution analysis. The solutions employ three-dimensional conformal meshes to handle cluster probes and other asymmetric assemblies. The conformal-mesh approach is essential for high-accuracy surface integrals of net electrode currents. ETherm3 performs coupled calculations of RF electric fields in conductive dielectrics and thermal transport via dynamic solutions of the bioheat equation. The boundary-value RF field solution is updated periodically to reflect changes in material properties. ETherm3 features advanced material models with the option for arbitrary temperature variations of thermal and electrical conductivity, perfusion rate, and other quantities. The code handles irreversible changes by switching the material reference of individual elements at specified transition temperatures. ETherm3 is controlled through a versatile interpreter language to enable complex run sequences. The code can automatically maintain constant current or power, switch to different states in response to temperature or impedance information, and adjust parameters on the basis of user-supplied control functions. In this paper, we discuss the physical basis and novel features of the code suite and review application examples.
Phase transitions at finite temperature and dimensional reduction for fermions and bosons
Kocic, Aleksandar
1995-01-01
In a recent Letter we discussed the fact that large-N expansions and computer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Neveu model is mean field theory. This was seen to be a counterexample to the standard 'sigma model' scenario which predicts the 2D Ising model universality class. In this article we present more evidence, both theoretical and numerical, that this result is correct. We develop a physical picture for our results and discuss the width of the scaling region (Ginzburg criterion), 1/N corrections, and differences between the dynamics of BCS superconductors and Gross-Neveu models. Lattices as large as 12 \\times 72^2 are simulated for both the N=12 and N=4 cases and the numerical evidence for mean field scaling is quite compelling. We point out that the amplitude ratio for the model's susceptibility is a particulartly good observable for distinguishing between the dimensional reduction and the mean field sceneri...
International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
Tutschke, W; Yang, C
2004-01-01
There is almost no field in Mathematics which does not use Mathe matical Analysis. Computer methods in Applied Mathematics, too, are often based on statements and procedures of Mathematical Analysis. An important part of Mathematical Analysis is Complex Analysis because it has many applications in various branches of Mathematics. Since the field of Complex Analysis and its applications is a focal point in the Vietnamese research programme, the Hanoi University of Technology organized an International Conference on Finite or Infinite Dimensional Complex Analysis and Applications which took place in Hanoi from August 8 - 12, 2001. This conference th was the 9 one in a series of conferences which take place alternately in China, Japan, Korea and Vietnam each year. The first one took place th at Pusan University in Korea in 1993. The preceding 8 conference was th held in Shandong in China in August 2000. The 9 conference of the was the first one which took place above mentioned series of conferences in Vietnam....
Institute of Scientific and Technical Information of China (English)
Xian-Qian Wu; Xi Wang; Yan-Peng Wei; Hong-Wei Song; Chen-Guang Huang
2012-01-01
Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and resistance to corrosion fatigue,cracking,etc.Compressive residual stress and dent profile are important factors to evaluate the effectiveness of shot peening process.In this paper,the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated.Firstly,dimensionless relations of processing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were deduced by dimensional analysis method.Secondly,the influence of each dimensionless parameter on dimensionless variables was investigated by the finite element method.Furthermore,related empirical formulas were given for each dimensionless parameter based on the simulation results.Finally,comparison was made and good agreement was found between the simulation results and the empirical formula,which shows that a useful approach is provided in this paper for analyzing the influence of each individual parameter.
Li, Zuoping; Alonso, Jorge E; Kim, Jong-Eun; Davidson, James S; Etheridge, Brandon S; Eberhardt, Alan W
2006-09-01
Three-dimensional finite element (FE) models of human pubic symphyses were constructed from computed tomography image data of one male and one female cadaver pelvis. The pubic bones, interpubic fibrocartilaginous disc and four pubic ligaments were segmented semi-automatically and meshed with hexahedral elements using automatic mesh generation schemes. A two-term viscoelastic Prony series, determined by curve fitting results of compressive creep experiments, was used to model the rate-dependent effects of the interpubic disc and the pubic ligaments. Three-parameter Mooney-Rivlin material coefficients were calculated for the discs using a heuristic FE approach based on average experimental joint compression data. Similarly, a transversely isotropic hyperelastic material model was applied to the ligaments to capture average tensile responses. Linear elastic isotropic properties were assigned to bone. The applicability of the resulting models was tested in bending simulations in four directions and in tensile tests of varying load rates. The model-predicted results correlated reasonably with the joint bending stiffnesses and rate-dependent tensile responses measured in experiments, supporting the validity of the estimated material coefficients and overall modeling approach. This study represents an important and necessary step in the eventual development of biofidelic pelvis models to investigate symphysis response under high-energy impact conditions, such as motor vehicle collisions.
A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids
Energy Technology Data Exchange (ETDEWEB)
Bungartz, H.J. [Technische Universitaet Muenchen (Germany)
1996-12-31
In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.
Temperature Distribution of Three-Dimensional Photovoltaic Panel by Using Finite Element Simulation
Directory of Open Access Journals (Sweden)
Leow Wai Zhe
2016-10-01
Full Text Available The low electricity performance of a photovoltaic (PV panel has been concerned in the PV application system. The effect of environmental and operating condition was affected the performance of the PV panel. In this research work, the main objective is to perform a three-dimensional geometry model of monocrystalline silicon PV panel with and without cooling system by using finite element method. In the case of a cooling system, the effect of the Direct Current (DC fan flow rate on the temperature distribution of PV panel was investigated. The electrical behaviour of this PV panel is obtained based on the average temperature of the PV panel obtained and average solar irradiance from site location. According to the experimental results, PV panel with cooling system can be significant to provide better performance than the PV panel without cooling system in the same environmental condition. For the effect of flow rate of DC fan in the PV panel with cooling system, the performance of this PV panel has been improved as increasing in flow rate of DC fan.
Hano, Mitsuo; Hotta, Masashi
A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.
Dobson, C A; Sisias, G; Phillips, R; Fagan, M J; Langton, C M
2006-04-01
Stereolithography (STL) models of complex cancellous bone structures have been produced from three-dimensional micro-computed tomography data sets of human cancellous bone histological samples from four skeletal sites. The STL models have been mechanically tested and the derived stiffness compared with that predicted by finite element analysis. The results show a strong correlation (R2 = 0.941) between the predicted and calculated stiffnesses of the structures and show promise for the use of STL as an additional technique to complement the use of finite element models, for the assessment of the mechanical properties of complex cancellous bone structures.
Finite element analysis of three dimensional crack growth by the use of a boundary element sub model
DEFF Research Database (Denmark)
Lucht, Tore
2009-01-01
A new automated method to model non-planar three dimensional crack growth is proposed which combines the advantages of both the boundary element method and the finite element method. The proposed method links the two methods by a submodelling strategy in which the solution of a global finite...... element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering...
Mir-Kasimov, R M
1994-01-01
The concept of the one -- dimensional quantum mechanics in the relativistic configurational space (RQM) is reviewed briefly. The Relativistic Schroedinger equation (RSE) arising here is the finite -- difference equation with the step equal to the Compton wave length of the particle. The different generalizations of the Dirac -- Infeld-- Hall factorizarion method for this case are constructed. This method enables us to find out all possible finite-difference generalizations of the most important nonrelativistic integrable case -- the harmonic oscillator. As it was shown in \\cite{kmn},\\cite{mir6} the case of RQM the harmonic oscillator = q -- oscillator. It is also shown that the relativistic and nonrelativistic QM's are different representations of the same theory. The transformation connecting these two representations is found in explicit form. It could be considered as the generalization of the Kontorovich -- Lebedev transformation.
Holographic energy loss in non-relativistic backgrounds
Atashi, Mahdi; Farahbodnia, Mitra
2016-01-01
In this paper, we study some aspects of energy loss in non-relativistic theories from holography. We analyze the energy lost by a rotating heavy point particle along a circle of radius $l$ with angular velocity $\\omega$ in theories with general dynamical exponent $z$ and hyperscaling violation exponent $\\theta$. It is shown that this problem provides a novel perspective on the energy loss in such theories. A general computation at zero and finite temperature is done and it is shown that how the total energy loss rate depends non-trivially on two characteristic exponents $(z,\\theta)$. We find that at zero temperature there is a special radius $l_c$ where the energy loss is independent of different values of $(z,\\theta)$. Also, there is a crossover between a regime in which the energy loss is dominated by the linear drag force and by the radiation because of the acceleration of the rotating particle. We discover different behaviors at finite temperature case.
Kastening, Boris
2012-10-01
Anisotropy effects on the finite-size critical behavior of a two-dimensional Ising model on a general triangular lattice in an infinite-strip geometry with periodic, antiperiodic, and free boundary conditions (bc) in the finite direction are investigated. Exact results are obtained for the scaling functions of the finite-size contributions to the free energy density. With ξ(>) the largest and ξ(temperature near criticality, we find that the dependence of these functions on the ratio ξ() and on the angle parametrizing the orientation of the correlation volume is of geometric nature. Since the scaling functions are independent of the particular microscopic realization of the anisotropy within the two-dimensional Ising model, our results provide a limited verification of universality. We explain our observations by considering finite-size scaling of free energy densities of general weakly anisotropic models on a d-dimensional film (i.e., in an L×∞(d-1) geometry) with bc in the finite direction that are invariant under a shear transformation relating the anisotropic and isotropic cases. This allows us to relate free energy scaling functions in the presence of an anisotropy to those of the corresponding isotropic system. We interpret our results as a simple and transparent case of anisotropic universality, where, compared to the isotropic case, scaling functions depend additionally on the shape and orientation of the correlation volume. We conjecture that this universality extends to cases where the geometry and/or the bc are not invariant under the shear transformation and argue in favor of validity of two-scale factor universality for weakly anisotropic systems.
Finite-size scaling relations for a four-dimensional Ising model on Creutz cellular automatons
Merdan, Z.; Güzelsoy, E.
2011-06-01
The four-dimensional Ising model is simulated on Creutz cellular automatons using finite lattices with linear dimensions 4 ≤ L ≤ 8. The temperature variations and finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for 7, 14, and 21 independent simulations. Approximate values for the critical temperature of the infinite lattice of Tc(∞) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without the logarithmic factor), 6.6921(22) (without the logarithmic factor), 6.6909(2) (without the logarithmic factor), 6.6822(13) (with the logarithmic factor), 6.6819(11) (with the logarithmic factor), and 6.6808(8) (with the logarithmic factor) are obtained from the intersection points of the specific heat curves, the Binder parameter curves, and straight line fits of specific heat maxima for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the results, 6.6802(1) and 6.6808(8), are in very good agreement with the results of a series expansion of Tc(∞), 6.6817(15) and 6.6802(2), the dynamic Monte Carlo value Tc(∞) = 6.6803(1), the cluster Monte Carlo value Tc(∞) = 6.680(1), and the Monte Carlo value using the Metropolis-Wolff cluster algorithm Tc(∞) = 6.6802632 ± 5 . 10-5. The average values calculated for the critical exponent of the specific heat are α =- 0.0402(15), - 0.0393(12), - 0.0391(11) with 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the result, α =- 0.0391(11), agrees with the series expansions result, α =- 0.12 ± 0.03 and the Monte Carlo result using the Metropolis-Wolff cluster algorithm, α ≥ 0 ± 0.04. However, α =- 0.0391(11) is inconsistent with the renormalization group prediction of α = 0.
Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
Griffin, Tom; Horava, Petr; Yan, Ziqi
2015-01-01
Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion $\\omega\\sim k^n$ ($n=2,3,\\ldots$), whose naturalness is protected by polynomial shift symmetries. Here we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of $n$ changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem.
Chen, Yung-Chuan; Tu, Yuan-Kun; Zhuang, Jun-Yan; Tsai, Yi-Jung; Yen, Cheng-Yo; Hsiao, Chih-Kun
2017-03-28
A three-dimensional dynamic elastoplastic finite element model was constructed and experimentally validated and was used to investigate the parameters which influence bone temperature during drilling, including the drill speed, feeding force, drill bit diameter, and bone density. Results showed the proposed three-dimensional dynamic elastoplastic finite element model can effectively simulate the temperature elevation during bone drilling. The bone temperature rise decreased with an increase in feeding force and drill speed, however, increased with the diameter of drill bit or bone density. The temperature distribution is significantly affected by the drilling duration; a lower drilling speed reduced the exposure duration, decreases the region of the thermally affected zone. The constructed model could be applied for analyzing the influence parameters during bone drilling to reduce the risk of thermal necrosis. It may provide important information for the design of drill bits and surgical drilling powers.
Energy Technology Data Exchange (ETDEWEB)
Kim, K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Petersson, N. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rodgers, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-10-25
Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examples and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.
Energy Technology Data Exchange (ETDEWEB)
Kulak, R. F.; Fiala, C.
1980-03-01
This report presents the formulations used in the NEPTUNE code. Specifically, it describes the finite-element formulation of a three-dimensional hexahedral element for simulating the behavior of either fluid or solid continua. Since the newly developed hexahedral element and the original triangular plate element are finite elements, they are compatible in the sense that they can be combined arbitrarily to simulate complex reactor components in three-dimensional space. Because rate-type constitutive relations are used in conjunction with a velocity-strain tensor, the formulation is applicable to large deformation problems. This development can be used to simulate (1) the fluid adjacent to reactor components and (2) the concrete fill found in large reactor head closures.
DEFF Research Database (Denmark)
Domadiya, Parthkumar Gandalal; Manconi, Elisabetta; Vanali, Marcello
2016-01-01
vibration and noise transmission. The aim of this paper is to investigate, numerically and experimentally, stop-bands in periodic one-dimensional structures. Two methods for pre-dicting stop-bands are described: the first method applies to infinite periodic structures using a wave approach; the second...... method deals with the evaluation of a vibration level difference (VLD) in a finite periodic structure embedded within an infinite one-dimensional waveguide. This VLD is defined to predict the performance in terms of noise and vibration insulation of periodic cells embedded in an otherwise uniform...
Energy Technology Data Exchange (ETDEWEB)
Lee, Kyoung Soo; Kim, Man Won; Lee, Sung Ho [KHNP Central Research Institute, Daejeon (Korea, Republic of)
2013-01-15
Numerous dissimilar metal welds are used to connect carbon steel and stainless steel in nuclear power plants. Recently, some cracks have occurred in the dissimilar metal welds, and welding residual stress is considered as a contributing factor to the cracks. In this study, welding residual stresses in dissimilar butt weld piping were evaluated by the 3-dimensional (3-D) finite element method. Welding residual stresses along the circumference of heat affected zones as well as weld regions were obtained through the analysis, which could not be obtainable with 2-dimensional (2-D) analysis. The differences between 2-D analysis and 3-D analysis are presented in this paper.
Mass of nonrelativistic meson from leading twist distribution amplitudes
Energy Technology Data Exchange (ETDEWEB)
Braguta, V. V., E-mail: braguta@mail.ru [Institute for High Energy Physics (Russian Federation)
2011-01-15
In this paper distribution amplitudes of pseudoscalar and vector nonrelativistic mesons are considered. Using equations of motion for the distribution amplitudes, relations are derived which allow one to calculate the masses of nonrelativistic pseudoscalar and vector meson if the leading twist distribution amplitudes are known. These relations can be also rewritten as relations between the masses of nonrelativistic mesons and infinite series of QCD operators, what can be considered as an exact version of Gremm-Kapustin relation in NRQCD.
Institute of Scientific and Technical Information of China (English)
LIU Yu-zeng; HAI Yong; ZHAO Hui
2012-01-01
Background Given that three-dimensional finite element models have been successfully used to analyze biomechanics in orthopedics-related research,this study aimed to establish a finite element model of the pelvic bone and three-fin acetabular component and evaluate biomechanical changes in this model after implantation of a three-fin acetabular prosthesis in a superior segmental bone defect of the acetabulum.Methods In this study,three-dimensional finite element models of the pelvic bone and three-fin acetabular component were first established.The prosthesis model was characterized by three different conformational fins to facilitate and optimize the prosthetic design.The spongy and cortical bones were evaluated using a different modulus of elasticity in this established model.Results The maximum and minimum von Mises stresses on the fins of the acetabular component were 15.2 and 0.74,respectively.The maximum and minimum micromotion between the three-fin acetabular component and the acetabulum bone interface were 27 and 13 μm,respectively.A high primary stability and implied better clinical outcome were revealed.Conclusion Finite element analysis may be an optimal strategy for biomechanics-related research of prosthetic design for segmental acetabular bone defects.
Institute of Scientific and Technical Information of China (English)
Chaojun Yan; Wenbiao Peng; Haijun Li
2007-01-01
@@ The alternate-direction implicit finite difference beam propagation method (FD-BPM) is used to analyze the two-dimensional (2D) symmetrical multimode interference (MMI) couplers. The positions of the images at the output plane and the length of multimode waveguide are accurately determined numerically. In order to reduce calculation time, the parallel processing of the arithmetic is implemented by the message passing interface and the simulation is accomplished by eight personal computers.
Energy Technology Data Exchange (ETDEWEB)
He, Pei-Song, E-mail: hepeisong@th.btbu.edu.cn; Zhao, Jia; Geng, Ai-Cong; Xu, Deng-Hui; Hu, Rong
2013-11-01
We prove that in a two-dimensional homogeneous boson system with Rashba spin–orbit coupling, Bose–Einstein condensate with plane-wave order is unstable at finite temperature. The calculations are based on a nonlinear sigma model scheme. The density wave contributions to the thermal deletions are divergent in the infrared limit. The behavior of the divergence is different from that without spin–orbit coupling.
Mehanee, Salah; Zhdanov, Michael
2004-12-01
Numerical modeling of the quasi-static electromagnetic (EM) field in the frequency domain in a three-dimensional (3-D) inhomogeneous medium is a very challenging problem in computational physics. We present a new approach to the finite difference (FD) solution of this problem. The FD discretization of the EM field equation is based on the balance method. To compute the boundary values of the anomalous electric field we solve for, we suggest using the fast and accurate quasi-analytical (QA) approximation, which is a special form of the extended Born approximation. We call this new condition a quasi-analytical boundary condition (QA BC). This approach helps to reduce the size of the modeling domain without losing the accuracy of calculation. As a result, a larger number of grid cells can be used to describe the anomalous conductivity distribution within the modeling domain. The developed numerical technique allows application of a very fine discretization to the area with anomalous conductivity only because there is no need to move the boundaries too far from the inhomogeneous region, as required by the traditional Dirichlet or Neumann conditions for anomalous field with boundary values equal to zero. Therefore this approach increases the efficiency of FD modeling of the EM field in a medium with complex structure. We apply the QA BC and the traditional FD (with large grid and zero BC) methods to complicated models with high resistivity contrast. The numerical modeling demonstrates that the QA BC results in 5 times matrix size reduction and 2-3 times decrease in computational time.
Development of a Three-Dimensional Finite Element Chest Model for the 5(th) Percentile Female.
Kimpara, Hideyuki; Lee, Jong B; Yang, King H; King, Albert I; Iwamoto, Masami; Watanabe, Isao; Miki, Kazuo
2005-11-01
Several three-dimensional (3D) finite element (FE) models of the human body have been developed to elucidate injury mechanisms due to automotive crashes. However, these models are mainly focused on 50(th) percentile male. As a first step towards a better understanding of injury biomechanics in the small female, a 3D FE model of a 5(th) percentile female human chest (FEM-5F) has been developed and validated against experimental data obtained from two sets of frontal impact, one set of lateral impact, two sets of oblique impact and a series of ballistic impacts. Two previous FE models, a small female Total HUman Model for Safety (THUMS-AF05) occupant version 1.0Beta (Kimpara et al. 2002) and the Wayne State University Human Thoracic Model (WSUHTM, Wang 1995 and Shah et al. 2001) were integrated and modified for this model development. The model incorporated not only geometrical gender differences, such as location of the internal organs and structure of the bony skeleton, but also the biomechanical differences of the ribs due to gender. It includes a detailed description of the sternum, ribs, costal cartilage, thoracic spine, skin, superficial muscles, intercostal muscles, heart, lung, diaphragm, major blood vessels and simplified abdominal internal organs and has been validated against a series of six cadaveric experiments on the small female reported by Nahum et al. (1970), Kroell et al. (1974), Viano (1989), Talantikite et al. (1998) and Wilhelm (2003). Results predicted by the model were well-matched to these experimental data for a range of impact speeds and impactor masses. More research is needed in order to increase the accuracy of predicting rib fractures so that the mechanisms responsible for small female injury can be more clearly defined.
Three-dimensional finite element analysis of the foot during standing--a material sensitivity study.
Cheung, Jason Tak-Man; Zhang, Ming; Leung, Aaron Kam-Lun; Fan, Yu-Bo
2005-05-01
Information on the internal stresses/strains in the human foot and the pressure distribution at the plantar support interface under loading is useful in enhancing knowledge on the biomechanics of the ankle-foot complex. While techniques for plantar pressure measurements are well established, direct measurement of the internal stresses/strains is difficult. A three-dimensional (3D) finite element model of the human foot and ankle was developed using the actual geometry of the foot skeleton and soft tissues, which were obtained from 3D reconstruction of MR images. Except the phalanges that were fused, the interaction among the metatarsals, cuneiforms, cuboid, navicular, talus, calcaneus, tibia and fibula were defined as contact surfaces, which allow relative articulating movement. The plantar fascia and 72 major ligaments were simulated using tension-only truss elements by connecting the corresponding attachment points on the bone surfaces. The bony and ligamentous structures were embedded in a volume of soft tissues. The encapsulated soft tissue was defined as hyperelastic, while the bony and ligamentous structures were assumed to be linearly elastic. The effects of soft tissue stiffening on the stress distribution of the plantar surface and bony structures during balanced standing were investigated. Increases of soft tissue stiffness from 2 and up to 5 times the normal values were used to approximate the pathologically stiffened tissue behaviour with increasing stages of diabetic neuropathy. The results showed that a five-fold increase in soft tissue stiffness led to about 35% and 33% increase in the peak plantar pressure at the forefoot and rearfoot regions, respectively. This corresponded to about 47% decrease in the total contact area between the plantar foot and the horizontal support surface. Peak bone stress was found at the third metatarsal in all calculated cases with a minimal increase of about 7% with soft tissue stiffening.
Analysis of 3-dimensional finite element after reconstruction of impaired ankle deltoid ligament.
Ji, Yunhan; Tang, Xianzhong; Li, Yifan; Xu, Wei; Qiu, Wenjun
2016-12-01
We compared four repair techniques for impaired ankle ligament deltoideum, namely Wiltberger, Deland, Kitaoka and Hintermann using a 3-dimensional finite element. We built an ankle ligament deltoideum model, including six pieces of bone structures, gristles and main ligaments around the ankle. After testing the model, we built an impaired ligament deltoideum model plus four reconstruction models. Subsequently, different levels of force on ankles with different flexion were imposed and ankle biomechanics were compared. In the course of bending, from plantar flexion 20° to back flexion 20°, the extortion of talus decreased while the eversion increased. Four reconstruction models failed to bring back the impaired ankle to normal, with an obvious increase of extortion and eversion. The Kitaoka technique was useful to reduce the extortion angle in a consequential manner. Compared with the other three techniques, the Kitaoka technique produced better results for extortion angle and the difference was statistically significant. However, in case of eversion, there was no significant difference among the four techniques (P>0.05). Lateral ligament's stress in all the four models was different from the normal one. When the ankle was imposed with extortion moment of force, stress of anterior talofibular ligament with the Kitaoka reconstruction method was close to that of the complete deltoid ligament. When ankle was imposed with eversion moment of force, stress of anterior talofibular ligament with Kitaoka and Deland reconstruction methods were close to that of the complete deltoid ligament. We concluded that Kitaoka and Deland tendon reconstruction technique could recover impaired ankle deltoid ligament and re-established its normal biomechanics characteristics.
Energy Technology Data Exchange (ETDEWEB)
Parvan, A.S. [Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation); Horia Hulubei National Institute of Physics and Nuclear Engineering, Department of Theoretical Physics, Bucharest (Romania); Moldova Academy of Sciences, Institute of Applied Physics, Chisinau (Moldova, Republic of)
2015-09-15
In the present paper, the Tsallis statistics in the grand canonical ensemble was reconsidered in a general form. The thermodynamic properties of the nonrelativistic ideal gas of hadrons in the grand canonical ensemble was studied numerically and analytically in a finite volume and the thermodynamic limit. It was proved that the Tsallis statistics in the grand canonical ensemble satisfies the requirements of the equilibrium thermodynamics in the thermodynamic limit if the thermodynamic potential is a homogeneous function of the first order with respect to the extensive variables of state of the system and the entropic variable z = 1/(q - 1) is an extensive variable of state. The equivalence of canonical, microcanonical and grand canonical ensembles for the nonrelativistic ideal gas of hadrons was demonstrated. (orig.)
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
Németh, Z A
1997-01-01
The interaction of a spin 1/2 particle (described by the non-relativistic "Dirac" equation of Lévy-Leblond) with Chern-Simons gauge fields is studied. It is shown, that similarly to the four dimensional spinor models, there is a consistent possibility of coupling them also by axial or chiral type currents. Static self dual vortex solutions together with a vortex-lattice are found with the new couplings.
Energy shift of interacting non-relativistic fermions in noncommutative space
Directory of Open Access Journals (Sweden)
A. Jahan
2005-06-01
Full Text Available A local interaction in noncommutative space modifies to a non-local one. For an assembly of particles interacting through the contact potential, formalism of the quantum field theory makes it possible to take into account the effect of modification of the potential on the energy of the system. In this paper we calculate the energy shift of an assembly of non-relativistic fermions, interacting through the contact potential in the presence of the two-dimensional noncommutativity.
H-VERSION ADAPTIVE FINITE ELEMENT METHOD FOR THREE-DIMENSIONAL SEEPAGE PROBLEM
Institute of Scientific and Technical Information of China (English)
Feng Xue-min; Chen Sheng-hong
2003-01-01
The h-version adaptive finite element method for 3-D seepage problem is presented in this paper.The adaptive system includes 4 modules: 3-D mesh generation, finite element analysis for 3-D seepage, mesh error estimation and post-process.The effectiveness of this system is verified by the given example.
Institute of Scientific and Technical Information of China (English)
张秀玲
1999-01-01
A method of approaching to the infinite-dimensional linear operators by the finite-dimensional operators is discussed. It is shown that,for every infinite-dimensional operator A and every natural number n,there exists an n-dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n-dimensional optimal approximations to be unique is obtained.
Karatolios, Konstantinos; Wittek, Andreas; Nwe, Thet Htar; Bihari, Peter; Shelke, Amit; Josef, Dennis; Schmitz-Rixen, Thomas; Geks, Josef; Maisch, Bernhard; Blase, Christopher; Moosdorf, Rainer; Vogt, Sebastian
2013-11-01
Aortic wall strains are indicators of biomechanical changes of the aorta due to aging or progressing pathologies such as aortic aneurysm. We investigated the potential of time-resolved three-dimensional ultrasonography coupled with speckle-tracking algorithms and finite element analysis as a novel method for noninvasive in vivo assessment of aortic wall strain. Three-dimensional volume datasets of 6 subjects without cardiovascular risk factors and 2 abdominal aortic aneurysms were acquired with a commercial real time three-dimensional echocardiography system. Longitudinal and circumferential strains were computed offline with high spatial resolution using a customized commercial speckle-tracking software and finite element analysis. Indices for spatial heterogeneity and systolic dyssynchrony were determined for healthy abdominal aortas and abdominal aneurysms. All examined aortic wall segments exhibited considerable heterogenous in-plane strain distributions. Higher spatial resolution of strain imaging resulted in the detection of significantly higher local peak strains (p ≤ 0.01). In comparison with healthy abdominal aortas, aneurysms showed reduced mean strains and increased spatial heterogeneity and more pronounced temporal dyssynchrony as well as delayed systole. Three-dimensional ultrasound speckle tracking enables the analysis of spatially highly resolved strain fields of the aortic wall and offers the potential to detect local aortic wall motion deformations and abnormalities. These data allow the definition of new indices by which the different biomechanical properties of healthy aortas and aortic aneurysms can be characterized. Copyright © 2013 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.
Jiang, Zhongzheng; Zhao, Wenwen
2016-01-01
Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computational model, namely the nonlinear coupled constitutive relations(NCCR),was developed by R.S.Myong and applied successfully to one-dimensional shock wave structure and two-dimensional rarefied flows. In this paper, finite volume schemes, including LU-SGS time advance scheme, MUSCL interpolation and AUSMPW+ scheme, are fistly adopted to investigate NCCR model's validity and potential in three-dimensional complex hypersonic rarefied gas flows. Moreover, in order to solve the computational stability problems in 3D complex flows,a modified solution is developed for the NCCR model. Finally, the modified solu...
Atluri, S. N.; Nakagaki, M.; Kathiresan, K.
1980-01-01
In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.
Three-dimensional finite element analyses of the local mechanical behavior of riveted lap joints
Iyer, Kaushik Arjunan
Three-dimensional elastic-plastic finite element models of single and double rivet-row lap joints have been developed to evaluate local distortions and the mechanics of airframe-type 7075-T6 aluminum alloy riveted assemblies. Loading induced distortion features such as the excess assembly compliance, rivet tilt, local in- and out-of-plane slips and stress concentration factors are evaluated as functions of rivet countersinking, rivet material and friction coefficient. Computed features are examined to identify alterations in the proportions of in-plane and out-of-plane load transmission across rivet-panel interfaces and isolate global and lower-order effects present in the complex response of these multi-body assemblies. Analytical procedures are validated by comparing calculated and measured values of excess assembly compliance and local panel bending. Direct out-of-plane load transmission between the rivet heads and panels affects global deformation features such as remote panel bending and local features such as the panel stress concentration factor. The increase in stress concentration due to panel bending is self-limiting owing to decreasing in-plane load bearing with increasing rivet tilt, which is a composite reflection of the basic rivet deformation modes of shear and rotation. Calculations have also been performed to define approximate steady-state fretting fatigue conditions that lead to crack initiation at a panel hole surface in single and double rivet-row assemblies for countersunk and non-countersunk rivets. These account for and isolate effects of interference and clamping forces on fatigue performance by comparing computed circumferential variations of bulk residual stresses, cyclic stress range and mean stress. With interference, a non-countersunk assembly is shown to be as prone to crack initiation as a countersunk assembly. Frictional work due to fretting is evaluated and the physical location of fretting fatigue crack initiation is predicted by
Vachiratienchai, Chatchai; Siripunvaraporn, Weerachai
2013-02-01
For efficient inversion code, the forward modeling routine, the sensitivity calculation, and the inversion algorithm must be efficient. Here, the hybrid finite difference-finite element algorithm, which is fast and accurate even when the slope of the topography is greater than 45°, is used as the forward modeling routine to calculate the responses. The sensitivity calculation is adapted from the most efficient adjoint Green's function technique. Both of these algorithms are then driven with the data space Occam's inversion. This combination of modules makes it possible to obtain an efficient inversion code based on MATLAB for two-dimensional direct current (DC) resistivity data. To demonstrate its efficiency, numerical experiments with our code and with commercial software are performed on synthetic data and real field data collected in the western part of Thailand where limestone and cavities dominate the region. In general, our code takes substantially longer than the commercial code to run but converges to a solution with a lower misfit. The result shows that the efficiency of our code makes it practical for real field surveys.
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Parsons, T.
2002-01-01
The M = 7.8 1906 San Francisco earthquake cast a stress shadow across the San Andreas fault system, inhibiting other large earthquakes for at least 75 years. The duration of the stress shadow is a key question in San Francisco Bay area seismic hazard assessment. This study presents a three-dimensional (3-D) finite element simulation of post-1906 stress recovery. The model reproduces observed geologic slip rates on major strike-slip faults and produces surface velocity vectors comparable to geodetic measurements. Fault stressing rates calculated with the finite element model are evaluated against numbers calculated using deep dislocation slip. In the finite element model, tectonic stressing is distributed throughout the crust and upper mantle, whereas tectonic stressing calculated with dislocations is focused mostly on faults. In addition, the finite element model incorporates postseismic effects such as deep afterslip and viscoelastic relaxation in the upper mantle. More distributed stressing and postseismic effects in the finite element model lead to lower calculated tectonic stressing rates and longer stress shadow durations (17-74 years compared with 7-54 years). All models considered indicate that the 1906 stress shadow was completely erased by tectonic loading no later than 1980. However, the stress shadow still affects present-day earthquake probability. Use of stressing rate parameters calculated with the finite element model yields a 7-12% reduction in 30-year probability caused by the 1906 stress shadow as compared with calculations not incorporating interactions. The aggregate interaction-based probability on selected segments (not including the ruptured San Andreas fault) is 53-70% versus the noninteraction range of 65-77%.
Shalkhauser, Kurt A.; Bartos, Karen F.; Fite, E. B.; Sharp, G. R.
1992-01-01
Current research in high-efficiency, high-performance traveling wave tubes (TWT's) has led to the development of novel thermal/mechanical computer models for use with helical slow-wave structures. A three-dimensional, finite element computer model and analytical technique used to study the structural integrity and thermal operation of a high-efficiency, diamond-rod, K-band TWT designed for use in advanced space communications systems. This analysis focused on the slow-wave circuit in the radiofrequency section of the TWT, where an inherent localized heating problem existed and where failures were observed during earlier cold compression, or 'coining' fabrication technique that shows great potential for future TWT development efforts. For this analysis, a three-dimensional, finite element model was used along with MARC, a commercially available finite element code, to simulate the fabrication of a diamond-rod TWT. This analysis was conducted by using component and material specifications consistent with actual TWT fabrication and was verified against empirical data. The analysis is nonlinear owing to material plasticity introduced by the forming process and also to geometric nonlinearities presented by the component assembly configuration. The computer model was developed by using the high efficiency, K-band TWT design but is general enough to permit similar analyses to be performed on a wide variety of TWT designs and styles. The results of the TWT operating condition and structural failure mode analysis, as well as a comparison of analytical results to test data are presented.
CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION
Institute of Scientific and Technical Information of China (English)
Benyu Guo; Songnian He; Heping Ma
2002-01-01
A mixed Chebyshev spectral-finite element method is proposed for solving two-dimensionalunsteady Navier-Stokes equation. The generalized stability and convergence are proved.The numerical results show the advantages of this method.
Nonrelativistic effective field theory for axions
Braaten, Eric; Mohapatra, Abhishek; Zhang, Hong
2016-10-01
Axions can be described by a relativistic field theory with a real scalar field ϕ whose self-interaction potential is a periodic function of ϕ . Low-energy axions, such as those produced in the early Universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field ψ whose effective potential is a function of ψ*ψ . We determine the coefficients in the expansion of the effective potential to fifth order in ψ*ψ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to truncate the expansion of the effective potential in powers of ψ*ψ , we develop a sequence of systematically improvable approximations to the effective potential that resum terms of all orders in ψ*ψ .
Vortex dynamics in nonrelativistic Abelian Higgs model
Directory of Open Access Journals (Sweden)
A.A. Kozhevnikov
2015-11-01
Full Text Available The dynamics of the gauge vortex with arbitrary form of a contour is considered in the framework of the nonrelativistic Abelian Higgs model, including the possibility of the gauge field interaction with the fermion asymmetric background. The equations for the time derivatives of the curvature and the torsion of the vortex contour generalizing the Betchov–Da Rios equations in hydrodynamics, are obtained. They are applied to study the conservation of helicity of the gauge field forming the vortex, twist, and writhe numbers of the vortex contour. It is shown that the conservation of helicity is broken when both terms in the equation of the vortex motion are present, the first due to the exchange of excitations of the phase and modulus of the scalar field and the second one due to the coupling of the gauge field forming the vortex, with the fermion asymmetric background.
Thermal quantum electrodynamics of nonrelativistic charged fluids.
Buenzli, Pascal R; Martin, Philippe A; Ryser, Marc D
2007-04-01
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for nonrelativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems, which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It still has the r(-6) decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.
Thermal quantum electrodynamics of nonrelativistic charged fluids
Buenzli, Pascal R.; Martin, Philippe A.; Ryser, Marc D.
2007-04-01
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for nonrelativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems, which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It still has the r-6 decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.
Microscopic picture of non-relativistic classicalons
Energy Technology Data Exchange (ETDEWEB)
Berkhahn, Felix; Müller, Sophia; Niedermann, Florian; Schneider, Robert, E-mail: felix.berkhahn@physik.lmu.de, E-mail: sophia.x.mueller@physik.uni-muenchen.de, E-mail: florian.niedermann@physik.lmu.de, E-mail: robert.bob.schneider@physik.uni-muenchen.de [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 Munich (Germany)
2013-08-01
A theory of a non-relativistic, complex scalar field with derivatively coupled interaction terms is investigated. This toy model is considered as a prototype of a classicalizing theory and in particular of general relativity, for which the black hole constitutes a prominent example of a classicalon. Accordingly, the theory allows for a non-trivial solution of the stationary Gross-Pitaevskii equation corresponding to a black hole in the case of GR. Quantum fluctuations on this classical background are investigated within the Bogoliubov approximation. It turns out that the perturbative approach is invalidated by a high occupation of the Bogoliubov modes. Recently, it was proposed that a black hole is a Bose-Einstein condensate of gravitons that dynamically ensures to stay at the verge of a quantum phase transition. Our result is understood as an indication for that claim. Furthermore, it motivates a non-linear numerical analysis of the model.
Nonrelativistic Quantum Mechanics with Fundamental Environment
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
Nonrelativistic Effective Field Theory for Axions
Braaten, Eric; Zhang, Hong
2016-01-01
Axions can be described by a relativistic field theory with a real scalar field $\\phi$ whose self-interaction potential is a periodic function of $\\phi$. Low-energy axions, such as those produced in the early universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field $\\psi$ whose effective potential is a function of $\\psi^*\\psi$. We determine the coefficients in the expansion of the effective potential to fifth order in $\\psi^*\\psi$ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to expand the effective potential in powers of $\\psi^*\\psi$, we develop a sequence of systematically improvable approximations to the effective potential that include terms of all orders in $\\psi^*\\psi$.
Gravity duals for nonrelativistic conformal field theories.
Balasubramanian, Koushik; McGreevy, John
2008-08-08
We attempt to generalize the anti-de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.
Finite Size Scaling and "perfect" actions the three dimensional Ising model
Ballesteros, H G; Martín-Mayor, V; Muñoz-Sudupe, A
1998-01-01
Using Finite-Size Scaling techniques, we numerically show that the first irrelevant operator of the lattice $\\lambda\\phi^4$ theory in three dimensions is (within errors) completely decoupled at $\\lambda=1.0$. This interesting result also holds in the Thermodynamical Limit, where the renormalized coupling constant shows an extraordinary reduction of the scaling-corrections when compared with the Ising model. It is argued that Finite-Size Scaling analysis can be a competitive method for finding improved actions.
Bonabi, Farzad; Pedersen, Thomas G.
2017-04-01
The dipole moment formalism for the optical response of finite electronic structures breaks down in infinite ones, for which a momentum-based method is better suited. Focusing on simple chain structures, we compare the linear and nonlinear optical response of finite and infinite one-dimensional semiconductors. This comparison is then extended to cases including strong electro-static fields breaking translational invariance. For large electro-static fields, highly non-perturbative Franz–Keldysh (FK) features are observed in both linear and nonlinear spectra. It is demonstrated that dipole and momentum formalisms agree in the limit of large structures provided the intraband momentum contributions are carefully treated. This convergence is established even in the presence of non-perturbative electro-static fields.
Directory of Open Access Journals (Sweden)
P. V. Bulat
2015-07-01
Full Text Available One-dimensional unsteady gas dynamics problems are revealing tests for the accuracy estimation of numerical solution with respect to simulation of supersonic flows of inviscid compressible gas. Numerical solution of Euler equations describing flows of inviscid compressible gas and conceding continuous and discontinuous solutions is considered. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes. The numerical solutions computed are compared with the exact solution of Riemann problem. Monotonic correction of derivatives makes possible avoiding new extremes and ensures monotonicity of the numerical solution near the discontinuity, but it leads to the smoothness of the existing minimums and maximums and to the accuracy loss. Calculations with the use of WENO schemes give the possibility for obtaining accurate and monotonic solution with the presence of weak and strong gas dynamical discontinuities.
Horowitz, A; Sheinman, I; Lanir, Y; Perl, M; Sideman, S
1988-02-01
A two-dimensional incompressible plane-stress finite element is formulated for the simulation of the passive-state mechanics of thin myocardial strips. The formulation employs a total Lagrangian and materially nonlinear approach, being based on a recently proposed structural material law, which is derived from the histological composition of the tissue. The ensuing finite element allows to demonstrate the mechanical properties of a single myocardial layer containing uniformly directed fibers by simulating various loading cases such as tension, compression and shear. The results of these cases show that the fiber direction is considerably stiffer than the cross-fiber direction, that there is significant coupling between these two directions, and that the shear stiffness of the tissue is lower than its tensile and compressive stiffness.
Energy Technology Data Exchange (ETDEWEB)
Maker, B.N.
1995-04-14
This report provides a user`s manual for NIKE3D, a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Over twenty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a factorization method, for which case bandwidth minimization is optional. Data may be stored either in or out of core memory to allow for large analyses.
Energy Technology Data Exchange (ETDEWEB)
Stone, C.M.
1997-07-01
SANTOS is a finite element program designed to compute the quasistatic, large deformation, inelastic response of two-dimensional planar or axisymmetric solids. The code is derived from the transient dynamic code PRONTO 2D. The solution strategy used to compute the equilibrium states is based on a self-adaptive dynamic relaxation solution scheme, which is based on explicit central difference pseudo-time integration and artificial mass proportional damping. The element used in SANTOS is a uniform strain 4-node quadrilateral element with an hourglass control scheme to control the spurious deformation modes. Finite strain constitutive models for many common engineering materials are included. A robust master-slave contact algorithm for modeling sliding contact is implemented. An interface for coupling to an external code is also provided. 43 refs., 22 figs.
Energy Technology Data Exchange (ETDEWEB)
Zhu Jiuyun (Department of Physics, Hunan Normal University, Hunan 410006 (China)); Kuang Leman (Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin 300071 (China) Department of Physics and Institute of Physics, Hunan Normal University, Hunan 410081 (China))
1994-10-03
The even and odd coherent states (CSs) of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are constructed and some properties of these states are studied. Their quadrature squeezing and amplitude-squared squeezing are investigated in detail. It is shown that, while the squeezing behaviour of the even and odd CSs of the FDHSHO approaches that of the even and odd CSs of the usual harmonic oscillator as the dimension of the Hilbert space tends to infinity, this behaviour is nontrivally different if the dimension of the Hilbert space is finite. In the latter case, it is found that the even and odd CSs exhibit both amplitude-squared squeezing and quadrature squeezing. ((orig.))
Energy Technology Data Exchange (ETDEWEB)
Santhanam, Thalanayar S [Department of Physics Saint Louis University, Missouri, MO 63103 (United States); Santhanam, Balu [Department of Electrical and Computer Engineering, MSC01 1100 1, University of New Mexico Albuquerque, NM 87131-0001 (United States)], E-mail: santhats@slu.edu, E-mail: bsanthan@ece.unm.edu
2009-05-22
Quantum mechanics of a linear harmonic oscillator in a finite-dimensional Hilbert space satisfying the correct equations of motion is studied. The connections to Weyl's formulation of the algebra of bounded unitary operators in finite space as well as to a truncated quantized linear harmonic oscillator are discussed. It is pointed out that the discrete Fourier transformation (DFT) plays a central role in determining the actual form of the position, the momentum, the number and the Hamiltonian operators. The explicit form of these operators in different bases is exhibited for some low values of the dimension of the Hilbert space. In this formulation, it is shown that the Hamiltonian is indeed the logarithm of the DFT and that by modifying Weyl's framework to include position and momentum operators with non-uniformly spaced spectra the equations of motion are satisfied.
Kim, Kyungmok; Géringer, Jean; 10.1177/0954411911422843
2012-01-01
This paper describes a two-dimensional (2D) finite element simulation for fracture and fatigue behaviours of pure alumina microstructures such as those found at hip prostheses. Finite element models are developed using actual Al2O3 microstructures and a bilinear cohesive zone law. Simulation conditions are similar to those found at a slip zone in a dry contact between a femoral head and an acetabular cup of hip prosthesis. Contact stresses are imposed to generate cracks in the models. Magnitudes of imposed stresses are higher than those found at the microscopic scale. Effects of microstructures and contact stresses are investigated in terms of crack formation. In addition, fatigue behaviour of the microstructure is determined by performing simulations under cyclic loading conditions. It is shown that crack density observed in a microstructure increases with increasing magnitude of applied contact stress. Moreover, crack density increases linearly with respect to the number of fatigue cycles within a given con...
Deng, Yongbo; Korvink, Jan G.
2016-05-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
Deng, Yongbo; Korvink, Jan G
2016-05-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
Korvink, Jan G.
2016-01-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766
Vörtler, Horst L; Schäfer, Katja; Smith, William R
2008-04-17
We study the simulation cell size dependence of chemical potential isotherms in subcritical square-well fluids by means of series of canonical ensemble Monte Carlo simulations with increasing numbers of particles, for both three-dimensional bulk systems and two-dimensional planar layers, using Widom-like particle insertion methods. By estimating the corresponding vapor/liquid coexistence densities using a Maxwell-like equal area rule for the subcritical chemical potential isotherms, we are able to study the influence of system size not only on chemical potentials but also on the coexistence properties. The chemical potential versus density isotherms show van der Waals-like loops in the subcritical vapor/liquid coexistence range that exhibit distinct finite size effects for both two- and three-dimensional fluids. Generally, in agreement with recent findings for related studies of Lennard-Jones fluids, the loops shrink with increasing number of particles. In contrast to the subcritical isotherms themselves, the equilibrium vapor/liquid densities show only a weak system size dependence and agree quantitatively with the best-known literature values for three-dimensional fluids. This allows our approach to be used to accurately predict the phase coexistence properties. Our resulting phase equilibrium results for two-dimensional square-well fluids are new. Knowledge concerning finite size effects of square-well systems is important not only for the simulation of thermodynamic properties of simple fluids, but also for the simulation of models of more complex fluids (such as aqueous or polymer fluids) involving square-well interactions.
Agarwal, Sumit; Briant, Clyde L.; Krajewski, Paul E.; Bower, Allan F.; Taleff, Eric M.
2007-04-01
A finite element method was recently designed to model the mechanisms that cause superplastic deformation (A.F. Bower and E. Wininger, A Two-Dimensional Finite Element Method for Simulating the Constitutive Response and Microstructure of Polycrystals during High-Temperature Plastic Deformation, J. Mech. Phys. Solids, 2004, 52, p 1289-1317). The computations idealize the solid as a collection of two-dimensional grains, separated by sharp grain boundaries. The grains may deform plastically by thermally activated dislocation motion, which is modeled using a conventional crystal plasticity law. The solid may also deform by sliding on the grain boundaries, or by stress-driven diffusion of atoms along grain boundaries. The governing equations are solved using a finite element method, which includes a front-tracking procedure to monitor the evolution of the grain boundaries and surfaces in the solid. The goal of this article is to validate these computations by systematically comparing numerical predictions to experimental measurements of the elevated-temperature response of aluminum alloy AA5083 (M.-A. Kulas, W.P. Green, E.M. Taleff, P.E. Krajewski, and T.R. McNelley, Deformation Mechanisms in Superplastic AA5083 materials. Metall. Mater. Trans. A, 2005, 36(5), p 1249-1261). The experimental work revealed that a transition occurs from grain-boundary sliding to dislocation (solute-drag) creep at approximately 0.001/s for temperatures between 425 and 500 °C. In addition, increasing the grain size from 7 to 10 μm decreased the transition to significantly lower strain rates. Predictions from the finite element method accurately predict the effect of grain size on the transition in deformation mechanisms.
From Clifford Algebra of Nonrelativistic Phase Space to Quarks and Leptons of the Standard Model
Żenczykowski, Piotr
2015-01-01
We review a recently proposed Clifford-algebra approach to elementary particles. We start with: (1) a philosophical background that motivates a maximally symmetric treatment of position and momentum variables, and: (2) an analysis of the minimal conceptual assumptions needed in quark mass extraction procedures. With these points in mind, a variation on Born's reciprocity argument provides us with an unorthodox view on the problem of mass. The idea of space quantization suggests then the linearization of the nonrelativistic quadratic form ${\\bf p}^2 +{\\bf x}^2$ with position and momentum satisfying standard commutation relations. This leads to the 64-dimensional Clifford algebra ${Cl}_{6,0}$ of nonrelativistic phase space within which one identifies the internal quantum numbers of a single Standard Model generation of elementary particles (i.e. weak isospin, hypercharge, and color). The relevant quantum numbers are naturally linked to the symmetries of macroscopic phase space. It is shown that the obtained pha...
Chang, Weng-Long; Ren, Ting-Ting; Feng, Mang
2015-01-01
In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finite-dimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertex-cover problem is completed.
Energy Technology Data Exchange (ETDEWEB)
Neumann, A.U.; Derrida, B.
1988-10-01
We study the time evolution of two configurations submitted to the same thermal noise for several two dimensional models (Ising ferromagnet, symmetric spin glass, non symmetric spin glass). For all these models, we find a non zero critical temperature above which the two configurations always meet. Using finite size scaling ideas, we determine for these three models this dynamical phase transition and some of the critical exponents. For the ferromagnet, the transition T/sub c/ approx. = 2.25 coincides with the Curie temperature whereas for the two spin glass models +- J distribution of bonds) we obtain T/sub c/ approx. = 1.5-1.7.
Directory of Open Access Journals (Sweden)
Vineet K. Srivastava
2014-03-01
Full Text Available In this paper, an implicit logarithmic finite difference method (I-LFDM is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.
Finite size dependence of scaling functions of the three dimensional O(4) model in an external field
Engels, J
2014-01-01
We calculate universal finite size scaling functions for the order parameter and the longitudinal susceptibility of the three-dimensional O(4) model. The phase transition of this model is supposed to be in the same universality class as the chiral transition of two-flavor QCD. The scaling functions serve as a testing device for QCD simulations on small lattices, where, for example, pseudocritical temperatures are difficult to determine. In addition, we have improved the infinite volume limit parametrization of the scaling functions by using newly generated high statistics data for the 3d O(4) model in the high temperature region on an L=120 lattice.
Institute of Scientific and Technical Information of China (English)
YUAN; Yirang
2006-01-01
For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method,multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.
Nonrelativistic gauged quantum mechanics: From Kaluza–Klein compactifications to Bargmann structures
Energy Technology Data Exchange (ETDEWEB)
Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co
2015-08-14
Highlights: • Null compactification techniques are used to derive the nonrelativistic gauged Schrödinger equation. • Compactification of both Klein–Gordon and Maxwell theories are revisited. • Connections with Kaluza–Klein-like Bargmann frameworks are established. - Abstract: The Schrödinger equation for a spinless particle in presence of an external electromagnetic field is derived by means of null compactification of five dimensional massless Klein–Gordon theory and five–dimensional Maxwell electrodynamics. Connections with Kaluza–Klein-like Bargmann frameworks are established.
Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence
Lopez-Arcos, Cristhiam; Murugan, Jeff; Nastase, Horatiu
2016-05-01
We consider the nonrelativistic limit of the abelian reduction of the massive ABJM model proposed in [1], obtaining a supersymmetric version of the Jackiw-Pi model. The system exhibits an mathcal{N}=2 Super-Schrödinger symmetry with the Jackiw-Pi vortices emerging as BPS solutions. We find that this (2 + 1)-dimensional abelian field theory is dual to a certain (3+1)-dimensional gravity theory that differs somewhat from previously considered abelian condensed matter stand-ins for the ABJM model. We close by commenting on progress in the top-down realization of the AdS/CMT correspondence in a critical string theory.
Kring, J.; Gyekenyesi, J.; Mendelson, A.
1977-01-01
The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement fields in finite geometry bars containing central, surface, and double-edge cracks under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Normal stresses and the stress intensity factor variation along the crack periphery are calculated using the obtained displacement field. The reported results demonstrate the usefulness of this method in calculating stress intensity factors for commonly encountered crack geometries in finite solids.
One spatial dimensional finite volume three-body interaction for a short-range potential
Guo, Peng
2016-01-01
In this work, we use McGuire's model to describe scattering of three spinless identical particles in one spatial dimension, we first present analytic solutions of Faddeev's equation for scattering of three spinless particles in free space. The three particles interaction in finite volume is derived subsequently, and the quantization conditions by matching wave functions in free space and finite volume are presented in terms of two-body scattering phase shifts. The quantization conditions obtained in this work for short range interaction are L\\"uscher's formula like and consistent with Yang's results in \\cite{Yang:1967bm}.
Institute of Scientific and Technical Information of China (English)
LIU Wei; YANG Jun; TIAN Jing
2012-01-01
A three-dimensional time-domain algorithm, which is based on tile augmented KZK （Khokhlov-Zabolotskaya-Kuznetsov） equation, is proposed to simulate the nonlinear field of the parametric array. First, KZK equation is transformed into TBE （Transformed beam equation）. Then, the effects of diffraction （in parabolic approximation）, thermoviscous absorption, relax- ation, and nonlinearity are solved with finite difference methods. The numerical results of this code agree well with the theoretical and experimental results presented in previous studies, which demonstrates the validity of the three-dimensional algorithm. Using this code to calcu- late the nonlinear field of the parametric array in air, it is found that the small time interval is important to the accuracy of the simulation results of the difference frequency wave in the case of high sound pressure level, and the errors caused by taking relaxation absorption for thermoviscous absorption are influenced by the characteristic frequency.
Energy Technology Data Exchange (ETDEWEB)
Jiaxing, Cheng; Dongfa, Sheng [Southwest Forestry University, Yunnan (China)
2017-05-15
As an important supplement and development to crystallography, the applications about quasicrystal materials have played a core role in many fields, such as manufacturing and the space industry. Due to the sensitivity of quasicrystals to defects, the research on the fracture problem of quasicrystals has attracted a great deal of attention. We present a boundary collocation method to research fracture problems for a finite dimension rectangular one-dimensional hexagonal quasicrystal plate. Because mode I and mode II problems for one- dimensional hexagonal quasicrystals are like that for the classical elastic materials, only the anti-plane problem is discussed in this paper. The correctness of the present numerical method is verified through a comparison of the present results and the existing results. And then, the size effects on stress field, stress intensity factor and energy release rate are discussed in detail. The obtained results can provide valuable references for the fracture behavior of quasicrystals.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The mathematical model of the semiconductor device of heat conduction has been described by a system of four equations. The optimal order estimates in L2 norm are derived for the error in the approximates solution, putting forward a kind of characteristic finite difference fractional step methods.
Finite size scaling analysis of intermittency moments in the two dimensional Ising model
Burda, Z; Peschanski, R; Wosiek, J
1993-01-01
Finite size scaling is shown to work very well for the block variables used in intermittency studies on a 2-d Ising lattice. The intermittency exponents so derived exhibit the expected relations to the magnetic critical exponent of the model. Email contact: pesch@amoco.saclay.cea.fr
NEW ERROR EXPANSION FOR ONE-DIMENSIONAL FINITE ELEMENTS AND ULTRACONVERGENCE
Institute of Scientific and Technical Information of China (English)
Chen Chuanmiao; Xie Ziqing; Liu Jinghong
2005-01-01
Based on an improved orthogonal expansion in an element, a new error expression of n-degree finite element approximation uh to two-point boundary value problem is derived, and then superconvergence of two order for both function and derivatives are obtained.
Non-relativistic particles in a thermal bath
Directory of Open Access Journals (Sweden)
Vairo Antonio
2014-04-01
Full Text Available Heavy particles are a window to new physics and new phenomena. Since the late eighties they are treated by means of effective field theories that fully exploit the symmetries and power counting typical of non-relativistic systems. More recently these effective field theories have been extended to describe non-relativistic particles propagating in a medium. After introducing some general features common to any non-relativistic effective field theory, we discuss two specific examples: heavy Majorana neutrinos colliding in a hot plasma of Standard Model particles in the early universe and quarkonia produced in heavy-ion collisions dissociating in a quark-gluon plasma.
Covariant geometric quantization of non-relativistic Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the Schrodinger representation of V^*Q. We show that this quantization is equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R, that makes the quantum algebra of non-relativistic mechanics an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra, which provides quantum evolution in non-relativistic mechanics as a parallel transport along time.
New approach to nonrelativistic diffeomorphism invariance and its applications
Banerjee, Rabin
2015-01-01
A comprehensive account of a new structured algorithm for obtaining nonrelativistic diffeomorphism invariances in both space and spacetime by gauging the Galilean symmetry in a generic nonrelativistic field theoretical model is provided. % where the original (global) symmetry is localised. Various applications like the obtention of nonrelativistic diffeomorphism invariance, the introduction of Chern-Simons term and its role in fractional quantum Hall effect, induction of diffeomorphism in irrotational fluid model, abstraction of Newton-Cartan geometry and the emergence of Horava-Lifshitz gravity are discussed in details.
Manos, T
2015-01-01
We study the quantum kicked rotator in the classically fully chaotic regime $K=10$ and for various values of the quantum parameter $k$ using Izrailev's $N$-dimensional model for various $N \\le 3000$, which in the limit $N \\rightarrow \\infty$ tends to the exact quantized kicked rotator. By numerically calculating the eigenfunctions in the basis of the angular momentum we find that the localization length ${\\cal L}$ for fixed parameter values has a certain distribution, in fact its inverse is Gaussian distributed, in analogy and in connection with the distribution of finite time Lyapunov exponents of Hamilton systems. However, unlike the case of the finite time Lyapunov exponents, this distribution is found to be independent of $N$, and thus survives the limit $N=\\infty$. This is different from the tight-binding model of Anderson localization. The reason is that the finite bandwidth approximation of the underlying Hamilton dynamical system in the Shepelyansky picture (D.L. Shepelyansky, {\\em Phys. Rev. Lett.} {...
Gonzales, Matthew J; Sturgeon, Gregory; Krishnamurthy, Adarsh; Hake, Johan; Jonas, René; Stark, Paul; Rappel, Wouter-Jan; Narayan, Sanjiv M; Zhang, Yongjie; Segars, W Paul; McCulloch, Andrew D
2013-07-01
High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 mm, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology. Copyright © 2013 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Arunachalam Sangeetha
2012-01-01
Full Text Available Context: To understand the effect of masticatory and parafunctional forces on the integrity of the prosthesis and the underlying cement layer. Aims: The purpose of this study was to evaluate the stress pattern in the cement layer and the fixed prosthesis, on subjecting a three-dimensional finite element model to simulated occlusal loading. Materials and Methods: Three-dimensional finite element model was simulated to replace missing mandibular first molar with second premolar and second molar as abutments. The model was subjected to a range of occlusal loads (20, 30, 40 MPa in two different directions - vertical and 30° to the vertical. The cements (zinc phosphate, polycarboxylate, glass ionomer, and composite were modeled with two cement thicknesses - 25 and 100 μm. Stresses were determined in certain reference points in fixed prosthesis and the cement layer. Statistical Analysis Used: The stress values are mathematic calculations without variance; hence, statistical analysis is not routinely required. Results: Stress levels were calculated according to Von Mises criteria for each node. Maximum stresses were recorded at the occlusal surface, axio-gingival corners, followed by axial wall. The stresses were greater with lateral load and with 100-μm cement thickness. Results revealed higher stresses for zinc phosphate cement, followed by composites. Conclusions: The thinner cement interfaces favor the success of the prosthesis. The stresses in the prosthesis suggest rounding of axio-gingival corners and a well-established finish line as important factors in maintaining the integrity of the prosthesis.
Institute of Scientific and Technical Information of China (English)
DAI Fu-hong; ZHANG Bo-ming; DU Shan-yi
2008-01-01
A three-dimensional finite element analysis of process-induced residual stress in resin transfer mold-ing (RTM) process is presented. The finite element method ( FEM ) was employed to solve the coupled equa-tions involved in the transient heat transfer and the cure kinetics of the resin, and the distributions of internal temperature and cure degree of the composite at any instant time were obtained. The self-consistent field micro-mechanics model was used to predict the cure-dependent mechanical properties of the composites. Thermal ex-pansion and cure shrinkage were included in the analysis. The thermo-elastie mechanical governing equationswere solved using the incremental stress-strain relationship based FEM and the residual stress development was predicted. The present results were validated by the comparisons with the pertinent literature. The numerical example of a half cylinder was presented. The results show that it is necessary to carry out the three-dimensional analysis due to the complex distributions of temperatures, cure degrees and process-induced stress for thick parts, which can be predicted at any point within composite structures in the present analysis.
Lu, Shijun; Wang, Zhendong; Ni, Xiaoyu; Wang, Lin
2013-02-01
To reconstruct a three-dimensional nonlinear finite element model of mandibular teeth with three-pieces segment arch, and analyze the mechanical properties of intrusive arch and the biomechanical characteristics of three-pieces segment arch. Three-dimensional nonlinear finite element model of mandible with three-pieces segment arch was reconstructed by multi-slice spiral CT scanning, Mimics, CATIA and Anasys software. Then, the mechanical properties of intrusive arch, the movement trend and stress distribution of three-pieces segment arch were calculated by Anasys software. In the range of 5 degrees-25 degrees, with the degree of intrusive arch increased, the force of intrusive arch also increased rapidly. The maximal force was 0.604 8 N in 30 degrees; the force was about 0.59 N in 30 degrees-65 degrees range. In condition of three-pieces segment arch mechanics, lateral incisor tipped labially and intruded; the first moral tipped distally and rotating; other teeth did not move clearly. The largest stress distribution in the whole arch was in the one-third labial cervical area of the lateral incisor root and the root bifurcations of first moral. Under an appropriate intrusive force, three-pieces segment arch can intrude incisors and control the extrusion of posterior teeth. It can be used to correct the deep overbite, especially with high mandibular planes, gummy smile or adult patients.
Joshi, Shrikrishna Nandkishor; Bolar, Gururaj
2017-06-01
Control of part deflection and deformation during machining of low rigidity thin-wall components is an important aspect in the manufacture of desired quality products. This paper presents a comparative study on the effect of geometry constraints on the product quality during machining of thin-wall components made of an aerospace alloy aluminum 2024-T351. Three-dimensional nonlinear finite element (FE) based simulations of machining of thin-wall parts were carried out by considering three variations in the wall constraint viz. free wall, wall constrained at one end, and wall with constraints at both the ends. Lagrangian formulation based transient FE model has been developed to simulate the interaction between the workpiece and helical milling cutter. Johnson-Cook material and damage model were adopted to account for material behavior during machining process; damage initiation and chip separation. A modified Coulomb friction model was employed to define the contact between the cutting tool and the workpiece. The numerical model was validated with experimental results and found to be in good agreement. Based on the simulation results it was noted that deflection and deformation were maximum in the thin-wall constrained at one end in comparison with those obtained in other cases. It was noted that three dimensional finite element simulations help in a better way to predict the product quality during precision manufacturing of thin-wall components.
A Finite-Element Solution of the Navier-Stokes Equations for Two-Dimensional and Axis-Symmetric Flow
Directory of Open Access Journals (Sweden)
Sven Ø. Wille
1980-04-01
Full Text Available The finite element formulation of the Navier-Stokes equations is derived for two-dimensional and axis-symmetric flow. The simple triangular, T6, isoparametric element is used. The velocities are interpolated by quadratic polynomials and the pressure is interpolated by linear polynomials. The non-linear simultaneous equations are solved iteratively by the Newton-Raphson method and the element matrix is given in the Newton-Raphson form. The finite element domain is organized in substructures and an equation solver which works on each substructure is specially designed. This equation solver needs less storage in the computer and is faster than the traditional banded equation solver. To reduce the amount of input data an automatic mesh generator is designed. The input consists of the coordinates of eight points defining each substructure with the corresponding boundary conditions. In order to interpret the results they are plotted on a calcomp plotter. Examples of plots of the velocities, the streamlines and the pressure inside a two-dimensional flow divider and an axis-symmetric expansion of a tube are shown for various Reynolds numbers.
Investigation of quasi-one-dimensional finite phononic crystal with conical section
Indian Academy of Sciences (India)
Zhiqiang Fu; Shuyu Lin; Shi Chen; Xiaojun Xian; Chenghui Wang
2014-12-01
In this paper, we studied the propagation of elastic longitudinal waves in quasi-onedimensional (1D) finite phononic crystal with conical section, and derived expressions of frequencyresponse functions. It is found that, contrary to the 1D phononic crystal with a constant section, the value of attenuation inside the band gaps decreases quickly when cross-sectional area increases, and the initial frequency also decreases, but the cut-off frequency increases, thus the width of the band gap increases. The effects of lattice constant and the filling fraction on the band gap are also analysed, and the change trends of the initial frequency and cut-off frequency are consistent with those of constant section. It is shown that the results using this method are in good agreement with the results analysed by the finite element software, ANSYS.We hope that the results will be helpful in practical applications of phononic crystals.
Finite element formulation for fluid-structure interaction in three-dimensional space
Energy Technology Data Exchange (ETDEWEB)
Kulak, R. F.
1979-01-01
A development is presented for a three-dimension hexahedral hydrodynamic finite-element. Using trilinear shape functions and assuming a constant pressure field in each element, simple relations were obtained for internal nodal forces. Because the formulation was based upon a rate approach it was applicable to problems involving large displacements. This element was incorporated into an existing plate-shell finite element code. Diagonal mass matrices were used and the resulting discrete equations of motion were solved using explicit temporal integrator. Results for several problems were presented which compare numerical predictions to closed form analytical solutions. In addition, the fluid-structure interaction problem of a fluid-filled, cylindrical vessel containing internal cylinders was studied. The internal cylinders were cantilever supported from the top cover of the vessel and were periodically located circumferentially at a fixed radius. A pressurized cylindrical cavity located at the bottom of the vessel at its centerline provided the loading.
Stress analysis of three-dimensional finite element model of malunion calcaneus during gait
Institute of Scientific and Technical Information of China (English)
刘立峰; 蔡锦方; 梁进
2004-01-01
Objective: To analyze the stress distribution of calcaneus with posterior articular facet compressed after fracture and talus during gait. Methods: A wedge under the posterior articular was transected from a normal finite element model of calcaneus and talus to simulate malformation of compression of the posterior facet after fracture of calcaneus. The model was used to simulate for three subphases of the stance during the gait(heel-strike, midstance, push-off) and calculate the finite element. The results were compared with normal situation. Results: The stress distribution within the bone in situation of malformation was obtained and regions of elevated stresses for three subphases were located. The results were significantly different from that of normal situation. Conclusion: The simulation of calcaneus and talus in malformation has important clinic implication and can provide an insight into the factors contributing to many clinic pathogenic changes after fracture of calcaneus.
Directory of Open Access Journals (Sweden)
Vishal Shrishail Kudagi
2017-01-01
Full Text Available Background and Objectives: Connecting the contralateral upper molars by means of a transpalatal arch (TPA is thought to decrease the tendency of the molars to move mesially in response to orthodontic force (i.e., provide orthodontic anchorage. This study was hence conducted to investigate the effects of the TPA on the displacement of the molars and stresses generated in the periodontium during orthodontic tooth movement using the finite element method (FEM. Materials and Methods: A three-dimensional (3D model was generated using medical modeling software (Mimics using the computed tomography slice images of the skull which were obtained at a slice thickness of 1 mm. From this, the finite element model was built using HyperMesh and analysis was performed using PATRAN software (MSC Software Corporation, 4675 MacArthur Court, Newport Beach, California 92660. The 3D finite element models were fabricated in two versions such as maxillary first molars including their associated periodontal ligament and alveolar bone one with TPA and another without TPA. Both were subjected to orthodontic forces, and the resultant stress patterns and displacements between the models with and without TPA were determined. Results: The stress and displacement plots in this study failed to show any significant differences in stress and displacement within the periodontium of molars, between the two models – one with TPA and the other without, in response to the orthodontic force. Interpretation and Conclusion: The results of the current finite element analysis, therefore, suggest that the presence of a TPA brings about no change in the initial dental and periodontal stress distribution and displacement.
Laser heating of finite two-dimensional dust clusters: A. Experiments
Energy Technology Data Exchange (ETDEWEB)
Schablinski, Jan; Block, Dietmar; Piel, Alexander [Institut fuer Experimentelle und Angewandte Physik, Christian-Albrechts-Universitaet zu Kiel, 24098 Kiel (Germany); Melzer, Andre [Institut fuer Physik, Ernst-Moritz-Arndt-Universitaet Greifswald, 17487 Greifswald (Germany); Thomsen, Hauke; Kaehlert, Hanno; Bonitz, Michael [Institut fuer Theoretische Physik und Astrophysik, Christian-Albrechts-Universitaet zu Kiel, 24098 Kiel (Germany)
2012-01-15
Laser manipulation allows to control the kinetic particle temperature in dusty plasmas. Different methods of laser heating for plasma crystals are benchmarked experimentally. The methods are analyzed with respect to homogeneity and isotropy in a spatial, temporal, and statistical sense. It is shown that it is possible to achieve particle dynamics very close to thermal equilibrium and that laser heating methods allow for a detailed study of phase transitions in finite size systems.
Comment on "Quantum phase for an arbitrary system with finite-dimensional Hilbert space"
Hall, Michael J. W.; Pegg, David T.
2012-01-01
A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical 'time' or 'age' observable, with the period T rescaled to 2\\pi. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phas...
Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case
Gan, Yan-Biao; Xu, Ai-Guo; Zhang, Guang-Cai; Zhang, Ping; Zhang, Lei; Li, Ying-Jun
2008-07-01
Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.
Nonrelativistic limit of solution of radial quasipotential equations
Energy Technology Data Exchange (ETDEWEB)
Minh, Vu.X.; Kadyshevskii, V.G.; Zhidkov, E.P.
1986-10-01
For the S-wave case, solutions of relativistic radial quasipotential equations that degenerate in the limit c ..-->.. infinity into the Jost solutions of the corresponding nonrelativistic radial Schrodinger equations are found.
Isotropic Landau levels of relativistic and non-relativistic fermions in 3D flat space
Li, Yi; Wu, Congjun
2012-02-01
The usual Landau level quantization, as demonstrated in the 2D quantum Hall effect, is crucially based on the planar structure. In this talk, we explore its 3D counterpart possessing the full 3D rotational symmetry as well as the time reversal symmetry. We construct the Landau level Hamiltonians in 3 and higher dimensional flat space for both relativistic and non-relativistic fermions. The 3D cases with integer fillings are Z2 topological insulators. The non-relativistic version describes spin-1/2 fermions coupling to the Aharonov-Casher SU(2) gauge field. This system exhibits flat Landau levels in which the orbital angular momentum and the spin are coupled with a fixed helicity. Each filled Landau level contributes one 2D helical Dirac Fermi surface at an open boundary, which demonstrates the Z2 topological nature. A natural generalization to Dirac fermions is found as a square root problem of the above non-relativistic version, which can also be viewed as the Dirac equation defined on the phase space. All these Landau level problems can be generalized to arbitrary high dimensions systematically. [4pt] [1] Yi Li and Congjun Wu, arXiv:1103.5422.[0pt] [2] Yi Li, Ken Intriligator, Yue Yu and Congjun Wu, arXiv:1108.5650.
Corrections to the Nonrelativistic Ground Energy of a Helium Atom
Institute of Scientific and Technical Information of China (English)
段一士; 刘玉孝; 张丽杰
2004-01-01
Considering the nuclear motion, we present the nonrelativistic ground energy of a helium atom by using a simple effective variational wavefunction with a flexible parameter k. Based on the result, the relativistic and radiative corrections to the nonrelativistic Hamiltonian are discussed. The high precision value of the helium ground energy is evaluated to be -2.90338 a.u. With the relative error 0.00034%.
Institute of Scientific and Technical Information of China (English)
Yan Liang; Chang Zhen; Xu Zhengwei; Liu Tuanjiang; He Baorong; Hao Dingjun
2014-01-01
Background Previous studies have suggested that percutaneous vertebroplasty might alter vertebral stress transfer,leading to adjacent vertebral failure.However,no three-dimensional finite element study so far accounted for the stress distributions on different cement volumes.The purpose of this study was to evaluate the stress distributions on the endplate under different loading conditions after augmentation with various volumes of bone cement.Methods L2-L3 motion segment data were obtained from CT scans of the lumbar spine from a cadaver of a young man who had no abnormal findings on roentgenograms.Three-dimensional model of L2-L3 was established using Mimics software,and finite element model of L2-L3 functional spinal unit (FSU) was established using Ansys10.0 software.For simulating percutaneous vertebral augmentation,polymethylmethacrylate (PMMA) was deposited into the bipedicle of the L2 vertebra.The percentage of PMMA volume varied between 15％ and 30％.The stress distributions on the endplate of the augmented vertebral body were calculated under three different loading conditions.Results In general,the stress level monotonically increased with bone cement volume.Under each loading condition,the stress change on the L2 superior and inferior endplates in three kinds of finite element models shows monotonic increase.Compared with the stress-increasing region of the endplate,the central part of the L2 endplate was subject to the greatest stress under three kinds of loading conditions,especially on the superior endplate and under flexion.Conclusions The finite element models of FSU are useful to optimize the planning for vertebroplasty.The bone cement volume might have an influence on the endplate of the augmentation,especially the superior endplate.It should be noted that the optimization of bone cement volume is patient specific; the volume of the bone cement should be based on the size,body mineral density,and stiffness of the vertebrae of individual
Three-dimensional finite element model for lesion correspondence in breast imaging
Qiu, Yan; Li, Lihua; Goldgof, Dmitry; Sarkar, Sudeep; Anton, Sorin; Clark, Robert A.
2004-05-01
Predicting breast tissue deformation is of great significance in several medical applications such as biopsy, diagnosis, and surgery. In breast surgery, surgeons are often concerned with a specific portion of the breast, e.g., tumor, which must be located accurately beforehand. Also clinically it is important for combining the information provided by images from several modalities or at different times, for the detection/diagnosis, treatment planning and guidance of interventions. Multi-modality imaging of the breast obtained by X-ray mammography, MRI is thought to be best achieved through some form of data fusion technique. However, images taken by these various techniques are often obtained under entirely different tissue configurations, compression, orientation or body position. In these cases some form of spatial transformation of image data from one geometry to another is required such that the tissues are represented in an equivalent configuration. We propose to use a 3D finite element model for lesion correspondence in breast imaging. The novelty of the approach lies in the following facts: (1) Finite element is the most accurate technique for modeling deformable objects such as breast. The physical soundness and mathematical rigor of finite element method ensure the accuracy and reliability of breast modeling that is essential for lesion correspondence. (2) When both MR and mammographic images are available, a subject-specific 3D breast model will be built from MRIs. If only mammography is available, a generic breast model will be used for two-view mammography reading. (3) Incremental contact simulation of breast compression allows accurate capture of breast deformation and ensures the quality of lesion correspondence. (4) Balance between efficiency and accuracy is achieved through adaptive meshing. We have done intensive research based on phantom and patient data.
Jiang, Zhongzheng; Zhao, Wenwen; Chen, Weifang
2016-11-01
Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computation model, namely the nonlinear coupled constitutive relations (NCCR), was developed by R.S. Myong and applied successfully to one-dimensional shock wave structure and two-dimensional rarefied flows. In this paper, finite volume schemes, including LU-SGS time advance scheme, MUSCL interpolation and AUSMPW+ scheme, are firstly adopted to investigate NCCR model's validity and potential in three-dimensional complex hypersonic rarefied gas flows. Moreover, in order to solve the computational stability problems in 3D complex flows, a modified solution is developed for the NCCR model. Finally, the modified solution is tested for a slip complex flow over a 3D hollow cylinder-flare configuration. The numerical results show that the NCCR model by the modified solution yields good solutions in better agreement with the DSMC results and experimental data than NSF equations, and imply NCCR model's great potential capability in further application.
A finite point method for adaptive-three-dimensional compressible flow calculations
Ortega, Enrique; Oñate Ibáñez de Navarra, Eugenio; Idelsohn Barg, Sergio Rodolfo
2009-01-01
Electronic version of an article published as "International journal for numerical methods in fluids", vol. 60, no 9, 2009, p. 937-971. DOI:10.1002/fld.1892 The finite point method (FPM) is a meshless technique, which is based on both, a weighted least-squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM...
WONDY V: a one-dimensional finite-difference wave-propagation code
Energy Technology Data Exchange (ETDEWEB)
Kipp, M.E.; Lawrence, R.J.
1982-06-01
WONDY V solves the finite difference analogs to the Lagrangian equations of motion in one spatial dimension (planar, cylindrical, or spherical). Simulations of explosive detonation, energy deposition, plate impact, and dynamic fracture are possible, using a variety of existing material models. In addition, WONDY has proven to be a powerful tool in the evaluation of new constitutive models. A preprocessor is available to allocate storage arrays commensurate with problem size, and automatic rezoning may be employed to improve resolution. This document provides a description of the equations solved, available material models, operating instructions, and sample problems.
Energy Technology Data Exchange (ETDEWEB)
Christe, P.; Flume, R.
1987-04-09
We investigate the structure of the linear differential operators whose solutions determine the four-point correlations of primary operators in the d=2 conformally invariant SU(2) sigma-model with Wess-Zumino term and the d=2 critical statistical systems with central Virasoro charge smaller than one. Factorisation properties of the differential operators are related to a finite closure of the operator algebras. We recover the selection and fusion rules of Fateev, Zamolodchikov and Gepner, Witten for the SU(2) sigma-model. It is outlined how the results of the SU(2) model can be used for the identification of closed operator algebras in the statistical model.
Energy Technology Data Exchange (ETDEWEB)
Christe, P.; Flume, R.
1986-10-01
We investigate the structure of the linear differential operators whose solutions determine the four point correlations of primary operators in the d=2 conformally invariant SU(2) sigma-model with Wess-Zumino term and the d=2 critical statistical systems with central Virasoro charge smaller than one. Factorisation properties of the differential operators are related to a finite closure of the operator algebras. We recover the selection and fusion rules of Fateev, Zamolodchikov and Gepner, Witten for the SU(2) sigma-model. It is outlined how the results of the SU(2) model can be used for the identification of closed operator algebras in the statistical model.
Benchmarking high order finite element approximations for one-dimensional boundary layer problems
Malagu, M.; Benvenuti, E.; Simone, A.
2013-01-01
In this article we investigate the application of high order approximation techniques to one-dimensional boundary layer problems. In particular, we use second order differential equations and coupled second order differential equations as case studies. The accuracy and convergence rate of numerical
Two-dimensional time-domain finite-difference modeling for viscoelastic seismic wave propagation
Fan, Na; Zhao, Lian-Feng; Xie, Xiao-Bi; Ge, Zengxi; Yao, Zhen-Xing
2016-09-01
Real Earth media are not perfectly elastic. Instead, they attenuate propagating mechanical waves. This anelastic phenomenon in wave propagation can be modeled by a viscoelastic mechanical model consisting of several standard linear solids. Using this viscoelastic model, we approximate a constant Q over a frequency band of interest. We use a four-element viscoelastic model with a trade-off between accuracy and computational costs to incorporate Q into 2-D time-domain first-order velocity-stress wave equations. To improve the computational efficiency, we limit the Q in the model to a list of discrete values between 2 and 1000. The related stress and strain relaxation times that characterize the viscoelastic model are pre-calculated and stored in a database for use by the finite-difference calculation. A viscoelastic finite-difference scheme that is second order in time and fourth order in space is developed based on the MacCormack algorithm. The new method is validated by comparing the numerical result with analytical solutions that are calculated using the generalized reflection/transmission coefficient method. The synthetic seismograms exhibit greater than 95 per cent consistency in a two-layer viscoelastic model. The dispersion generated from the simulation is consistent with the Kolsky-Futterman dispersion relationship.
Two-Dimensional Large Deformation Finite Element Analysis for the Pulling-up of Plate Anchor
Institute of Scientific and Technical Information of China (English)
WANG Dong; HU Yu-xia; JIN Xia
2006-01-01
Based on mesh regeneration and stress interpolation from an old mesh to a new one, a large deformation finite element model is developed for the study of the behaviour of circular plate anchors subjected to uplift loading. For the determination of the distributions of stress components across a clay foundation, the Recovery by Equilibrium in Patches is extended to plastic analyses. ABAQUS, a commercial finite element package, is customized and linked into our program so as to keep automatic and efficient running of large deformation calculation. The quality of stress interpolation is testified by evaluations of Tresca stress and nodal reaction forces. The complete pulling-up processes of plate anchors buried in homogeneous clay are simulated, and typical pulling force-displacement responses of a deep anchor and a shallow anchor are compared. Different from the results of previous studies, large deformation analysis is of the capability of estimating the breakaway between the anchor bottom and soils. For deep anchors, the variation of mobilized uplift resistance with anchor settlement is composed of three stages, and the initial buried depths of anchors affect the separation embedment slightly. The uplift bearing capacity of deep anchors is usually higher than that of shallow anchors.
Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem
Bramble, James H.
2010-01-01
We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.
Efficient inversion of three-dimensional finite element models of volcano deformation
Charco, M.; Galán del Sastre, P.
2014-03-01
Numerical techniques, as such as finite element method, allow for the inclusion of features, such as topography and/or mechanical heterogeneities, for the interpretation of volcanic deformation. However, models based on these numerical techniques usually are not suitable to be included in non-linear estimations of source parameters based on explorative optimization schemes because they require a calculation of the numerical approach for every evaluation of the misfit function. We present a procedure for finite element (FE) models that can be combined with explorative inversion schemes. The methodology is based on including a body force term representing an infinitesimal source in the model formulation that is responsible for pressure (volume) changes in the medium. This provides significant savings in both the time required for mesh generation and actual computational time of the numerical approach. Furthermore, we develop an inversion algorithm to estimate those parameters that characterize the changes in location and pressure (volume) of deformation sources. Both provide FE inversions in a single step, avoiding remeshing and assembly of the linear system of algebraic equations that define the numerical approach and/or the automatic mesh generation. After providing the theoretical basis for the model, the numerical approach and the algorithm for the inversions, we test the methodology using a synthetic example in a stratovolcano. Our results suggest that the FE inversion methodology can be considered suitable for efficiently save time in quantitative interpretations of volcano deformation.
Institute of Scientific and Technical Information of China (English)
陈普庆; 夏伟; 周照耀; 朱权利; 李元元
2004-01-01
The application of a combined finite-discrete element modeling approach to simulate the three-dimensional microscopic compaction behavior of single-layer metal powder system was described. The process was treated as a static problem, with kinematical component being neglected. Due to ill condition, Cholesky's method failed to solve the system equations, while conjugate gradient method was tried and yielded good results. Deformation of the particles was examined and compared with the results of physical modeling experiments. In both cases, the inner particles were deformed from sphere to polygonal column, with the edges turning from arc to straight line. The edge number of a particle was equal to the number of particles surrounding it. And the experiments show that the ductile metal particles can be densified only by their plastic deformation without the occurrence of rearrangement phenomenon.
Directory of Open Access Journals (Sweden)
Liu Bing
2014-10-01
Full Text Available Earthquake action is the main external factor which influences long-term safe operation of civil construction, especially of the high-rise building. Applying time-history method to simulate earthquake response process of civil construction foundation surrounding rock is an effective method for the anti-knock study of civil buildings. Therefore, this paper develops a civil building earthquake disaster three-dimensional dynamic finite element numerical simulation system. The system adopts the explicit central difference method. Strengthening characteristics of materials under high strain rate and damage characteristics of surrounding rock under the action of cyclic loading are considered. Then, dynamic constitutive model of rock mass suitable for civil building aseismic analysis is put forward. At the same time, through the earthquake disaster of time-history simulation of Shenzhen Children’s Palace, reliability and practicability of system program is verified in the analysis of practical engineering problems.
Indian Academy of Sciences (India)
Smitadhi Ganguly; A Nandi; S Neogy
2014-06-01
Unlike structural dynamics, the three-dimensional finite-element model of non-axisymmetric rotors on orthotropic bearings generates a large gyroscopic system with parametric stiffness. The present work explores the use of mass-lumping in stability analysis of such systems. Using a variant of Hill’s method, the problem reduces to a generalized Eigen value problem of order $nm \\times nm$, with as the order of the system in state vector representation and as the number of terms in the assumed solution. The matrices in both the sides of the Eigen value problem are expressed in terms of Kronecker products where the mass-matrix appears twice as a sub-matrix in both the sides of the equation. A particular one or both of them can be made diagonal. Both options produce sufficiently accurate results with considerable savings, even with a coarse mesh.
Institute of Scientific and Technical Information of China (English)
Cheng Ying; Huang Qiao-Jian; Liu Xiao-Jun
2008-01-01
This paper uses finite element method to obtain the three-dimensional temperature field of laser-induced transient thermal grating (TTG) for two-layered structure of diamond film on ZnSe substrate.The numerical results indicate that unique two-times heating process is gradually experienced in the area between two adjacent grating stripes.However,there is a little change for the temperature field along the depth direction for the diamond film due to its great thermal conductivity.It further finds that the thickness of the diamond film has a significant influence on the temperature field in diamond/ZnSe system.The results are useful for the application of laser-induced TTG technique in film/substrate system.
Lu, Chang; Han, Ke; Li, Jing; Wang, Bing; Lu, Guo-hua
2008-05-01
To establish a 3-dimensional finite element model. The coordinate data of the vertebras were obtained from the CT scan images of Chinese 50th percentile healthy male adult volunteers' cervical spine, converted into point cloud data, and stored as ASCII file using Mimics software. CATIA software was used to preprocess and Geomagic software was used to establish the geometry model of the C0 approximately C7 cervical spine. The geometry model was meshed by Hypermesh software. Mapped mesh method was used to mesh cortical bone, trabecular bone, intervertebral disk, ligaments, etc. Some material parameters were defined from other available material parameters using proportion and function scale method. The model had 22 512 solid elements and 14 180 shell/membrane elements. The model was validated by the cervical spine drop test. The model has good biofidelity and can be used to study the dynamic response and injury mechanism of the cervical spine in the car accidents.
Directory of Open Access Journals (Sweden)
B. U. Musa
2017-04-01
Full Text Available The C++ programming language was used to implement three-dimensional (3-D finite-difference time-domain (FDTD technique to simulate radiation of high frequency electromagnetic waves in free space. To achieve any meaningful results the computational domain of interest should have to be truncated in some way and this is achieved by applying absorbing boundary conditions. A uniaxial perfectly matched layer (UPML absorbing boundary condition is used in this work. The discretised equations of the UPML in FDTD time stepping scheme were derived and has been successfully implemented using the computer program. Simulation results showed that the UPML behaves as an absorber. This was confirmed by comparing the results with another boundary condition, the Mur ABC.
Energy Technology Data Exchange (ETDEWEB)
Xiong Yuhong [Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616 (United States); Hofmeister, William H. [Center for Laser Applications, University of Tennessee Space Institute, Tullahoma, TN 37388 (United States); Cheng Zhao [Earth Mechanics Inc., Oakland, CA 94621 (United States); Smugeresky, John E. [Sandia National Laboratories, Livermore, CA 94551 (United States); Lavernia, Enrique J. [Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616 (United States); Schoenung, Julie M., E-mail: jmschoenung@ucdavis.edu [Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616 (United States)
2009-10-15
Laser deposition is being used for the fabrication of net shapes from a broad range of materials, including tungsten carbide-cobalt (WC-Co) cermets (composites composed of a metallic phase and a hard refractory phase). During deposition, an unusual thermal condition is created for cermets, resulting in rather complex microstructures. To provide a fundamental insight into the evolution of such microstructures, we studied the thermal behavior of WC-Co cermets during laser deposition involving complementary results from in situ high-speed thermal imaging and three-dimensional finite element modeling. The former allowed for the characterization of temperature gradients and cooling rates in the vicinity of the molten pool, whereas the latter allowed for simulation of the entire sample. By combining the two methods, a more robust analysis of the thermal behavior was achieved. The model and the imaging results correlate well with each other and with the alternating sublayers observed in the microstructure.
Institute of Scientific and Technical Information of China (English)
YUAN Si; HE Xue-feng
2006-01-01
Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM),the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient.This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea,implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
Murthy, P. L. N.; Chamis, C. C.
1985-01-01
A computational procedure is described for evaluating End-Notch-Flexure (ENF) and Mixed-Mode-Flexure (MMF) interlaminar fracture toughness in unidirectional fiber composites. The procedure consists of a three-dimensional finite element analysis in conjunction with the strain energy release rate concept and with composite micromechanics. The procedure is used to analyze select cases of ENF and MMF. The strain energy release rate predicted by this procedure is in good agreement with limited experimental data. The procedure is used to identify significant parameters associated with interlaminar fracture toughness. It is also used to determine the critical strain energy release rate and its attendant crack length in ENF and/or MMF. This computational procedure has considerable versatility/generality and provides extensive information about interlaminar fracture toughness in fiber composites.
Aarts, Gert
2010-01-01
The three-dimensional XY model is studied at finite chemical potential using complex Langevin dynamics. The validity of the approach is probed at small chemical potential using imaginary chemical potential and continuity arguments, and at larger chemical potential by comparison with the world line method. While complex Langevin works for larger beta, we find that it fails for smaller beta, in the region of the phase diagram corresponding to the disordered phase. Diagnostic tests are developed to identify symptoms correlated with incorrect convergence. We argue that the erroneous behaviour at smaller beta is not due to the sign problem, but rather resembles dynamics observed in complex Langevin simulations of simple models with complex noise.
Çelik Köycü, Berrak; Imirzalioğlu, Pervin; Özden, Utku Ahmet
2016-01-01
Functional occlusal loads and intraoral temperature changes create stress in teeth. The purpose of this study was to evaluate the impact of simultaneous thermomechanical loads on stress distribution related to inlay restored teeth by three-dimensional finite element analysis. A mandibular first molar was constructed with tooth structures, surrounding bone and inlays of Type II gold alloy, ceramic, and composite resin. Stress patterns on the restorative materials, adhesive resin, enamel and dentin were analyzed after simulated temperature changes from 36°C to 4 or 60°C for 2 s with 200-N oblique loading. The results showed that the three types of inlays had similar stress distribution in the tooth structures and restorative materials. Concerning the adhesive resin, the composite resin inlay model exhibited lower stresses than ceramic and gold alloy inlays. Simultaneous thermomechanical loads caused high stress patterns in inlay-restored teeth. Composite resin inlays may be the better choice to avoid adhesive failure.
Schneider, T.; Botta, N.; Geratz, K. J.; Klein, R.
1999-11-01
When attempting to compute unsteady, variable density flows at very small or zero Mach number using a standard finite volume compressible flow solver one faces at least the following difficulties: (i) Spatial pressure variations vanish as the Mach number M→0, but they do affect the velocity field at leading order; (ii) the resulting spatial homogeneity of the leading order pressure implies an elliptic divergence constraint for the energy flux; (iii) violations of this constraint crucially affect the transport of mass, preventing a code to properly advect even a constant density distribution. We overcome these difficulties through a new algorithm for constructing numerical fluxes in the context of multi-dimensional finite volume methods in conservation form. The construction of numerical fluxes involves: (1) An explicit upwind step yielding predictions for the nonlinear convective flux components. (2) A first correction step that introduces pressure gradients which guarantee compliance of the convective fluxes with a divergence constraint. This step requires the solution of a first Poisson-type equation. (3) A second projection step which provides the yet unknown (non-convective) pressure contribution to the total flux of momentum. This second projection requires the solution of another Poisson-type equation and yields the cell centered velocity field at the new time. This velocity field exactly satisfies a divergence constraint consistent with the asymptotic limit. Step (1) can be done by any standard finite volume compressible flow solver. The input to steps (2) and (3) involves solely the fluxes from step (1) and is independent of how these were obtained. Thus, our approach allows any such solver to be extended to compute variable density incompressible flows.
Popov, Alexander P.; Gloria Pini, Maria; Rettori, Angelo
2016-03-01
The metastable states of a finite-size chain of N classical spins described by the chiral XY-model on a discrete one-dimensional lattice are calculated by means of a general theoretical method recently developed by one of us. This method allows one to determine all the possible equilibrium magnetic states in an accurate and systematic way. The ground state of a chain consisting of N classical XY spins is calculated in the presence of (i) a symmetric ferromagnetic exchange interaction, favoring parallel alignment of nearest neighbor spins, (ii) a uniaxial anisotropy, favoring a given direction in the film plane, and (iii) an antisymmetric Dzyaloshinskii-Moriya interaction (DMI), favoring perpendicular alignment of nearest neighbor spins. In addition to the ground state with a non-uniform helical spin arrangement, which originates from the energy competition in the finite-size chain with open boundary conditions, we have found a considerable number of higher-energy equilibrium states. In the investigated case of a chain with N=10 spins and a DMI much smaller than the in-plane uniaxial anisotropy, it turns out that a metastable (unstable) state of the finite chain is characterized by a configuration where none (at least one) of the inner spins is nearly parallel to the hard axis. The role of the DMI is to establish a unique rotational sense for the helical ground state. Moreover, the number of both metastable and unstable equilibrium states is doubled with respect to the case of zero DMI. This produces modifications in the Peierls-Nabarro potential encountered by a domain wall during its displacement along the discrete spin chain.
Guo, Guifang; Long, Bo; Cheng, Bo; Zhou, Shiqiong; Xu, Peng; Cao, Binggang
In order to better understand the thermal abuse behavior of high capacities and large power lithium-ion batteries for electric vehicle application, a three-dimensional thermal model has been developed for analyzing the temperature distribution under abuse conditions. The model takes into account the effects of heat generation, internal conduction and convection, and external heat dissipation to predict the temperature distribution in a battery. Three-dimensional model also considers the geometrical features to simulate oven test, which are significant in larger cells for electric vehicle application. The model predictions are compared to oven test results for VLP 50/62/100S-Fe (3.2 V/55 Ah) LiFePO 4/graphite cells and shown to be in great agreement.
A Study of Two-Dimensional Unsteady Breaking Waves in Finite-Depth Water
2010-01-01
1880). [8] J. H. Duncan, “An experimental investigation of breaking waves produced by a towed hydrofoil ,” Proc. R. Soc. London, Ser. A 377, 331(1981...measured the drag per unit length due to quasi-steady breaking waves generated with a submerged hydrofoil . His measurements illustrated that the... hydrofoil . Proc. R. Soc. London Ser. A 377, 331-348. DUNCAN, J. H. 1983 The breaking and non-breaking wave resistance of a two- dimensional hydrofoil . J
Documentation of finite-difference model for simulation of three-dimensional ground-water flow
Trescott, Peter C.; Larson, S.P.
1976-01-01
User experience has indicated that the documentation of the model of three-dimensional ground-water flow (Trescott and Larson, 1975) should be expanded. This supplement is intended to fulfill that need. The original report emphasized the theory of the strongly implicit procedure, instructions for using the groundwater-flow model, and practical considerations for application. (See also W76-02962 and W76-13085) (Woodard-USGS)
Wang, Morten M. T.; Sheu, Tony W. H.
1997-09-01
Our work is an extension of the previously proposed multivariant element. We assign this refined element as a compact mixed-order element in the sense that use of this element offers a much smaller bandwidth. The analysis is implemented on quadratic hexahedral elements with a view to analysing a three-dimensional incompressible viscous flow problem using a method formulated within the mixed finite element context. The idea of constructing such a stable element is to bring the marker-and-cell (MAC) grid lay-out to the finite element context. This multivariant element can thus be classified as a discontinuous pressure element. We have several reasons for advocating the proposed multivariant element. The primary advantage gained is its ability to reduce the bandwidth of the matrix equation, as compared with its univariant counterparts, so that it can be effectively stored in a compressed row storage (CRS) format. The resulting matrix equation can be solved efficiently by a multifrontal solver owing to its reduced bandwidth. The coding is, however, complicated by the appearance of restricted degrees of freedom at mid-face nodes. Through analytic study this compact multivariant element has a marked advantage over the multivariant element of Gupta et al. in that both bandwidth and computation time have been drastically reduced.
Merdan, Ziya; Kürkçü, Cihan; Öztürk, Mustafa K.
2014-12-01
The four-dimensional ferromagnetic Ising model in external magnetic field is simulated on the Creutz cellular automaton algorithm using finite-size lattices with linear dimension 4 ≤ L ≤ 8. The critical temperature value of infinite lattice, Tc χ ( ∞ ) = 6 , 680 (1) obtained for h = 0 agrees well with the values T c ( ∞ ) ≈ 6.68 obtained previously using different methods. Moreover, h = 0.00025 in our work also agrees with all the results obtained from h = 0 in the literature. However, there are no works for h ≠ 0 in the literature. The value of the field critical exponent (δ = 3.0136(3)) is in good agreement with δ = 3 which is obtained from scaling law of Widom. In spite of the finite-size scaling relations of | M L ( t ) | and χ L ( t ) for 0 ≤ h ≤ 0.001 are verified; however, in the cases of 0.0025 ≤ h ≤ 0.1 they are not verified.
Directory of Open Access Journals (Sweden)
Hassan Badreddine
2017-01-01
Full Text Available The current work focuses on the development and application of a new finite volume immersed boundary method (IBM to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Arthur J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States); Dreger, Douglas S. [Univ. of California, Berkeley, CA (United States); Pitarka, Arben [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-06-15
We performed three-dimensional (3D) anelastic ground motion simulations of the South Napa earthquake to investigate the performance of different finite rupture models and the effects of 3D structure on the observed wavefield. We considered rupture models reported by Dreger et al. (2015), Ji et al., (2015), Wei et al. (2015) and Melgar et al. (2015). We used the SW4 anelastic finite difference code developed at Lawrence Livermore National Laboratory (Petersson and Sjogreen, 2013) and distributed by the Computational Infrastructure for Geodynamics. This code can compute the seismic response for fully 3D sub-surface models, including surface topography and linear anelasticity. We use the 3D geologic/seismic model of the San Francisco Bay Area developed by the United States Geological Survey (Aagaard et al., 2008, 2010). Evaluation of earlier versions of this model indicated that the structure can reproduce main features of observed waveforms from moderate earthquakes (Rodgers et al., 2008; Kim et al., 2010). Simulations were performed for a domain covering local distances (< 25 km) and resolution providing simulated ground motions valid to 1 Hz.
Katyal, A. K.; Kaluarachchi, J. J.; Parker, J. C.
1991-05-01
The manual describes a two-dimensional finite element model for coupled multiphase flow and multicomponent transport in planar or radially symmetric vertical sections. Flow and transport of three fluid phases, including water, nonaqueous phase liquid (NAPL), and gas are considered by the program. The program can simulate flow only or coupled flow and transport. The flow module can be used to analyze two phases, water and NAPL, with the gas phase held at constant pressure, or explicit three-phase flow of water, NAPL, and gas at various pressures. The transport module can handle up to five components which partition among water, NAPL, gas and solid phases assuming either local equilibrium or first-order mass transfer. Three phase permeability-saturation-capillary pressure relations are defined by an extension of the van Genuchten model. The governing equations are solved using an efficient upstream-weighted finite element scheme. The required inputs for flow and transport analysis are described. Detailed instructions for creating data files needed to run the program and examples of input and output files are given in appendices.
Liu, Pengcheng; Archuleta, Ralph J.
2004-02-01
We present a new procedure to invert for kinematic source parameters on a finite fault. On the basis of the reciprocity relation of the Green's functions, we use a newly developed fourth-order viscoelastic finite-difference algorithm to calculate three-dimensional (3-D) Green's functions (actually the tractions) on the fault. We invert the data for the unknown source parameters at the nodes (or corners) of the subfaults. The source parameters within a subfault area are allowed to vary; this variation is calculated through bilinear interpolation of the four nodal quantities. We have developed a global nonlinear inversion algorithm that is based on simulated annealing methods to solve efficiently for the nodal parameters. We apply this method to the 1989 Loma Prieta, California, M 6.9 earthquake for both a 1-D and 3-D velocity structure. We show (1) the bilinear interpolation technique reduces the dependence of inversion results on the subfault size by naturally including the effects of nearby subfaults. (2) While the number of synthetic seismograms that must be computed is greatly increased by the bilinear interpolation, the structure of the inversion method minimizes the actual numbers of computations. (3) As expected, complexity in the velocity structure is mapped into the source parameters that describe the rupture process; there are significant differences between faulting models derived from 1-D and 3-D structural models.
Directory of Open Access Journals (Sweden)
Filip Keulemans
2015-01-01
Full Text Available The aim of this study was to evaluate the influence of different framework materials on biomechanical behaviour of anterior two-unit cantilever resin-bonded fixed dental prostheses (RBFDPs. A three-dimensional finite element model of a two-unit cantilever RBFDP replacing a maxillary lateral incisor was created. Five framework materials were evaluated: direct fibre-reinforced composite (FRC-Z250, indirect fibre-reinforced composite (FRC-ES, gold alloy (M, glass ceramic (GC, and zirconia (ZI. Finite element analysis was performed and stress distribution was evaluated. A similar stress pattern, with stress concentrations in the connector area, was observed in RBFDPs for all materials. Maximal principal stress showed a decreasing order: ZI > M > GC > FRC-ES > FRC-Z250. The maximum displacement of RBFDPs was higher for FRC-Z250 and FRC-ES than for M, GC, and ZI. FE analysis depicted differences in location of the maximum stress at the luting cement interface between materials. For FRC-Z250 and FRC-ES, the maximum stress was located in the upper part of the proximal area of the retainer, whereas, for M, GC, and ZI, the maximum stress was located at the cervical outline of the retainer. The present study revealed differences in biomechanical behaviour between all RBFDPs. The general observation was that a RBFDP made of FRC provided a more favourable stress distribution.
Guevara, Cristi
2012-01-01
We study the global behavior of finite energy solutions to the $d$-dimensional focusing nonlinear Schr\\"odinger equation (NLS), $i \\partial_t u+\\Delta u+ |u|^{p-1}u=0, $ with initial data $u_0\\in H^1,\\; x \\in R^n$. The nonlinearity power $p$ and the dimension $d$ are such that the scaling index $s=\\frac{d}2-\\frac2{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle.
Pan, Xue; Chen, Li-Zhu; Wu, Yuan-Fang
2016-09-01
The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). This has been calculated to the sixth order in experiments. Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign. Supported by Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University for Doctor (2016RC004), Major State Basic Research Development Program of China (2014CB845402) and National Natural Science Foundation of China (11405088, 11221504)
An Efficient Multiple-Dimensional Finite Element Solution for Water Flow in Variably Saturated Soils
Institute of Scientific and Technical Information of China (English)
QI Xue-bin; ZHANG Xiao-xian; PANG Hong-bin
2008-01-01
Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots;its quantitative description is usually based on the Richards' equation.Because of the nonlinearity of the Richards' equation and the complexity of natural soils,most practical simulations rely on numerical solutions with the nonlinearity solved by iterations.The commonly used iterations for solving the nonlinearity are Picard and Newton methods with the former converging at first-order rate and the later at second-order rate.A recent theoretical analysis by the authors,however,revealed that for solving the diffusive flow,the classical Picard method is actually a chord-Newton method,converging at a rate faster than first order;its linear convergence rate is due to the treatment of the gravity term.To improve computational efficiency,a similar chord-Newton method as for solving the diffusive term was proposed to solve the gravity term.Testing examples for one-dimensional flow showed significant improvement.The core of this method is to produce a diagonally dominant matrix in the linear system so as to improve the iteration-toiteration stability and hence the convergence.In this paper,we develop a similar method for multiple-dimensional flow and compare its performance with the classical Picard and Newton methods for water flow in soils characterised by a wide range of van Genuchten parameters.
Two Dimensional Finite Element Analysis for the Effect of a Pressure Wave in the Human Brain
Ponce L., Ernesto; Ponce S., Daniel
2008-11-01
Brain injuries in people of all ages is a serious, world-wide health problem, with consequences as varied as attention or memory deficits, difficulties in problem-solving, aggressive social behavior, and neuro degenerative diseases such as Alzheimer's and Parkinson's. Brain injuries can be the result of a direct impact, but also pressure waves and direct impulses. The aim of this work is to develop a predictive method to calculate the stress generated in the human brain by pressure waves such as high power sounds. The finite element method is used, combined with elastic wave theory. The predictions of the generated stress levels are compared with the resistance of the arterioles that pervade the brain. The problem was focused to the Chilean mining where there are some accidents happen by detonations and high sound level. There are not formal medical investigation, however these pressure waves could produce human brain damage.
Danza, Matteo; Palmieri, Annalisa; Farinella, Francesca; Brunelli, Giorgio; Carinci, Francesco; Girardi, Ambra; Spinelli, Giuseppe
2009-01-01
The aim of research was to study spiral family implant by finite element analysis (FEA) inserted in different bone qualities connected with abutments of different angulations. The biomechanical behaviour of 4.2 × 13 mm dental implants, connecting screw, straight and 15° and 25° angulated abutments subjected to static loads, in contact with high and poor bone qualities was evaluated by FEA. The lowest stress value was found in the system composed by implants and straight abut-ments loaded with a vertical force, while the highest stress value was found in implants with 15° angulated abutment loaded with an angulated force. In addition, we found the lower the bone quality, the higher the distribution of the stress within the bone. Spiral family implants can be used successfully in low bone quality but applying a straight force is recommended.
Puzyrev, Vladimir; Koldan, Jelena; de la Puente, Josep; Houzeaux, Guillaume; Vázquez, Mariano; Cela, José María
2013-05-01
We present a nodal finite-element method that can be used to compute in parallel highly accurate solutions for 3-D controlled-source electromagnetic forward-modelling problems in anisotropic media. Secondary coupled-potential formulation of Maxwell's equations allows to avoid the singularities introduced by the sources, while completely unstructured tetrahedral meshes and mesh refinement support an accurate representation of geological and bathymetric complexity and improve the solution accuracy. Different complex iterative solvers and an efficient pre-conditioner based on the sparse approximate inverse are used for solving the resulting large sparse linear system of equations. Results are compared with the ones of other researchers to check the accuracy of the method. We demonstrate the performance of the code in large problems with tens and even hundreds of millions of degrees of freedom. Scalability tests on massively parallel computers show that our code is highly scalable.
Institute of Scientific and Technical Information of China (English)
袁益让
1996-01-01
The software for oil-gas transport and accumulation is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. This thesis, from actual conditions such as the effects of gravitation, buoyancy and capillary pressure, puts forward for the two class boundary value problem a kind of characteristic mixed finite element scheme by making use of the change of region, time step modified techniques of handling boundary value condition, negative norm estimate and the theory of prior estimates. Optimal order estimates in L2 norm are derived for the error in approximate solutions. Thus the well-known theoretical problem proposed by J. Douglas, Jr has been thoroughly and completely solved.
Maxwell-Chern-Simons Models: Their Symmetries, Exact Solutions and Non-relativistic Limits
Directory of Open Access Journals (Sweden)
J. Niederle
2010-01-01
Full Text Available Two Maxwell-Chern-Simons (MCS models in the (1 + 3-dimensional space-space are discussed and families of their exact solutions are found. In contrast to the Carroll-Field-Jackiw (CFE model [2] these systems are relativistically invariant and include the CFJ model as a particular sector.Using the InNonNu-Wigner contraction a Galilei-invariant non-relativistic limit of the systems is found, which makes possible to find a Galilean formulation of the CFJ model.
Time as an Observable in Nonrelativistic Quantum Mechanics
Hahne, G. E.
2003-01-01
The argument follows from the viewpoint that quantum mechanics is taken not in the usual form involving vectors and linear operators in Hilbert spaces, but as a boundary value problem for a special class of partial differential equations-in the present work, the nonrelativistic Schrodinger equation for motion of a structureless particle in four- dimensional space-time in the presence of a potential energy distribution that can be time-as well as space-dependent. The domain of interest is taken to be one of two semi-infinite boxes, one bounded by two t=constant planes and the other by two t=constant planes. Each gives rise to a characteristic boundary value problem: one in which the initial, input values on one t=constant wall are given, with zero asymptotic wavefunction values in all spatial directions, the output being the values on the second t=constant wall; the second with certain input values given on both z=constant walls, with zero asymptotic values in all directions involving time and the other spatial coordinates, the output being the complementary values on the z=constant walls. The first problem corresponds to ordinary quantum mechanics; the second, to a fully time-dependent version of a problem normally considered only for the steady state (time-independent Schrodinger equation). The second problem is formulated in detail. A conserved indefinite metric is associated with space-like propagation, where the sign of the norm of a unidirectional state corresponds to its spatial direction of travel.
A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection
Buell, Jeffrey C.
1988-01-01
A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.
Spectral Properties of the Two-Dimensional Laplacian with a Finite Number of Point Interactions
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1997-01-01
We discuss spectral properties of the Laplacian with multiple ($N$) point interactions in two-dimensional bounded regions. A mathematically sound formulation for the problem is given within the framework of the self-adjoint extension of a symmetric (Hermitian) operator in functional analysis. The eigenvalues of this system are obtained as the poles of a transition matrix which has size $N$. Closely examining a generic behavior of the eigenvalues of the transition matrix as a function of the energy, we deduce the general condition under which point interactions have a substantial effect on statistical properties of the spectrum.
A static analysis of metal matrix composite spur gear by three-dimensional finite element method
Ganesan, N.; Vijayarangan, S.
1993-03-01
A number of engineering components have recently been made using metal matrix composite (MMC) materials, due to their overwhelming advantages, such as light weight high strength, higher dimensional stability and minimal attack by environment, when compared with polymer-based composite materials, even though the cost of MMCs are very high. Power transmission gears are one such area able to make use of MMC materials. Here an attempt is made to study and compare the performance of gears made of MMC materials with that of conventional steel material gears. It may be concluded from this study that MMC materials are highly suitable for making gears that are to transmit even fairly large power.
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2011-05-09
A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. - Highlights: A new family of Poisson structures is globally characterized and analyzed. Such family is globally defined for arbitrary values of the dimension and the rank. Global construction of Casimir invariants and Darboux canonical form is provided. Very diverse and previously known solutions of physical interest are generalized.
A COMPLETE THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS OF THE BAR-BAR TENSILE IMPACT APPARATUS
Institute of Scientific and Technical Information of China (English)
万华培; 汪洋; 夏源明
2003-01-01
A complete three-dimensional FEM model of the Bar-Bar Tensile Impact Apparatus (BTIA) is constructed, in which the slots in the bars and the glue layers between the bars and the flat-shaped specimen are included. For elastic-plastic specimen material, Ly12cz aluminum alloy, the process of tensile impact experiments is simulated and the matching relation between the specimen geometry and the bars is investigated. Based on the FEM analysis, an iterative method is proposed to design a reasonable specimen geometry for obtaining the true dynamic stress-strain relation for a certain specimen material.
Energy Technology Data Exchange (ETDEWEB)
Popov, Alexander P., E-mail: APPopov@mephi.ru [Department of Molecular Physics, National Research Nuclear University MEPhI, Kashirskoe shosse 31, 115409 Moscow (Russian Federation); Gloria Pini, Maria, E-mail: mariagloria.pini@isc.cnr.it [Istituto dei Sistemi Complessi del CNR (CNR-ISC), Unità di Firenze, Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Rettori, Angelo [Dipartimento di Fisica ed Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino (Italy)
2016-03-15
The metastable states of a finite-size chain of N classical spins described by the chiral XY-model on a discrete one-dimensional lattice are calculated by means of a general theoretical method recently developed by one of us. This method allows one to determine all the possible equilibrium magnetic states in an accurate and systematic way. The ground state of a chain consisting of N classical XY spins is calculated in the presence of (i) a symmetric ferromagnetic exchange interaction, favoring parallel alignment of nearest neighbor spins, (ii) a uniaxial anisotropy, favoring a given direction in the film plane, and (iii) an antisymmetric Dzyaloshinskii–Moriya interaction (DMI), favoring perpendicular alignment of nearest neighbor spins. In addition to the ground state with a non-uniform helical spin arrangement, which originates from the energy competition in the finite-size chain with open boundary conditions, we have found a considerable number of higher-energy equilibrium states. In the investigated case of a chain with N=10 spins and a DMI much smaller than the in-plane uniaxial anisotropy, it turns out that a metastable (unstable) state of the finite chain is characterized by a configuration where none (at least one) of the inner spins is nearly parallel to the hard axis. The role of the DMI is to establish a unique rotational sense for the helical ground state. Moreover, the number of both metastable and unstable equilibrium states is doubled with respect to the case of zero DMI. This produces modifications in the Peierls–Nabarro potential encountered by a domain wall during its displacement along the discrete spin chain. - Highlights: • A finite-size chain of N classical spins within the XY-chiral model is investigated. • Using a systematic theoretical method, all equilibrium states are calculated for N=10. • The ground state has a non-uniform helical order with unique rotational sense. • Metastable states contain a domain wall whose energy
Zhang, Gong; Yuan, Hai; Chen, Xianshuai; Wang, Weijun; Chen, Jianyu; Liang, Jimin; Zhang, Peng
2016-01-01
Background/Purpose. This three-dimensional finite element study observed the stress distribution characteristics of 12 types of dental implants and their surrounding bone tissues with various structured abutments, implant threads, and healing methods under different amounts of concentrated loading. Materials and Methods. A three-dimensional geometrical model of a dental implant and its surrounding bone tissue was created; the model simulated a screw applied with a preload of 200 N or a torque...
Institute of Scientific and Technical Information of China (English)
SU Jia-can; LI Zhuo-dong; CAO Lie-hu; YU Bao-qing; ZHANG Chun-cai; LI Ming
2009-01-01
To explore the mechanical behavioroflum-bar spine loaded by stress and provide the mechanical ba-sis for clinical analysis and judgement of lumbar spine frac-tare classification, mechanical distribution and static stress. Methods: By means of computer simulation method, the constructed lumbar spine three-dimensional model was introduced into three-dimensional finite element analysis by software Ansys 7.0. The lumbar spine mechanical be-havior in different parts of the stress loading were calculated. Impact load is 0-8000 N. The peak value was 8000 N. The loading time is 0-40 minutes. The values of the main stress, stress distribution and the lumbar spine unit displacement in the direction of main stress were analyzed. Results: The lumbar spine model was divided into a total of 121 239 nodes, 112 491 units. It could objectively reflect the true anatomy of lumbar spine and its biomechani-cal behavior and obtain the end-plate images under differ-ent stress. The stress distribution on the lumbar interverte-bral disc (L-L) under the axial, lateral flexion and extension stress, and the displacement trace of the corresponding pro-cessus articularis were analyzed. Conclusion: It is helpful to analyze the stress distribu-tion of lumbar spine and units displacement in static stress loading in the clinical research of lumbar spine injury and the distribution of internal stress.
Watari, Minoru
2009-06-01
Two problems exist in the current studies on the application of the lattice Boltzmann method (LBM) to rarefied gas dynamics. First, most studies so far are applications of two-dimensional models. The numbers of velocity particles are small. Consequently, the boundary-condition methods of these studies are not directly applicable to a multispeed finite-difference lattice Boltzmann method (FDLBM) that has many velocity particles. Second, the LBM and FDLBM share their origins with the Boltzmann equation. Therefore, the results of LBM and FDLBM studies should be verified by the results of the continuous Boltzmann equation. In my review to date on the LBM studies, it appears that such verifications were seldom done. In this study, velocity slip and temperature jump simulations in the slip-flow regime were conducted using a three-dimensional FDLBM model. The results were compared with preceding theoretical studies based on the continuous Boltzmann equation. The results agreed with the theory with errors of a few percent. To further improve the accuracy of the FDLBM, it seems necessary to increase the number of velocity particles.
Gupta, Anurag; Kohli, Virender S; Hazarey, Pushpa V; Kharbanda, Om P; Gunjal, Amit
2009-06-01
This study was designed to evaluate patterns of stress generation in the temporomandibular joint after mandibular protraction, by using a 3-dimensional finite element method. The results of the initial investigation are reported here in Part 1. The effects of varying the construction bite are reported in Part 2. A 3-dimensional computer-aided design model was developed from the magnetic resonance images of a growing boy (age, 12 years), by using I-DEAS NX (version 11.0, Siemens PLM Software, Plano, Tex). The model simulated mandibular protraction, with 5 mm of sagittal advancement and 4 mm of vertical opening. Stress distributions on the condylar neck, the glenoid fossa, and the articular disc in the anteroposterior and mediolateral directions were assessed. Tensile stresses were located on the posterosuperior aspects and compressive stresses on the anterior and anterosuperior aspects of the condylar head. Tensile stresses were found in the posterior region of the glenoid fossa near the attachment of the posterior connective tissues. These results suggest that, on mandibular protraction, the mandibular condyle experiences tensile stresses in the posterosuperior aspect that might help explain condylar growth in this direction. Similarly, on the glenoid fossa, tensile stresses are created in the region of posterior connective tissues; this might be correlated with the increased cellular activity in this region. Further study with variable vertical heights of the construction bites is needed.
Zhang, Xiangfeng; Wang, Chao; Xia, Xi; Deng, Feng; Zhang, Yi
2015-06-01
This study aims to construct a three-dimensional finite element model of a maxillary anterior teeth retraction force system in light wire technique and to investigate the difference of hydrostatic pressure and initial displacement of upper anterior teeth under different torque values of tip back bend. A geometric three-dimensional model of the maxillary bone, including all the upper teeth, was achieved via CT scan. To construct the force model system, lingual brackets and wire were constructed by using the Solidworks. Brackets software, and wire were assembled to the teeth. ANASYS was used to calculate the hydrostatic pressure and the initial displacement of maxillary anterior teeth under different tip-back bend moments of 15, 30, 45, 60, and 75 Nmm when the class II elastic force was 0.556 N. Hydrostatic pressure was concentrated in the root apices and cervical margin of upper anterior teeth. Distal tipping and relative intrusive displacement were observed. The hydrostatic pressure and initial displacement of upper canine were greater than in the central and lateral incisors. This hydrostatic pressure and initial intrusive displacement increased with an increase in tip-back bend moment. Lingual retraction force system of maxillary anterior teeth in light wire technique can be applied safely and controllably. The type and quantity of teeth movement can be controlled by the alteration of tip-back bend moment.
Rajagopal, K. R.; Srinivasa, A. R.
2016-08-01
The aim of this paper is to develop a new unified class of 3D nonlinear anisotropic finite deformation inelasticity model that (1) exhibits rate-independent or dependent hysteretic response (i.e., response wherein reversal of the external stimuli does not cause reversal of the path in state space) with or without yield surfaces. The hysteresis persists with quasistatic loading. (2) Encompasses a wide range of different types of inelasticity models (such as Mullins effect in rubber, rock and soil mechanics, traditional metal plasticity, hysteretic behavior of shape memory materials) into a simple unified framework that is relatively easy to implement in computational schemes and (3) does not require any a priori particular notion of plastic strain or yield function. The core idea behind the approach is the development of an system of implicit rate equations that allow for the continuity of the response but with different rates along different directions. The theory, which is in purely mechanical setting, subsumes and generalizes many commonly used approaches for hypoelasticity and rate-independent plasticity. We illustrate its capability by modeling the Mullins effect which is the inelastic behavior of certain rubbery materials. We are able to simulate the entire cyclic response without the use of additional internal variables, i.e., the entire response is modeled by using an implicit function of stress and strain measures and their rates.
ImageParser: a tool for finite element generation from three-dimensional medical images
Directory of Open Access Journals (Sweden)
Yamada T
2004-10-01
Full Text Available Abstract Background The finite element method (FEM is a powerful mathematical tool to simulate and visualize the mechanical deformation of tissues and organs during medical examinations or interventions. It is yet a challenge to build up an FEM mesh directly from a volumetric image partially because the regions (or structures of interest (ROIs may be irregular and fuzzy. Methods A software package, ImageParser, is developed to generate an FEM mesh from 3-D tomographic medical images. This software uses a semi-automatic method to detect ROIs from the context of image including neighboring tissues and organs, completes segmentation of different tissues, and meshes the organ into elements. Results The ImageParser is shown to build up an FEM model for simulating the mechanical responses of the breast based on 3-D CT images. The breast is compressed by two plate paddles under an overall displacement as large as 20% of the initial distance between the paddles. The strain and tangential Young's modulus distributions are specified for the biomechanical analysis of breast tissues. Conclusion The ImageParser can successfully exact the geometry of ROIs from a complex medical image and generate the FEM mesh with customer-defined segmentation information.
Numerical simulation of shallow-water flooding using a two-dimensional finite volume model
Institute of Scientific and Technical Information of China (English)
YUAN Bing; SUN Jian; YUAN De-kui; TAO Jian-hua
2013-01-01
A 2-D Finite Volume Model (FVM) is developed for shallow water flows over a complex topography with wetting and drying processes.The numerical fluxes are computed using the Harten,Lax,and van Leer (HLL) approximate Riemann solver.Second-order accuracy is achieved by employing the MUSCL reconstruction method with a slope limiter in space and an explicit two-stage Runge-Kutta method for time integration.A simple and efficient method is introduced to deal with the wetting and drying processes without any correction of the numerical flux term or the source term.In this new method,a switch of alternative schemes is used to compute the water depths at the cell interface to obtain the numerical flux.The model is verified against benchmark tests with analytical solutions and laboratory experimental data.The numerical results show that the model can simulate different types of flood waves from the ideal flood wave to cases over complex terrains.The satisfactory performance indicates an extensive application prospect of the present model in view of its simplicity and effectiveness.
Electron acceleration in a nonrelativistic shock with very high Alfv\\'en Mach number
Matsumoto, Y; Hoshino, M
2013-01-01
Electron acceleration associated with various plasma kinetic instabilities in a nonrelativistic, very-high-Alfv\\'en Mach-number ($M_A \\sim 45$) shock is revealed by means of a two-dimensional fully kinetic PIC simulation. Electromagnetic (ion Weibel) and electrostatic (ion-acoustic and Buneman) instabilities are strongly activated at the same time in different regions of the two-dimensional shock structure. Relativistic electrons are quickly produced predominantly by the shock surfing mechanism with the Buneman instability at the leading edge of the foot. The energy spectrum has a high-energy tail exceeding the upstream ion kinetic energy accompanying the main thermal population. This gives a favorable condition for the ion acoustic instability at the shock front, which in turn results in additional energization. The large-amplitude ion Weibel instability generates current sheets in the foot, implying another dissipation mechanism via magnetic reconnection in a three-dimensional shock structure in the very-hi...
Dyer, Gregory C; Preu, Sascha; Vinh, N Q; Allen, S James; Reno, John L; Shaner, Eric A
2016-01-01
We measured a change in the current transport of an antenna-coupled, multi-gate, GaAs/AlGaAs field-effect transistor when terahertz electromagnetic waves irradiated the transistor and attribute the change to bolometric heating of the electrons in the two-dimensional electron channel. The observed terahertz absorption spectrum indicates coherence between plasmons excited under adjacent biased device gates. The experimental results agree quantitatively with a theoretical model we developed that is based on a generalized plasmonic transmission line formalism and describes an evolution of the plasmonic spectrum with increasing electron density modulation from homogeneous to the crystal limit. These results demonstrate an electronically induced and dynamically tunable plasmonic band structure.
Institute of Scientific and Technical Information of China (English)
Fa-yong Zhang
2004-01-01
The three-dimensional nonlinear Schrodinger equation with weakly damped that possesses a global attractor are considered. The dynamical properties of the discrete dynamical system which generate by a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete dynamical system.
Institute of Scientific and Technical Information of China (English)
Muhammad Ashfaq Ahmad; Lin Jie; Qian Yan; Ma Zhi-Min; Ma Ai-Qun; Liu Shu-Tian
2007-01-01
This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.
Two-dimensional finite volume method for dam-break flow simulation
Institute of Scientific and Technical Information of China (English)
M.ALIPARAST
2009-01-01
A numerical model based upon a second-order upwind cell-center finite volume method on unstructured triangular grids is developed for solving shallow water equations.The assumption of a small depth downstream instead of a dry bed situation changes the wave structure and the propagation speed of the front which leads to incorrect results.The use of Harten-Lax-vau Leer (HLL) allows handling of wet/dry treatment.By usage of the HLL approximate Riemann solver,also it make possible to handle discontinuous solutions.As the assumption of a very small depth downstream of the dam can change the nature of the dam break flow problem which leads to incorrect results,the HLL approximate Riemann solver is used for the computation of inviscid flux functions,which makes it possible to handle discontinuous solutions.A multidimensional slope-limiting technique is applied to achieve second-order spatial accuracy and to prevent spurious oscillations.To alleviate the problems associated with numerical instabilities due to small water depths near a wet/dry boundary,the friction source terms are treated in a fully implicit way.A third-order Runge-Kutta method is used for the time integration of semi-discrete equations.The developed numerical model has been applied to several test cases as well as to real flows.The tests are tested in two cases:oblique hydraulic jump and experimental dam break in converging-diverging flume.Numerical tests proved the robustness and accuracy of the model.The model has been applied for simulation of dam break analysis of Torogh in Irun.And finally the results have been used in preparing EAP (Emergency Action Plan).
An Investigation of Dimensional Scaling Using Cervical Spine Motion Segment Finite Element Models.
Singh, Dilaver; Cronin, Duane S
2017-02-15
The paucity of experimental data for validating computational models of different statures underscores the need for appropriate scaling methods so that models can be verified and validated using experimental data. Scaling was investigated using 50(th) percentile male (M50) and 5(th) percentile female (F05) cervical spine motion segment (C4-C5) finite element models subject to tension, flexion and extension loading. Two approaches were undertaken: geometric scaling of the models to investigate size effects (volumetric scaling) and scaling of the force-displacement or moment-angle model results (data scaling). Three sets of scale factors were considered: global (body mass), regional (neck dimensions) and local (segment tissue dimensions). Volumetric scaling of the segment models from M50 to F05, and vice-versa, produced correlations that were good or excellent in both tension and flexion (0.825-0.991); however, less agreement was found in extension (0.550-0.569). The reduced correlation in extension was attributed to variations in shape between the models leading to nonlinear effects such as different time to contact for the facet joints and posterior processes. Data scaling of the responses between the M50 and F05 models produced similar trends to volumetric scaling, with marginally greater correlations. Overall, the local tissue level and neck region level scale factors produced better correlations than the traditional global scaling. The scaling methods work well for a given subject, but are limited in applicability between subjects with different morphology, where nonlinear effects may dominate the response.
Two-dimensional finite-element modeling of periodical interdigitated full organic solar cells
Granero, P.; Balderrama, V. S.; Ferré-Borrull, J.; Pallarès, J.; Marsal, L. F.
2013-01-01
By means of finite-element numerical modeling, we analyze the influence of the nanostructured dissociation interface geometry on the behavior of interdigitated heterojunction full organic solar cells. A systematic analysis of light absorption, exciton diffusion, and carrier transport, all in the same numerical framework, is carried out to obtain their dependence on the interface geometrical parameters: pillar diameter and height, and nanostructure period. Cells are constituted of poly(3-hexylthiophene) (P3HT) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-(6,6)C61. Results show that light absorption is maximum for pillar heights of 80 nm and 230 nm. However, due to the short exciton diffusion length of organic materials, the analysis of the exciton diffusion process reveals that the 80 nm thickness gives rise to a higher photocurrent, except for the smaller pillar diameters. In terms of efficiency, it has been observed that the charge carrier transport is weakly dependent on the geometric parameters of the nanostructured interface if compared with the exciton diffusion process. The optimal cell is a device with a pillar height of 80 nm, a structure period of 25 nm, and a ratio of the nanopillar diameter to the period of 0.75, with an efficiency 3.6 times higher than the best planar bilayer reference device. This structure is such that it reaches a compromise between having a high proportion of P3HT to increase light absorption but preserving a small pillar diameter and interpillar distance to ensure an extended exciton dissociation interface.
Fields and fluids on curved non-relativistic spacetimes
Geracie, Michael; Roberts, Matthew M
2015-01-01
We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works. In this approach the derivative operator is defined by a Galilean spin connection valued in the Lie algebra of the Galilean group. This includes the usual spin connection plus an additional "boost connection" which parameterizes the freedom in the derivative operator not fixed by torsion or metric compatibility. As an example of this approach we develop the theory of non-relativistic dissipative fluids and find significant differences in both equations of motion and allowed transport coefficients from those found previously. Our approach also immediately generalizes to systems with independent mass and charge currents as would arise in multicomponent fluids. Along the way we also discuss how to write general locally Galilean invariant non-relativistic actions for multiple particle species at any order in derivatives. A detailed review of the geometry and its rela...
Nonrelativistic Fermions in Magnetic Fields a Quantum Field Theory Approach
Espinosa, Olivier R; Lepe, S; Méndez, F
2001-01-01
The statistical mechanics of nonrelativistic fermions in a constant magnetic field is considered from the quantum field theory point of view. The fermionic determinant is computed using a general procedure that contains all possible regularizations. The nonrelativistic grand-potential can be expressed in terms polylogarithm functions, whereas the partition function in 2+1 dimensions and vanishing chemical potential can be compactly written in terms of the Dedekind eta function. The strong and weak magnetic fields limits are easily studied in the latter case by using the duality properties of the Dedekind function.
Nonrelativistic factorizable scattering theory of multicomponent Calogero-Sutherland model
Ahn, C; Nam, S; Ahn, Changrim; Lee, Kong Ju Bock; Nam, Soonkeon
1995-01-01
We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable S-matrix theory with SU(N)-invariance. We find complete solutions of the Yang-Baxter equations without implementing the crossing symmetry, and one of them is identified with the scattering amplitudes derived from the Schr\\"{o}dinger equation of the Calogero-Sutherland model. This particular solution is of interest in that it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the SU(N)-invariant Yang-Baxter equations.
On the Failure of Multiconfiguration Methods in the Nonrelativistic Limit
Esteban, Maria J; Savin, Andreas
2009-01-01
The multiconfiguration Dirac-Fock method allows to calculate the state of relativistic electrons in atoms or molecules. This method has been known for a long time to provide certain wrong predictions in the nonrelativistic limit. We study in full mathematical details the nonlinear model obtained in the nonrelativistic limit for Be-like atoms. We show that the method with sp+pd configurations in the J=1 sector leads to a symmetry breaking phenomenon in the sense that the ground state is never an eigenvector of L^2 or S^2. We thereby complement and clarify some previous studies.
A three-dimensional finite element model of an adherent eukaryotic cell
Directory of Open Access Journals (Sweden)
McGarry J. G.
2004-04-01
Full Text Available Mechanical stimulation is known to cause alterations in the behaviour of cells adhering to a substrate. The mechanisms by which forces are transduced into biological responses within the cell remain largely unknown. Since cellular deformation is likely involved, further understanding of the biomechanical origins of alterations in cellular response can be aided by the use of computational models in describing cellular structural behaviour and in determining cellular deformation due to imposed loads of various magnitudes. In this paper, a finite element modelling approach that can describe the biomechanical behaviour of adherent eukaryotic cells is presented. It fuses two previous modelling approaches by incorporating, in an idealised geometry, all cellular components considered structurally significant, i.e. prestressed cytoskeleton, cytoplasm, nucleus and membrane components. The aim is to determine if we can use this model to describe the non-linear structural behaviour of an adherent cell and to determine the contribution of the various cellular components to cellular stability. Results obtained by applying forces (in the picoNewton range to the model membrane nodes suggest a key role for the cytoskeleton in determining cellular stiffness. The model captures non-linear structural behaviours such as strain hardening and prestress effects (in the region of receptor sites, and variable compliance along the cell surface. The role of the cytoskeleton in stiffening a cell during the process of cell spreading is investigated by applying forces to five increasingly spread cell geometries. Parameter studies reveal that material properties of the cytoplasm (elasticity and compressibility also have a large influence on cellular stiffness. The computational model of a single cell developed here is proposed as one that is sufficiently complex to capture the non-linear behaviours of the cell response to forces whilst not being so complex that the parameters
Institute of Scientific and Technical Information of China (English)
LI Ping; MAO Jing; PENG Zhou; XIE Hui
2007-01-01
In order to study mechanical stress on root from orthodontic tooth movement by sliding mechanics, a 3-dimensional finite element model incorporating all layers of a human mandibular dental arch with orthodontic appliance has been developed to simulate mechanical stress on root from the orthodontic tooth movement. Simulated orthodontic force of 2 N at 0, 30 and 45 degree from the horizontal axis was applied to the crown of the teeth. The finite element analysis showed when or- thodontic forces were applied to the tooth, the stress was mainly concentrated at the neck of the tooth decreasing uniformly to the apex and crown. The highest stress on the root was 0.621 N/ram2 for cer- vical margin of the canine, and 0.114 N/mm2 for apical region of the canine. The top of canine crown showed the largest amount of displacement (2.417 μm), while the lowest amount of displacement was located at the apical region of canine (0.043 μm). In conclusion, this model might enable one to simulate orthodontic tooth movements clinically. Sliding force at 2 N is ideal to ensure the bodily or- thodontic tooth movement. The highest stress concentration in the roots was always localized at the cervical margin when orthodontic force of 2 N at 0, 30 and 45 degree from the horizontal axis, so there may be the same risk of root resorption when orthodontic force of 2 N at 0, 30 and 45 degree was used in clinic cases.
Chen, Wen-Ming; Lee, Sung-Jae; Lee, Peter Vee Sin
2015-02-26
Therapeutic footwear with specially-made insoles is often used in people with diabetes and rheumatoid arthritis to relieve ulcer risks and pain due to high pressures from areas beneath bony prominences of the foot, in particular to the metatarsal heads (MTHs). In a three-dimensional finite element study of the foot and footwear with sensitivity analysis, effects of geometrical variations of a therapeutic insole, in terms of insole thicknesses and metatarsal pad (MP) placements, on local peak plantar pressure under MTHs and stress/strain states within various forefoot tissues, were determined. A validated musculoskeletal finite element model of the human foot was employed. Analyses were performed in a simulated muscle-demanding instant in gait. For many design combinations, increasing insole thicknesses consistently reduce peak pressures and internal tissue strain under MTHs, but the effects reach a plateau when insole becomes very thick (e.g., a value of 12.7mm or greater). Altering MP placements, however, showed a proximally- and a distally-placed MP could result in reverse effects on MTH pressure-relief. The unsuccessful outcome due to a distally-placed MP may attribute to the way it interacts with plantar tissue (e.g., plantar fascia) adjacent to the MTH. A uniform pattern of tissue compression under metatarsal shaft is necessary for a most favorable pressure-relief under MTHs. The designated functions of an insole design can best be achieved when the insole is very thick, and when the MP can achieve a uniform tissue compression pattern adjacent to the MTH.
A finite difference solution to 2-dimensional radiative transfer equation for small-animal imaging
Jin, Meng; Jiao, Yuting; Gao, Feng; Zhao, Huijuan
2010-02-01
Diffuse optical tomography (DOT) has been increasingly studied in the past decades. In DOT, the radiative transfer equation (RTE) and its P1 approximation, i.e. the diffuse equation (DE), have been used as the forward models. Since the DE-based DOT fails where biological tissue has a void-like region and when the source-detector separation is less than 5 mean free pathlengths, as in the situations of small animal imaging, the RTE-based DOT methodology has become a focus of investigation. Therefore, the complete formalism of the RTE is attracting more and more interest. It is clear that the quality of the reconstructed image depends strongly on the accuracy of the forward model. In this paper, A FDM was developed for solving two-dimensional RTE in a 2cm×2cm square homogeneous tissue with two groups of the optical properties and different schemes of the spatial and solid angle discretization. The results of the FDM are compared with the MC simulations. It is shown that when the step size of the spatial mesh becomes small, more discretized angle number is needed.
Directory of Open Access Journals (Sweden)
S. N. S. Jamaludin
2014-01-01
Full Text Available The composition of hydroxyapatite (HA as the ceramic phase and titanium (Ti as the metallic phase in HA/Ti functionally graded materials (FGMs shows an excellent combination of high biocompatibility and high mechanical properties in a structure. Because the gradation of these properties is one of the factors that affects the response of the functionally graded (FG plates, this paper is presented to show the domination of the grading parameter on the displacement and stress distribution of the plates. A three-dimensional (3D thermomechanical model of a 20-node brick quadratic element is used in the simulation of the thermoelastic behaviors of HA/Ti FG plates subjected to constant and functional thermal, mechanical, and thermomechanical loadings. The convergence properties of the present results are examined thoroughly in order to assess the accuracy of the theory applied and to compare them with the established research results. Instead of the grading parameter, this study reveals that the loading field distribution can be another factor that reflects the thermoelastic properties of the HA/Ti FG plates. The FG structure is found to be able to withstand the thermal stresses while preserving the high toughness properties and thus shows its ability to operate at high temperature.
A multi-dimensional finite volume cell-centered direct ALE solver for hydrodynamics
Clair, G.; Ghidaglia, J.-M.; Perlat, J.-P.
2016-12-01
In this paper we describe a second order multi-dimensional scheme, belonging to the class of direct Arbitrary Lagrangian-Eulerian (ALE) methods, for the solution of non-linear hyperbolic systems of conservation law. The scheme is constructed upon a cell-centered explicit Lagrangian solver completed with an edge-based upwinded formulation of the numerical fluxes, computed from the MUSCL-Hancock method, to obtain a full ALE formulation. Numerical fluxes depend on nodal grid velocities which are either set or computed to avoid most of the mesh problems typically encountered in purely Lagrangian simulations. In order to assess the robustness of the scheme, most results proposed in this paper have been obtained by computing the grid velocities as a fraction of the Lagrangian nodal velocities, the ratio being set before running the test case. The last part of the paper describes preliminary results about the triple point test case run in the ALE framework by computing the grid velocities with the fully adaptive Large Eddy Limitation (L.E.L.) method proposed in [1]. Such a method automatically computes the grid velocities at each node defining the mesh from the local characteristics of the flow. We eventually discuss the advantages and the drawback of the coupling.
Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios
Hobrecht, Hendrik; Hucht, Alfred
2017-02-01
We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function Z on an L× M square lattice, wrapped around a torus with aspect ratio ρ =L/M . By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a 2× 2 transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films ρ \\to 0 . Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.
Wu, Zhi-fang; Lei, Yong-hua; Li, Wen-jie; Liao, Sheng-hui; Zhao, Zi-jin
2013-02-01
To explore an effective method to construct and validate a finite element model of the unilateral cleft lip and palate(UCLP) craniomaxillary complex with sutures, which could be applied in further three-dimensional finite element analysis (FEA). One male patient aged 9 with left complete lip and palate cleft was selected and CT scan was taken at 0.75mm intervals on the skull. The CT data was saved in Dicom format, which was, afterwards, imported into Software Mimics 10.0 to generate a three-dimensional anatomic model. Then Software Geomagic Studio 12.0 was used to match, smoothen and transfer the anatomic model into a CAD model with NURBS patches. Then, 12 circum-maxillary sutures were integrated into the CAD model by Solidworks (2011 version). Finally meshing by E-feature Biomedical Modeler was done and a three-dimensional finite element model with sutures was obtained. A maxillary protraction force (500 g per side, 20° downward and forward from the occlusal plane) was applied. Displacement and stress distribution of some important craniofacial structures were measured and compared with the results of related researches in the literature. A three-dimensional finite element model of UCLP craniomaxillary complex with 12 sutures was established from the CT scan data. This simulation model consisted of 206 753 individual elements with 260 662 nodes, which was a more precise simulation and a better representation of human craniomaxillary complex than the formerly available FEA models. By comparison, this model was proved to be valid. It is an effective way to establish the three-dimensional finite element model of UCLP cranio-maxillary complex with sutures from CT images with the help of the following softwares: Mimics 10.0, Geomagic Studio 12.0, Solidworks and E-feature Biomedical Modeler.
Energy Technology Data Exchange (ETDEWEB)
Bellucci, S. [INFN, Laboratori Nazionali di Frascati, Frascati (Italy); Bezerra de Mello, E.R. [Universidade Federal da Parai ba, Departamento de Fisica, 58.059-970, Joao Pessoa, PB (Brazil); Braganca, E. [INFN, Laboratori Nazionali di Frascati, Frascati (Italy); Universidade Federal da Parai ba, Departamento de Fisica, 58.059-970, Joao Pessoa, PB (Brazil); Saharian, A.A. [Yerevan State University, Department of Physics, Yerevan (Armenia)
2016-06-15
We evaluate the fermion condensate and the expectation values of the charge and current densities for a massive fermionic field in (2+1)-dimensional conical spacetime with a magnetic flux located at the cone apex. The consideration is done for both irreducible representations of the Clifford algebra. The expectation values are decomposed into the vacuum expectation values and contributions coming from particles and antiparticles. All these contributions are periodic functions of the magnetic flux with the period equal to the flux quantum. Related to the non-invariance of the model under the parity and time-reversal transformations, the fermion condensate and the charge density have indefinite parity with respect to the change of the signs of the magnetic flux and chemical potential. The expectation value of the radial current density vanishes. The azimuthal current density is the same for both the irreducible representations of the Clifford algebra. It is an odd function of the magnetic flux and an even function of the chemical potential. The behavior of the expectation values in various asymptotic regions of the parameters are discussed in detail. In particular, we show that for points near the cone apex the vacuum parts dominate. For a massless field with zero chemical potential the fermion condensate and charge density vanish. Simple expressions are derived for the part in the total charge induced by the planar angle deficit and magnetic flux. Combining the results for separate irreducible representations, we also consider the fermion condensate, charge and current densities in parity and time-reversal symmetric models. Possible applications to graphitic nanocones are discussed. (orig.)
Miksat, J.; Müller, T. M.; Wenzel, F.
2008-07-01
Finite difference (FD) simulation of elastic wave propagation is an important tool in geophysical research. As large-scale 3-D simulations are only feasible on supercomputers or clusters, and even then the simulations are limited to long periods compared to the model size, 2-D FD simulations are widespread. Whereas in generally 3-D heterogeneous structures it is not possible to infer the correct amplitude and waveform from 2-D simulations, in 2.5-D heterogeneous structures some inferences are possible. In particular, Vidale & Helmberger developed an approach that simulates 3-D waveforms using 2-D FD experiments only. However, their method requires a special FD source implementation technique that is based on a source definition which is not any longer used in nowadays FD codes. In this paper, we derive a conversion between 2-D and 3-D Green tensors that allows us to simulate 3-D displacement seismograms using 2-D FD simulations and the actual ray path determined in the geometrical optic limit. We give the conversion for a source of a certain seismic moment that is implemented by incrementing the components of the stress tensor. Therefore, we present a hybrid modelling procedure involving 2-D FD and kinematic ray-tracing techniques. The applicability is demonstrated by numerical experiments of elastic wave propagation for models of different complexity.
A review of finite size effects in quasi-zero dimensional superconductors.
Bose, Sangita; Ayyub, Pushan
2014-11-01
Quantum confinement and surface effects (SEs) dramatically modify most solid state phenomena as one approaches the nanometer scale, and superconductivity is no exception. Though we may expect significant modifications from bulk superconducting properties when the system dimensions become smaller than the characteristic length scales for bulk superconductors-such as the coherence length or the penetration depth-it is now established that there is a third length scale which ultimately determines the critical size at which Cooper pairing is destroyed. In quasi-zero-dimensional (0D) superconductors (e.g. nanocrystalline materials, isolated or embedded nanoparticles), one may define a critical particle diameter below which the mean energy level spacing arising from quantum confinement becomes equal to the bulk superconducting energy gap. The so-called Anderson criterion provides a remarkably accurate estimate of the limiting size for the destabilization of superconductivity in nanosystems. This review of size effects in quasi-0D superconductors is organized as follows. A general summary of size effects in nanostructured superconductors (section 1) is followed by a brief overview of their synthesis (section 2) and characterization using a variety of techniques (section 3). Section 4 reviews the size-evolution of important superconducting parameters-the transition temperature, critical fields and critical current-as the Anderson limit is approached from above. We then discuss the effect of thermodynamic fluctuations (section 5), which become significant in confined systems. Improvements in fabrication methods and the increasing feasibility of addressing individual nanoparticles using scanning probe techniques have lately opened up new directions in the study of nanoscale superconductivity. Section 6 reviews both experimental and theoretical aspects of the recently discovered phenomena of 'parity effect' and 'shell effect' that lead to a strong, non-monotonic size
Chang, Chih-Ling; Chen, Chen-Sheng; Yeung, Tze Cheung; Hsu, Ming-Lun
2012-01-01
The objective of this study was to analyze and compare the stresses in two different bone-implant interface conditions in anisotropic three-dimensional finite element models (FEMs) of an osseointegrated implant of either commercially pure titanium or yttrium-partially stabilized zirconia (Y-PSZ) in combination with different superstructures (gold alloy or Y-PSZ crown) in the posterior maxilla. Three-dimensional FEMs were created of a first molar section of the maxilla into which was embedded an implant, connected to an abutment and superstructure, using commercial software. Two versions of the FEM were constructed; these allowed varying assignment of properties (either a bonded and or a contact interface), so that all experimental variables could be investigated in eight groups. Compact and cancellous bone were modeled as fully orthotropic and transversely isotropic, respectively. Oblique (200-N vertical and 40-N horizontal) occlusal loading was applied at the central and distal fossae of the crown. Maximum von Mises and compressive stresses in the compact bone in the two interfaces were lower in the zirconia implant groups than in the titanium implant groups. A similar pattern of stress distribution in cancellous bone was observed, not only on the palatal side of the platform but also in the apical area of both types of implants. The biomechanical parameters of the new zirconia implant generated a performance similar to that of the titanium implant in terms of displacement, stresses on the implant, and the bone-implant interface; therefore, it may be a viable alternative, especially for esthetic regions.
Pellizzer, Eduardo Piza; Verri, Fellippo Ramos; de Moraes, Sandra Lúcia Dantas; Falcón-Antenucci, Rosse Mary; de Carvalho, Paulo Sérgio Perri; Noritomi, Pedro Yoshito
2013-08-01
The aim of this study was to evaluate the stress distribution in implants of regular platforms and of wide diameter with different sizes of hexagon by the 3-dimensional finite element method. We used simulated 3-dimensional models with the aid of Solidworks 2006 and Rhinoceros 4.0 software for the design of the implant and abutment and the InVesalius software for the design of the bone. Each model represented a block of bone from the mandibular molar region with an implant 10 mm in length and different diameters. Model A was an implant 3.75 mm/regular hexagon, model B was an implant 5.00 mm/regular hexagon, and model C was an implant 5.00 mm/expanded hexagon. A load of 200 N was applied in the axial, lateral, and oblique directions. At implant, applying the load (axial, lateral, and oblique), the 3 models presented stress concentration at the threads in the cervical and middle regions, and the stress was higher for model A. At the abutment, models A and B showed a similar stress distribution, concentrated at the cervical and middle third; model C showed the highest stresses. On the cortical bone, the stress was concentrated at the cervical region for the 3 models and was higher for model A. In the trabecular bone, the stresses were less intense and concentrated around the implant body, and were more intense for model A. Among the models of wide diameter (models B and C), model B (implant 5.00 mm/regular hexagon) was more favorable with regard to distribution of stresses. Model A (implant 3.75 mm/regular hexagon) showed the largest areas and the most intense stress, and model B (implant 5.00 mm/regular hexagon) showed a more favorable stress distribution. The highest stresses were observed in the application of lateral load.
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary coordinat
A brief introduction to non-relativistic supergravity
Energy Technology Data Exchange (ETDEWEB)
Zojer, Thomas [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen (Netherlands)
2016-04-15
Non-relativistic geometries have received more attention lately. We review our attempts to construct supersymmetric extensions of this so-called Newton-Cartan geometry in three space-time dimensions. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary
Non-relativistic classical mechanics for spinning particles
Salesi, G
2004-01-01
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which suggests classical interpretations for tunnel effect and quantum potential.
Spacetime Variation of Lorentz-Violation Coefficients at Nonrelativistic Scale
Lane, Charles D
2016-01-01
When the Standard-Model Extension (SME) is applied in curved spacetime, the Lorentz-violation coefficients must depend on spacetime position. This work describes some of the consequences of this spacetime variation. We focus on effects that appear at a nonrelativistic scale and extract sensitivity of completed experiments to derivatives of SME coefficient fields.
Theory of non-relativistic three-particle scattering
Malfliet, R.; Ruijgrok, Th.
1967-01-01
A new method, using asymptotically stationary states, is developed to calculate the S-matrix for the scattering of a non-relativistic particle by the bound state of two other particles. For the scattering with breakup of this bound state, we obtain a simplified form of the Faddeev integral
Pan, Xue; Wu, Yuan-Fang
2016-01-01
The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). The order has been calculated to the sixth one at experiments. The corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class with QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that when the critical point is approached from the crossover side, the sixth order cumulant is negative. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising mod...
Directory of Open Access Journals (Sweden)
Francesca Capelli
2016-05-01
Full Text Available Power devices intended for high-voltage systems must be tested according to international standards, which includes the short-time withstand current test and peak withstand current test. However, these tests require very special facilities which consume huge amounts of electrical power. Therefore, mathematical tools to simulate such tests are highly appealing since they allow reproducing the electromagnetic and thermal behavior of the test object in a fast and economical manner. In this paper, a three-dimensional finite element method (3D-FEM approach to simulate the transient thermal behavior of substation connectors is presented and validated against experimental data. To this end, a multiphysics 3D-FEM method is proposed, which considers both the connector and the reference power conductors. The transient and steady-state temperature profiles of both the conductors and connector provided by the 3D-FEM method prove its suitability and accuracy as compared to experimental data provided by short-circuit tests conducted in two high-current laboratories. The proposed simulation tool, which was proven to be accurate and realistic, may be particularly useful during the design and optimization phases of substation connectors since it allows anticipating the results of mandatory laboratory tests.
Jacobsen, P H; Wakefieldt, A J; O'Doherty, D M; Rees, J S
2006-12-01
Three dimensional finite element models of an upper second premolar and molar with full veneer gold crown preparations were developed from extracted samples. The cement lute width was kept constant at 40 microm, but the height and preparation taper were varied. For both models the preparation height was either 1.5 mm (short preparation) or 3 mm (long preparation). The preparation taper was either 10 degree or 30 degree, giving a total of eight models. Each model was loaded with a 10 N horizontal load, a 10 N vertical load or a 10 N load distributed across the occlusal surface. The maximum shear stress and the maximum Von Mises' stress in the cement lute of each model were recorded. For the premolar, the maximum shear stresses ranged from 0.3-5.43 MPa and the maximum Von Mises' stress ranged from 1.44-14.98 MPa. For the molar, the maximum shear stresses ranged from 0.15-5.22 MPa and the maximum Von Mises' stress ranged from 0.3 7-15.02 MPa. The stress fields were consistently higher in the premolar with a 30 degree preparation taper compared to the 10 degree taper. The attainment of a cavity taper of 100 is still important to minimise stress in the cement lute and is particularly important in teeth with a lower preparation surface area such as a premolar
Bohling, G.C.; Butler, J.J.
2001-01-01
We have developed a program for inverse analysis of two-dimensional linear or radial groundwater flow problems. The program, 1r2dinv, uses standard finite difference techniques to solve the groundwater flow equation for a horizontal or vertical plane with heterogeneous properties. In radial mode, the program simulates flow to a well in a vertical plane, transforming the radial flow equation into an equivalent problem in Cartesian coordinates. The physical parameters in the model are horizontal or x-direction hydraulic conductivity, anisotropy ratio (vertical to horizontal conductivity in a vertical model, y-direction to x-direction in a horizontal model), and specific storage. The program allows the user to specify arbitrary and independent zonations of these three parameters and also to specify which zonal parameter values are known and which are unknown. The Levenberg-Marquardt algorithm is used to estimate parameters from observed head values. Particularly powerful features of the program are the ability to perform simultaneous analysis of heads from different tests and the inclusion of the wellbore in the radial mode. These capabilities allow the program to be used for analysis of suites of well tests, such as multilevel slug tests or pumping tests in a tomographic format. The combination of information from tests stressing different vertical levels in an aquifer provides the means for accurately estimating vertical variations in conductivity, a factor profoundly influencing contaminant transport in the subsurface. ?? 2001 Elsevier Science Ltd. All rights reserved.
Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang
2015-10-01
For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and has a high resolution. Moreover, we evaluate and compare the performance of the uniform mesh WENO scheme and the parallel AMR&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.
Tanaka, E; del Pozo, R; Tanaka, M; Asai, D; Hirose, M; Iwabe, T; Tanne, K
2004-07-01
The aim of this study was to evaluate the differences of stress distribution in the temporomandibular joint (TMJ) disc during jaw opening between the subjects with and without internal derangement of TMJ (TMJ-ID). Three symptom-free volunteers and three symptomatic patients with anterior disc displacement were selected as normal and TMJ-ID subjects, respectively. For each subject, magnetic resonance images (MRI) were taken in the axial, sagittal and coronal directions. Using MRI taken, six three-dimensional finite element models of TMJ were developed. For each subject, the condylar movements during jaw opening were recorded and used as the loading condition for stress analysis. By comparing the calculated disc displacement to the measured one from MRI, the frictional coefficients were mu = 0.001 for the normal subjects, but mu = 0.01-0.001 for the TMJ-ID subjects. For the normal subjects, relatively high stresses were found at the anterior and lateral portions of the disc throughout jaw opening. In the connective tissues, the stress level was higher in the TMJ-ID than in the normal subjects. It is suggested that the disc displacement induces the change of stress distribution in the disc and the increase of frictional coefficients between articular surfaces, resulting in the secondary tissue damage.
Li, Lei-Ting; Lin, Y. C.; Li, Ling; Shen, Lu-Ming; Wen, Dong-Xu
2015-03-01
Three-dimensional crystal plasticity finite element (CPFE) method is used to investigate the hot compressive deformation behaviors of 7075 aluminum alloy. Based on the grain morphology and crystallographic texture of 7075 aluminum alloy, the microstructure-based representative volume element (RVE) model was established by the pole figure inversion approach. In order to study the macroscopic stress-strain response and microstructural evolution, the CPFE simulations are performed on the established microstructure-based RVE model. It is found that the simulated stress-strain curves and deformation texture well agree with the measured results of 7075 aluminum alloy. With the increasing deformation degree, the remained initial weak Goss texture component tends to be strong and stable, which may result in the steady flow stress. The grain orientation and grain misorientation have significant effects on the deformation heterogeneity during hot compressive deformation. In the rolling-normal plane, the continuity of strain and misorientation can maintain across the low-angle grain boundaries, while the discontinuity of strain and misorientation is observed at the high-angle grain boundaries. The simulated results demonstrate that the developed CPFE model can well describe the hot compressive deformation behaviors of 7075 aluminum alloy under elevated temperatures.
Peery, Jeffrey T; Klute, Glenn K; Blevins, Joanna J; Ledoux, William R
2006-09-01
Amputees who wear prosthetic limbs often experience discomfort from blisters and sores due to mechanical insult; these skin conditions are exacerbated by elevated skin temperatures and excessive perspiration within the prosthetic socket. The goal of this study was to create a tool for developing new prostheses that accommodate varying thermal loads arising from everyday activities. A three-dimensional thermal model of a transtibial residual limb and prosthesis was constructed using the finite element (FE) method. Transverse computerized tomography (CT) scans were used to specify the geometry of the residual limb and socket. Thermal properties from the literature were assigned to both biological tissue and prosthetic socket elements. The purpose of this work was to create a model that would aid in testing the effect of new prosthesis designs on skin temperature. To validate its output, the model was used to predict the skin temperature distribution in a common prosthetic socket system (silicone liner, wool sock, and carbon fiber socket) at rest with no mechanical loading. Skin temperatures were generally elevated near muscle and decreased anteriorly and at the distal end. Experimental temperature measurements taken at the skin-prosthesis interface of five human subjects were used to validate the model. Data extracted from the thermal model at anterior, posterior, lateral, and medial locations were typically within one standard deviation of experimental results; the mean temperatures were within 0.3 degree C for each section and were within 0.1 degree C overall.
Miura, Shoko; Kasahara, Shin; Yamauchi, Shinobu; Egusa, Hiroshi
2017-06-01
The purpose of this study were: to perform stress analyses using three-dimensional finite element analysis methods; to analyze the mechanical stress of different framework designs; and to investigate framework designs that will provide for the long-term stability of both cantilevered fixed partial dentures (FPDs) and abutment teeth. An analysis model was prepared for three units of cantilevered FPDs that assume a missing mandibular first molar. Four types of framework design (Design 1, basic type; Design 2, framework width expanded buccolingually by 2 mm; Design 3, framework height expanded by 0.5 mm to the occlusal surface side from the end abutment to the connector area; and Design 4, a combination of Designs 2 and 3) were created. Two types of framework material (yttrium-oxide partially stabilized zirconia and a high precious noble metal gold alloy) and two types of abutment material (dentin and brass) were used. In the framework designs, Design 1 exhibited the highest maximum principal stress value for both zirconia and gold alloy. In the abutment tooth, Design 3 exhibited the highest maximum principal stress value for all abutment teeth. In the present study, Design 4 (the design with expanded framework height and framework width) could contribute to preventing the concentration of stress and protecting abutment teeth. © 2017 Eur J Oral Sci.
Wu, J S; Chen, J H
1996-04-01
The purpose of this study is to clarify the mechanical behaviour of spinal motion segments through a proper numerical model. The model constructed can give correct information and provide medical fields with valuable guidance in solving clinical problems occurring in the spine. A three-dimensional poroelastic finite element model of spinal motion segments is constructed and a mixed formulation is introduced. The geometry of the model is automatically formed from a series of CT-scanning images. Vertebral column, intervertebral joint, facet joints and ligaments are all included in the model. The contact surface of facet joints is considered as the inclined boundary. Such inclination is imposed when the contact surface is under compression. Ligaments surrounding the vertebral body and the intervertebral disc are put into the model when they are under tension. Iteration is implemented in the computing process to meet such boundary characteristics of facet joints and ligaments. Prediction of the mechanical behaviour in the segment under long term creep loading, is demonstrated using the current algorithm. Results show that the model and corresponding numerical procedures developed here can simulate the mechanical behaviour of the spinal motion segments properly.
Ozevin, Didem; Fazel, Hossein; Cox, Justin; Hardman, William; Kessler, Seth S.; Timmons, Alan
2014-04-01
Gearbox components of aerospace structures are typically made of brittle materials with high fracture toughness, but susceptible to fatigue failure due to continuous cyclic loading. Structural Health Monitoring (SHM) methods are used to monitor the crack growth in gearbox components. Damage detection methodologies developed in laboratory-scale experiments may not represent the actual gearbox structural configuration, and are usually not applicable to real application as the vibration and wave properties depend on the material, structural layers and thicknesses. Also, the sensor types and locations are key factors for frequency content of ultrasonic waves, which are essential features for pattern recognition algorithm development in noisy environments. Therefore, a deterministic damage detection methodology that considers all the variables influencing the waveform signature should be considered in the preliminary computation before any experimental test matrix. In order to achieve this goal, we developed two dimensional finite element models of a gearbox cross section from front view and shaft section. The cross section model consists of steel revolving teeth, a thin layer of oil, and retention plate. An ultrasonic wave up to 1 MHz frequency is generated, and waveform histories along the gearbox are recorded. The received waveforms under pristine and cracked conditions are compared in order to analyze the crack influence on the wave propagation in gearbox, which can be utilized by both active and passive SHM methods.
Robbins, Joshua; Voth, Thomas
2011-06-01
Material response to dynamic loading is often dominated by microstructure such as grain topology, porosity, inclusions, and defects; however, many models rely on assumptions of homogeneity. We use the probabilistic finite element method (WK Liu, IJNME, 1986) to introduce local uncertainty to account for material heterogeneity. The PFEM uses statistical information about the local material response (i.e., its expectation, coefficient of variation, and autocorrelation) drawn from knowledge of the microstructure, single crystal behavior, and direct numerical simulation (DNS) to determine the expectation and covariance of the system response (velocity, strain, stress, etc). This approach is compared to resolved grain-scale simulations of the equivalent system. The microstructures used for the DNS are produced using Monte Carlo simulations of grain growth, and a sufficient number of realizations are computed to ensure a meaningful comparison. Finally, comments are made regarding the suitability of one-dimensional PFEM for modeling material heterogeneity. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence
Lopez-Arcos, Cristhiam; Nastase, Horatiu
2015-01-01
We consider the nonrelativistic limit of the abelian reduction of the massive ABJM model proposed in \\cite{Mohammed:2012gi}, obtaining a supersymmetric version of the Jackiw-Pi model. The system exhibits an ${\\cal N}=2$ Super-Schr\\"odinger symmetry with the Jackiw-Pi vortices emerging as BPS solutions. We find that this $(2+1)$-dimensional abelian field theory is dual to a certain (3+1)-dimensional gravity theory that differs somewhat from previously considered abelian condensed matter stand-ins for the ABJM model. We close by commenting on progress in the top-down realization of the AdS/CMT correspondence in a critical string theory.
Institute of Scientific and Technical Information of China (English)
LI Li-li; WANG Zhong-yi; BAI Zhong-cheng; MAO Yong; GAO Bo; XIN Hai-tao; ZHOU Bing; ZHANG Yong; LIU Bing
2006-01-01
Background It is very difficult and relatively unpredictable to preserve and restore severely weakened pulpless roots. To provide much needed benefit basis for clinical practice, this study was carried out to analyze the stress distribution in weakened roots restored with different cements in combination with titanium alloy posts. Finite element analysis (FEA) was employed in the study.Methods A pseudo three-dimensional model of a maxillary central incisor with flared root canal, theoretically restored with titanium alloy posts in combination with different cements, was established. The analysis was performed by use of ANSYS software. The tooth was assumed to be isotropic, homogenous and elastic. A load of 100 N at an angle of 45°to the longitudinal axis was applied at the palatal surface of the crown. The distributions of stresses in weakened roots filled with cements of different elastic modulus were analyzed by the three-dimensional FEA model.Results Several stress trends were observed when the stress cloud atlas obtained in the study was analyzed. With the increase of the elastic modulus of cements from 1.8 GPa to 22.4 GPa, the stress values in dentin decreased from 39.58 MPa to 31.43 MPa and from 24.51 MPa to 20.76 MPa (respectively, for maximum principle stress values and Von Mises stress values). When Panavia F and zinc phosphate cement were used, the stress peak values in dentin were very small with no significant difference observed, and the Von Mises stress values were 20.87 MPa and 20.76 MPa respectively. On the other hand, maximum principle stress value and Von Mises stress value in cement layer increased with the increase of the elastic modulus of cements.Conclusions The result of this study demonstrated that elastic modulus was indeed one of the important parameters to evaluate property of the cements. Our three-dimensional FEA model study also found that the cement with elastic modulus similar to that of dentin could reinforce weakened root and
Construction of the ground state in nonrelativistic QED by continuous flows
Bach, Volker; Könenberg, Martin
For a nonrelativistic hydrogen atom minimally coupled to the quantized radiation field we construct the ground state projection P by a continuous approximation scheme as an alternative to the iteration scheme recently used by Fröhlich, Pizzo, and the first author [V. Bach, J. Fröhlich, A. Pizzo, Infrared-finite algorithms in QED: The groundstate of an atom interacting with the quantized radiation field, Comm. Math. Phys. (2006), doi: 10.1007/s00220-005-1478-3]. That is, we construct P=limP as the limit of a continuously differentiable family ()t⩾0 of ground state projections of infrared regularized Hamiltonians H. Using the ODE solved by this family of projections, we show that the norm ‖P‖ of their derivative is integrable in t which in turn yields the convergence of P by the fundamental theorem of calculus.
GenASiS: General Astrophysical Simulation System. II. Nonrelativistic Hydrodynamics
Cardall, Christian Y; Endeve, Eirik; Mezzacappa, Anthony
2012-01-01
In this paper, the second in a series, we document the algorithms and solvers for compressible nonrelativistic hydrodynamics implemented in GenASiS (General Astrophysical Simulation System)---a new code being developed initially and primarily, though by no means exclusively, for the simulation of core-collapse supernovae. In the Mathematics division of GenASiS we introduce Solvers, which includes finite-volume updates for generic hyperbolic BalanceEquations and ordinary differential equation integration Steps. We also introduce the Physics division of GenASiS; this extends the Manifolds division of Mathematics into physical Spaces, defines StressEnergies, and combines these into Universes. We benchmark the hydrodynamics capabilities of GenASiS against many standard test problems; the results illustrate the basic competence of our implementation, demonstrate the manifest superiority of the HLLC over the HLL Riemann solver in a number of interesting cases, and provide preliminary indications of the code's abili...
Horowitz, A; Sheinman, I; Lanir, Y
1988-02-01
A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.
Energy Technology Data Exchange (ETDEWEB)
Nakra Mohajer, Soukaina; El Harouny, El Hassan [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); El Khamkhami, Jamal [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); and others
2016-09-15
Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.
Three particles in a finite volume
Polejaeva, Kathryn
2012-01-01
Within the non-relativistic potential scattering theory, we derive a generalized version of the L\\"uscher formula, which includes three-particle inelastic channels. Faddeev equations in a finite volume are discussed in detail. It is proved that, even in the presence of the three-particle intermediate states, the discrete spectrum in a finite box is determined by the infinite-volume elements of the scattering S-matrix up to corrections, exponentially suppressed at large volumes.
Zhou, Chenggang; Landau, D. P.; Schulthess, Thomas C.
2006-01-01
By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in $2+\\epsilon$ dimensions. We found that the long length scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $\\sigma$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dime...
Greene, Jethro H; Taflove, Allen
2003-10-01
We report the initial three-dimensional finite-difference time-domain modeling of a vertically coupled photonic racetrack. The modeling reveals details of the full suite of space-time behavior of electromagnetic-wave phenomena involved in guiding, coupling, multimoding, dispersion, and radiation. This behavior is not easily obtainable by analytical or full-vector frequency-domain methods, measurements of terminal properties, or near-field scanning optical microscopy.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A three-dimensional finite-element simulation of stretching technological parameters of heavy forgings is performed by using ANSYS program. The law of internal stress distribution with different bt/h (tool width ratio) and different bb/h (blank width ratio) is studied. Consequently, the critical tool width ratio( bt/h )cr and blank width ratio( bb/h )cr leading no bi-axial tension are obtained. It lays a credible foundation for designing reasonable stretching technology.
Directory of Open Access Journals (Sweden)
Saraswati Acharya
2015-08-01
Full Text Available Objective: To deal the implication of metabolic reaction relying on dermal thicknesses of males and females for temperature distribution on the layers of dermal part at various atmospheric temperatures. Methods: The mathematical model involving bioheat equation has been solved using finite element method and Crank-Nicolson technique to numerically investigate two dimensional temperature distributions. Initially, human dermal region under consideration is divided into six parts: stratum corneum, stratum germinativum, papillary region, reticular region, fatty layer and muscle part of subcutaneous tissue. Pennes bioheat equation is used considering the suitable physical and physiological parameters that affect the heat regulation in the layers. Computer simulation has been used for numerical results and graph of the temperatures profiles. Results: Lower percentage of muscle mass and higher percentage of adipose tissue in subcutaneous part of females result lower metabolic rate compared to males. Metabolism is considered as a heat source within the body tissue. The study delineates that when the metabolic heat generation S increases, body temperature rises and when S decreases, it goes down. In higher ambient temperature T∞ effect of S is lower as compared to lower T∞. Conclusions: Males and females would differ in their physiological responses in temperature distribution due to differences in metabolic heat production between genders. The thinner layers of males lead to higher values of skin temperature than thicker layer of females. Thickness plays a significant role in temperature distributions in human males and females body. Current understanding of human thermoregulation is based on male patterns; studies on women are still relatively rare and involve only small number of subjects. So it is still necessary for micro level study for temperature distribution model on the dermal layers of males and females.
Connector design in a long-span-fixed dental prosthesis: A three-dimensional finite element analysis
Directory of Open Access Journals (Sweden)
B H Harshitha Gowda
2013-01-01
Full Text Available Objectives: The goal of every prosthetic management is to simulate nature and be in harmony with nature within the physiological limits. The occlusal forces on a fixed dental prosthesis are transmitted to the surrounding structures through pontics, connectors and retainers and more stresses are seen at the connector region. To analyze the stress patterns in cast and soldered connectors between the two pontics and between the retainer and pontic of a four unit fixed dental prosthesis on axial and non axial loading and also to observe and ascertain the need to modify the design of the rigid connectors. Materials and Methods: Subsequently four models each of cast and soldered connectors with cylindrical and triangular design, of dimension 3 × 4 mm and thickness 0.5 mm was designed for the study. The first premolar and second molar were considered as the abutments and 2 nd premolar and 1 st molar as the pontics. The analysis was done using ANSYS version 8.0 software and by placing axial and non-axial load of 40 Newtons each. Results: Von Misses stresses were observed at the connector region between the two pontics, especially in the cervical region. Conclusion: The cylindrical cast connectors showed less stress in comparison to triangular design and the difference in the stress distribution of cast and soldered connectors were marginal. Clinical Significance: The occlusal forces on a fixed dental prosthesis are transmitted to the surrounding structures through pontics, connectors and retainers with maximum stresses concentrated at the connectors. Hence this three-dimensional finite element analysis study investigated stress distribution in a four unit posterior fixed dental prosthesis, having cylindrical and triangular connector designs.
Huang, C.-S.; Chen, J.-J.; Yeh, H.-D.
2016-01-01
This study develops a three-dimensional (3-D) mathematical model for describing transient hydraulic head distributions due to pumping at a radial collector well (RCW) in a rectangular confined or unconfined aquifer bounded by two parallel streams and no-flow boundaries. The streams with low-permeability streambeds fully penetrate the aquifer. The governing equation with a point-sink term is employed. A first-order free surface equation delineating the water table decline induced by the well is considered. Robin boundary conditions are adopted to describe fluxes across the streambeds. The head solution for the point sink is derived by applying the methods of finite integral transform and Laplace transform. The head solution for a RCW is obtained by integrating the point-sink solution along the laterals of the RCW and then dividing the integration result by the sum of lateral lengths. On the basis of Darcy's law and head distributions along the streams, the solution for the stream depletion rate (SDR) can also be developed. With the aid of the head and SDR solutions, the sensitivity analysis can then be performed to explore the response of the hydraulic head to the change in a specific parameter such as the horizontal and vertical hydraulic conductivities, streambed permeability, specific storage, specific yield, lateral length, and well depth. Spatial head distributions subject to the anisotropy of aquifer hydraulic conductivities are analyzed. A quantitative criterion is provided to identify whether groundwater flow at a specific region is 3-D or 2-D without the vertical component. In addition, another criterion is also given to allow for the neglect of vertical flow effect on SDR. Conventional 2-D flow models can be used to provide accurate head and SDR predictions if satisfying these two criteria.
Institute of Scientific and Technical Information of China (English)
XIAO Jinbiao; LIU Xu; CAI Chun; FAN Hehong; SUN Xiaohan
2006-01-01
A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method (3D-FV-BPM) formulation along the longitudinal direction. The cross-coupling terms (CCTs) are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.
Institute of Scientific and Technical Information of China (English)
SaraswatiAcharya; Dil Bahadur Gurung; Vinod Prakash Saxena
2015-01-01
Objective: To deal the implication of metabolic reaction relying on dermal thicknesses of males and females for temperature distribution on the layers of dermal part at various atmospheric temperatures. Methods: The mathematical model involving bioheat equation has been solved using finite element method and Crank-Nicolson technique to numerically investigate two dimensional temperature distributions. Initially, human dermal region under consideration is divided into six parts: stratum corneum, stratum germinativum, papillary region, reticular region, fatty layer and muscle part of subcutaneous tissue. Pennes bioheat equation is used considering the suitable physical and physiological parameters that affect the heat regulation in the layers. Computer simulation has been used for numerical results and graph of the temperatures profiles. Results: Lower percentage of muscle mass and higher percentage of adipose tissue in subcutaneous part of females result lower metabolic rate compared to males. Metabolism is considered as a heat source within the body tissue. The study delineates that when the metabolic heat generation S increases, body temperature rises and when S decreases, it goes down. In higher ambient temperature T∞ effect of S is lower as compared to lower T∞. Conclusions: Males and females would differ in their physiological responses in temperature distribution due to differences in metabolic heat production between genders. The thinner layers of males lead to higher values of skin temperature than thicker layer of females. Thickness plays a significant role in temperature distributions in human males and females body. Current understanding of human thermoregulation is based on male patterns; studies on women are still relatively rare and involve only small number of subjects. So it is still necessary for micro level study for temperature distribution model on the dermal layers of males and females.
Institute of Scientific and Technical Information of China (English)
Wen Xue; Kunzheng Wang; Wei Ling
2006-01-01
Objective: To study the alternation of distribution of the stress in the necrotic femoral head with different kinds of grafting materials by using three-dimensional element methods and find out the most optimal one with sound biomechanical principles before clinical application. Methods: We prepared a three dimension finite element model of central femoral head necrosis with surface modeling technique (spiral ct)and calculated the peak stress index of necrotic portion in three situations:core drilling in 14 mm diameter and grafting with titanium,fibula,polylactide. Results: The peak stress index of normal femoral head was 0.05,but in osteonecrotic femoral head, the peak stress index was 13 times of the normal (0.67). The value of necrotic portion with big shallow angle (0.67) was larger than the one with small deep angle (0.49). Core drilling in 14 mm diameter and grafting with titanium, fibula and polyactide could diminish the bad stress in the necrotic portion respectirdy. The decrease volume in small necrotic area (90°) is marked(38%), while in big necrotic area (150°) it was indistinctive(10%). In the same necrotic portion, the decrease volume with titanium was(38%) larger than with the fibula (37 % ), and also larger than with the polyactide(29% ). Conclusion: In necrotic portion of femoral head, the badshess could produce 13times of the normal one. Grafting with titanium, fibula and polyactide could reduce the bad stress respectively. The effect of titanium is most marked, second is fibula and polyactide is indistinctive. The effect was in big necrotic portion is bad, the best effect was in small necrotic portion.
Directory of Open Access Journals (Sweden)
A. Monzavi
2004-06-01
Full Text Available Statement of Problem: Currently there are three recognized theories about the diameter of prepared dowel space in endodontically treated teeth. Diameter of the dowel is commonly contributed to the root fracture.Purpose: This study used a 3 dimensional (3D finite element method to predict stress distribution in endodontically treated central maxillary tooth with cast post and core with various post diameter according to three philosophies about post diameter (Conservational,Proportional, Preservational.Materials and Methods: In this study three 3D models of central maxillary incisors with different post diameter were created and depend on the size of post called narrow, medium and thick model with post diameter of 1.1mm, 1.7 mm and 2.6 mm of in (CEJrespectively. A load of 100 N was applied to cingulum fossa from lingual direction with 45-degree angle to long axis of tooth and maximum tensile, compressive and Von Misses stresses and their distribution in dentin and post was studied.Results: The post in narrow, medium and thick models produced a similar magnitude of tensile, compressive and Von Misses stresses in dentin. Stress distribution was also similar in all models. Peak stresses in dentin were slightly decreased when post diameter increased from narrow to thick model. In all models peak tensile stresses in dentin occurred in the coronally one third of the lingual surface of the root, whereas peak compressive stresseswere evident in the coronal one third of the facial surface of the root.Conclusion: There were not significant differences stress distribution pattern and magnitude in dentin between the three theories of post diameter.
Wang, Shuai; Wang, Yu; Zi, Yanyang; Li, Bing; He, Zhengjia
2015-10-01
A novel reduced-order modeling method is presented in this paper for dynamics analysis of rotating impeller-shaft-bearing assembly with cracked impellers. Based on three-dimensional finite element model, the complex component mode synthesis (CMS) method is employed to generate an efficient reduced-order model (ROM) for studying the effects of crack on the global vibration of the rotating assembly. First, a modeling framework for impeller-shaft-bearing systems in rotating frame is presented. Rotational effects, including Coriolis matrix and centrifugal softening, have been taken into account. Then, the governing equation of motion of the damped gyroscopic system is reduced by the complex CMS method. Finally, the obtained ROM is employed to study the effects of crack on assembly's vibration. During the steady-state response analysis, external excitations on the impeller due to rotor-stator interactions have been taken into account, which was however neglected in previous investigations on rotordynamics. Numerical results show that the lower-order eigenvalues and the unbalance response of the assembly are not sensitive to the local crack on impeller. Nevertheless, the flexible coupling between impeller and shaft becomes more complex when the air flow-induced excitations are considered. Under EO1 traveling wave excitations, a crack leads to slight changes in the assembly's response. In contrast, the effect of crack becomes significant when the assembly is excited by EO2 and higher EO excitations. Moreover, the nonlinear crack breathing effects affect the assembly's response obviously. Finally, a potential technique for detecting the crack on impeller during operation is discussed.
Non-relativistic twistor theory and Newton--Cartan geometry
Dunajski, Maciej
2015-01-01
We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle ${\\mathcal O}\\oplus{\\mathcal O}(2)$. We show that the Newton--Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton--Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non--trivial on twistor lines. The resulting geometries agree with non--relativistic limits of anti-self-dual gravitational instantons.
Nonrelativistic parallel shocks in unmagnetized and weakly magnetized plasmas
Niemiec, Jacek; Bret, Antoine; Wieland, Volkmar
2012-01-01
We present results of 2D3V particle-in-cell simulations of non-relativistic plasma collisions with absent or parallel large-scale magnetic field for parameters applicable to the conditions at young supernova remnants. We study the collision of plasma slabs of different density, leading to two different shocks and a contact discontinuity. Electron dynamics play an important role in the development of the system. While non-relativistic shocks in both unmagnetized and magnetized plasmas can be mediated by Weibel-type instabilities, the efficiency of shock-formation processes is higher when a large-scale magnetic field is present. The electron distributions downstream of the forward and reverse shocks are generally isotropic, whereas that is not always the case for the ions. We do not see any significant evidence of pre-acceleration, neither in the electron population nor in the ion distribution.
Do non-relativistic neutrinos constitute the dark matter?
Nieuwenhuizen, T.M.
2009-01-01
The dark matter of the Abell 1689 Galaxy Cluster is modeled by thermal, non-relativistic gravitating fermions and its galaxies and X-ray gas by isothermal distributions. A fit yields a mass of h(70)(1/2) (12/(g) over bar)(1)/(4) 1.445(30) eV. A dark-matter fraction Omega(nu) = h(70)(-3/2) 0.1893(39)
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Energy Technology Data Exchange (ETDEWEB)
Geracie, Michael, E-mail: mgeracie@uchicago.edu; Prabhu, Kartik, E-mail: kartikp@uchicago.edu; Roberts, Matthew M., E-mail: matthewroberts@uchicago.edu [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-10-15
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print http://arxiv.org/abs/1503.02680 ], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
Three-dimensional Finite Element Analysis of Switched Reluctance Motor%开关磁阻电机的三维有限元分析
Institute of Scientific and Technical Information of China (English)
熊春宇; 王艳芹; 吴春梅; 李欣欣
2013-01-01
为了解决二维有限元分析开关磁阻电机磁场不准确的问题,采用了三维建模方法,对开关磁阻电机的整个场域进行三维有限元分析.基于整体建模的方法,利用三维有限元数值进行分析计算,准确描述开关磁阻电机的端部磁场效应.在三维有限元分析加载电流时,提出了“跑道线圈”这一概念.该概念在考虑了端部效应的同时,也解决了立体模型施加载荷时出现的方向选择困难的问题.采用通用磁标势法对非线性方程组进行求解,得出了最大电感和最小电感位置处的磁感应强度和磁场强度分布.%To solve the problem that two-dimensional finite element analysis of magnetic field of switched reluctance motor is not accurate enough, by using the method of three-dimensional modeling, three-dimensional finite element analysis of entire field of switched reluctance motor is accomplished. Based on the overall modeling method, and by adopting three-dimensional finite element analysis values, the end portion magnetic effect of the switched reluctance motor is described precisely. The concept of racetrack coil is put forward during three-dimensional finite element analyzing of loading current. In addition, the problem of difficulty of selecting direction of applying load for three-dimensional model is also resolved. The nonlinear equations are solved with universal magnetic scalar potential method, and the distribution of magnetic induction and magnetic field intensity at the positions of maximum and minimum induction are found.
Virial Theorem for Non-relativistic Quantum Fields in D Spatial Dimensions
Lin, Chris L
2015-01-01
The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in lower-dimensional systems. The potential appearance of a Jacobian $J$ due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the $J=1$ case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, $J=1$, is not natural, and the generalization to the case $J\
Non-relativistic Schroedinger theory on q-deformed quantum spaces III, Scattering theory
Wachter, H
2007-01-01
This is the third part of a paper about non-relativistic Schroedinger theory on q-deformed quantum spaces like the braided line or the three-dimensional q-deformed Euclidean space. Propagators for the free q-deformed particle are derived and their basic properties are discussed. A time-dependent formulation of scattering is proposed. In this respect, q-analogs of the Lippmann-Schwinger equation are given. Expressions for their iterative solutions are written down. It is shown how to calculate S-matrices and transition probabilities. Furthermore, attention is focused on the question what becomes of unitarity of S-matrices in a q-deformed setting. The examinations are concluded by a discussion of the interaction picture and its relation to scattering processes.
Indian Academy of Sciences (India)
Bilge Inan; Ahmet Refik Bahadir
2013-10-01
This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.
Settle, Sean O.
2013-01-01
The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.
Institute of Scientific and Technical Information of China (English)
ZHONG Yan-lin; WANG You; WANG Hai-peng; RONG Ke; XIE Le
2011-01-01
Objective: To create a 3-dimensional finite element model of knee ligaments and to analyse the stress changes of lateral collateral ligament (LCL) with or without displaced movements at different knee flexion conditions.Methods: A four-major-ligament contained knee specimen from an adult died of skull injury was prepared for CT scanning with the detectable ligament insertion footprints,locations and orientations precisely marked in advance. The CT scanning images were converted to a 3-dimensional model of the knee with the 3-dimensional reconstruction technique and transformed into finite element model by the software of ANSYS. The model was validated using experimental and numerical results obtained by other scientists.The natural stress changes of LCL at five different knee flexion angles (0°, 30°, 60°, 90°, 120°) and under various motions of anterior-posterior tibial translation, tibial varus rotation and internal-external tibial rotation were measured.Results: The maximum stress reached to 87%-113%versus natural stress in varus motion at early 30° of knee flexions. The stress values were smaller than the peak value of natural stress at 0° (knee full extension) when knee bending was over 60° of flexion in anterior-posterior tibial translation and internal-external rotation.Conclusion: LCL is vulnerable to varus motion in almost all knee bending positions and susceptible to anterlor-posterior tibial translation or internal-external rotation at early 30° of knee flexions.
Spacetime Variation of Lorentz-Violation Coefficients at Nonrelativistic Scale
Lane, Charles D
2016-01-01
The notion of uniform and/or constant tensor fields of rank $>0$ is incompatible with general curved spacetimes. This work considers the consequences of certain tensor-valued coefficients for Lorentz violation in the Standard-Model Extension varying with spacetime position. We focus on two of the coefficients, $a_\\mu$ and $b_\\mu$, that characterize Lorentz violation in massive fermions, particularly in those fermions that constitute ordinary matter. We calculate the nonrelativistic hamiltonian describing these effects, and use it to extract the sensitivity of several precision experiments to coefficient variation.
Δ - Δ resonance in the nonrelativistic quark model
Cvetič, M.; Golli, B.; Mankoč-Borštnik, N.; Rosina, M.
1980-06-01
The Δ - Δ resonance is treated in the nonrelativistic quark model. The trial wave function is a colour singlet including N-N, Δ - Δ and coloured baryon channels. The effective Δ - Δ potential is repulsive at all distances for T=0, S=1, L=0,2,4 while for T=3, S=0, L=0 and T=0, S=3, L=0 it has a minimum. The GCM calculation gives for the latter state the binding emergy ∼ -40 MeV.
Conservation of energy and momentum in nonrelativistic plasmas
Energy Technology Data Exchange (ETDEWEB)
Sugama, H.; Watanabe, T.-H. [National Institute for Fusion Science, Toki 509-5292 (Japan); Graduate University for Advanced Studies, Toki 509-5292 (Japan); Nunami, M. [National Institute for Fusion Science, Toki 509-5292 (Japan)
2013-02-15
Conservation laws of energy and momentum for nonrelativistic plasmas are derived from applying Noether's theorem to the action integral for the Vlasov-Poisson-Ampere system [Sugama, Phys. Plasmas 7, 466 (2000)]. The symmetric pressure tensor is obtained from modifying the asymmetric canonical pressure tensor with using the rotational symmetry of the action integral. Differences between the resultant conservation laws and those for the Vlasov-Maxwell system including the Maxwell displacement current are clarified. These results provide a useful basis for gyrokinetic conservation laws because gyrokinetic equations are derived as an approximation of the Vlasov-Poisson-Ampere system.
Scattering theory the quantum theory of nonrelativistic collisions
Taylor, John R
2006-01-01
This graduate-level text is intended for any student of physics who requires a thorough grounding in the quantum theory of nonrelativistic scattering. It is designed for readers who are already familiar with the general principles of quantum mechanics and who have some small acquaintance with scattering theory. Study of this text will allow students of atomic or nuclear physics to begin reading the literature and tackling real problems, with a complete grasp of the underlying principles. For students of high-energy physics, it provides the necessary background for later study of relativistic p
Singh, Gurpreet; Tan, Eng Leong; Chen, Zhi Ning
2012-02-01
This Letter presents a split-step (SS) finite-difference time-domain (FDTD) method for the efficient analysis of two-dimensional (2-D) photonic crystals (PhCs) with anisotropic media. The proposed SS FDTD method is formulated with perfectly matched layer boundary conditions and caters for inhomogeneous anisotropic media. Furthermore, the proposed method is derived using the efficient SS1 splitting formulas with simpler right-hand sides that are more efficient and easier to implement. A 2-D PhC cavity with anisotropic media is used as an example to validate the efficiency of the proposed method.
Wada, Yuji; Koyama, Daisuke; Nakamura, Kentaro
2014-12-01
The direct finite-difference fluid simulation of acoustic streaming on a fine-meshed three-dimensional model using a graphics processing unit (GPU)-based calculation array is discussed. Airflows are induced by an acoustic traveling wave when an intense sound field is generated in a gap between a bending transducer and a reflector. The calculation results showed good agreement with measurements in a pressure distribution. Several flow vortices were observed near the boundary layer of the reflector and the transducer, which have often been observed near the boundary of acoustic tubes, but have not been observed in previous calculations for this type of ultrasonic air pump.
Energy Technology Data Exchange (ETDEWEB)
Hutula, D.N.; Wiancko, B.E.
1980-03-01
ACCEPT is a three-dimensional finite element computer program for analysis of large-deformation elastic-plastic-creep response of Zircaloy tubes subjected to temperature, surface pressures, and axial force. A twenty-mode, tri-quadratic, isoparametric element is used along with a Zircaloy materials model. A linear time-incremental procedure with residual force correction is used to solve for the time-dependent response. The program features an algorithm which automatically chooses the time step sizes to control the accuracy and numerical stability of the solution. A contact-separation capability allows modeling of interaction of reactor fuel rod cladding with fuel pellets or external supports.
Institute of Scientific and Technical Information of China (English)
LI Yuguo; LUO Ming; PEI Jianxin
2013-01-01
In this paper,we extend the scope of numerical simulations of marine controlled-source electromagnetic (CSEM) fields in a particular case of anisotropy (dipping anisotropy) to the general case of anisotropy by using an adaptive finite element approach.In comparison to a dipping anisotropy case,the first order spatial derivatives of the strike-parallel components arise in the partial differential equations for generally anisotropic media,which cause a non-symmetric linear system of equations for finite element modeling.The adaptive finite element method is employed to obtain numerical solutions on a sequence of refined unstructured triangular meshes,which allows for arbitrary model geometries including bathymetry and dipping layers.Numerical results of a 2D anisotropic model show both anisotropy strike and dipping angles have great influence on the marine CSEM responses.
Finite-temperature scaling close to Ising-nematic quantum critical points in two-dimensional metals
Punk, Matthias
2016-11-01
We study finite-temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent z =2 , in contrast to z =3 found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to Ω /γ (T ) at small momenta, where γ (T ) is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte Carlo simulations at finite temperature, where results consistent with z =2 were found.
Yang, Heng
2007-12-01
Resonance properties of the Earth-ionosphere cavity were predicted by W. O. Schumann in 1952. Since then observations of electromagnetic signals in the frequency range 1-500 Hz have become a powerful tool for variety of remote sensing applications, which in recent years included studies of thunderstorm related transient luminous events in the middle atmosphere and related lightning discharges. In this thesis, a three dimensional Finite Difference Time Domain (FDTD) model is developed to study the propagation of the extremely low frequency (ELF) waves in the Earth-ionosphere cavity and in similar cavities on other celestial bodies of the Solar System. A comparison of the results from this FDTD model with a set of classical eigen-frequency (fn) and quality factor ( Qn) solutions for laterally uniform spherically symmetric Earth-ionosphere cavity and with recent observations of Schumann resonance (SR) during solar proton events (SPEs) and X-ray bursts is provided. The FDTD fn and Qn solutions for the uniform cavity appear to be in excellent agreement (within several %) with well-known experimental results documented in the literature. The related analysis indicates that the frequency of the first SR mode decreases during SPEs and increases during X-ray bursts by a fraction of a Hz, in agreement with physical arguments presented in previously published literature and with observations. The FDTD model is extended to include the effects of the geomagnetic field on SR parameters. A higher penetration height of SR electric and magnetic components is found with the presence of the geomagnetic field. In a realistic cavity, the conductivity distribution is not laterally uniform and spherically symmetric, but varies with local time and seasons reflecting related variations in the effects of solar radiation on the conductivity of the lower ionosphere. The global lightning activity in the three main areas (Africa, South-East Asia, and South America) also has diurnal and seasonal