A finite area scheme for shallow granular flows on three-dimensional surfaces

Science.gov (United States)

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.

Preservation theorems on finite structures

International Nuclear Information System (INIS)

Hebert, M.

1994-09-01

This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs

Mixed finite element simulations in two-dimensional groundwater flow problems

International Nuclear Information System (INIS)

Kimura, Hideo

1989-01-01

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

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

Energy Technology Data Exchange (ETDEWEB)

Thapliyal, Kishore, E-mail: tkishore36@yahoo.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India)

2016-03-15

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

International Nuclear Information System (INIS)

Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban

2016-01-01

Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them. -- Highlights: •Tomograms are constructed for open quantum systems. •Finite and infinite dimensional quantum systems are studied. •Finite dimensional systems (phase states, single & two qubit spin states) are studied. •A dissipative harmonic oscillator is considered as an infinite dimensional system. •Both pure dephasing as well as dissipation effects are studied.

Ultraviolet finiteness of N = 8 supergravity, spontaneously broken by dimensional reduction

International Nuclear Information System (INIS)

Sezgin, E.; Nieuwenhuizen, P. van

1982-06-01

The one-loop corrections to scalar-scalar scattering in N = 8 supergravity with 4 masses from dimensional reduction, are finite. We discuss various mechanisms that cancel the cosmological constant and infra-red divergences due to finite but non-vanishing tadpoles. (author)

Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces

International Nuclear Information System (INIS)

Robinson, James C

2009-01-01

This paper treats the embedding of finite-dimensional subsets of a Banach space B into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X − X is finite, d H (X − X) k are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hölder continuous inverse when the box-counting dimension of X is finite and k > 2d B (X). A related argument shows that if the Assouad dimension of X − X is finite and k > d A (X − X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L ∞ (X)

Integrable finite-dimensional systems related to Lie algebras

International Nuclear Information System (INIS)

Olshanetsky, M.A.; Perelomov, A.M.

1979-01-01

Some solvable finite-dimensional classical and quantum systems related to the Lie algebras are considered. The dynamics of these systems is closely related to free motion on symmetric spaces. In specific cases the systems considered describe the one-dimensional n-body problem recently considered by many authors. The review represents from general and universal point of view the results obtained during the last few years. Besides, it contains some results both of physical and mathematical type

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.

Quantum Finance: The Finite Dimensional Case

OpenAIRE

Chen, Zeqian

2001-01-01

In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of the binomial market. Furthermore, we re-deduce the Cox-Ross-Rubinstein binomial option pricing form...

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.

Alfven-wave particle interaction in finite-dimensional self-consistent field model

International Nuclear Information System (INIS)

Padhye, N.; Horton, W.

1998-01-01

A low-dimensional Hamiltonian model is derived for the acceleration of ions in finite amplitude Alfven waves in a finite pressure plasma sheet. The reduced low-dimensional wave-particle Hamiltonian is useful for describing the reaction of the accelerated ions on the wave amplitudes and phases through the self-consistent fields within the envelope approximation. As an example, the authors show for a single Alfven wave in the central plasma sheet of the Earth's geotail, modeled by the linear pinch geometry called the Harris sheet, the time variation of the wave amplitude during the acceleration of fast protons

Low-dimensional filiform Lie algebras over finite fields

OpenAIRE

Falcón Ganfornina, Óscar Jesús; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vasek, Vladimir (Coordinador); Shmaliy, Yuriy S. (Coordinador); Trcek, Denis (Coordinador); Kobayashi, Nobuhiko P. (Coordinador); Choras, Ryszard S. (Coordinador); Klos, Zbigniew (Coordinador)

2011-01-01

In this paper we use some objects of Graph Theory to classify low-dimensional filiform Lie algebras over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As results, which can be applied in several branches of Physics or Engineering, for instance, we find out that there exist, up to isomorphism, six 6-dimensional filiform Lie algebras over Z/pZ, for p = 2, 3, 5. Pl...

Finite-dimensional representations of the quantum superalgebra Uq[gl(2/2)]: 1. Typical representations at generic q

International Nuclear Information System (INIS)

Nguyen Anh Ky.

1993-05-01

In the present paper we construct all typical finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)] at generic deformation parameter q. As in the non-deformed case the finite-dimensional U q [gl(2/2)]-module W q obtained is irreducible and can be decomposed into finite-dimensional irreducible U q [l(2)+gl(2)]submodules V i q . (authohor). 32 refs

Determination of two dimensional axisymmetric finite element model for reactor coolant piping nozzles

International Nuclear Information System (INIS)

Choi, S. N.; Kim, H. N.; Jang, K. S.; Kim, H. J.

2000-01-01

The purpose of this paper is to determine a two dimensional axisymmetric model through a comparative study between a three dimensional and an axisymmetric finite element analysis of the reactor coolant piping nozzle subject to internal pressure. The finite element analysis results show that the stress adopting the axisymmetric model with the radius of equivalent spherical vessel are well agree with that adopting the three dimensional model. The radii of equivalent spherical vessel are 3.5 times and 7.3 times of the radius of the reactor coolant piping for the safety injection nozzle and for the residual heat removal nozzle, respectively

Finite element method for radiation heat transfer in multi-dimensional graded index medium

International Nuclear Information System (INIS)

Liu, L.H.; Zhang, L.; Tan, H.P.

2006-01-01

In graded index medium, ray goes along a curved path determined by Fermat principle, and curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectories, a finite element method based on discrete ordinate equation is developed to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two particular test problems of radiative transfer are taken as examples to verify this finite element method. The predicted dimensionless net radiative heat fluxes are determined by the proposed method and compared with the results obtained by finite volume method. The results show that the finite element method presented in this paper has a good accuracy in solving the multi-dimensional radiative transfer problem in semitransparent graded index medium

Irreducible quantum group modules with finite dimensional weight spaces

DEFF Research Database (Denmark)

Pedersen, Dennis Hasselstrøm

a finitely generated U q -module which has finite dimensional weight spaces and is a sum of those. Our approach follows the procedures used by S. Fernando and O. Mathieu to solve the corresponding problem for semisimple complex Lie algebra modules. To achieve this we have to overcome a number of obstacles...... not present in the classical case. In the process we also construct twisting functors rigerously for quantum group modules, study twisted Verma modules and show that these admit a Jantzen filtration with corresponding Jantzen sum formula....

Finite-dimensional approximation for operator equations of Hammerstein type

International Nuclear Information System (INIS)

Buong, N.

1992-11-01

The purpose of this paper is to establish convergence rate for a method of finite-dimensional approximation to solve operator equation of Hammerstein type in real reflexive Banach space. In order to consider a numerical example an iteration method is proposed in Hilbert space. (author). 25 refs

Perfect 3-dimensional lattice actions for 4-dimensional quantum field theories at finite temperature

International Nuclear Information System (INIS)

Kerres, U.; Mack, G.; Palma, G.

1994-12-01

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bololiubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for φ 4 -theory and scalar electrodynamics. The Balaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here. (orig.)

A complementarity-based approach to phase in finite-dimensional quantum systems

International Nuclear Information System (INIS)

Klimov, A B; Sanchez-Soto, L L; Guise, H de

2005-01-01

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

A three-dimensional cell-based smoothed finite element method for elasto-plasticity

International Nuclear Information System (INIS)

Lee, Kye Hyung; Im, Se Yong; Lim, Jae Hyuk; Sohn, Dong Woo

2015-01-01

This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

A three-dimensional cell-based smoothed finite element method for elasto-plasticity

Energy Technology Data Exchange (ETDEWEB)

Lee, Kye Hyung; Im, Se Yong [KAIST, Daejeon (Korea, Republic of); Lim, Jae Hyuk [KARI, Daejeon (Korea, Republic of); Sohn, Dong Woo [Korea Maritime and Ocean University, Busan (Korea, Republic of)

2015-02-15

This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

The structure of the Hamiltonian in a finite-dimensional formalism based on Weyl's quantum mechanics

International Nuclear Information System (INIS)

Santhanam, T.S.; Madivanane, S.

1982-01-01

Any discussion on finite-dimensional formulation of quantum mechanics involves the Sylvester matrix (finite Fourier transform). In the usual formulation, a remarkable relation exists that gives the Fourier transform as the exponential of the Hamiltonian of a simple harmonic oscillator. In this paper, assuming that such a relation holds also in the finite dimensional case, we extract the logarithm of the Sylvester matrix and in some cases this can be interpreted as the Hamiltonian of the truncated oscillator. We calculate the Hamiltonian matrix explicitly for some special cases of n = 3,4. (author)

Calculation of two-dimensional thermal transients by the finite element method

International Nuclear Information System (INIS)

Fontoura Rodrigues, J.L.A. da; Barcellos, C.S. de

1981-01-01

The linear heat conduction through anisotropic and/or heterogeneous matter, in either two-dimensional fields with any kind of geometry or three-dimensional fields with axial symmetry is analysed. It only accepts time-independent boundary conditions and it is possible to have internal heat generation. The solution is obtained by modal analysis employing the finite element method under Galerkin formulation. (Author) [pt

Finite size effects and chiral symmetry breaking in quenched three-dimensional QED

International Nuclear Information System (INIS)

Hands, S.; Kogut, J.B.

1990-01-01

Finite size effects and the chiral condensate are studied in three-dimensional QED by the Lanczos and the conjugate-gradient algorithms. Very substantial finite size effects are observed, but studies on L 3 lattices with L ranging from 8 to 80 indicate the development of a non-vanishing chiral condensate in the continuum limit of the theory. The systematics of the finite size effects and the fermion mass dependence in the conjugate-gradient algorithm are clarified in this extensive study. (orig.)

Theory of finite-entanglement scaling at one-dimensional quantum critical points.

Science.gov (United States)

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.

Finite-size scaling in two-dimensional superfluids

International Nuclear Information System (INIS)

Schultka, N.; Manousakis, E.

1994-01-01

Using the x-y model and a nonlocal updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two-dimensional superfluid on large-size square lattices LxL up to 400x400. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of L values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization-group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson renormalization group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments

[Three dimensional finite element model of a modified posterior cervical single open-door laminoplasty].

Science.gov (United States)

Wang, Q; Yang, Y; Fei, Q; Li, D; Li, J J; Meng, H; Su, N; Fan, Z H; Wang, B Q

2017-06-06

Objective: To build a three-dimensional finite element models of a modified posterior cervical single open-door laminoplasty with short-segmental lateral mass screws fusion. Methods: The C(2)-C(7) segmental data were obtained from computed tomography (CT) scans of a male patient with cervical spondylotic myelopathy and spinal stenosis.Three-dimensional finite element models of a modified cervical single open-door laminoplasty (before and after surgery) were constructed by the combination of software package MIMICS, Geomagic and ABAQUS.The models were composed of bony vertebrae, articulating facets, intervertebral disc and associated ligaments.The loads of moments 1.5Nm at different directions (flexion, extension, lateral bending and axial rotation)were applied at preoperative model to calculate intersegmental ranges of motion.The results were compared with the previous studies to verify the validation of the models. Results: Three-dimensional finite element models of the modified cervical single open- door laminoplasty had 102258 elements (preoperative model) and 161 892 elements (postoperative model) respectively, including C(2-7) six bony vertebraes, C(2-3)-C(6-7) five intervertebral disc, main ligaments and lateral mass screws.The intersegmental responses at the preoperative model under the loads of moments 1.5 Nm at different directions were similar to the previous published data. Conclusion: Three-dimensional finite element models of the modified cervical single open- door laminoplasty were successfully established and had a good biological fidelity, which can be used for further study.

Finite-size scaling of clique percolation on two-dimensional Moore lattices

Science.gov (United States)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

International Nuclear Information System (INIS)

Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

2008-01-01

Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

Equilibrium charge distribution on a finite straight one-dimensional wire

Science.gov (United States)

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.

Equilibrium charge distribution on a finite straight one-dimensional wire

International Nuclear Information System (INIS)

Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Farouk, Ahmed; Alkhambashi, Majid

2017-01-01

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. (paper)

Bipartite discrimination of independently prepared quantum states as a counterexample to a parallel repetition conjecture

Science.gov (United States)

Akibue, Seiseki; Kato, Go

2018-04-01

For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a composite system consisting of N subsystems, where each subsystem is shared between two parties and the state of each subsystem is randomly sampled from a particular ensemble comprising the Bell states. We show that the success probability of perfectly identifying the state converges to 1 as N →∞ if the entropy of the probability distribution associated with the ensemble is less than 1, even if the success probability is less than 1 for any finite N . In other words, the nonlocality of the N -fold ensemble asymptotically disappears if the probability distribution associated with each ensemble is concentrated. Furthermore, we show that the disappearance of the nonlocality can be regarded as a remarkable counterexample of a fundamental open question in theoretical computer science, called a parallel repetition conjecture of interactive games with two classically communicating players. Measurements for the discrimination task include a projective measurement of one party represented by stabilizer states, which enable the other party to perfectly distinguish states that are sampled with high probability.

Stress-intensity factor equations for cracks in three-dimensional finite bodies

Science.gov (United States)

Newman, J. C., Jr.; Raju, I. S.

1981-01-01

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Three dimensional finite element linear analysis of reinforced concrete structures

International Nuclear Information System (INIS)

Inbasakaran, M.; Pandarinathan, V.G.; Krishnamoorthy, C.S.

1979-01-01

A twenty noded isoparametric reinforced concrete solid element for the three dimensional linear elastic stress analysis of reinforced concrete structures is presented. The reinforcement is directly included as an integral part of the element thus facilitating discretization of the structure independent of the orientation of reinforcement. Concrete stiffness is evaluated by taking 3 x 3 x 3 Gauss integration rule and steel stiffness is evaluated numerically by considering three Gaussian points along the length of reinforcement. The numerical integration for steel stiffness necessiates the conversion of global coordiantes of the Gaussian points to nondimensional local coordinates and this is done by Newton Raphson iterative method. Subroutines for the above formulation have been developed and added to SAP and STAP routines for solving the examples. The validity of the reinforced concrete element is verified by comparison of results from finite element analysis and analytical results. It is concluded that this finite element model provides a valuable analytical tool for the three dimensional elastic stress analysis of concrete structures like beams curved in plan and nuclear containment vessels. (orig.)

Spherical harmonics solutions of multi-dimensional neutron transport equation by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1977-01-01

A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)

Quantum phase space points for Wigner functions in finite-dimensional spaces

OpenAIRE

Luis Aina, Alfredo

2004-01-01

We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas.

Quantum phase space points for Wigner functions in finite-dimensional spaces

International Nuclear Information System (INIS)

Luis, Alfredo

2004-01-01

We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas

Three-Dimensional Phase Field Simulations of Hysteresis and Butterfly Loops by the Finite Volume Method

International Nuclear Information System (INIS)

Xi Li-Ying; Chen Huan-Ming; Zheng Fu; Gao Hua; Tong Yang; Ma Zhi

2015-01-01

Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg–Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems. (paper)

Peculiarities of cyclotron magnetic system calculation with the finite difference method using two-dimensional approximation

International Nuclear Information System (INIS)

Shtromberger, N.L.

1989-01-01

To design a cyclotron magnetic system the legitimacy of two-dimensional approximations application is discussed. In all the calculations the finite difference method is used, and the linearization method with further use of the gradient conjugation method is used to solve the set of finite-difference equations. 3 refs.; 5 figs

Absolute continuity of autophage measures on finite-dimensional vector spaces

Energy Technology Data Exchange (ETDEWEB)

Raja, C R.E. [Stat-Math Unit, Indian Statistical Institute, Bangalore (India); [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)]. E-mail: creraja@isibang.ac.in

2002-06-01

We consider a class of measures called autophage which was introduced and studied by Szekely for measures on the real line. We show that the autophage measures on finite-dimensional vector spaces over real or Q{sub p} are infinitely divisible without idempotent factors and are absolutely continuous with bounded continuous density. We also show that certain semistable measures on such vector spaces are absolutely continuous. (author)

One-Dimensional Finite Elements An Introduction to the FE Method

CERN Document Server

Öchsner, Andreas

2013-01-01

 This textbook presents finite element methods using exclusively  one-dimensional elements. The aim is to present the complex methodology in  an easily understandable but mathematically correct fashion. The approach of  one-dimensional elements enables the reader to focus on the understanding of  the principles of basic and advanced mechanical problems. The reader easily  understands the assumptions and limitations of mechanical modeling as well  as the underlying physics without struggling with complex mathematics. But  although the description is easy it remains scientifically correct.   The approach using only one-dimensional elements covers not only standard  problems but allows also for advanced topics like plasticity or the  mechanics of composite materials. Many examples illustrate the concepts and  problems at the end of every chapter help to familiarize with the topics.

Approximate approaches to the one-dimensional finite potential well

International Nuclear Information System (INIS)

Singh, Shilpi; Pathak, Praveen; Singh, Vijay A

2011-01-01

The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (m i ) is taken to be distinct from mass outside (m o ). A relevant parameter is the mass discontinuity ratio β = m i /m o . To correctly account for the mass discontinuity, we apply the BenDaniel-Duke boundary condition. We obtain approximate solutions for two cases: when the well is shallow and when the well is deep. We compare the approximate results with the exact results and find that higher-order approximations are quite robust. For the shallow case, the approximate solution can be expressed in terms of a dimensionless parameter σ l = 2m o V 0 L 2 /ℎ 2 (or σ = β 2 σ l for the deep case). We show that the lowest-order results are related by a duality transform. We also discuss how the energy upscales with L (E∼1/L γ ) and obtain the exponent γ. Exponent γ → 2 when the well is sufficiently deep and β → 1. The ratio of the masses dictates the physics. Our presentation is pedagogical and should be useful to students on a first course on elementary quantum mechanics or low-dimensional semiconductors.

Mappings with closed range and finite dimensional linear spaces

International Nuclear Information System (INIS)

Iyahen, S.O.

1984-09-01

This paper looks at two settings, each of continuous linear mappings of linear topological spaces. In one setting, the domain space is fixed while the range space varies over a class of linear topological spaces. In the second setting, the range space is fixed while the domain space similarly varies. The interest is in when the requirement that the mappings have a closed range implies that the domain or range space is finite dimensional. Positive results are obtained for metrizable spaces. (author)

Calculation of two-dimensional thermal transients by the method of finite elements

International Nuclear Information System (INIS)

Fontoura Rodrigues, J.L.A. da.

1980-08-01

The unsteady linear heat conduction analysis throught anisotropic and/or heterogeneous matter, in either two-dimensional fields with any kind of geometry or three-dimensional fields with axial symmetry is presented. The boundary conditions and the internal heat generation are supposed time - independent. The solution is obtained by modal analysis employing the finite element method under Galerkin formulation. Optionally, it can be used with a reduced resolution method called Stoker Economizing Method wich allows a decrease on the program processing costs. (Author) [pt

Non-Linear Three Dimensional Finite Elements for Composite Concrete Structures

Directory of Open Access Journals (Sweden)

O. Kohnehpooshi

Full Text Available Abstract The current investigation focused on the development of effective and suitable modelling of reinforced concrete component with and without strengthening. The modelling includes physical and constitutive models. New interface elements have been developed, while modified constitutive law have been applied and new computational algorithm is utilised. The new elements are the Truss-link element to model the interaction between concrete and reinforcement bars, the interface element between two plate bending elements and the interface element to represent the interfacial behaviour between FRP, steel plates and concrete. Nonlinear finite-element (FE codes were developed with pre-processing. The programme was written using FORTRAN language. The accuracy and efficiency of the finite element programme were achieved by analyzing several examples from the literature. The application of the 3D FE code was further enhanced by carrying out the numerical analysis of the three dimensional finite element analysis of FRP strengthened RC beams, as well as the 3D non-linear finite element analysis of girder bridge. Acceptable distributions of slip, deflection, stresses in the concrete and FRP plate have also been found. These results show that the new elements are effective and appropriate to be used for structural component modelling.

The finite - dimensional star and grade star irreducible representation of SU(n/1)

International Nuclear Information System (INIS)

Han Qi-zhi.

1981-01-01

We derive the conditions of star and grade star representations of SU(n/1) and give some examples of them. We also give a brief review of the finite - dimensional irreducible representations of SU(n/1). (author)

Acoustic Wave Propagation Modeling by a Two-dimensional Finite-difference Summation-by-parts Algorithm

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.

Gauge theory for finite-dimensional dynamical systems

International Nuclear Information System (INIS)

Gurfil, Pini

2007-01-01

Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently ''disordered'' flow into a regular dynamical process, and that there exists a strong connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse fields, including quantum mechanics, chemistry, rigid-body dynamics, and information theory

Finite-dimensional representations of the quantum superalgebra Uq[gl(2/2)] II: Nontypical representations at generic q

International Nuclear Information System (INIS)

Nguyen Anh Ky; Stoilova, N.I.

1994-11-01

The construction approach proposed in the previous paper Ref.1 allows us there and in the present paper to construct at generic deformation parameter q all finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)]. The finite-dimensional U q [gl(2/2)]-modules W q constructed in Ref.1 are either irreducible or indecomposable. If a module W q is indecomposable, i.e. when the condition (4.41) in Ref.1 does not hold, there exists an invariant maximal submodule of W q , to say I q k , such that the factor-representation in the factor-module W q /I q k is irreducible and called nontypical. Here, in this paper, indecomposable representations and nontypical finite-dimensional representations of the quantum Lie superalgebra U q [gl(2/2)] are considered and classified as their module structures are analyzed and the matrix elements of all nontypical representations are written down explicitly. (author). 23 refs

A finite element method for calculating the 3-dimensional magnetic fields of cyclotron

International Nuclear Information System (INIS)

Zhao Xiaofeng

1986-01-01

A series of formula of the finite element method (scalar potential) for calculating the three-dimensional magnetic field of the main magnet of a sector focused cyclotron, and the realization method of the periodic boundary conditions in the code are given

On the development of a three-dimensional finite-element groundwater flow model of the saturated zone, Yucca Mountain, Nevada

International Nuclear Information System (INIS)

Czarnecki, J.B.; Faunt, C.C.; Gable, C.W.; Zyvoloski, G.A.

1996-01-01

Development of a preliminary three-dimensional model of the saturated zone at Yucca Mountain, the potential location for a high-level nuclear waste repository, is presented. The development of the model advances the technology of interfacing: (1)complex three-dimensional hydrogeologic framework modeling; (2) fully three-dimensional, unstructured, finite-element mesh generation; and (3) groundwater flow, heat, and transport simulation. The three-dimensional hydrogeologic framework model is developed using maps, cross sections, and well data. The framework model data are used to feed an automated mesh generator, designed to discretize irregular three-dimensional solids,a nd to assign materials properties from the hydrogeologic framework model to the tetrahedral elements. The mesh generator facilitated the addition of nodes to the finite-element mesh which correspond to the exact three-dimensional position of the potentiometric surface based on water-levels from wells. A ground water flow and heat simulator is run with the resulting finite- element mesh, within a parameter-estimation program. The application of the parameter-estimation program is designed to provide optimal values of permeability and specified fluxes over the model domain to minimize the residual between observed and simulated water levels

Three-dimensional finite element impact analysis of a nuclear waste truck cask

International Nuclear Information System (INIS)

Miller, J.D.

1985-01-01

This paper presents a three-dimensional finite element impact analysis of a hypothetical accident event for the preliminary design of a shipping cask which is used to transport radioactive waste by standard tractor-semitrailer truck. The nonlinear dynamic structural analysis code DYNA3D run on Sandia's Cray-1 computer was used to calculate the effects of the cask's closure-end impacting a rigid frictionless surface on an edge of its external impact limiter after a 30-foot fall. The center of gravity of the cask (made of 304 stainless steel and depleted uranium) was assumed to be directly above the impact point. An elastic-plastic material constitutive model was used to calculate the nonlinear response of the cask components to the transient loading. Interactive color graphics (PATRAN and MOVIE BYU) were used throughout the analysis, proving to be extremely helpful for generation and verification of the geometry and boundary conditions of the finite element model and for interpretation of the analysis results. Results from the calculations show the cask sustained large localized deformations. However, these were almost entirely confined to the impact limiters built into the cask. The closure sections were determined to remain intact, and leakage would not be expected after the event. As an example of a large three-dimensional finite element dynamic impact calculation, this analysis can serve as an excellent benchmark for computer aided design procedures

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Directory of Open Access Journals (Sweden)

Djordjevich Alexandar

2017-12-01

Full Text Available The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity. Included are the firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.

Three-dimensional finite element analysis of implant-assisted removable partial dentures.

Science.gov (United States)

Eom, Ju-Won; Lim, Young-Jun; Kim, Myung-Joo; Kwon, Ho-Beom

2017-06-01

Whether the implant abutment in implant-assisted removable partial dentures (IARPDs) functions as a natural removable partial denture (RPD) tooth abutment is unknown. The purpose of this 3-dimensional finite element study was to analyze the biomechanical behavior of implant crown, bone, RPD, and IARPD. Finite element models of the partial maxilla, teeth, and prostheses were generated on the basis of a patient's computed tomographic data. The teeth, surveyed crowns, and RPDs were created in the model. With the generated components, four 3-dimensional finite element models of the partial maxilla were constructed: tooth-supported RPD (TB), implant-supported RPD (IB), tooth-tissue-supported RPD (TT), and implant-tissue-supported RPD (IT) models. Oblique loading of 300 N was applied on the crowns and denture teeth. The von Mises stress and displacement of the denture abutment tooth and implant system were identified. The highest von Mises stress values of both IARPDs occurred on the implants, while those of both natural tooth RPDs occurred on the frameworks of the RPDs. The highest von Mises stress of model IT was about twice that of model IB, while the value of model TT was similar to that of model TB. The maximum displacement was greater in models TB and TT than in models IB and IT. Among the 4 models, the highest maximum displacement value was observed in the model TT and the lowest value was in the model IB. Finite element analysis revealed that the stress distribution pattern of the IARPDs was different from that of the natural tooth RPDs and the stress distribution of implant-supported RPD was different from that of implant-tissue-supported RPD. When implants are used for RPD abutments, more consideration concerning the RPD design and the number or location of the implant is necessary. Copyright © 2016 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

Simulation of three-dimensional, time-dependent, incompressible flows by a finite element method

International Nuclear Information System (INIS)

Chan, S.T.; Gresho, P.M.; Lee, R.L.; Upson, C.D.

1981-01-01

A finite element model has been developed for simulating the dynamics of problems encountered in atmospheric pollution and safety assessment studies. The model is based on solving the set of three-dimensional, time-dependent, conservation equations governing incompressible flows. Spatial discretization is performed via a modified Galerkin finite element method, and time integration is carried out via the forward Euler method (pressure is computed implicitly, however). Several cost-effective techniques (including subcycling, mass lumping, and reduced Gauss-Legendre quadrature) which have been implemented are discussed. Numerical results are presented to demonstrate the applicability of the model

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.

Development of three-dimensional transport code by the double finite element method

International Nuclear Information System (INIS)

Fujimura, Toichiro

1985-01-01

Development of a three-dimensional neutron transport code by the double finite element method is described. Both of the Galerkin and variational methods are adopted to solve the problem, and then the characteristics of them are compared. Computational results of the collocation method, developed as a technique for the vaviational one, are illustrated in comparison with those of an Ssub(n) code. (author)

An efficicient data structure for three-dimensional vertex based finite volume method

Science.gov (United States)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

A counterexample of the Euler condition: the Appell–Hamel dynamical system on a horizontally moving plate

International Nuclear Information System (INIS)

Shan-Shan, Xu; Shu-Min, Li; Jamal, Berakdar

2009-01-01

As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the Apell–Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces. (general)

The finite-dimensional Freeman thesis.

Science.gov (United States)

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.

Theoretical formulation of finite-dimensional discrete phase spaces: I. Algebraic structures and uncertainty principles

International Nuclear Information System (INIS)

Marchiolli, M.A.; Ruzzi, M.

2012-01-01

We propose a self-consistent theoretical framework for a wide class of physical systems characterized by a finite space of states which allows us, within several mathematical virtues, to construct a discrete version of the Weyl–Wigner–Moyal (WWM) formalism for finite-dimensional discrete phase spaces with toroidal topology. As a first and important application from this ab initio approach, we initially investigate the Robertson–Schrödinger (RS) uncertainty principle related to the discrete coordinate and momentum operators, as well as its implications for physical systems with periodic boundary conditions. The second interesting application is associated with a particular uncertainty principle inherent to the unitary operators, which is based on the Wiener–Khinchin theorem for signal processing. Furthermore, we also establish a modified discrete version for the well-known Heisenberg–Kennard–Robertson (HKR) uncertainty principle, which exhibits additional terms (or corrections) that resemble the generalized uncertainty principle (GUP) into the context of quantum gravity. The results obtained from this new algebraic approach touch on some fundamental questions inherent to quantum mechanics and certainly represent an object of future investigations in physics. - Highlights: ► We construct a discrete version of the Weyl–Wigner–Moyal formalism. ► Coherent states for finite-dimensional discrete phase spaces are established. ► Discrete coordinate and momentum operators are properly defined. ► Uncertainty principles depend on the topology of finite physical systems. ► Corrections for the discrete Heisenberg uncertainty relation are also obtained.

A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems

International Nuclear Information System (INIS)

Xia Tiecheng; Chen Xiaohong; Chen Dengyuan

2004-01-01

An eigenvalue problem and the associated new Lax integrable hierarchy of nonlinear evolution equations are presented in this paper. As two reductions, the generalized nonlinear Schroedinger equations and the generalized mKdV equations are obtained. Zero curvature representation and bi-Hamiltonian structure are established for the whole hierarchy based on a pair of Hamiltonian operators (Lenard's operators), and it is shown that the hierarchy of nonlinear evolution equations is integrable in Liouville's sense. Thus the hierarchy of nonlinear evolution equations has infinitely many commuting symmetries and conservation laws. Moreover the eigenvalue problem is nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalue functions. Finally finite-dimensional Liouville integrable system are found, and the involutive solutions of the hierarchy of equations are given. In particular, the involutive solutions are developed for the system of generalized nonlinear Schroedinger equations

Three-dimensional linear fracture mechanics analysis by a displacement-hybrid finite-element model

International Nuclear Information System (INIS)

Atluri, S.N.; Kathiresan, K.; Kobayashi, A.S.

1975-01-01

This paper deals with a finite-element procedures for the calculation of modes I, II and III stress intensity factors, which vary, along an arbitrarily curved three-dimensional crack front in a structural component. The finite-element model is based on a modified variational principle of potential energy with relaxed continuity requirements for displacements at the inter-element boundary. The variational principle is a three-field principle, with the arbitrary interior displacements for the element, interelement boundary displacements, and element boundary tractions as variables. The unknowns in the final algebraic system of equations, in the present displacement hybrid finite element model, are the nodal displacements and the three elastic stress intensity factors. Special elements, which contain proper square root and inverse square root crack front variations in displacements and stresses, respectively, are used in a fixed region near the crack front. Interelement displacement compatibility is satisfied by assuming an independent interelement boundary displacement field, and using a Lagrange multiplier technique to enforce such interelement compatibility. These Lagrangean multipliers, which are physically the boundary tractions, are assumed from an equilibrated stress field derived from three-dimensional Beltrami (or Maxwell-Morera) stress functions that are complete. However, considerable care should be exercised in the use of these stress functions such that the stresses produced by any of these stress function components are not linearly dependent

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.

Fermi surface of the one-dimensional Hubbard model. Finite-size effects

Energy Technology Data Exchange (ETDEWEB)

Bourbonnais, C.; Nelisse, H.; Reid, A.; Tremblay, A.M.S. (Dept. de Physique and Centre de Recherche en Physique du Solide (C.R.P.S.), Univ. de Sherbrooke, Quebec (Canada))

1989-12-01

The results reported here, using a standard numerical algorithm and a simple low temperature extrapolation, appear consistent with numerical results of Sorella et al. for the one-dimensional Hubbard model in the half-filled and quarter-filled band cases. However, it is argued that the discontinuity at the Fermi level found in the quarter-filled case is likely to come from the zero-temperature finite-size dependence of the quasiparticle weight Z, which is also discussed here. (orig.).

Quantum limits to information about states for finite dimensional Hilbert space

International Nuclear Information System (INIS)

Jones, K.R.W.

1990-01-01

A refined bound for the correlation information of an N-trial apparatus is developed via an heuristic argument for Hilbert spaces of arbitrary finite dimensionality. Conditional upon the proof of an easily motivated inequality it was possible to find the optimal apparatus for large ensemble quantum Inference, thereby solving the asymptotic optimal state determination problem. In this way an alternative inferential uncertainty principle, is defined which is then contrasted with the usual Heisenberg uncertainty principle. 6 refs

Solution of the multigroup diffusion equation for two-dimensional triangular regions by finite Fourier transformation

International Nuclear Information System (INIS)

Takeshi, Y.; Keisuke, K.

1983-01-01

The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method

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...

Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

Science.gov (United States)

Nazarov, Anton

2012-11-01

In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent

Reparametrization in the path integral over finite dimensional manifold with a time-dependent metric

International Nuclear Information System (INIS)

Storchak, S.N.

1988-01-01

The path reparametrization procedure in the path integral is considered using the methods of stochastic processes for diffusion on finite dimensional manifold with a time-dependent metric. the reparametrization Jacobian has been obtained. The formulas of reparametrization for a symbolic presentation of the path integral have been derived

A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space

International Nuclear Information System (INIS)

Bagchi, B.

1995-01-01

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.))

Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

Ordering, symbols and finite-dimensional approximations of path integrals

International Nuclear Information System (INIS)

Kashiwa, Taro; Sakoda, Seiji; Zenkin, S.V.

1994-01-01

We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are independent of the type of symbols up to terms of O(ε), where ε of is infinitesimal time interval determining the accuracy of the approximations. A new class of such approximations is found for both c-number and Grassmannian dynamical variables. The actions determined by the approximations are non-local and have no classical continuum limit except the cases of pq- and qp-ordering. As an explicit example the fermionic oscillator is considered in detail. (author)

Two-dimensional finite element heat transfer model of softwood. Part II, Macrostructural effects

Science.gov (United States)

Hongmei Gu; John F. Hunt

2006-01-01

A two-dimensional finite element model was used to study the effects of structural features on transient heat transfer in softwood lumber with various orientations. Transient core temperature was modeled for lumber samples “cut” from various locations within a simulated log. The effects of ring orientation, earlywood to latewood (E/L) ratio, and ring density were...

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.

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

Science.gov (United States)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

Quantum key distribution for composite dimensional finite systems

Science.gov (United States)

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.

Application of finite-element method to three-dimensional nuclear reactor analysis

International Nuclear Information System (INIS)

Cheung, K.Y.

1985-01-01

The application of the finite element method to solve a realistic one-or-two energy group, multiregion, three-dimensional static neutron diffusion problem is studied. Linear, quadratic, and cubic serendipity box-shape elements are used. The resulting sets of simultaneous algebraic equations with thousands of unknowns are solved by the conjugate gradient method, without forming the large coefficient matrix explicitly. This avoids the complicated data management schemes to store such a large coefficient matrix. Three finite-element computer programs: FEM-LINEAR, FEM-QUADRATIC and FEM-CUBIC were developed, using the linear, quadratic, and cubic box-shape elements respectively. They are self-contained, using simple nodal labeling schemes, without the need for separate finite element mesh generating routines. The efficiency and accuracy of these computer programs are then compared among themselves, and with other computer codes. The cubic element model is not recommended for practical usage because it gives almost identical results as the quadratic model, but it requires considerably longer computation time. The linear model is less accurate than the quadratic model, but it requires much shorter computation time. For a large 3-D problem, the linear model is to be preferred since it gives acceptable accuracy. The quadratic model may be used if improved accuracy is desired

Geometrical bucklings for two-dimensional regular polygonal regions using the finite Fourier transformation

International Nuclear Information System (INIS)

Mori, N.; Kobayashi, K.

1996-01-01

A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)

Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures

Science.gov (United States)

Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.

2012-01-01

A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.

Primary decomposition of zero-dimensional ideals over finite fields

Science.gov (United States)

Gao, Shuhong; Wan, Daqing; Wang, Mingsheng

2009-03-01

A new algorithm is presented for computing primary decomposition of zero-dimensional ideals over finite fields. Like Berlekamp's algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invariant subspace equals the number of primary components, and a basis of the invariant subspace yields a complete decomposition. Unlike previous approaches for decomposing multivariate polynomial systems, the new method does not need primality testing nor any generic projection, instead it reduces the general decomposition problem directly to root finding of univariate polynomials over the ground field. Also, it is shown how Groebner basis structure can be used to get partial primary decomposition without any root finding.

On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra

Energy Technology Data Exchange (ETDEWEB)

Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Institute of Gravitation and Cosmology, Moscow (Russian Federation)

2017-10-15

A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions H{sub s}(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials - the so-called fluxbrane polynomials. These polynomials depend upon integration constants q{sub s}, s = 1,.., n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ{sup s} over a proper 2d submanifold are finite and obey the relations q{sub s} Φ{sup s} = 4πn{sub s}h{sub s}, where the h{sub s} > 0 are certain constants (related to dilatonic coupling vectors) and the n{sub s} are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s = 1,.., n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A{sub 1}, A{sub 2}, A{sub 3}, C{sub 2}, G{sub 2} and A{sub 1} + A{sub 1} are presented. (orig.)

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

Science.gov (United States)

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.

Current singularities at finitely compressible three-dimensional magnetic null points

International Nuclear Information System (INIS)

Pontin, D.I.; Craig, I.J.D.

2005-01-01

The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed

Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs

Energy Technology Data Exchange (ETDEWEB)

Sergyeyev, Artur, E-mail: Artur.Sergyeyev@math.slu.cz [Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava (Czech Republic)

2012-06-04

In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.

Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs

International Nuclear Information System (INIS)

Sergyeyev, Artur

2012-01-01

In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized Stäckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given. -- Highlights: ► We consider the multiparameter coupling constant metamorphosis (MCCM). ► The latter is also known as the generalized Stäckel transform. ► This transform is extended to general (non-Hamiltonian) finite-dimensional dynamical systems. ► The extended transform preserves integrability just as the original MCCM. ► A simple formula for transforming solutions under MCCM is given.

FEAST: a two-dimensional non-linear finite element code for calculating stresses

International Nuclear Information System (INIS)

Tayal, M.

1986-06-01

The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%

Study of two-dimensional transient cavity fields using the finite-difference time-domain technique

Energy Technology Data Exchange (ETDEWEB)

Crisp, J.L.

1988-06-01

This work is intended to be a study into the application of the finite-difference time-domain, or FD-TD technique, to some of the problems faced by designers of equipment used in modern accelerators. In particular it discusses using the FD-TD algorithm to study the field distribution of a simple two-dimensional cavity in both space and time. 18 refs.

Study of two-dimensional transient cavity fields using the finite-difference time-domain technique

International Nuclear Information System (INIS)

Crisp, J.L.

1988-06-01

This work is intended to be a study into the application of the finite-difference time-domain, or FD-TD technique, to some of the problems faced by designers of equipment used in modern accelerators. In particular it discusses using the FD-TD algorithm to study the field distribution of a simple two-dimensional cavity in both space and time. 18 refs

Normal Modes of Magnetized Finite Two-Dimensional Yukawa Crystals

Science.gov (United States)

Marleau, Gabriel-Dominique; Kaehlert, Hanno; Bonitz, Michael

2009-11-01

The normal modes of a finite two-dimensional dusty plasma in an isotropic parabolic confinement, including the simultaneous effects of friction and an external magnetic field, are studied. The ground states are found from molecular dynamics simulations with simulated annealing, and the influence of screening, friction, and magnetic field on the mode frequencies is investigated in detail. The two-particle problem is solved analytically and the limiting cases of weak and strong magnetic fields are discussed.[4pt] [1] C. Henning, H. K"ahlert, P. Ludwig, A. Melzer, and M.Bonitz. J. Phys. A 42, 214023 (2009)[2] B. Farokhi, M. Shahmansouri, and P. K. Shukla. Phys.Plasmas 16, 063703 (2009)[3] L. Cândido, J.-P. Rino, N. Studart, and F. M. Peeters. J. Phys.: Condens. Matter 10, 11627--11644 (1998)

Chiral ward-Takahashi identities at finite temperature and chiral phase transition in (2+1) dimensional chiral Gross-Neveu model

International Nuclear Information System (INIS)

Shen Kun; Qiu Zhongping

1993-01-01

Chiral Ward-Takahashi identities at finite temperature are derived in (2+1) dimensional chiral Gross-Neveu model. In terms of these identities, fermion mass generation and the mass spectra of bound states are investigate at finite temperature. Taking the fermion mass as an order parameter, the authors discuss the phase structure and chiral phase transition and obtain the critical temperature

hree-Dimensional Finite Element Simulation of the Buried Pipe Problem in Geogrid Reinforced Soil

Directory of Open Access Journals (Sweden)

Mohammed Yousif Fattah

2016-05-01

Full Text Available Buried pipeline systems are commonly used to transport water, sewage, natural oil/gas and other materials. The beneficial of using geogrid reinforcement is to increase the bearing capacity of the soil and decrease the load transfer to the underground structures. This paper deals with simulation of the buried pipe problem numerically by finite elements method using the newest version of PLAXIS-3D software. Rajkumar and Ilamaruthi's study, 2008 has been selected to be reanalyzed as 3D problem because it is containing all the properties needed by the program such as the modulus of elasticity, Poisson's ratio, angle of internal friction. It was found that the results of vertical crown deflection for the model without geogrid obtained from PLAXIS-3D are higher than those obtained by two-dimensional plane strain by about 21.4% while this percent becomes 12.1 for the model with geogrid, but in general, both have the same trend. The two dimensional finite elements analysis predictions of pipe-soil system behavior indicate an almost linear displacement of pipe deflection with applied pressure while 3-D analysis exhibited non-linear behavior especially at higher loads.

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

International Nuclear Information System (INIS)

Ishiguro, Misako; Higuchi, Kenji

1983-01-01

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

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

Science.gov (United States)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Finite volume model for two-dimensional shallow environmental flow

Science.gov (United States)

Simoes, F.J.M.

2011-01-01

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

International Nuclear Information System (INIS)

Franke, H.P.

1976-05-01

The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

Study of structural attachments of a pool type LMFBR vessel through seismic analysis of a simplified three dimensional finite element model

International Nuclear Information System (INIS)

Ahmed, H.; Ma, D.

1979-01-01

A simplified three dimensional finite element model of a pool type LMFBR in conjunction with the computer program ANSYS is developed and scoping results of seismic analysis are produced. Through this study various structural attachments of a pool type LMFBR like the reactor vessel skirt support, the pump support and reactor shell-support structure interfaces are studied. This study also provides some useful results on equivalent viscous damping approach and some improvements to the treatment of equivalent viscous damping are recommended. This study also sets forth pertinent guidelines for detailed three dimensional finite element seismic analysis of pool type LMFBR

Three-dimensional analysis of eddy current with the finite element method

International Nuclear Information System (INIS)

Takano, Ichiro; Suzuki, Yasuo

1977-05-01

The finite element method is applied to three-dimensional analysis of eddy current induced in a large Tokamak device (JT-60). Two techniques to study the eddy current are presented: those of ordinary vector potential and modified vector potential. The latter is originally developed for decreasing dimension of the global matrix. Theoretical treatment of these two is given. The skin effect for alternate current flowing in the circular loop of rectangular cross section is examined as an example of the modified vector potential technique, and the result is compared with analytical one. This technique is useful in analysis of the eddy current problem. (auth.)

Three-dimensional finite element modelling of the uniaxial tension test

DEFF Research Database (Denmark)

Østergaard, Lennart; Stang, Henrik

2002-01-01

. 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......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...... 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....

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...

Finite-time barriers to front propagation in two-dimensional fluid flows

Science.gov (United States)

Mahoney, John R.; Mitchell, Kevin A.

2015-08-01

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 et al. [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind."

Application of three dimensional finite element modeling for the simulation of machining processes

International Nuclear Information System (INIS)

Fischer, C.E.; Wu, W.T.; Chigurupati, P.; Jinn, J.T.

2004-01-01

For many years, metal cutting simulations have been performed using two dimensional approximations of the actual process. Factors such as chip morphology, cutting force, temperature, and tool wear can all be predicted on the computer. However, two dimensional simulation is limited to processes which are orthogonal, or which can be closely approximated as orthogonal.Advances in finite element technology, coupled with continuing improvement in the availability of low cost, high performance computer hardware, have made the three dimensional simulation of a large variety of metal cutting processes practical. Specific improvements include efficient FEM solvers, and robust adaptive remeshing. As researchers continue to gain an improved understanding of wear, material representation, tool coatings, fracture, and other such phenomena, the machining simulation system also must adapt to incorporate these evolving models.To demonstrate the capabilities of the 3D simulation system, a variety of drilling, milling, and turning processes have been simulated and will be presented in this paper. Issues related to computation time and simulation accuracy will also be addressed

Stability and Existence Results for Quasimonotone Quasivariational Inequalities in Finite Dimensional Spaces

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.

Stability and Existence Results for Quasimonotone Quasivariational Inequalities in Finite Dimensional Spaces

International Nuclear Information System (INIS)

Castellani, Marco; Giuli, Massimiliano

2016-01-01

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

A three-dimensional finite element model for biomechanical analysis of the hip.

Science.gov (United States)

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.

FINITE VOLUME METHOD FOR SOLVING THREE-DIMENSIONAL ELECTRIC FIELD DISTRIBUTION

Directory of Open Access Journals (Sweden)

Paţiuc V.I.

2011-04-01

Full Text Available The paper examines a new approach to finite volume method which is used to calculate the electric field spatially homogeneous three-dimensional environment. It is formulated the problem Dirihle with building of the computational grid on base of space partition, which is known as Delone triangulation with the use of Voronoi cells. It is proposed numerical algorithm for calculating the potential and electric field strength in the space formed by a cylinder placed in the air. It is developed algorithm and software which were for the case, when the potential on the inner surface of the cylinder has been assigned and on the outer surface and the bottom of cylinder it was assigned zero potential. There are presented results of calculations of distribution in the potential space and electric field strength.

FREESURF: A three-dimensional finite-element model for simulating groundwater flow into and around an excavation

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)

Evaluation of the parameters affecting bone temperature during drilling using a three-dimensional dynamic elastoplastic finite element model.

Science.gov (United States)

Chen, Yung-Chuan; Tu, Yuan-Kun; Zhuang, Jun-Yan; Tsai, Yi-Jung; Yen, Cheng-Yo; Hsiao, Chih-Kun

2017-11-01

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.

State switching kinetics for quasi-one-dimensional nanosystems: Effects of Finite length and irradiation

Energy Technology Data Exchange (ETDEWEB)

Petukhov, B. V., E-mail: petukhov@ns.crys.ras.ru [Russian Academy of Sciences, Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” (Russian Federation)

2017-01-15

The state switching in an extended quasi-one-dimensional material is modeled by the stochastic formation of local new-state nuclei and their subsequent growth along the system axis. An analytical approach is developed to describe the influence of defects, dividing a sample into an ensemble of finite-length segments, on its state switching kinetics. As applied to magnetic systems, the method makes it possible to calculate magnetization curves for different defect concentrations and parameters of material.

Three-dimensional reconstruction and modeling of middle ear biomechanics by high-resolution computed tomography and finite element analysis.

Science.gov (United States)

Lee, Chia-Fone; Chen, Peir-Rong; Lee, Wen-Jeng; Chen, Jyh-Horng; Liu, Tien-Chen

2006-05-01

To present a systematic and practical approach that uses high-resolution computed tomography to derive models of the middle ear for finite element analysis. This prospective study included 31 subjects with normal hearing and no previous otologic disorders. Temporal bone images obtained from 15 right ears and 16 left ears were used for evaluation and reconstruction. High-resolution computed tomography of temporal bone was performed using simultaneous acquisition of 16 sections with a collimated slice thickness of 0.625 mm. All images were transferred to an Amira visualization system for three-dimensional reconstruction. The created three-dimensional model was translated into two commercial modeling packages, Patran and ANSYS, for finite element analysis. The characteristic dimensions of the model were measured and compared with previously published histologic section data. This result confirms that the geometric model created by the proposed method is accurate except that the tympanic membrane is thicker than when measured by the histologic section method. No obvious difference in the geometrical dimension between right and left ossicles was found (P > .05). The three-dimensional model created by finite element method and predicted umbo and stapes displacements are close to the bounds of the experimental curves of Nishihara's, Huber's, Gan's, and Sun's data across the frequency range of 100 to 8000 Hz. The model includes a description of the geometry of the middle ear components and dynamic equations of vibration. The proposed method is quick, practical, low-cost, and, most importantly, noninvasive as compared with histologic section methods.

Simple one-dimensional finite element algorithm with multi-dimensional capabilities

International Nuclear Information System (INIS)

Pepper, D.W.; Baker, A.J.

1978-01-01

The application of the finite element procedure for the solution of partial differential equations is gaining widespread acceptance. The ability of the finite element procedure to solve problems which are arbitrarily shaped as well as the alleviation of boundary condition problems is well known. By using local interpolation functionals over each subdomain, or element, a set of linearized algebraic equations are obtained which can be solved using any direct, iterative, or inverse numerical technique. Subsequent use of an explicit or implicit integration procedure permits closure of the solution over the global domain

Nonlinear Conservation Laws and Finite Volume Methods

Science.gov (United States)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Broken bridges: a counter-example of the ER=EPR conjecture

International Nuclear Information System (INIS)

Chen, Pisin; Wu, Chih-Hung; Yeom, Dong-han

2017-01-01

In this paper, we provide a counter-example to the ER=EPR conjecture. In an anti-de Sitter space, we construct a pair of maximally entangled but separated black holes. Due to the vacuum decay of the anti-de Sitter background toward a deeper vacuum, these two parts can be trapped by bubbles. If these bubbles are reasonably large, then within the scrambling time, there should appear an Einstein-Rosen bridge between the two black holes. Now by tracing more details on the bubble dynamics, one can identify parameters such that one of the two bubbles either monotonically shrinks or expands. Because of the change of vacuum energy, one side of the black hole would evaporate completely. Due to the shrinking of the apparent horizon, a signal of one side of the Einstein-Rosen bridge can be viewed from the opposite side. We analytically and numerically demonstrate that within a reasonable semi-classical parameter regime, such process can happen. Bubbles are a non-perturbative effect, which is the crucial reason that allows the transmission of information between the two black holes through the Einstein-Rosen bridge, even though the probability is highly suppressed. Therefore, the ER=EPR conjecture cannot be generic in its present form and its validity maybe restricted.

Broken bridges: a counter-example of the ER=EPR conjecture

Energy Technology Data Exchange (ETDEWEB)

Chen, Pisin; Wu, Chih-Hung; Yeom, Dong-han, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: b02202007@ntu.edu.tw, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)

2017-06-01

In this paper, we provide a counter-example to the ER=EPR conjecture. In an anti-de Sitter space, we construct a pair of maximally entangled but separated black holes. Due to the vacuum decay of the anti-de Sitter background toward a deeper vacuum, these two parts can be trapped by bubbles. If these bubbles are reasonably large, then within the scrambling time, there should appear an Einstein-Rosen bridge between the two black holes. Now by tracing more details on the bubble dynamics, one can identify parameters such that one of the two bubbles either monotonically shrinks or expands. Because of the change of vacuum energy, one side of the black hole would evaporate completely. Due to the shrinking of the apparent horizon, a signal of one side of the Einstein-Rosen bridge can be viewed from the opposite side. We analytically and numerically demonstrate that within a reasonable semi-classical parameter regime, such process can happen. Bubbles are a non-perturbative effect, which is the crucial reason that allows the transmission of information between the two black holes through the Einstein-Rosen bridge, even though the probability is highly suppressed. Therefore, the ER=EPR conjecture cannot be generic in its present form and its validity maybe restricted.

A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank

Science.gov (United States)

Fu, Yuchen; Shelley-Abrahamson, Seth

2016-06-01

We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for U_q(sl_N). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov.

Steady finite-Reynolds-number flows in three-dimensional collapsible tubes

Science.gov (United States)

Hazel, Andrew L.; Heil, Matthias

2003-07-01

A fully coupled finite-element method is used to investigate the steady flow of a viscous fluid through a thin-walled elastic tube mounted between two rigid tubes. The steady three-dimensional Navier Stokes equations are solved simultaneously with the equations of geometrically nonlinear Kirchhoff Love shell theory. If the transmural (internal minus external) pressure acting on the tube is sufficiently negative then the tube buckles non-axisymmetrically and the subsequent large deformations lead to a strong interaction between the fluid and solid mechanics. The main effect of fluid inertia on the macroscopic behaviour of the system is due to the Bernoulli effect, which induces an additional local pressure drop when the tube buckles and its cross-sectional area is reduced. Thus, the tube collapses more strongly than it would in the absence of fluid inertia. Typical tube shapes and flow fields are presented. In strongly collapsed tubes, at finite values of the Reynolds number, two ’jets‘ develop downstream of the region of strongest collapse and persist for considerable axial distances. For sufficiently high values of the Reynolds number, these jets impact upon the sidewalls and spread azimuthally. The consequent azimuthal transport of momentum dramatically changes the axial velocity profiles, which become approximately uTheta-shaped when the flow enters the rigid downstream pipe. Further convection of momentum causes the development of a ring-shaped velocity profile before the ultimate return to a parabolic profile far downstream.

Convergence rates and finite-dimensional approximations for nonlinear ill-posed problems involving monotone operators in Banach spaces

International Nuclear Information System (INIS)

Nguyen Buong.

1992-11-01

The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs

Numerical and algebraic studies for the control of finite-dimensional quantum systems

Energy Technology Data Exchange (ETDEWEB)

Sander, Uwe

2010-11-18

In this thesis, two aspects of control theory, namely controllability and optimal control, are applied to quantum systems. The presented results are based on group theoretical techniques and numerical studies. By Lie-algebraic analysis, the controllability properties of systems with an arbitrary topology are described and related to the symmetries existing in these systems. We find that symmetry precludes full controllability. Our work investigates well-known control systems and gives rules for the design of new systems. Furthermore, theoretical and numerical concepts are instrumental to studying quantum channels: Their capacities are optimised using gradient flows on the unitary group in order to find counterexamples to a long-established additivity conjecture. The last part of this thesis presents and benchmarks a modular optimal control algorithm known as GRAPE. Numerical tests show how the interplay of its modules can be optimised for higher performance, and how the algorithm performs in comparison to a Krotov-type optimal control algorithm. It is found that GRAPE performs particularly well when aiming for high qualities. (orig.)

Numerical and algebraic studies for the control of finite-dimensional quantum systems

International Nuclear Information System (INIS)

Sander, Uwe

2010-01-01

In this thesis, two aspects of control theory, namely controllability and optimal control, are applied to quantum systems. The presented results are based on group theoretical techniques and numerical studies. By Lie-algebraic analysis, the controllability properties of systems with an arbitrary topology are described and related to the symmetries existing in these systems. We find that symmetry precludes full controllability. Our work investigates well-known control systems and gives rules for the design of new systems. Furthermore, theoretical and numerical concepts are instrumental to studying quantum channels: Their capacities are optimised using gradient flows on the unitary group in order to find counterexamples to a long-established additivity conjecture. The last part of this thesis presents and benchmarks a modular optimal control algorithm known as GRAPE. Numerical tests show how the interplay of its modules can be optimised for higher performance, and how the algorithm performs in comparison to a Krotov-type optimal control algorithm. It is found that GRAPE performs particularly well when aiming for high qualities. (orig.)

Numerical simulation of potato slices drying using a two-dimensional finite element model

Directory of Open Access Journals (Sweden)

Beigi Mohsen

2017-01-01

Full Text Available An experimental and numerical study was conducted to investigate the process of potato slices drying. For simulating the moisture transfer in the samples and predict the dehydration curves, a two-dimensional finite element model was developed and programmed in Compaq Visual Fortran, version 6.5. The model solved the Fick’s second law for slab in a shrinkage system to calculate the unsteady two-dimensional moisture transmission in rectangular coordinates (x,y. Moisture diffusivity and moisture transfer coefficient were determined by minimizing the sum squares of residuals between experimental and numerical predicted data. Shrinkage kinetics of the potato slices during dehydration was determined experimentally and found to be a linear function of removed moisture. The determined parameters were used in the mathematical model. The predicted moisture content values were compared to the experimental data and the validation results demonstrated that the dynamic drying curves were predicted by the methodology very well.

Finite Element Analysis of Three-Dimensional (3D Auxetic Textile Composite under Compression

Directory of Open Access Journals (Sweden)

Jifang Zeng

2018-03-01

Full Text Available This paper reports a finite element (FE analysis of three-dimensional (3D auxetic textile composite by using commercial software ANSYS 15 under compression. The two-dimensional (2D FE model was first developed and validated by experiment. Then, the validated model was used to evaluate effects of structural parameters and constituent material properties. For the comparison, 3D non-auxetic composite that was made with the same constituent materials and structural parameters, but with different yarn arrangement in the textile structure was also analyzed at the same time. The analysis results showed that the auxetic and non-auxetic composites have different compression behaviors and the auxetic composite has better the energy absorption capacity than the non-auxetic composite under the same compression stress. The study has provided us a guidance to design and fabricate auxetic composites with the required mechanical behavior by appropriately selecting structural parameters and constituent materials.

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

A solution of two-dimensional magnetohydrodynamic flow using the finite volume method

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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.

Electromagnetic-field amplification in finite one-dimensional photonic crystals

International Nuclear Information System (INIS)

Gorelik, V. S.; Kapaev, V. V.

2016-01-01

The electromagnetic-field distribution in a finite one-dimensional photonic crystal is studied using the numerical solution of Maxwell’s equations by the transfer-matrix method. The dependence of the transmission coefficient T on the period d (or the wavelength λ) has the characteristic form with M–1 (M is the number of periods in the structure) maxima with T = 1 in the allowed band of an infinite crystal and zero values in the forbidden band. The field-modulus distribution E(x) in the structure for parameters that correspond to the transmission maxima closest to the boundaries of forbidden bands has maxima at the center of the structure; the value at the maximum considerably exceeds the incident-field strength. For the number of periods M ~ 50, more than an order of magnitude increase in the field amplification is observed. The numerical results are interpreted with an analytic theory constructed by representing the solution in the form of a linear combination of counterpropagating Floquet modes in a periodic structure.

Highly arc-transitive digraphs -- counterexamples and structure

OpenAIRE

DeVos, Matt; Mohar, Bojan; Šámal, Robert

2011-01-01

We resolve two problems of [Cameron, Praeger, and Wormald -- Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica 1993]. First, we construct a locally finite highly arc-transitive digraph with universal reachability relation. Second, we provide constructions of 2-ended highly arc transitive digraphs where each `building block' is a finite bipartite graph that is not a disjoint union of complete bipartite graphs. This was conjectured impossible in the above pa...

SANTOS - a two-dimensional finite element program for the quasistatic, large deformation, inelastic response of solids

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.

Theoretical background and implementation of the finite element method for multi-dimensional Fokker-Planck equation analysis

Czech Academy of Sciences Publication Activity Database

Král, Radomil; Náprstek, Jiří

2017-01-01

Roč. 113, November (2017), s. 54-75 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GP14-34467P; GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : Fokker-Planck equation * finite element method * simplex element * multi-dimensional problem * non-symmetric operator Subject RIV: JM - Building Engineering OBOR OECD: Mechanical engineering Impact factor: 3.000, year: 2016 https://www.sciencedirect.com/science/ article /pii/S0965997817301904

Supersymmetric theories and finiteness

International Nuclear Information System (INIS)

Helayel-Neto, J.A.

1989-01-01

We attempt here to present a short survey of the all-order finite Lagrangian field theories known at present in four-and two-dimensional space-times. The question of the possible relevance of these ultraviolet finite models in the formulation of consistent unified frameworks for the fundamental forces is also addressed to. (author)

Evaluating the effects of modeling errors for isolated finite three-dimensional targets

Science.gov (United States)

Henn, Mark-Alexander; Barnes, Bryan M.; Zhou, Hui

2017-10-01

Optical three-dimensional (3-D) nanostructure metrology utilizes a model-based metrology approach to determine critical dimensions (CDs) that are well below the inspection wavelength. Our project at the National Institute of Standards and Technology is evaluating how to attain key CD and shape parameters from engineered in-die capable metrology targets. More specifically, the quantities of interest are determined by varying the input parameters for a physical model until the simulations agree with the actual measurements within acceptable error bounds. As in most applications, establishing a reasonable balance between model accuracy and time efficiency is a complicated task. A well-established simplification is to model the intrinsically finite 3-D nanostructures as either periodic or infinite in one direction, reducing the computationally expensive 3-D simulations to usually less complex two-dimensional (2-D) problems. Systematic errors caused by this simplified model can directly influence the fitting of the model to the measurement data and are expected to become more apparent with decreasing lengths of the structures. We identify these effects using selected simulation results and present experimental setups, e.g., illumination numerical apertures and focal ranges, that can increase the validity of the 2-D approach.

Parallel DSMC Solution of Three-Dimensional Flow Over a Finite Flat Plate

Science.gov (United States)

Nance, Robert P.; Wilmoth, Richard G.; Moon, Bongki; Hassan, H. A.; Saltz, Joel

1994-01-01

This paper describes a parallel implementation of the direct simulation Monte Carlo (DSMC) method. Runtime library support is used for scheduling and execution of communication between nodes, and domain decomposition is performed dynamically to maintain a good load balance. Performance tests are conducted using the code to evaluate various remapping and remapping-interval policies, and it is shown that a one-dimensional chain-partitioning method works best for the problems considered. The parallel code is then used to simulate the Mach 20 nitrogen flow over a finite-thickness flat plate. It is shown that the parallel algorithm produces results which compare well with experimental data. Moreover, it yields significantly faster execution times than the scalar code, as well as very good load-balance characteristics.

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

Biomechanical Property of a Newly Designed Assembly Locking Compression Plate: Three-Dimensional Finite Element Analysis

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.

Three-dimensional finite element analysis of residual magnetic field for ferromagnets under early damage

International Nuclear Information System (INIS)

Yao, Kai; Shen, Kai; Wang, Zheng-Dao; Wang, Yue-Sheng

2014-01-01

In this study, 3D finite element analysis is presented by calculating the residual magnetic field signals of ferromagnets under the plastic deformation. The contour maps of tangential and normal RMF gradients are given, and the 3D effect is discussed. The results show that the tangential peak–peak amplitude and normal peak–vale amplitude are remarkably different in 2D and 3D simulations, but the tangential peak–peak width and normal peak–vale width are similar. Moreover, some key points are capable of capturing the plastic-zone shape, especially when the lift-off is small enough. The present study suggests an effective defect identification method with Metal magnetic memory (MMM) technique. - Highlights: • Three-dimensional (3D) finite element analysis is presented by calculating the residual magnetic field signals of ferromagnets under the plastic deformation. • The contour maps of gradients of the tangential and normal residual magnetic fields are given, and the 3D effect is discussed. • The present study suggests an effective defect identification method with metal magnetic memory technique

Development of a three-dimensional neutron transport code DFEM based on the double finite element method

International Nuclear Information System (INIS)

Fujimura, Toichiro

1996-01-01

A three-dimensional neutron transport code DFEM has been developed by the double finite element method to analyze reactor cores with complex geometry as large fast reactors. Solution algorithm is based on the double finite element method in which the space and angle finite elements are employed. A reactor core system can be divided into some triangular and/or quadrangular prism elements, and the spatial distribution of neutron flux in each element is approximated with linear basis functions. As for the angular variables, various basis functions are applied, and their characteristics were clarified by comparison. In order to enhance the accuracy, a general method is derived to remedy the truncation errors at reflective boundaries, which are inherent in the conventional FEM. An adaptive acceleration method and the source extrapolation method were applied to accelerate the convergence of the iterations. The code structure is outlined and explanations are given on how to prepare input data. A sample input list is shown for reference. The eigenvalue and flux distribution for real scale fast reactors and the NEA benchmark problems were presented and discussed in comparison with the results of other transport codes. (author)

Numerical and Experimental Investigation of Stop-Bands in Finite and Infinite Periodic One-Dimensional Structures

DEFF Research Database (Denmark)

Domadiya, Parthkumar Gandalal; Manconi, Elisabetta; Vanali, Marcello

2016-01-01

Adding periodicity to structures leads to wavemode interaction, which generates pass- and stop-bands. The frequencies at which stop-bands occur are related to the periodic nature of the structure. Thus structural periodicity can be shaped in order to design vibro-acoustic filters for reducing...... 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...

A two dimensional finite difference time domain analysis of the quiet zone fields of an anechoic chamber

Science.gov (United States)

Ryan, Deirdre A.; Luebbers, Raymond J.; Nguyen, Truong X.; Kunz, Karl S.; Steich, David J.

1992-01-01

Prediction of anechoic chamber performance is a difficult problem. Electromagnetic anechoic chambers exist for a wide range of frequencies but are typically very large when measured in wavelengths. Three dimensional finite difference time domain (FDTD) modeling of anechoic chambers is possible with current computers but at frequencies lower than most chamber design frequencies. However, two dimensional FDTD (2D-FTD) modeling enables much greater detail at higher frequencies and offers significant insight into compact anechoic chamber design and performance. A major subsystem of an anechoic chamber for which computational electromagnetic analyses exist is the reflector. First, an analysis of the quiet zone fields of a low frequency anechoic chamber produced by a uniform source and a reflector in two dimensions using the FDTD method is presented. The 2D-FDTD results are compared with results from a three dimensional corrected physical optics calculation and show good agreement. Next, a directional source is substituted for the uniform radiator. Finally, a two dimensional anechoic chamber geometry, including absorbing materials, is considered, and the 2D-FDTD results for these geometries appear reasonable.

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

Science.gov (United States)

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.

Entangled photon pair generation by spontaneous parametric down-conversion in finite-length one-dimensional photonic crystals

International Nuclear Information System (INIS)

Centini, M.; Sciscione, L.; Sibilia, C.; Bertolotti, M.; Perina, J. Jr.; Scalora, M.; Bloemer, M.J.

2005-01-01

A description of spontaneous parametric down-conversion in finite-length one-dimensional nonlinear photonic crystals is developed using semiclassical and quantum approaches. It is shown that if a suitable averaging is added to the semiclassical model, its results are in very good agreement with the quantum approach. We propose two structures made with GaN/AlN that generate both degenerate and nondegenerate entangled photon pairs. Both structures are designed so as to achieve a high efficiency of the nonlinear process

Three-dimensional finite elements for the analysis of soil contamination using a multiple-porosity approach

Science.gov (United States)

El-Zein, Abbas; Carter, John P.; Airey, David W.

2006-06-01

A three-dimensional finite-element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non-equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro-pores of aggregated topsoils, as well as non-equilibrium sorption. A Galerkin weighted-residual statement for the three-dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer.

Finite quantum field theories

International Nuclear Information System (INIS)

Lucha, W.; Neufeld, H.

1986-01-01

We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)

Partially-massless higher-spin algebras and their finite-dimensional truncations

International Nuclear Information System (INIS)

Joung, Euihun; Mkrtchyan, Karapet

2016-01-01

The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS d+1 are studied. The algebras involving PM generators up to depth 2 (ℓ−1) are defined as the maximal symmetries of free conformal scalar field with 2 ℓ order wave equation in d dimensions. We review the construction of these algebras by quotienting certain ideals in the universal enveloping algebra of (A)dS d+1 isometries. We discuss another description in terms of Howe duality and derive the formula for computing trace in these algebras. This enables us to explicitly calculate the bilinear form for this one-parameter family of algebras. In particular, the bilinear form shows the appearance of additional ideal for any non-negative integer values of ℓ−d/2 , which coincides with the annihilator of the one-row ℓ-box Young diagram representation of so d+2 . Hence, the corresponding finite-dimensional coset algebra spanned by massless and PM generators is equivalent to the symmetries of this representation.

Efficient Finite Element Models for Calculation of the No-load losses of the Transformer

Directory of Open Access Journals (Sweden)

Kamran Dawood

2017-10-01

Full Text Available Different transformer models are examined for the calculation of the no-load losses using finite element analysis. Two-dimensional and three-dimensional finite element analyses are used for the simulation of the transformer. Results of the finite element method are also compared with the experimental results. The Result shows that 3-dimensional provide high accuracy as compared to the 2 dimensional full and half model. However, the 2-dimensional half model is the less time-consuming method as compared to the 3 and 2-dimensional full model. Simulation time duration taken by the different models of the transformer is also compared. The difference between the 3-dimensional finite element method and experimental results are less than 3%. These numerical methods can help transformer designers to minimize the development of the prototype transformers.

Finite-temperature symmetry restoration in the four-dimensional Φ4 model with four components

International Nuclear Information System (INIS)

Jansen, K.

1990-01-01

The finite-temperature symmetry restoration in the four-dimensional φ 4 theory with four components and with an infinite self-coupling is studied by means of Monte Carlo simulations on lattices with time extensions L t =4,5,6 and space extensions 12 3 -28 3 . The numerical calculations are done by means of the Wolff cluster algorithm which is very efficient for simulations near a phase transition. The numerical results are in good agreement with an improved one-loop expansion and with the 1/N-expansion, indicating that in the electroweak theory the symmetry restoration temperature T sr is about 350 GeV. (orig.)

Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions

International Nuclear Information System (INIS)

Barrios, Dolores; Lopez, Guillermo L; Martinez-Finkelshtein, A; Torrano, Emilio

1999-01-01

The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a positive result is obtained. The convergence domain of the sequence of resolvents can be described in this case in terms of matrices involved in the representation. This result is applied to tridiagonal complex matrices to establish conditions for the convergence of Chebyshev continued fractions on sets in the complex domain. In the particular case of compact perturbations this result is improved and a connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is established

Some efficient Lagrangian mesh finite elements encoded in ZEPHYR for two dimensional transport calculations

International Nuclear Information System (INIS)

Mordant, Maurice.

1981-04-01

To solve a multigroup stationary neutron transport equation in two-dimensional geometries (X-Y), (R-O) or (R-Z) generally on uses discrete ordinates and rectangular meshes. The way to do it is then well known, well documented and somewhat obvious. If one needs to treat awkward geometries or distorted meshes, things are not so easy and the way to do it is no longer straightforward. We have studied this problem at Limeil Nuclear Center and as an alternative to Monte Carlo methods and code we have implemented in ZEPHYR code at least two efficient finite element solutions for Lagrangian meshes involving any kind of triangles and quadrilaterals

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space

Science.gov (United States)

Crisford, Toby; Santos, Jorge E.

2017-05-01

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

International Conference on Finite or Infinite Dimensional Complex Analysis and Applications

CERN Document Server

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....

NCEL: two dimensional finite element code for steady-state temperature distribution in seven rod-bundle

International Nuclear Information System (INIS)

Hrehor, M.

1979-01-01

The paper deals with an application of the finite element method to the heat transfer study in seven-pin models of LMFBR fuel subassembly. The developed code NCEL solves two-dimensional steady state heat conduction equation in the whole subassembly model cross-section and enebles to perform the analysis of thermal behaviour in both normal and accidental operational conditions as eccentricity of the central rod or full or partial (porous) blockage of some part of the cross-flow area. The heat removal is simulated by heat sinks in coolant under conditions of subchannels slug flow approximation

Application of space-and-angle finite element method to the three-dimensional neutron transport problems

International Nuclear Information System (INIS)

Fujimura, T.; Nakahara, Y.; Matsumura, M.

1983-01-01

A double finite element method (DFEM), in which both the space-and-angle finite elements are employed, has been formulated and computer codes have been developed to solve the static multigroup neutron transport problems in the three-dimensional geometry. Two methods, Galerkin's weighted residual and variational are used to apply the DFEM to the transport equation. The variational principle requires complicated formulation than the Galerkin method, but the boundary conditions can be automatically incorporated and each plane equation becomes symmetric. The system equations are solved over the planar layers which we call plane iteration. The coarse mesh rebalancing technique is used for the inner iteration and the outer iteration is accelerated by extra-polation. Numerical studies of these two DFEM algorithms have been done in comparison between them and also with THe CITATION and TWOTRAN-II results. It has been confirmed that in the case of variational formulation an adaptive acceleration method of the SSOR iteration works effectively and the ray effects are mitigated in both DFEM algorithms. (author)

Finite-element three-dimensional ground-water (FE3DGW) flow model - formulation, program listings and users' manual

International Nuclear Information System (INIS)

Gupta, S.K.; Cole, C.R.; Bond, F.W.

1979-12-01

The Assessment of Effectiveness of Geologic Isolation Systems (AEGIS) Program is developing and applying the methodology for assessing the far-field, long-term post-closure safety of deep geologic nuclear waste repositories. AEGIS is being performed by Pacific Northwest Laboratory (PNL) under contract with the Office of Nuclear Waste Isolation (OWNI) for the Department of Energy (DOE). One task within AEGIS is the development of methodology for analysis of the consequences (water pathway) from loss of repository containment as defined by various release scenarios. Analysis of the long-term, far-field consequences of release scenarios requires the application of numerical codes which simulate the hydrologic systems, model the transport of released radionuclides through the hydrologic systems to the biosphere, and, where applicable, assess the radiological dose to humans. Hydrologic and transport models are available at several levels of complexity or sophistication. Model selection and use are determined by the quantity and quality of input data. Model development under AEGIS and related programs provides three levels of hydrologic models, two levels of transport models, and one level of dose models (with several separate models). This document consists of the description of the FE3DGW (Finite Element, Three-Dimensional Groundwater) Hydrologic model third level (high complexity) three-dimensional, finite element approach (Galerkin formulation) for saturated groundwater flow

Inelastic analysis of finite length and depth cracked tubes

International Nuclear Information System (INIS)

Reich, M.; Gardner, D.; Prachuktam, S.; Chang, T.Y.

1977-01-01

Steam generator tube failure can at times result in reactor safety problems and subsequent premature reactor shutdown. This paper concerns itself with the prediction of the failure pressures for typical PWR steam generator tubes with longitudinal finite length and finite depth cracks. Only local plastic overload failure is considered since the material is non-notch sensitive. Non-linear finite element analyses are carried out to determine the burst pressures of steam generator tubes containing longitudinal cracks located on the outer surface of the tubes. The non-linearities considered herein include elastic-plastic material behaviour and large deformations. A non-proprietary general purpose non-linear finite element program, NFAP was adopted for the analysis. Due to the asymmetric nature of the cracks, two-dimensional as well as three-dimensional finite element analyses, were performed. The analysis clearly shows that for short cracks axial effects play a significant role. For long cracks, they are not important since two-dimensional conditions predominate and failure is governed by circumferential or hoop stress conditions. (Auth.)

Features of finite quantum field theories

International Nuclear Information System (INIS)

Boehm, M.; Denner, A.

1987-01-01

We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)

Inelastic analysis of finite length and depth cracked tubes

International Nuclear Information System (INIS)

Reich, M.; Gardner, D.; Prachuktam, S.; Chang, T.Y.

1977-01-01

Steam generator tube failure can at times result in reactor safety problems and subsequent premature reactor shutdowns. This paper concerns itself with the prediction of the failure pressures for typical PWR steam generator tubes with longitudinal finite length and finite depth cracks. Only local plastic overload failure is considered since the material is non-notch sensitive. Non-linear finite element analyses are carried out to determine the burst pressures of steam generator tubes containing longitudinal cracks located on the outer surface of the tubes. The non-linearities considered herein include elastic-plastic material behavior and large deformations. A non-proprietary general purpose non-linear finite element program, NFAP was adopted for the analysis. Due to the asymmetric nature of the cracks, two-dimensional, as well as three-dimensional finite element analyses, were performed. The two-dimensional element and its formulations are similar to those of NONSAP. The three-dimensional isoparametric element with elastic-plastic material characteristics together with the large deformation formulations used in NFAP are described in the Report BNL-20684. The numerical accuracy of the program was investigated and checked with known solutions of benchmark problems. In addition to the three-dimensional element which was specifically inserted into NFAP for this problem, other features such as direct pressure inputs for isoparametric elements, automatic load increment adjustments for convergent non-linear solutions, and automatic bandwidth reduction schemes are incorporated into the program thus allowing for a more economical evaluation of three-dimensional inelastic analysis. In summary the analysis clearly shows that for short cracks axial effects play a significant role. For long cracks, they are not important since two-dimensional conditions predominate and failure is governed by circumferential or hoop stress conditions

Finite-Element Software for Conceptual Design

DEFF Research Database (Denmark)

Lindemann, J.; Sandberg, G.; Damkilde, Lars

2010-01-01

and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...

Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions

International Nuclear Information System (INIS)

Carpenter, D.C.

1997-01-01

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

DIF3D: a code to solve one-, two-, and three-dimensional finite-difference diffusion theory problems

International Nuclear Information System (INIS)

Derstine, K.L.

1984-04-01

The mathematical development and numerical solution of the finite-difference equations are summarized. The report provides a guide for user application and details the programming structure of DIF3D. Guidelines are included for implementing the DIF3D export package on several large scale computers. Optimized iteration methods for the solution of large-scale fast-reactor finite-difference diffusion theory calculations are presented, along with their theoretical basis. The computational and data management considerations that went into their formulation are discussed. The methods utilized include a variant of the Chebyshev acceleration technique applied to the outer fission source iterations and an optimized block successive overrelaxation method for the within-group iterations. A nodal solution option intended for analysis of LMFBR designs in two- and three-dimensional hexagonal geometries is incorporated in the DIF3D package and is documented in a companion report, ANL-83-1

Three-dimensional Finite Elements Method simulation of Total Ionizing Dose in 22 nm bulk nFinFETs

Energy Technology Data Exchange (ETDEWEB)

Chatzikyriakou, Eleni, E-mail: ec3g12@soton.ac.uk; Potter, Kenneth; Redman-White, William; De Groot, C.H.

2017-02-15

Highlights: • Simulation of Total Ionizing Dose using the Finite Elements Method. • Carrier generation, transport and trapping in the oxide. • Application in three-dimensional bulk FinFET model of 22 nm node. • Examination of trapped charge in the Shallow Trench Isolation. • Trapped charge dependency of parasitic transistor current. - Abstract: Finite Elements Method simulation of Total Ionizing Dose effects on 22 nm bulk Fin Field Effect Transistor (FinFET) devices using the commercial software Synopsys Sentaurus TCAD is presented. The simulation parameters are extracted by calibrating the charge trapping model to experimental results on 400 nm SiO{sub 2} capacitors irradiated under zero bias. The FinFET device characteristics are calibrated to the Intel 22 nm bulk technology. Irradiation simulations of the transistor performed with all terminals unbiased reveal increased hardness up to a total dose of 1 MRad(SiO{sub 2}).

A two-dimensional, finite-element methods for calculating TF coil response to out-of-plane Lorentz forces

International Nuclear Information System (INIS)

Witt, R.J.

1989-01-01

Toroidal field (TF) coils in fusion systems are routinely operated at very high magnetic fields. While obtaining the response of the coil to in-plane loads is relatively straightforward, the same is not true for the out-of-plane loads. Previous treatments of the out-of-plane problem have involved large, three-dimensional finite element idealizations. A new treatment of the out-of-plane problem is presented here; the model is two-dimensional in nature, and consumes far less CPU-time than three-dimensional methods. The approach assumes there exists a region of torsional deformation in the inboard leg and a bending region in the outboard leg. It also assumes the outboard part of the coil is attached to a torque frame/cylinder, which experiences primarily torsional deformation. Three-dimensional transition regions exist between the inboard and outboard legs and between the outboard leg and the torque frame. By considering several idealized problems of cylindrical shells subjected to moment distributions, it is shown that the size of these three-dimensional regions is quite small, and that the interaction between the torsional and bending regions can be treated in an equivalent two-dimensional fashion. Equivalent stiffnesses are derived to model penetration into and twist along the cylinders. These stiffnesses are then used in a special substructuring analysis to couple the three regions together. Results from the new method are compared to results from a 3D continuum model. (orig.)

Electrical machine analysis using finite elements

CERN Document Server

Bianchi, Nicola

2005-01-01

OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I

3-dimensional earthquake response analysis of embedded reactor building using hybrid model of boundary elements and finite elements

International Nuclear Information System (INIS)

Muto, K.; Motosaka, M.; Kamata, M.; Masuda, K.; Urao, K.; Mameda, T.

1985-01-01

In order to investigate the 3-dimensional earthquake response characteristics of an embedded structure with consideration for soil-structure interaction, the authors have developed an analytical method using 3-dimensional hybrid model of boundary elements (BEM) and finite elements (FEM) and have conducted a dynamic analysis of an actual nuclear reactor building. This paper describes a comparative study between two different embedment depths in soil as elastic half-space. As the results, it was found that the earthquake response intensity decreases with the increase of the embedment depth and that this method was confirmed to be effective for investigating the 3-D response characteristics of embedded structures such as deflection pattern of each floor level, floor response spectra in high frequency range. (orig.)

Finite element computational fluid mechanics

International Nuclear Information System (INIS)

Baker, A.J.

1983-01-01

This book analyzes finite element theory as applied to computational fluid mechanics. It includes a chapter on using the heat conduction equation to expose the essence of finite element theory, including higher-order accuracy and convergence in a common knowledge framework. Another chapter generalizes the algorithm to extend application to the nonlinearity of the Navier-Stokes equations. Other chapters are concerned with the analysis of a specific fluids mechanics problem class, including theory and applications. Some of the topics covered include finite element theory for linear mechanics; potential flow; weighted residuals/galerkin finite element theory; inviscid and convection dominated flows; boundary layers; parabolic three-dimensional flows; and viscous and rotational flows

Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

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.

Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

International Nuclear Information System (INIS)

Nakra Mohajer, Soukaina; El Harouny, El Hassan; Ibral, Asmaa; El Khamkhami, Jamal

2016-01-01

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.

Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

Science.gov (United States)

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.

Orthogonality preserving infinite dimensional quadratic stochastic operators

International Nuclear Information System (INIS)

Akın, Hasan; Mukhamedov, Farrukh

2015-01-01

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators

Stark effect in finite-barrier quantum wells, wires, and dots

International Nuclear Information System (INIS)

Pedersen, Thomas Garm

2017-01-01

The properties of confined carriers in low-dimensional nanostructures can be controlled by external electric fields and an important manifestation is the Stark shift of quantized energy levels. Here, a unifying analytic theory for the Stark effect in arbitrary dimensional nanostructures is presented. The crucial role of finite potential barriers is stressed, in particular, for three-dimensional confinement. Applying the theory to CdSe quantum dots, finite barriers are shown to improve significantly the agreement with experiments. (paper)

The analysis of three-dimensional effects of nitanium palatal expander 2 and hyrax maxillary expansion appliances on craniofacial structures: A finite element study

Directory of Open Access Journals (Sweden)

Avinash Kumar

2017-01-01

Full Text Available Objectives: To analyze three-dimensional effects of stress distribution and displacement on the craniofacial structures, following the application of forces from Nitanium Palatal Expander 2 (NPE2 and Hyrax appliance in early mixed dentition period using finite element analysis. Materials and Methods: Three-dimensional finite element models of the young dried human skull, NPE2 and Hyrax were constructed, and the initial activation of the expanders was simulated to carry out the analysis and to evaluate the von misses stresses and displacement on the craniofacial structures. Results: Both the models demonstrated the highest stresses at the mid-palatal suture, with maximum posterior dislocation. The inferior nasal floor showed highest downward displacement and point A showed outward, backward, and upward displacement in both the models. The pattern of stress distribution was almost similar in both the groups, but NPE2 revealed lower magnitude stresses than Hyrax. The cusp of the erupting canine and the mesiobuccal cusp of the second molar showed outward, backward, and downward displacement signifying eruption pattern following maxillary expansion. Conclusions: Nickel titanium palatal expander-2 and Hyrax produced similar stress pattern in early mixed dentition period finite element model. We conclude from this finite element method study that NPE2 is equally effective as Hyrax when used in early mixed dentition period as it exhibits orthopedic nature of expansion with minimal residual stresses in the craniofacial structures.

Finite element analysis of stresses in fixed prosthesis and cement layer using a three-dimensional model

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.

A Note on Symplectic, Multisymplectic Scheme in Finite Element Method

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke

2001-01-01

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``

Linear finite element method for one-dimensional diffusion problems

Energy Technology Data Exchange (ETDEWEB)

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

2011-07-01

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

On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions

KAUST Repository

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.

A two-dimensional finite element method for analysis of solid body contact problems in fuel rod mechanics

International Nuclear Information System (INIS)

Nissen, K.L.

1988-06-01

Two computer codes for the analysis of fuel rod behavior have been developed. Fuel rod mechanics is treated by a two-dimensional, axisymmetric finite element method. The program KONTAKT is used for detailed examinations on fuel rod sections, whereas the second program METHOD2D allows instationary calculations of whole fuel rods. The mechanical contact of fuel and cladding during heating of the fuel rod is very important for it's integrity. Both computer codes use a Newton-Raphson iteration for the solution of the nonlinear solid body contact problem. A constitutive equation is applied for the dependency of contact pressure on normal approach of the surfaces which are assumed to be rough. If friction is present on the contacting surfaces, Coulomb's friction law is used. Code validation is done by comparison with known analytical solutions for special problems. Results of the contact algorithm for an elastic ball pressing against a rigid surface are confronted with Hertzian theory. Influences of fuel-pellet geometry as well as influences of discretisation of displacements and stresses of a single fuel pellet are studied. Contact of fuel and cladding is calculated for a fuel rod section with two fuel pellets. The influence of friction forces between fuel and cladding on their axial expansion is demonstrated. By calculation of deformations and temperatures during an instationary fuel rod experiment of the CABRI-series the feasibility of two-dimensional finite element analysis of whole fuel rods is shown. (orig.) [de

Implicit three-dimensional finite-element formulation for the nonlinear structural response of reactor components

International Nuclear Information System (INIS)

Kulak, R.F.; Belytschko, T.B.

1975-09-01

The formulation of a finite-element procedure for the implicit transient and static analysis of plate/shell type structures in three-dimensional space is described. The triangular plate/shell element can sustain both membrane and bending stresses. Both geometric and material nonlinearities can be treated, and an elastic-plastic material law has been incorporated. The formulation permits the element to undergo arbitrarily large rotations and translations; but, in its present form it is restricted to small strains. The discretized equations of motion are obtained by a stiffness method. An implicit integration algorithm based on trapezoidal integration formulas is used to integrate the discretized equations of motion in time. To ensure numerical stability, an iterative solution procedure with equilibrium checks is used

Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

Science.gov (United States)

Newman, J. C., Jr.; Raju, I. S.

1984-01-01

Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.

Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators

Science.gov (United States)

Pervishko, Anastasiia A.; Yudin, Dmitry; Shelykh, Ivan A.

2018-02-01

Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect within recently proposed Brillouin-Wigner perturbation theory that allows us to map a time-dependent problem into a stationary one. Our analysis reveals that both the gap and the components of the group velocity of the surface states can be tuned in a controllable fashion by adjusting the intensity of the driving field within an experimentally accessible range and demonstrate the effect of light-induced band inversion in the spectrum of the surface states for high enough values of the pump.

Three-Dimensional Finite Difference Simulation of Ground Motions from the August 24, 2014 South Napa Earthquake

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.

Three-dimensional photoacoustic tomography based on graphics-processing-unit-accelerated finite element method.

Science.gov (United States)

Peng, Kuan; He, Ling; Zhu, Ziqiang; Tang, Jingtian; Xiao, Jiaying

2013-12-01

Compared with commonly used analytical reconstruction methods, the frequency-domain finite element method (FEM) based approach has proven to be an accurate and flexible algorithm for photoacoustic tomography. However, the FEM-based algorithm is computationally demanding, especially for three-dimensional cases. To enhance the algorithm's efficiency, in this work a parallel computational strategy is implemented in the framework of the FEM-based reconstruction algorithm using a graphic-processing-unit parallel frame named the "compute unified device architecture." A series of simulation experiments is carried out to test the accuracy and accelerating effect of the improved method. The results obtained indicate that the parallel calculation does not change the accuracy of the reconstruction algorithm, while its computational cost is significantly reduced by a factor of 38.9 with a GTX 580 graphics card using the improved method.

Analysis of Elastic-Plastic J Integrals for 3-Dimensional Cracks Using Finite Element Alternating Method

International Nuclear Information System (INIS)

Park, Jai Hak

2009-01-01

SGBEM(Symmetric Galerkin Boundary Element Method)-FEM alternating method has been proposed by Nikishkov, Park and Atluri. In the proposed method, arbitrarily shaped three-dimensional crack problems can be solved by alternating between the crack solution in an infinite body and the finite element solution without a crack. In the previous study, the SGBEM-FEM alternating method was extended further in order to solve elastic-plastic crack problems and to obtain elastic-plastic stress fields. For the elastic-plastic analysis the algorithm developed by Nikishkov et al. is used after modification. In the algorithm, the initial stress method is used to obtain elastic-plastic stress and strain fields. In this paper, elastic-plastic J integrals for three-dimensional cracks are obtained using the method. For that purpose, accurate values of displacement gradients and stresses are necessary on an integration path. In order to improve the accuracy of stress near crack surfaces, coordinate transformation and partitioning of integration domain are used. The coordinate transformation produces a transformation Jacobian, which cancels the singularity of the integrand. Using the developed program, simple three-dimensional crack problems are solved and elastic and elastic-plastic J integrals are obtained. The obtained J integrals are compared with the values obtained using a handbook solution. It is noted that J integrals obtained from the alternating method are close to the values from the handbook

Study of a method to solve the one speed, three dimensional transport equation using the finite element method and the associated Legendre function

International Nuclear Information System (INIS)

Fernandes, A.

1991-01-01

A method to solve three dimensional neutron transport equation and it is based on the original work suggested by J.K. Fletcher (42, 43). The angular dependence of the flux is approximated by associated Legendre functions and the finite element method is applied to the space components is presented. When the angular flux, the scattering cross section and the neutrons source are expanded in associated Legendre functions, the first order neutron transport equation is reduced to a coupled set of second order diffusion like equations. These equations are solved in an iterative way by the finite element method to the moments. (author)

Quarter elliptical crack growth using three dimensional finite element method and crack closure technique

Energy Technology Data Exchange (ETDEWEB)

Gozin, Mohammad-Hosein; Aghaie-Khafri, Mehrdad [K. N. Toosi University of Technology, Tehran (Korea, Republic of)

2014-06-15

Shape evolution of a quarter-elliptical crack emanating from a hole is studied. Three dimensional elastic-plastic finite element analysis of the fatigue crack closure was considered and the stress intensity factor was calculated based on the duplicated elastic model at each crack tip node. The crack front node was advanced proportional to the imposed effective stress intensity factor. Remeshing was applied at each step of the crack growth and solution mapping algorithm was considered. Crack growth retardation at free surfaces was successfully observed. A MATLAB-ABAQUS interference code was developed for the first time to perform crack growth on the basis of crack closure. Simulation results indicated that crack shape is sensitive to the remeshing strategy. Predictions based on the proposed models were in good agreement with Carlson's experiments results.

Quantum operations that cannot be implemented using a small mixed environment

International Nuclear Information System (INIS)

Zalka, Christof; Rieffel, Eleanor

2002-01-01

To implement any quantum operation (a.k.a. ''superoperator'' or ''CP map'') on a d-dimensional quantum system, it is enough to apply a suitable overall unitary transformation to the system and a d 2 -dimensional environment which is initialized in a fixed pure state. It has been suggested that a d-dimensional environment might be enough if we could initialize the environment in a mixed state of our choosing. In this note we show with elementary means that certain explicit quantum operations cannot be realized in this way. Our counterexamples map some pure states to pure states, giving strong and easily manageable conditions on the overall unitary transformation. Everything works in the more general setting of quantum operations from d-dimensional to d ' -dimensional spaces, so we place our counterexamples within this more general framework

Three-dimensional simulation of diamagnetic cavity formation by a finite-sized plasma beam

International Nuclear Information System (INIS)

Thomas, V.A.

1989-01-01

The problem of collisionless coupling between a plasma beam and a background plasma is examined using a three-dimensional hybrid code. The beam is assumed to be moving parallel to an ambient magnetic field at a speed greater than the local Alfven speed. In addition, the beam has a finite spatial extent in the directions perpendicular to the magnetic field and is uniform and infinite in the direction parallel to the ambient magnetic field. Such a system is susceptible to coupling of the beam ions with the background ions via an electromagnetic ion beam instability. This instability isotropizes the beam and energizes the background plasma. A large-amplitude Alfven wave traveling radially away from the interaction region is associated with the energized background plasma. The process described here is one which may be responsible for the formation of diamagnetic cavities observed in the solar wind. copyright American Geophysical Union 1989

Comparison of Neck Screw and Conventional Fixation Techniques in Mandibular Condyle Fractures Using 3-Dimensional Finite Element Analysis.

Science.gov (United States)

Conci, Ricardo Augusto; Tomazi, Flavio Henrique Silveira; Noritomi, Pedro Yoshito; da Silva, Jorge Vicente Lopes; Fritscher, Guilherme Genehr; Heitz, Claiton

2015-07-01

To compare the mechanical stress on the mandibular condyle after the reduction and fixation of mandibular condylar fractures using the neck screw and 2 other conventional techniques according to 3-dimensional finite element analysis. A 3-dimensional finite element model of a mandible was created and graphically simulated on a computer screen. The model was fixed with 3 different techniques: a 2.0-mm plate with 4 screws, 2 plates (1 1.5-mm plate and 1 2.0-mm plate) with 4 screws, and a neck screw. Loads were applied that simulated muscular action, with restrictions of the upper movements of the mandible, differentiation of the cortical and medullary bone, and the virtual "folds" of the plates and screws so that they could adjust to the condylar surface. Afterward, the data were exported for graphic visualization of the results and quantitative analysis was performed. The 2-plate technique exhibited better stability in regard to displacement of fractures, deformity of the synthesis materials, and minimum and maximum tension values. The results with the neck screw were satisfactory and were similar to those found when a miniplate was used. Although the study shows that 2 isolated plates yielded better results compared with the other groups using other fixation systems and methods, the neck screw could be an option for condylar fracture reduction. Copyright © 2015 American Association of Oral and Maxillofacial Surgeons. Published by Elsevier Inc. All rights reserved.

The dimensional reduction in a multi-dimensional cosmology

International Nuclear Information System (INIS)

Demianski, M.; Golda, Z.A.; Heller, M.; Szydlowski, M.

1986-01-01

Einstein's field equations are solved for the case of the eleven-dimensional vacuum spacetime which is the product R x Bianchi V x T 7 , where T 7 is a seven-dimensional torus. Among all possible solutions, the authors identify those in which the macroscopic space expands and the microscopic space contracts to a finite size. The solutions with this property are 'typical' within the considered class. They implement the idea of a purely dynamical dimensional reduction. (author)

Lectures on zeta functions over finite fields

OpenAIRE

Wan, Daqing

2007-01-01

These are the notes from the summer school in G\\"ottingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over finite fields, focusing on moment zeta functions and zeta functions of affine toric hypersurfaces.

Fourier analysis of finite element preconditioned collocation schemes

Science.gov (United States)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

A Finite Segment Method for Skewed Box Girder Analysis

Directory of Open Access Journals (Sweden)

Xingwei Xue

2018-01-01

Full Text Available A finite segment method is presented to analyze the mechanical behavior of skewed box girders. By modeling the top and bottom plates of the segments with skew plate beam element under an inclined coordinate system and the webs with normal plate beam element, a spatial elastic displacement model for skewed box girder is constructed, which can satisfy the compatibility condition at the corners of the cross section for box girders. The formulation of the finite segment is developed based on the variational principle. The major advantage of the proposed approach, in comparison with the finite element method, is that it can simplify a three-dimensional structure into a one-dimensional structure for structural analysis, which results in significant saving in computational times. At last, the accuracy and efficiency of the proposed finite segment method are verified by a model test.

On infinite-dimensional state spaces

International Nuclear Information System (INIS)

Fritz, Tobias

2013-01-01

It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V −1 U 2 V=U 3 , then finite-dimensionality entails the relation UV −1 UV=V −1 UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V −1 U 2 V=U 3 holds only up to ε and then yields a lower bound on the dimension.

On infinite-dimensional state spaces

Science.gov (United States)

Fritz, Tobias

2013-05-01

It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

Science.gov (United States)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Multigrid Finite Element Method in Calculation of 3D Homogeneous and Composite Solids

Directory of Open Access Journals (Sweden)

A.D. Matveev

2016-12-01

Full Text Available In the present paper, a method of multigrid finite elements to calculate elastic three-dimensional homogeneous and composite solids under static loading has been suggested. The method has been developed based on the finite element method algorithms using homogeneous and composite three-dimensional multigrid finite elements (MFE. The procedures for construction of MFE of both rectangular parallelepiped and complex shapes have been shown. The advantages of MFE are that they take into account, following the rules of the microapproach, heterogeneous and microhomogeneous structures of the bodies, describe the three-dimensional stress-strain state (without any simplifying hypotheses in homogeneous and composite solids, as well as generate small dimensional discrete models and numerical solutions with a high accuracy.

A set of pathological tests to validate new finite elements

Indian Academy of Sciences (India)

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

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

Finite size scaling and lattice gauge theory

International Nuclear Information System (INIS)

Berg, B.A.

1986-01-01

Finite size (Fisher) scaling is investigated for four dimensional SU(2) and SU(3) lattice gauge theories without quarks. It allows to disentangle violations of (asymptotic) scaling and finite volume corrections. Mass spectrum, string tension, deconfinement temperature and lattice β-function are considered. For appropriate volumes, Monte Carlo investigations seem to be able to control the finite volume continuum limit. Contact is made with Luescher's small volume expansion and possibly also with the asymptotic large volume behavior. 41 refs., 19 figs

A finite element evaluation of mechanical function for 3 distal extension partial dental prosthesis designs with a 3-dimensional nonlinear method for modeling soft tissue.

Science.gov (United States)

Nakamura, Yoshinori; Kanbara, Ryo; Ochiai, Kent T; Tanaka, Yoshinobu

2014-10-01

The mechanical evaluation of the function of partial removable dental prostheses with 3-dimensional finite element modeling requires the accurate assessment and incorporation of soft tissue behavior. The differential behaviors of the residual ridge mucosa and periodontal ligament tissues have been shown to exhibit nonlinear displacement. The mathematic incorporation of known values simulating nonlinear soft tissue behavior has not been investigated previously via 3-dimensional finite element modeling evaluation to demonstrate the effect of prosthesis design on the supporting tissues. The purpose of this comparative study was to evaluate the functional differences of 3 different partial removable dental prosthesis designs with 3-dimensional finite element analysis modeling and a simulated patient model incorporating known viscoelastic, nonlinear soft tissue properties. Three different designs of distal extension removable partial dental prostheses were analyzed. The stress distributions to the supporting abutments and soft tissue displacements of the designs tested were calculated and mechanically compared. Among the 3 dental designs evaluated, the RPI prosthesis demonstrated the lowest stress concentrations on the tissue supporting the tooth abutment and also provided wide mucosa-borne areas of support, thereby demonstrating a mechanical advantage and efficacy over the other designs evaluated. The data and results obtained from this study confirmed that the functional behavior of partial dental prostheses with supporting abutments and soft tissues are consistent with the conventional theories of design and clinical experience. The validity and usefulness of this testing method for future applications and testing protocols are shown. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application.

Science.gov (United States)

Carson, Cantwell G; Levine, Jonathan S

2016-09-01

The concept of a finite body Dirichlet tessellation has been extended to that of a finite body Delaunay 'triangulation' to provide a more meaningful description of the spatial distribution of nonspherical secondary phase bodies in 2- and 3-dimensional images. A finite body triangulation (FBT) consists of a network of minimum edge-to-edge distances between adjacent objects in a microstructure. From this is also obtained the characteristic object chords formed by the intersection of the object boundary with the finite body tessellation. These two sets of distances form the basis of a parsimonious homogeneity estimation. The characteristics of the spatial distribution are then evaluated with respect to the distances between objects and the distances within them. Quantitative analysis shows that more physically representative distributions can be obtained by selecting subgraphs, such as the relative neighbourhood graph and the minimum spanning tree, from the finite body tessellation. To demonstrate their potential, we apply these methods to 3-dimensional X-ray computed tomographic images of foamed cement and their 2-dimensional cross sections. The Python computer code used to estimate the FBT is made available. Other applications for the algorithm - such as porous media transport and crack-tip propagation - are also discussed. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

Characterization of resonances using finite size effects

International Nuclear Information System (INIS)

Pozsgay, B.; Takacs, G.

2006-01-01

We develop methods to extract resonance widths from finite volume spectra of (1+1)-dimensional quantum field theories. Our two methods are based on Luscher's description of finite size corrections, and are dubbed the Breit-Wigner and the improved ''mini-Hamiltonian'' method, respectively. We establish a consistent framework for the finite volume description of sufficiently narrow resonances that takes into account the finite size corrections and mass shifts properly. Using predictions from form factor perturbation theory, we test the two methods against finite size data from truncated conformal space approach, and find excellent agreement which confirms both the theoretical framework and the numerical validity of the methods. Although our investigation is carried out in 1+1 dimensions, the extension to physical 3+1 space-time dimensions appears straightforward, given sufficiently accurate finite volume spectra

Analysis of distances between inclusions in finite one-dimensional binary stochastic materials

International Nuclear Information System (INIS)

Griesheimer, D. P.; Millman, D. L.

2009-01-01

In this paper we develop a statistical distribution for the number of inclusions present in a one-dimensional binary stochastic material of a finite length. From this distribution, an analytic solution for the expected number of inclusions present in a given problem is derived. For cases where the analytical solution for the expected number of inclusions is prohibitively expensive to compute, a simple, empirically-derived, approximation for the expected value is presented. A series of numerical experiments are used to bound the error of this approximation over the domain of interest. Finally, the above approximations are used to develop a methodology for determining the distribution of distances between adjacent inclusions in the material, subject to known problem conditions including: the total length of the problem, the length of each inclusion, and the expected volume fraction of inclusions in the problem. The new method is shown to be equivalent to the use of the infinite medium nearest neighbor distribution with an effective volume fraction to account for the finite nature of the material. Numerical results are presented for a wide range of problem parameters, in order to demonstrate the accuracy of this method and identify conditions where the method breaks down. In general, the technique is observed to produce excellent results (absolute error less than 1 10-6) for problems with inclusion volume fractions less than 0.8 and a ratio of problem length to inclusion length greater than 25. For problems that do not fall into this category, the accuracy of the method is shown to be dependent on the particular combination of these parameters. A brief discussion of the relevance of this method for Monte Carlo chord length sampling algorithms is also provided. (authors)

Three-dimensional modeling with finite element codes

Energy Technology Data Exchange (ETDEWEB)

Druce, R.L.

1986-01-17

This paper describes work done to model magnetostatic field problems in three dimensions. Finite element codes, available at LLNL, and pre- and post-processors were used in the solution of the mathematical model, the output from which agreed well with the experimentally obtained data. The geometry used in this work was a cylinder with ports in the periphery and no current sources in the space modeled. 6 refs., 8 figs.

A non conforming finite element method for computing eigenmodes of resonant cavities

International Nuclear Information System (INIS)

Touze, F.; Le Meur, G.

1990-06-01

We present here a non conforming finite element in R 3 . This finite element, built on tetrahedrons, is particularly suited for computing eigenmodes. The main advantage of this element is that it preserves some structural properties of the space in which the solutions of the Maxwell's equations are to be found. Numerical results are presented for both two-dimensional and three-dimensional cases

A Liouville integrable hierarchy, symmetry constraint, new finite-dimensional integrable systems, involutive solution and expanding integrable models

International Nuclear Information System (INIS)

Sun Yepeng; Chen Dengyuan

2006-01-01

A new spectral problem and the associated integrable hierarchy of nonlinear evolution equations are presented in this paper. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. An explicit symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the hierarchy. Moreover, the corresponding Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative, new finite-dimensional completely integrable Hamiltonian systems in the Liouville sense. Further, an involutive representation of solution of each equation in the hierarchy is given. Finally, expanding integrable models of the hierarchy are constructed by using a new Loop algebra

Fracture analysis of one-dimensional hexagonal quasicrystals: Researches of a finite dimension rectangular plate by boundary collocation method

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.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, T S; Adams, M L [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B; Zika, M R [Lawrence Livermore National Lab., Livermore, CA (United States)

2005-07-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

Finite elements methods in mechanics

CERN Document Server

Eslami, M Reza

2014-01-01

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

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

Science.gov (United States)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

The finite element method its basis and fundamentals

CERN Document Server

Zienkiewicz, Olek C; Zhu, JZ

2013-01-01

The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob

New method for solving three-dimensional Schroedinger equation

International Nuclear Information System (INIS)

Melezhik, V.S.

1990-01-01

The method derived recently for solving a multidimensional scattering problem is applied to a three-dimensional Schroedinger equation. As compared with direct three-dimensional calculations of finite elements and finite differences, this approach gives sufficiently accurate upper and lower approximations to the helium-atom binding energy, which demonstrates its efficiency. 15 refs.; 1 fig.; 2 tabs

Implementation of Unsplit Perfectly Matched Layer Absorbing Boundary Condition in 3 Dimensional Finite Difference Time Domain Method

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.

Finite elements for partial differential equations: An introductory survey

International Nuclear Information System (INIS)

Succi, S.

1988-03-01

After presentation of the basic ideas behind the theory of the Finite Element Method, the application of the method to three equations of particular interest in Physics and Engineering is discussed in some detail, namely, a one-dimensional Sturm-Liouville problem, a two-dimensional linear Fokker-Planck equation and a two-dimensional nonlinear Navier-Stokes equation. 6 refs, 8 figs

Finite-dimensional attractor for a composite system of wave/plate equations with localized damping

International Nuclear Information System (INIS)

Bucci, Francesca; Toundykov, Daniel

2010-01-01

The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping

Human vocal tract resonances and the corresponding mode shapes investigated by three-dimensional finite-element modelling based on CT measurement.

Science.gov (United States)

Vampola, Tomáš; Horáček, Jaromír; Laukkanen, Anne-Maria; Švec, Jan G

2015-04-01

Resonance frequencies of the vocal tract have traditionally been modelled using one-dimensional models. These cannot accurately represent the events in the frequency region of the formant cluster around 2.5-4.5 kHz, however. Here, the vocal tract resonance frequencies and their mode shapes are studied using a three-dimensional finite element model obtained from computed tomography measurements of a subject phonating on vowel [a:]. Instead of the traditional five, up to eight resonance frequencies of the vocal tract were found below the prominent antiresonance around 4.7 kHz. The three extra resonances were found to correspond to modes which were axially asymmetric and involved the piriform sinuses, valleculae, and transverse vibrations in the oral cavity. The results therefore suggest that the phenomenon of speaker's and singer's formant clustering may be more complex than originally thought.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)

2005-07-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

Finite-element analysis of dynamic fracture

Science.gov (United States)

Aberson, J. A.; Anderson, J. M.; King, W. W.

1976-01-01

Applications of the finite element method to the two dimensional elastodynamics of cracked structures are presented. Stress intensity factors are computed for two problems involving stationary cracks. The first serves as a vehicle for discussing lumped-mass and consistent-mass characterizations of inertia. In the second problem, the behavior of a photoelastic dynamic tear test specimen is determined for the time prior to crack propagation. Some results of a finite element simulation of rapid crack propagation in an infinite body are discussed.

A new hierarchy of generalized derivative nonlinear Schroedinger equations, its bi-Hamiltonian structure and finite-dimensional involutive system

International Nuclear Information System (INIS)

Yan, Z.; Zhang, H.

2001-01-01

In this paper, an isospectral problem and one associated with a new hierarchy of nonlinear evolution equations are presented. As a reduction, a representative system of new generalized derivative nonlinear Schroedinger equations in the hierarchy is given. It is shown that the hierarchy possesses bi-Hamiltonian structures by using the trace identity method and is Liouville integrable. The spectral problem is non linearized as a finite-dimensional completely integrable Hamiltonian system under a constraint between the potentials and spectral functions. Finally, the involutive solutions of the hierarchy of equations are obtained. In particular, the involutive solutions of the system of new generalized derivative nonlinear Schroedinger equations are developed

Three dimensional stress analysis of nozzle-to-shell intersections by the finite element method and a auto-mesh generation program

International Nuclear Information System (INIS)

Fujihara, Hirohiko; Ueda, Masahiro

1975-01-01

In the design of chemical reactors or nuclear pressure vessels it is often important to evaluate the stress distribution in nozzle-to-shell intersections. The finite element method is a powerful tool for stress analysis, but it has a defects to require troublesome work in preparing input data. Specially, the mesh data of oblique nozzles and tangential nozzles, in which stress concentration is very high, are very difficult to be prepared. The authors made a mesh generation program which can be used to any nozzle-to-shell intersections, and combining this program with a three dimensional stress analysis program by the finite element method they made the stress analysis of nozzle-to-shell intersections under internal pressure. Consequently, stresses, strains and deformations of nozzles nonsymmetrical to spherical shells and nozzles tangential to cylindrical shells were made clear and it was shown that the curvature of the inner surface of the nozzle corner was a controlling factor in reducing stress concentration. (auth.)

Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics.

Science.gov (United States)

Lizana, L; Ambjörnsson, T

2009-11-01

We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Delta diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function rhoT(yT,t|yT,0) that a tagged particle T (T=1,...,N) is at position yT at time t given that it at time t=0 was at position yT,0. Using a Bethe ansatz we obtain the N -particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T , we arrive at an exact expression for rhoT(yT,t|yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N , maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for rhoT(yT,t|yT,0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time tparticle concentration and D is the diffusion constant for each particle, the tagged particle undergoes a normal diffusion; (B) for times much larger than the collision time t >taucoll but times smaller than the equilibrium time ttaue , rhoT(yT,t|yT,0) approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems.

Efficacy of transpalatal arch as an anchorage reinforcing unit during orthodontic space closure: A three-dimensional finite element study

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.

Finite N=1 SUSY gauge field theories

International Nuclear Information System (INIS)

Kazakov, D.I.

1986-01-01

The authors give a detailed description of the method to construct finite N=1 SUSY gauge field theories in the framework of N=1 superfields within dimensional regularization. The finiteness of all Green functions is based on supersymmetry and gauge invariance and is achieved by a proper choice of matter content of the theory and Yukawa couplings in the form Y i =f i (ε)g, where g is the gauge coupling, and the function f i (ε) is regular at ε=0 and is calculated in perturbation theory. Necessary and sufficient conditions for finiteness are determined already in the one-loop approximation. The correspondence with an earlier proposed approach to construct finite theories based on aigenvalue solutions of renormalization-group equations is established

Two Dimensional Finite Element Model to Study Calcium Distribution in Oocytes

Science.gov (United States)

Naik, Parvaiz Ahmad; Pardasani, Kamal Raj

2015-06-01

Cytosolic free calcium concentration is a key regulatory factor and perhaps the most widely used means of controlling cellular function. Calcium can enter cells through different pathways which are activated by specific stimuli including membrane depolarization, chemical signals and calcium depletion of intracellular stores. One of the important components of oocyte maturation is differentiation of the Ca2+ signaling machinery which is essential for egg activation after fertilization. Eggs acquire the ability to produce the fertilization-specific calcium signal during oocyte maturation. The calcium concentration patterns required during different stages of oocyte maturation are still not completely known. Also the mechanisms involved in calcium dynamics in oocyte cell are still not well understood. In view of above a two dimensional FEM model has been proposed to study calcium distribution in an oocyte cell. The parameters such as buffers, ryanodine receptor, SERCA pump and voltage gated calcium channel are incorporated in the model. Based on the biophysical conditions the initial and boundary conditions have been framed. The model is transformed into variational form and Ritz finite element method has been employed to obtain the solution. A program has been developed in MATLAB 7.10 for the entire problem and executed to obtain numerical results. The numerical results have been used to study the effect of buffers, RyR, SERCA pump and VGCC on calcium distribution in an oocyte cell.

Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections

Science.gov (United States)

Hermanns, M.; Kimchi, I.; Knolle, J.

2018-03-01

Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples - they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)2IrO3 iridates and RuCl3. In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.

A contribution to quantum cryptography in finite-dimensional systems including further results from the field of quantum information theory

International Nuclear Information System (INIS)

Ranade, Kedar S.

2009-01-01

This PhD thesis deals with quantum-cryptographic protocols which allow general finite-dimensional quantum systems (qudits) as carriers of information in contrast to the predominantly used two-dimensional quantum systems (qubits). The main focus of investigations is the maximum tolerable error rate of such protocols and its behaviour as a function of the dimension of the information carriers. For this purpose, several concepts are introduced which allow the treatment of this problem. In particular, protocols are presented which work up to a maximum tolerate error rate, and it is shown that a wide class of protocols cannot be used for higher error rates. Among other things, it turns out that the maximum tolerable error rate for two-basis protocols increases up to 50% for high dimensions. Apart from the above-mentioned main subjects of this thesis, some other results from the field of quantum information theory are given, which were achieved during this PhD project. (orig.)

Multisymplectic Structure－Preserving in Simple Finite Element Method in High Dimensional Case

Institute of Scientific and Technical Information of China (English)

BAIYong-Qiang; LIUZhen; PEIMing; ZHENGZhu-Jun

2003-01-01

In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems in high-dhnensjonal space. With uniform mesh, we find that, the numerical scheme derived from finite element method can keep a preserved multisymplectic structure.

Interactive finite difference preprocessor for three-dimensional fluid flow systems. [PREFLO

Energy Technology Data Exchange (ETDEWEB)

Kleinstreuer, C. (Rensselaer Polytechnic Inst., Troy, NY); Patterson, M.R.

1981-06-01

A preprocessor, called PREFLO, consisting of data processing modules combined with a flexible finite difference grid generator is described. This economical, interactive computer code is a useful research tool contributing significantly to the accurate analysis and modeling of large and/or geometrically complex flow systems. PREFLO (PREprocessor for fluid FLOw problems), written in FORTRAN IV, consists of four modules which in turn call various subroutines. The main programs accomplish the following tasks: (1) system identification and selection of appropriate finite difference algorithms; (2) input devices for storage of natural flow boundaries; (3) interactive generation of finite difference meshes and display of computer graphics; (4) preparation of all data files for the source program. The computation of the velocity field near a power plant site is outlined to illustrate the capabilities and application of PREFLO.

Effective permittivity of finite inhomogeneous objects

NARCIS (Netherlands)

Raghunathan, S.B.; Budko, N.V.

2010-01-01

A generalization of the S-parameter retrieval method for finite three-dimensional inhomogeneous objects under arbitrary illumination and observation conditions is presented. The effective permittivity of such objects may be rigorously defined as a solution of a nonlinear inverse scattering problem.

[Remodeling simulation of human femur under bed rest and spaceflight circumstances based on three dimensional finite element analysis].

Science.gov (United States)

Yang, Wenting; Wang, Dongmei; Lei, Zhoujixin; Wang, Chunhui; Chen, Shanguang

2017-12-01

Astronauts who are exposed to weightless environment in long-term spaceflight might encounter bone density and mass loss for the mechanical stimulus is smaller than normal value. This study built a three dimensional model of human femur to simulate the remodeling process of human femur during bed rest experiment based on finite element analysis (FEA). The remodeling parameters of this finite element model was validated after comparing experimental and numerical results. Then, the remodeling process of human femur in weightless environment was simulated, and the remodeling function of time was derived. The loading magnitude and loading cycle on human femur during weightless environment were increased to simulate the exercise against bone loss. Simulation results showed that increasing loading magnitude is more effective in diminishing bone loss than increasing loading cycles, which demonstrated that exercise of certain intensity could help resist bone loss during long-term spaceflight. At the end, this study simulated the bone recovery process after spaceflight. It was found that the bone absorption rate is larger than bone formation rate. We advise that astronauts should take exercise during spaceflight to resist bone loss.

Dynamic analysis of a needle insertion for soft materials: Arbitrary Lagrangian-Eulerian-based three-dimensional finite element analysis.

Science.gov (United States)

Yamaguchi, Satoshi; Tsutsui, Kihei; Satake, Koji; Morikawa, Shigehiro; Shirai, Yoshiaki; Tanaka, Hiromi T

2014-10-01

Our goal was to develop a three-dimensional finite element model that enables dynamic analysis of needle insertion for soft materials. To demonstrate large deformation and fracture, we used the arbitrary Lagrangian-Eulerian (ALE) method for fluid analysis. We performed ALE-based finite element analysis for 3% agar gel and three types of copper needle with bevel tips. To evaluate simulation results, we compared the needle deflection and insertion force with corresponding experimental results acquired with a uniaxial manipulator. We studied the shear stress distribution of agar gel on various time scales. For 30°, 45°, and 60°, differences in deflections of each needle between both sets of results were 2.424, 2.981, and 3.737mm, respectively. For the insertion force, there was no significant difference for mismatching area error (p<0.05) between simulation and experimental results. Our results have the potential to be a stepping stone to develop pre-operative surgical planning to estimate an optimal needle insertion path for MR image-guided microwave coagulation therapy and for analyzing large deformation and fracture in biological tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.

The finite element solution of two-dimensional transverse magnetic scattering problems on the connection machine

International Nuclear Information System (INIS)

Hutchinson, S.; Costillo, S.; Dalton, K.; Hensel, E.

1990-01-01

A study is conducted of the finite element solution of the partial differential equations governing two-dimensional electromagnetic field scattering problems on a SIMD computer. A nodal assembly technique is introduced which maps a single node to a single processor. The physical domain is first discretized in parallel to yield the node locations of an O-grid mesh. Next, the system of equations is assembled and then solved in parallel using a conjugate gradient algorithm for complex-valued, non-symmetric, non-positive definite systems. Using this technique and Thinking Machines Corporation's Connection Machine-2 (CM-2), problems with more than 250k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Hemoholtz wave equations are presented in this paper. Solutions are demonstrated for a wide range of objects. A summary of performance data is given for the set of test problems

Three-dimensional finite element analysis of different implant configurations for a mandibular fixed prosthesis.

Science.gov (United States)

Fazi, Giovanni; Tellini, Simone; Vangi, Dario; Branchi, Roberto

2011-01-01

The distribution of stresses in bone, implants, and prosthesis were analyzed via three-dimensional finite element modeling in different implant configurations for a fixed implant-supported prosthesis in an edentulous mandible. A finite element model was created with data obtained from computed tomographic scans of a human mandible. Anisotropic characteristics for cortical and cancellous bone were incorporated into the model. Six different configurations of intraforaminal implants were tested, with the number of implants varying from three to five and the distal implants inserted either parallel to the other implants or tilted distally by 17 or 34 degrees. A prosthetic structure connecting the implants was designed, with 20-mm posterior cantilevers for the parallel implant configurations, and a load of 200 N was applied to the distal portion of the cantilevers. Stresses were measured at the level of the implant, the prosthetic structure, and the bone. Bone-level stresses were analyzed at the implant-bone interface, at the external cortical bone surface, distal to the terminal implant, and in the cancellous bone along the implant body. A three-parallel-implant configuration resulted in higher stress in the implant and bone than configurations with four or five parallel implants. Configurations with the distal implants tilted resulted in a more favorable stress distribution at all levels. In parallel-implant configurations for fixed implant-supported mandibular prostheses, four and five implants resulted in similar stress distribution in the bone, framework, and implants. A distribution of four implants with the distal implants tilted 34 degrees (ie, the "All-on-Four" configuration) resulted in a favorable reduction of stresses in the bone, framework, and implants.

Numerical Simulations of Finite-Length Effects in Diocotron Modes

Science.gov (United States)

Mason, Grant W.; Spencer, Ross L.

2000-10-01

Over a decade ago Driscoll and Fine(C. F. Driscoll and K. S. Fine, Phys. Fluids B 2) (6), 1359, June 1990. reported experimental observations of an exponential instability in the self-shielded m=1 diocotron mode for an electron plasma confined in a Malmberg-Penning trap. More recently, Finn et al(John M. Finn, Diego del-Castillo-Negrete and Daniel C. Barnes, Phys. Plasmas 6) (10), 3744, October 1999. have given a theoretical explanation of the instability as a finite-length end effect patterned after an analogy to theory for shallow water fluid vortices. However, in a test case selected for comparison, the growth rate in the experiment exceeds the theoretical value by a factor of two. We present results from a two-dimensional, finite length drift-kinetic code and a fully three-dimensional particle-in-cell code written to explore details of finite-length effects in diocotron modes.

ZONE: a finite element mesh generator

International Nuclear Information System (INIS)

Burger, M.J.

1976-05-01

The ZONE computer program is a finite-element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated to describe pressure boundary conditions. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. The output from ZONE is essentially the input file to NAOS, HONDO, and other axisymmetric finite element programs. 14 figures

Finite action for three dimensional gravity with a minimally coupled scalar field

International Nuclear Information System (INIS)

Gegenberg, Jack; Martinez, Cristian; Troncoso, Ricardo

2003-01-01

Three-dimensional gravity with a minimally coupled self-interacting scalar is considered. The falloff of the fields at infinity is assumed to be slower than that of a localized distribution of matter in the presence of a negative cosmological constant. However, the asymptotic symmetry group remains to be the conformal group. The counterterm Lagrangian needed to render the action finite is found by demanding that the action attain an extremum for the boundary conditions implied by the above falloff of the fields at infinity. These counterterms explicitly depend on the scalar field. As a consequence, the Brown-York stress-energy tensor acquires a nontrivial contribution from the matter sector. Static circularly symmetric solutions with a regular scalar field are explored for a one-parameter family of potentials. Their masses are computed via the Brown-York quasilocal stress-energy tensor, and they coincide with the values obtained from the Hamiltonian approach. The thermal behavior, including the transition between different configurations, is analyzed, and it is found that the scalar black hole can decay into the Banados-Teitelboim-Zanelli solution irrespective of the horizon radius. It is also shown that the AdS conformal field theory correspondence yields the same central charge as for pure gravity

Grid integration policies of gas-fired cogeneration in Peninsular Malaysia: Fallacies and counterexamples

Energy Technology Data Exchange (ETDEWEB)

Shaaban, M., E-mail: m.shaaban@fke.utm.my [Centre of Electrical Energy Systems, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru (Malaysia); Azit, A.H. [Tenaga Nasional Berhad, Wisma TNB, Jalan Timur, 46200 Petaling Jaya, Selangor (Malaysia); Nor, K.M. [Centre of Electrical Energy Systems, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru (Malaysia)

2011-09-15

Despite the abundance of natural gas reserves in Malaysia coupled with serious government thrusts to promote cogeneration, its (cogeneration) development pace lags far off expectations. There are widespread fallacies among potential cogeneration developers and concerned professionals that cogeneration is uncompetitive in Malaysia due to existing policies of subsidized gas prices and grid-connection charges. This paper exposes these fallacies through counterexamples of practical cogeneration system design and evaluation of some segments of the industrial and service sectors in Peninsular Malaysia. The electrical and thermal characteristics of the cogeneration were modeled based on heat rate characteristics at partial loading patterns. A hierarchical mathematical programming approach that uses mixed-integer nonlinear optimization and dynamic programming principle, if necessary, is employed to determine the optimal size of cogeneration and its related auxiliary equipment as well as the optimal operation schedule. Financial assessment is integrated at a later stage to assess the economic viability of the system. Analyses of the cogeneration potential for several facilities of miscellaneous activities were carried out using various gas and electricity prices. Results obtained consistently rebuff the perpetuated fallacies and confirm that there is no real barrier to cogeneration development in Malaysia under current policies of gas prices and electricity tariffs. - Highlights: > Mixed-integer nonlinear programming and dynamic programming are used in the design. > Various loading levels are modeled and hourly operation schedule is determined. > Standby electricity charge has a minimal impact on cogeneration feasibility. > Gas and electricity prices are interrelated and affect cogeneration investment. > Under existing policies, there is no barrier to cogeneration adoption in Malaysia.

Grid integration policies of gas-fired cogeneration in Peninsular Malaysia: Fallacies and counterexamples

International Nuclear Information System (INIS)

Shaaban, M.; Azit, A.H.; Nor, K.M.

2011-01-01

Despite the abundance of natural gas reserves in Malaysia coupled with serious government thrusts to promote cogeneration, its (cogeneration) development pace lags far off expectations. There are widespread fallacies among potential cogeneration developers and concerned professionals that cogeneration is uncompetitive in Malaysia due to existing policies of subsidized gas prices and grid-connection charges. This paper exposes these fallacies through counterexamples of practical cogeneration system design and evaluation of some segments of the industrial and service sectors in Peninsular Malaysia. The electrical and thermal characteristics of the cogeneration were modeled based on heat rate characteristics at partial loading patterns. A hierarchical mathematical programming approach that uses mixed-integer nonlinear optimization and dynamic programming principle, if necessary, is employed to determine the optimal size of cogeneration and its related auxiliary equipment as well as the optimal operation schedule. Financial assessment is integrated at a later stage to assess the economic viability of the system. Analyses of the cogeneration potential for several facilities of miscellaneous activities were carried out using various gas and electricity prices. Results obtained consistently rebuff the perpetuated fallacies and confirm that there is no real barrier to cogeneration development in Malaysia under current policies of gas prices and electricity tariffs. - Highlights: → Mixed-integer nonlinear programming and dynamic programming are used in the design. → Various loading levels are modeled and hourly operation schedule is determined. → Standby electricity charge has a minimal impact on cogeneration feasibility. → Gas and electricity prices are interrelated and affect cogeneration investment. → Under existing policies, there is no barrier to cogeneration adoption in Malaysia.

[Three-dimensional finite element modeling and biomechanical simulation for evaluating and improving postoperative internal instrumentation of neck-thoracic vertebral tumor en bloc resection].

Science.gov (United States)

Qinghua, Zhao; Jipeng, Li; Yongxing, Zhang; He, Liang; Xuepeng, Wang; Peng, Yan; Xiaofeng, Wu

2015-04-07

To employ three-dimensional finite element modeling and biomechanical simulation for evaluating the stability and stress conduction of two postoperative internal fixed modeling-multilevel posterior instrumentation ( MPI) and MPI with anterior instrumentation (MPAI) with neck-thoracic vertebral tumor en bloc resection. Mimics software and computed tomography (CT) images were used to establish the three-dimensional (3D) model of vertebrae C5-T2 and simulated the C7 en bloc vertebral resection for MPI and MPAI modeling. Then the statistics and images were transmitted into the ANSYS finite element system and 20N distribution load (simulating body weight) and applied 1 N · m torque on neutral point for simulating vertebral displacement and stress conduction and distribution of motion mode, i. e. flexion, extension, bending and rotating. With a better stability, the displacement of two adjacent vertebral bodies of MPI and MPAI modeling was less than that of complete vertebral modeling. No significant differences existed between each other. But as for stress shielding effect reduction, MPI was slightly better than MPAI. From biomechanical point of view, two internal instrumentations with neck-thoracic tumor en bloc resection may achieve an excellent stability with no significant differences. But with better stress conduction, MPI is more advantageous in postoperative reconstruction.

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

Institute of Scientific and Technical Information of China (English)

Yirang YUAN; Qing YANG; Changfeng LI; Tongjun SUN

2017-01-01

Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

Exact vacuum polarization in 1 + 1 dimensional finite nuclei

International Nuclear Information System (INIS)

Ferree, T.C.

1992-01-01

There is considerable interest in the use of renormalizable quantum field theories to describe nuclear structure. In particular, theories which employ hadronic degrees of freedom are used widely and lead to efficient models which allow self-consistent solutions of the many-body problem. An interesting feature inherent to relativistic field theories (like QHD) is the presence of an infinite sea of negative energy fermion (nucleon) states, which interact dynamically with positive energy fermions via other fields. Such interactions give rise to, for example, vacuum polarization effects, in which virtual particle-antiparticle pairs interact with positive energy valence nucleons as well as with each other, and can significantly influence the ground and excited states of nuclear systems. Several authors have addressed this question in various approximations for finite nuclei, mostly based on extensions of results derived for a uniform system of nucleons. Some attempts have also been made to include vacuum effects in finite systems exactly, but the presence of a vector potential can be problematic when working in a spectral representation. In this paper, the author presents a computational method by which vacuum polarization effects in finite nuclei can be calculated exactly in the RHA by employing matrix diagonalization methods in a discrete Fourier representation of the Dirac equation, and an approximate method for including deep negative energy states based on a derivative expansion of the effective action. This efficient approach is shown to provide well-behaved vacuum polarization densities which remain so even in the presence of strong vector potential

Collapse in a forced three-dimensional nonlinear Schrodinger equation

DEFF Research Database (Denmark)

Lushnikov, P.M.; Saffman, M.

2000-01-01

We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation.......We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation....

Compressibility, zero sound, and effective mass of a fermionic dipolar gas at finite temperature

International Nuclear Information System (INIS)

Kestner, J. P.; Das Sarma, S.

2010-01-01

The compressibility, zero-sound dispersion, and effective mass of a gas of fermionic dipolar molecules is calculated at finite temperature for one-, two-, and three-dimensional uniform systems, and in a multilayer quasi-two-dimensional system. The compressibility is nonmonotonic in the reduced temperature, T/T F , exhibiting a maximum at finite temperature. This effect might be visible in a quasi-low-dimensional experiment, providing a clear signature of the onset of many-body quantum degeneracy effects. The collective mode dispersion and effective mass show similar nontrivial temperature and density dependence. In a quasi-low-dimensional system, the zero-sound mode may propagate at experimentally attainable temperatures.

A TQFT associated to the LMO invariant of three-dimensional manifolds

DEFF Research Database (Denmark)

Cheptea, Dorin; Le, Thang

2007-01-01

We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This is ......We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category...

Coulomb systems seen as critical systems: Finite-size effects in two dimensions

International Nuclear Information System (INIS)

Jancovici, B.; Manificat, G.; Pisani, C.

1994-01-01

It is known that the free energy at criticality of a finite two-dimensional system of characteristic size L has in general a term which behaves like log L as L → ∞; the coefficient of this term is universal. There are solvable models of two-dimensional classical Coulomb systems which exhibit the same finite-size correction (except for its sign) although the particle correlations are short-ranged, i.e., noncritical. Actually, the electrical potential and electrical field correlations are critical at all temperatures (as long as the Coulomb system is a conductor), as a consequence of the perfect screening property of Coulomb systems. This is why Coulomb systems have to exhibit critical finite-size effects

The Finite-Horizon Singular H∞ Control Problem With Dynamic Measurement Feedback

NARCIS (Netherlands)

Stoorvogel, A.A.; Trentelman, H.L.

1993-01-01

This paper is concerned with the finite-horizon version of the H∞ problem with measurement feedback. Given a finite-dimensional linear, time-varying system, together with a positive real number γ, we obtain necessary and sufficient conditions for the existence of a possibly time-varying dynamic

Finite-size scaling for quantum chains with an oscillatory energy gap

International Nuclear Information System (INIS)

Hoeger, C.; Gehlen, G. von; Rittenberg, V.

1984-07-01

We show that the existence of zeroes of the energy gap for finite quantum chains is related to a nonvanishing wavevector. Finite-size scaling ansaetze are formulated for incommensurable and oscillatory structures. The ansaetze are verified in the one-dimensional XY model in a transverse field. (orig.)

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.

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Science.gov (United States)

Wu, Xian-Qian; Wang, Xi; Wei, Yan-Peng; Song, Hong-Wei; Huang, Chen-Guang

2012-06-01

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.

Electrothermal Equivalent Three-Dimensional Finite-Element Model of a Single Neuron.

Science.gov (United States)

Cinelli, Ilaria; Destrade, Michel; Duffy, Maeve; McHugh, Peter

2018-06-01

We propose a novel approach for modelling the interdependence of electrical and mechanical phenomena in nervous cells, by using electrothermal equivalences in finite element (FE) analysis so that existing thermomechanical tools can be applied. First, the equivalence between electrical and thermal properties of the nerve materials is established, and results of a pure heat conduction analysis performed in Abaqus CAE Software 6.13-3 are validated with analytical solutions for a range of steady and transient conditions. This validation includes the definition of equivalent active membrane properties that enable prediction of the action potential. Then, as a step toward fully coupled models, electromechanical coupling is implemented through the definition of equivalent piezoelectric properties of the nerve membrane using the thermal expansion coefficient, enabling prediction of the mechanical response of the nerve to the action potential. Results of the coupled electromechanical model are validated with previously published experimental results of deformation for squid giant axon, crab nerve fibre, and garfish olfactory nerve fibre. A simplified coupled electromechanical modelling approach is established through an electrothermal equivalent FE model of a nervous cell for biomedical applications. One of the key findings is the mechanical characterization of the neural activity in a coupled electromechanical domain, which provides insights into the electromechanical behaviour of nervous cells, such as thinning of the membrane. This is a first step toward modelling three-dimensional electromechanical alteration induced by trauma at nerve bundle, tissue, and organ levels.

Electronic states in crystals of finite size quantum confinement of bloch waves

CERN Document Server

Ren, Shang Yuan

2017-01-01

This book presents an analytical theory of the electronic states in ideal low dimensional systems and finite crystals based on a differential equation theory approach. It provides precise and fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals, and offers new insights into some of the basic problems in low-dimensional systems, such as the surface states and quantum confinement effects, etc., some of which are quite different from what is traditionally believed in the solid state physics community. Many previous predictions have been confirmed in subsequent investigations by other authors on various relevant problems. In this new edition, the theory is further extended to one-dimensional photonic crystals and phononic crystals, and a general theoretical formalism for investigating the existence and properties of surface states/modes in semi-infinite one-dimensional crystals is developed. In addition, there are various revisions and improvements, including us...

Finite element simulation of moisture movement and solute transport in a large caisson

International Nuclear Information System (INIS)

Huyakorn, P.S.; Jones, B.G.; Parker, J.C.; Wadsworth, T.D.; White, H.O. Jr.

1987-01-01

The results of the solute transport experiments performed on compacted, crushed Bandelier Tuff in caisson B of the experimental cluster described by DePoorter (1981) are simulated. Both one- and three-dimensional simulations of solute transport have been performed using two selected finite element codes. Results of bromide and iodide tracer experiments conducted during near-steady flow conditions have been analyzed for pulse additions made on December 6, 1984, and followed over a period of up to 60 days. In addition, a pulse addition of nonconservative strontium tracer on September 28, 1984, during questionably steady flow conditions has been analyzed over a period of 240 days. One-dimensional finite element flow and transport simulations were carried out assuming the porous medium to be homogeneous and the injection source uniformly distributed. To evaluate effects of the nonuniform source distribution and also to investigate effects of inhomogeneous porous medium properties, three dimensional finite element analyses of transport were carried out. Implications of the three-dimensional effects for the design and analysis of future tracer studies are discussed

Effect of Oval Posts on Stress Distribution in Endodontically Treated Teeth: A Three-Dimensional Finite Element Analysis

Directory of Open Access Journals (Sweden)

Mojtaba Mahmoodi

2017-09-01

Full Text Available Introduction: In post-core crown restorations, the use of prefabricated composite posts concentrate stress at the cervical region and the use of metal posts (prefabricated and customized posts concentrates stress at the interfaces. Fiber reinforced composite posts (FRCs with oval cross-section (oval posts were proposed for post-core crown restorations to reduce the stress levels at the cervical region. The aim of the present study was to investigate the impact of oval cross-section composite posts on stress distribution of premolar with oval-shaped canal by using three-dimensional (3D finite element analysis. Materials and Methods: An extracted premolar tooth was mounted, sectioned, and photographed to create a 3D model. The surrounding tissues of the tooth, periodontal ligament, as well as cortical and trabecular bones were modeled. Seven taper posts with two different cross-section geometries (circular and oval shapes were modeled, as well. Then, the effect of post geometry, post material (carbon fiber and fiberglass, and cement material were investigated by 3D finite element analysis and the stress distribution results were compared. Results: In all the models, the highest stress levels of the dentin were accumulated at the coronal third of the root, and the highest stress levels at the bonding layers were accumulated at the cervical margin. Narrow circular posts induced the highest stress levels, whereas the stress levels were reduced by using thick oval posts. Application of elastic cement reduces the stress at the bonding layers but increases stress at the dentin. Conclusion: Finite element analysis showed that prefabricated oval posts are superior to traditional circular ones. The use of cement with low elastic modulus reduces the risk of debonding but raises the risk of root fracture.

Evaluation of stress patterns on maxillary posterior segment when intruded with mini implant anchorage: A three-dimensional finite element study

Directory of Open Access Journals (Sweden)

Nikhita Pekhale

2016-01-01

Full Text Available Introduction: The aim of this study is to evaluate stress and displacement effects of maxillary posterior intrusion mechanics with mini-implant anchorage by using finite element method. Materials and Methods: A computer stimulation of three-dimensional model maxilla with all teeth, PDL, bone, mini-implants, brackets, arch wire, force element, and transpalatal arch was constructed on the basis of average anatomic morphology. Finite element analysis was done to evaluate the amount of stress and its distribution during orthodontic intrusive force. Results: Increased Von Mises stress values were observed in mesio-cervical region of first molar. The middle third of second premolar and second molar and regions adjacent to force application sites also showed relatively high stress values. Minimum stress values were observed in apical region of first premolar as it is away from force application. Conclusion: Using three mini-implant and transpalatal arches, this study demonstrates that significant amount of true intrusion of maxillary molars could be obtained with lesser concentration of stresses in the apical area recorded.

An essential representation for a product system over a finitely ...

Indian Academy of Sciences (India)

25

2017-10-06

An essential representation for a product system over a finitely generated subsemigroup of Z d. S.P. Murugan and S. Sundar. October 6, 2017. Abstract. Let S ⊂ Zd be a finitely generated subsemigroup. Let E be a product system over S. We show that there exists an infinite dimensional separable Hilbert space. H and a ...

Numerical solution of recirculating flow by a simple finite element recursion relation

Energy Technology Data Exchange (ETDEWEB)

Pepper, D W; Cooper, R E

1980-01-01

A time-split finite element recursion relation, based on linear basis functions, is used to solve the two-dimensional equations of motion. Recirculating flow in a rectangular cavity and free convective flow in an enclosed container are analyzed. The relation has the advantage of finite element accuracy and finite difference speed and simplicity. Incorporating dissipation parameters in the functionals decreases numerical dispersion and improves phase lag.

Root Fernando-Kac subalgebras of finite type

OpenAIRE

Milev, Todor

2010-01-01

Let $\\mathfrak{g}$ be a finite-dimensional Lie algebra and $M$ be a $\\mathfrak{g}$-module. The Fernando-Kac subalgebra of $\\mathfrak{g}$ associated to $M$ is the subset $\\mathfrak{g}[M]\\subset\\mathfrak{g}$ of all elements $g\\in\\mathfrak{g}$ which act locally finitely on $M$. A subalgebra $\\mathfrak{l}\\subset\\mathfrak{g}$ for which there exists an irreducible module $M$ with $\\mathfrak{g}[M]=\\mathfrak{l}$ is called a Fernando-Kac subalgebra of $\\mathfrak{g}$. A Fernando-Kac subalgebra of $\\mat...

Approximation of the Frame Coefficients using Finite Dimensional Methods

DEFF Research Database (Denmark)

Christensen, Ole; Casazza, P.

1997-01-01

_i \\}_{i=1}^{n}$ of the frame and theorthogonal projection $P_n$ onto its span. For $f \\in \\h ,P_nf$ has a representation as a linear combination of $f_i , i=1,2,..n,$and the corresponding coefficients can be calculated using finite dimensionalmethods. We find conditions implying that those coefficients...

Topological terms induced by finite temperature and density fluctuations

International Nuclear Information System (INIS)

Niemi, A.J.; Department of Physics, The Ohio State University, Columbus, Ohio 43210)

1986-01-01

In (3+1)-dimensional finite-temperature and -density SU(2) gauge theories with left-handed fermions, the three-dimensional Chern-Simons term (topological mass) can be induced by radiative corrections. This result is derived by use of a family's index theorem which also implies that in many other quantum field theories various additional lower-dimensional topological terms can be induced. In the high-temperature limit these terms dominate the partition function, which suggests applications to early-Universe cosmology

Finite element formulation for a digital image correlation method

International Nuclear Information System (INIS)

Sun Yaofeng; Pang, John H. L.; Wong, Chee Khuen; Su Fei

2005-01-01

A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

Science.gov (United States)

Tay, Wei Choon; Tan, Eng Leong

2014-07-01

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

A two-dimensional finite element model of front surface current flow in cells under non-uniform, concentrated illumination

Energy Technology Data Exchange (ETDEWEB)

Mellor, A.; Domenech-Garret, J.L.; Chemisana, D.; Rosell, J.I. [Departament de Medi Ambient i C.S., University of Lleida, Av. Alcalde Rovira Roure 191, E25198 (Spain)

2009-09-15

A two-dimensional finite element model of current flow in the front surface of a PV cell is presented. In order to validate this model we perform an experimental test. Later, particular attention is paid to the effects of non-uniform illumination in the finger direction which is typical in a linear concentrator system. Fill factor, open circuit voltage and efficiency are shown to decrease with increasing degree of non-uniform illumination. It is shown that these detrimental effects can be mitigated significantly by reoptimization of the number of front surface metallization fingers to suit the degree of non-uniformity. The behavior of current flow in the front surface of a cell operating at open circuit voltage under non-uniform illumination is discussed in detail. (author)

Two dimensional finite element modelling for dynamic water diffusion through stratum corneum.

Science.gov (United States)

Xiao, Perry; Imhof, Robert E

2012-10-01

Solvents penetration through in vivo human stratum corneum (SC) has always been an interesting research area for trans-dermal drug delivery studies, and the importance of intercellular routes (diffuse in between corneocytes) and transcellular routes (diffuse through corneocytes) during diffusion is often debatable. In this paper, we have developed a two dimensional finite element model to simulate the dynamic water diffusion through the SC. It is based on the brick-and-mortar model, with brick represents corneocytes and mortar represents lipids, respectively. It simulates the dynamic water diffusion process through the SC from pre-defined initial conditions and boundary conditions. Although the simulation is based on water diffusions, the principles can also be applied to the diffusions of other topical applied substances. The simulation results show that both intercellular routes and transcellular routes are important for water diffusion. Although intercellular routes have higher flux rates, most of the water still diffuse through transcellular routes because of the high cross area ratio of corneocytes and lipids. The diffusion water flux, or trans-epidermal water loss (TEWL), is reversely proportional to corneocyte size, i.e. the larger the corneocyte size, the lower the TEWL, and vice versa. There is also an effect of the SC thickness, external air conditions and diffusion coefficients on the water diffusion through SC on the resulting TEWL. Copyright © 2012 Elsevier B.V. All rights reserved.

Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory

DEFF Research Database (Denmark)

Frier, Christian; Sørensen, John Dalsgaard

2003-01-01

A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...

Formation and 'self-healing' of magnetic islands in finite-β Helias equilibria

International Nuclear Information System (INIS)

Hayashi, T.; Sato, T.; Merkel, P.; Nuehrenberg, J.; Schwenn, U.

1994-01-01

The behaviour of finite-pressure-induced magnetic islands is numerically analyzed for three-dimensional magnetohydrodynamic equilibria of the Helias configuration by using a three-dimensional equilibrium code. It is found that an island chain is generated on the 5/6 rational surface, when such a surface appears in the plasma region of the finite-β equilibrium. The island chain, however, is not so dangerous as to destroy the plasma confinement even if it appears in a vanishingly small shear region. Thus, a high β equilibrium with clear magnetic surfaces can be realized. Moreover, it is definitely confirmed that the finite pressure effect sometimes exhibits an unexpectedly good aspect, namely, that the vacuum islands are removed as β increases, which can be called 'self-healing' of islands. This property can be explained by the numerically discovered fact that the phases of islands induced by the finite-pressure effect are always locked in the same phase regardless of β. (author)

Finite Source Effects in Microlensing Events

OpenAIRE

Gould, Andrew; Gaucherel, Cedric

1996-01-01

The computation of the magnification of a finite source by an arbitrary gravitational lens can be reduced from a two-dimensional to a one-dimensional integral using a generalization of Stoke's theorem. For a large source lensed by a planetary-system whose planet lies at the position where one of the two images would be in the absence of a planet, the integral can be done analytically. If the planet lies at the position of the major (unperturbed) image, the excess flux is the same as it would ...

Soliton pair creation at finite temperatures

International Nuclear Information System (INIS)

Grigoriev, D.Yu.; Rubakov, V.A.

1988-01-01

Creation of soliton-antisoliton pairs at finite temperature is considered within a (1+1)-dimensional model of a real scalar field. It is argued that at certain temperatures, the soliton pair creation in quantum theory can be investigated by studying classical field evolution in real time. The classical field equations are solved numerically, and the pair creation rate and average number of solitons are evaluated. No peculiar suppression of the rate is observed. Some results on the sphaleron transitions in (1+1)-dimensional abelian Higgs model are also presented. (orig.)

Three-dimensional optimization and sensitivity analysis of dental implant thread parameters using finite element analysis.

Science.gov (United States)

Geramizadeh, Maryam; Katoozian, Hamidreza; Amid, Reza; Kadkhodazadeh, Mahdi

2018-04-01

This study aimed to optimize the thread depth and pitch of a recently designed dental implant to provide uniform stress distribution by means of a response surface optimization method available in finite element (FE) software. The sensitivity of simulation to different mechanical parameters was also evaluated. A three-dimensional model of a tapered dental implant with micro-threads in the upper area and V-shaped threads in the rest of the body was modeled and analyzed using finite element analysis (FEA). An axial load of 100 N was applied to the top of the implants. The model was optimized for thread depth and pitch to determine the optimal stress distribution. In this analysis, micro-threads had 0.25 to 0.3 mm depth and 0.27 to 0.33 mm pitch, and V-shaped threads had 0.405 to 0.495 mm depth and 0.66 to 0.8 mm pitch. The optimized depth and pitch were 0.307 and 0.286 mm for micro-threads and 0.405 and 0.808 mm for V-shaped threads, respectively. In this design, the most effective parameters on stress distribution were the depth and pitch of the micro-threads based on sensitivity analysis results. Based on the results of this study, the optimal implant design has micro-threads with 0.307 and 0.286 mm depth and pitch, respectively, in the upper area and V-shaped threads with 0.405 and 0.808 mm depth and pitch in the rest of the body. These results indicate that micro-thread parameters have a greater effect on stress and strain values.

Three-dimensional finite-element analysis of the cellular convection phenomena in the Clinch River Breeder Reactor Plant prototype pump

International Nuclear Information System (INIS)

Silver, A.H.; Lee, J.Y.

1983-01-01

Cellular convection was studied rigorously during the development of the Clinch River Breeder Reactor Plant (CRBRP) Program Pumps. This paper presents the development of a three-dimensional finite-element heat transfer model which accounts for the cellular convection phenomena. A buoyancy driven cellular convection flow pattern is introduced in the annulus region between the upper inner structure and the pump tank. Steady-state thermal data were obtained for several test conditions for argon gas pressures up to 93 psig (741 kPa) and sodium operating temperatures to 1000 0 F (811 0 K). Test temperature distributions on the pump tank and inner structure were correlated with numerical results and excellent agreement was obtained

FINEDAN - an explicit finite-element calculation code for two-dimensional analyses of fast dynamic transients in nuclear reactor technology

International Nuclear Information System (INIS)

Adamik, V.; Matejovic, P.

1989-01-01

The problems are discussed of nonstationary, nonlinear dynamics of the continuum. A survey is presented of calculation methods in the given area with emphasis on the area of impact problems. A description is presented of the explicit finite elements method and its application to two-dimensional Cartesian and cylindrical configurations. Using the method the explicit calculation code FINEDAN was written which was tested in a series of verification calculations for different configurations and different types of continuum. The main characteristics are presented of the code and of some, of its practical applications. Envisaged trends of the development of the code and its possible applications in the technology of nuclear reactors are given. (author). 9 figs., 4 tabs., 10 refs

On the Geometrical Characteristics of Three-Dimensional Wireless Ad Hoc Networks and Their Applications

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available In a wireless ad hoc network, messages are transmitted, received, and forwarded in a finite geometrical region and the transmission of messages is highly dependent on the locations of the nodes. Therefore the study of geometrical relationship between nodes in wireless ad hoc networks is of fundamental importance in the network architecture design and performance evaluation. However, most previous works concentrated on the networks deployed in the two-dimensional region or in the infinite three-dimensional space, while in many cases wireless ad hoc networks are deployed in the finite three-dimensional space. In this paper, we analyze the geometrical characteristics of the three-dimensional wireless ad hoc network in a finite space in the framework of random graph and deduce an expression to calculate the distance probability distribution between network nodes that are independently and uniformly distributed in a finite cuboid space. Based on the theoretical result, we present some meaningful results on the finite three-dimensional network performance, including the node degree and the max-flow capacity. Furthermore, we investigate some approximation properties of the distance probability distribution function derived in the paper.

3-D thermal analysis using finite difference technique with finite element model for improved design of components of rocket engine turbomachines for Space Shuttle Main Engine SSME

Science.gov (United States)

Sohn, Kiho D.; Ip, Shek-Se P.

1988-01-01

Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.

Comparative effect of implant-abutment connections, abutment angulations, and screw lengths on preloaded abutment screw using three-dimensional finite element analysis: An in vitro study

OpenAIRE

Krishna Chaitanya Kanneganti; Dileep Nag Vinnakota; Srinivas Rao Pottem; Mahesh Pulagam

2018-01-01

Purpose: The purpose of this study is to compare the effect of implant-abutment connections, abutment angulations, and screw lengths on screw loosening (SL) of preloaded abutment using three dimensional (3D) finite element analysis. Materials and Methods: 3D models of implants (conical connection with hex/trilobed connections), abutments (straight/angulated), abutment screws (short/long), and crown and bone were designed using software Parametric Technology Corporation Creo and assembled t...

a constructive approach to the finite wavelet frames over prime fields

Indian Academy of Sciences (India)

6

The motivation of this paper is to establish an alternative constructive formulation for the wavelet coefficients of finite ... is a |G|-dimensional vector space with complex vector entries indexed by elements in the finite group G. The inner product of x,y ∈ CG is defined by .... Construction of Wavelet Frames over Prime Fields.

Finite micro-tab system for load control on a wind turbine

International Nuclear Information System (INIS)

Bach, A B; Lennie, M; Nayeri, C N; Paschereit, C O; Pechlivanoglou, G

2014-01-01

Finite micro-tabs have been investigated experimentally to evaluate the potential for load control on wind turbines. Two dimensional full span, as well as multiple finite tabs of various aspect ratios have been studied on an AH93W174 airfoil at different chord wise positions. A force balance was used to measure the aerodynamic loads. Furthermore, the wake vortex system consisting of the Karman vortex street as well as the tab tip vortices was analyzed with a 12-hole probe and hot wire anemometry. Finally, conventional oil paint as well as a quantitative digital flow analysis technique called SMARTviz were used to visualize the flow around the finite tab configurations. Results have shown that the devices are an effective solution to alleviate the airfoils overall load. The influence of the tab height, tab position as well as the finite tab aspect ratio on the lift and lift to drag ratio have been evaluated. It could be shown, that the lift difference can either be varied by changing the tab height as well as by altering the aspect ratio of the finite tabs. The drag of a two-dimensional flap is directly associated with the vortex street, while in the case of the finite tab, the solidity ratio of the tabs has the strongest effect on the drag. Therefore, the application of a finite tab system showed to improve the lift to drag ratio

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional Davey-Stewartson system on surface waves of finite depth

Science.gov (United States)

Zhao, Xue-Hui; Tian, Bo; Xie, Xi-Yang; Wu, Xiao-Yu; Sun, Yan; Guo, Yong-Jiang

2018-04-01

Under investigation in this paper is a (2+1)-dimensional Davey-Stewartson system, which describes the transformation of a wave-packet on water of finite depth. By virtue of the bell polynomials, bilinear form, Bäcklund transformation and Lax pair are got. One- and two-soliton solutions are obtained via the symbolic computation and Hirota method. Velocity and amplitude of the one-soliton solutions are relevant with the wave number. Graphical analysis indicates that soliton shapes keep unchanged and maintain their original directions and amplitudes during the propagation. Elastic overtaking and head-on interactions between the two solitons are described.

ACCEPT: a three-dimensional finite element program for large deformation elastic-plastic-creep analysis of pressurized tubes (LWBR/AWBA Development Program)

International Nuclear Information System (INIS)

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

Three-dimensional finite element model for flexible pavement analyses based field modulus measurements

International Nuclear Information System (INIS)

Lacey, G.; Thenoux, G.; Rodriguez-Roa, F.

2008-01-01

In accordance with the present development of empirical-mechanistic tools, this paper presents an alternative to traditional analysis methods for flexible pavements using a three-dimensional finite element formulation based on a liner-elastic perfectly-plastic Drucker-Pager model for granular soil layers and a linear-elastic stress-strain law for the asphalt layer. From the sensitivity analysis performed, it was found that variations of +-4 degree in the internal friction angle of granular soil layers did not significantly affect the analyzed pavement response. On the other hand, a null dilation angle is conservatively proposed for design purposes. The use of a Light Falling Weight Deflectometer is also proposed as an effective and practical tool for on-site elastic modulus determination of granular soil layers. However, the stiffness value obtained from the tested layer should be corrected when the measured peak deflection and the peak force do not occur at the same time. In addition, some practical observations are given to achieve successful field measurements. The importance of using a 3D FE analysis to predict the maximum tensile strain at the bottom of the asphalt layer (related to pavement fatigue) and the maximum vertical comprehensive strain transmitted to the top of the granular soil layers (related to rutting) is also shown. (author)

GITTAM program for numerical simulation of one-dimensional targets TIS. Part 2

International Nuclear Information System (INIS)

Arpishkin, Yu.P.; Basko, M.M.; Sokolovskij, M.V.

1989-01-01

A finite-difference algorithm for numeric solution of a system of one-dimensional hydrodynamics equation with heat conductivity, radiation diffusion and thermonuclear combustion is considered. The algorithm presented allows one to simulate one-dimensional thermonuclear targets for heavy-ion synthesis (HIS), irradiated with heavy ion beams. A brief description of a complex of GITTAM programs in which finite-difference algorithm for one-dimensional thermonuclear HIS target simulation is used, is given. 5 refs.; 3 figs

On the application of finite element method in the solution of steady state diffusion equation

International Nuclear Information System (INIS)

Ono, S.

1982-01-01

The solution of the steady state neutron diffusion equation is obtained by using the finite element method. Specifically the variational approach is used for one dimensional problems and the weighted residual method (Galerkin) for one and two dimensional problems. The spatial domain is divided into retangular elements and the neutron flux is approximated by linear (one dimensional case), and bilinear (two-dimensional case) functions. Numerical results are obtained with a FORTRAN IV computer program and compared with those obtained by the finite difference CITATION code. The results show that linear or bilinear functions, do not satisfactorily describe the differential parameters in highly heterogeneous reactor cases, but provide good results for integral parameters such as multiplication factor. (Author) [pt

Finite-element formulations for the thermal stress analysis of two- and three-dimensional thin ractor structures

International Nuclear Information System (INIS)

Kulak, R.F.; Kennedy, J.M.; Belytschko, T.B.; Schoeberle, D.F.

1977-01-01

This paper describes finite-element formulations for the thermal stress analysis of LMFBR structures. The first formulation is applicable to large displacement rotation problems in which the strains are small. For this formulation, a general temperature-dependent constituent relationship is derived from a Gibbs potential function and a temperature dependent yield surface. The temperature dependency of the yield surface is based upon a temperature-dependent, material-hardening model. The model uses a temperature-equivalent stress-plastic strain diagram which is generated from isothermal uniaxial stress-strain data. A second formulation is presented for problems characterized by both large displacement-rotations and large strains. Here a set of large strain hypoelastic-plastic relationships are developed to linearly relate the rate of stress to the rate of deformation. The temperature field is described through time-dependent values at mesh node points; the temperature fields in each element are then obtained by interpolation formulas. Hence, problems with both spatial and temporal dependent temperature fields can easily be treated. The above developments were incorporated into two ANL developed finite-element computer codes: the implicit version of STRAW and the 3D Implicit Structural Analysis Code. STRAW is a two-dimensional code with a plane stress/plane strain beam element. The 3D Implicit code has a triangular flat plate element which is capable of sustaining both membrane and bending loads. To insure numerical stability both codes are based on an iterative-incremental solution procedure with equilibrium checks based on an error in energy

A finite range coupled channel Born approximation code

International Nuclear Information System (INIS)

Nagel, P.; Koshel, R.D.

1978-01-01

The computer code OUKID calculates differential cross sections for direct transfer nuclear reactions in which multistep processes, arising from strongly coupled inelastic states in both the target and residual nuclei, are possible. The code is designed for heavy ion reactions where full finite range and recoil effects are important. Distorted wave functions for the elastic and inelastic scattering are calculated by solving sets of coupled differential equations using a Matrix Numerov integration procedure. These wave functions are then expanded into bases of spherical Bessel functions by the plane-wave expansion method. This approach allows the six-dimensional integrals for the transition amplitude to be reduced to products of two one-dimensional integrals. Thus, the inelastic scattering is treated in a coupled channel formalism while the transfer process is treated in a finite range born approximation formalism. (Auth.)

Discrete finite nilpotent Lie analogs: New models for unified gauge field theory

International Nuclear Information System (INIS)

Kornacker, K.

1978-01-01

To each finite dimensional real Lie algebra with integer structure constants there corresponds a countable family of discrete finite nilpotent Lie analogs. Each finite Lie analog maps exponentially onto a finite unipotent group G, and is isomorphic to the Lie algebra of G. Reformulation of quantum field theory in discrete finite form, utilizing nilpotent Lie analogs, should elminate all divergence problems even though some non-Abelian gauge symmetry may not be spontaneously broken. Preliminary results in the new finite representation theory indicate that a natural hierarchy of spontaneously broken symmetries can arise from a single unbroken non-Abelian gauge symmetry, and suggest the possibility of a new unified group theoretic interpretation for hadron colors and flavors

Three dimensional analysis of laterally loaded piles

International Nuclear Information System (INIS)

Yilmaz, C.

1987-01-01

In this study static analysis of laterally loaded pile is studied by the three models. The first model is the beam on discrete elastic springs. This model is analyzed using a flexibility method. The second model is the beam on a two-parameter elastic foundation. This model is analyzed using the linear finite element method. The third model is the finite element model, using the three-dimensional iso-parametric parabolic brick element. Three-dimensional pile group analysis is also performed using elastic constants of single pile obtained by any one of the above analyses. The main objective is to develop computer programs for each model related to single piles and to group analysis. Then, the deflections, rotations, moments, shears, stresses and strains of the single pile are obtained at any arbitrary point. Comparison is made between each model and with other studies such as Poulos 1971, Desai and Appel 1976. In addition, to provide a benchmark of three-dimensional finite element analysis, the Boussinesq problem is analyzed. (orig.)

Element-topology-independent preconditioners for parallel finite element computations

Science.gov (United States)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

An algorithm for the basis of the finite Fourier transform

Science.gov (United States)

Santhanam, Thalanayar S.

1995-01-01

The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

Composite resin reinforced with pre-tensioned fibers: a three-dimensional finite element study on stress distribution.

Science.gov (United States)

Jie, Lin; Shinya, Akikazu; Lassila, Lippo V J; Vallittu, Pekka K

2013-01-01

Pre-tensioned construction material is utilized in engineering applications of high strength demands. The purpose of this study was to evaluate the effect of the pre-tensioning fibers of fiber-reinforced composite (FRC) using three-dimensional finite element (FE) analysis. The 3D FE models of particulate composite resin (CR), FRC and composite resin reinforced with pre-tensioned fibers (PRE-T-FRC) were constructed. The uniaxial three-point bending test was simulated using FE analysis to calculate the principal stress distribution. In the FRC and PRE-T-FRC, stresses were higher than CR, and they were located in the fiber. However, the maximum principal stress value at the composite of PRE-T-FRC was lower than the FRC and CR. Composite resin reinforced with pre-tensioned fibers was advantageous for stress distribution and lowering the stress at the composite itself. Experimental studies on physical properties of pre-tensioned FRC are encouraged to be conducted.

Three-dimensional magnetic field computation on a distributed memory parallel processor

International Nuclear Information System (INIS)

Barion, M.L.

1990-01-01

The analysis of three-dimensional magnetic fields by finite element methods frequently proves too onerous a task for the computing resource on which it is attempted. When non-linear and transient effects are included, it may become impossible to calculate the field distribution to sufficient resolution. One approach to this problem is to exploit the natural parallelism in the finite element method via parallel processing. This paper reports on an implementation of a finite element code for non-linear three-dimensional low-frequency magnetic field calculation on Intel's iPSC/2

On higher order pyramidal finite elements

Czech Academy of Sciences Publication Activity Database

Liu, L.; Davies, K.B.; Křížek, Michal; Guan, L.

2011-01-01

Roč. 3, č. 2 (2011), s. 131-140 ISSN 2070-0733 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : pyramidal polynomial basis functions * finite element method * composite elements * three-dimensional mortar elements Subject RIV: BA - General Mathematics Impact factor: 0.750, year: 2011

Analysis of the finite deformation response of shape memory polymers: II. 1D calibration and numerical implementation of a finite deformation, thermoelastic model

International Nuclear Information System (INIS)

Volk, Brent L; Lagoudas, Dimitris C; Chen, Yi-Chao

2010-01-01

This study presents the analysis of the finite deformation response of a shape memory polymer (SMP). This two-part paper addresses the thermomechanical characterization of SMPs, the derivation of material parameters for a finite deformation phenomenological model, the numerical implementation of such a model, and the predictions from the model with comparisons to experimental data. Part II of this work presents the calibration of a previously developed thermoelastic constitutive model which is capable of handling finite deformations. The model is proposed in a general three-dimensional framework; however, this work focuses on reducing the model to one dimension and subsequently calibrating the model using experimental data obtained in part I. The one-dimensional numerical implementation of the model is presented, including the handling of the system of nonlinear equations and the integral term resulting from the constitutive model. The model is then used to predict the uniaxial shape memory effect. Results indicate good agreement between the model predictions and the experimental results, but the predictions do not capture the irrecoverable deformation present at the end of recovery

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.

JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

International Nuclear Information System (INIS)

Biffle, J.H.; Blanford, M.L.

1994-05-01

JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

International Nuclear Information System (INIS)

Biffle, J.H.

1993-02-01

JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

Exact effective action for (1+1)-dimensional fermions in an Abelian background at finite temperature and chemical potential

International Nuclear Information System (INIS)

Maciel, Soraya G.; Perez, Silvana

2008-01-01

In this paper we study the effects of a nonzero chemical potential in (1+1)-dimensional quantum field models at finite temperature. We particularly consider massless fermions in an Abelian gauge field background and calculate the effective action by evaluating the n-point functions. We find that the structure of the amplitudes corresponds to a generalization of the structure noted earlier in a calculation without a chemical potential (the associated integrals carry the dependence on the chemical potential). Our calculation shows that the chiral anomaly is unaffected by the presence of a chemical potential at finite temperature. However, unlike in the absence of a chemical potential, odd point functions do not vanish. We trace this to the fact that in the presence of a chemical potential the generalized charge conjugation symmetry of the theory allows for such amplitudes. In fact, we find that all the even point functions are even functions of μ, while the odd point functions are odd functions of μ which is consistent with this generalized charge conjugation symmetry. We show that the origin of the structure of the amplitudes is best seen from a formulation of the theory in terms of left- and right-handed spinors. The calculations are also much simpler in this formulation and it clarifies many other aspects of the theory.

A Three-Dimensional, Immersed Boundary, Finite Volume Method for the Simulation of Incompressible Heat Transfer Flows around Complex Geometries

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.

Application of the finite element method to neutronics problems with inhomogeneous boundray conditions

International Nuclear Information System (INIS)

Yoo, K.J.

1982-01-01

The albedo boundary conditions are incorporated into the finite element method using bicubic Hermite element functions in order to reduce the computer memory and computation time in two-group diffusion calculations by excluding the reflector regions in computation space. The basis functions at the core-reflector interfaces are newly established to satisfy the albedo boundary conditions, and then the ''weak'' form of two-group diffusion equations is discretized using the principle of the weighted residual method in combination with the Galerkin approximation. The discretized two-group diffusion equation is then solved by the Gaussian elimination method with the scaled column pivoting algorithm in one-dimensional problem and Gauss-Seidel method in two-dimensional problem. Prior to the application of the method to two-group diffusion problems, the same method is applied to the one-speed neutron transport equation in a bare slab reactor with the vacuum boundary condition to confirm its usefulness in the diffusion calculations. To investigate the applicability of our diffusion method, several numerical calculations are performed: two-dimensional IAEA benchmark problem and two-dimensional ZION problem. The results are compared with the available results from the conventional finite difference and other finite element methods. If the albedo values are appropriately adjusted, our results of the two-dimensional IAEA benchmark problem are agreed within 0.002% of ksub(eff) with the fine mesh PDQ results. Comparing with CITATION results, one-eighth of core memory and one-fifteenth of computing time are required to obtain the same accuracy even though no acceleration technique is used in the present case. Also, it is found that the results are comparable with the other finite element results. However, no significant saving is obtained in computation time comparing with the other finite element results, where the reflector regions are explicity included. This mainly comes from

Adaptive mixed finite element methods for Darcy flow in fractured porous media

KAUST Repository

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-01-01

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

Adaptive mixed finite element methods for Darcy flow in fractured porous media

KAUST Repository

Chen, Huangxin

2016-09-21

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

A finite element conjugate gradient FFT method for scattering

Science.gov (United States)

Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

1991-01-01

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

Three dimensional periodic foundations for base seismic isolation

International Nuclear Information System (INIS)

Yan, Y; Mo, Y L; Cheng, Z; Shi, Z; Menq, F; Tang, Y

2015-01-01

Based on the concept of phononic crystals, periodic foundations made of periodic materials are investigated in this paper. The periodic foundations can provide low frequency band gaps, which cover the main frequency ranges of seismic waves. Therefore, the periodic foundations are able to protect the upper structures during earthquake events. In this paper, the basic theory of three dimensional periodic foundations is studied and the finite element method was used to conduct the sensitivity study. A simplified three-dimensional periodic foundation with a superstructure was tested in the field and the feasibility of three dimensional periodic foundations was proved. The test results showed that the response of the upper structure with the three dimensional periodic foundation was reduced under excitation waves with the main frequency falling in the attenuation zones. The finite element analysis results are consistent with the experimental data, indicating that three dimensional periodic foundations are a feasible way of reducing seismic vibrations. (paper)

Infinite-dimensional Z2sup(k)-supermanifolds

International Nuclear Information System (INIS)

Molotkov, V.

1984-10-01

In this paper the theory of finite-dimensional supermanifolds of Berezin, Leites and Kostant is generalized in two directions. First, we introduce infinite-dimensional supermanifolds ''locally isomorphic'' to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped with some additional structure) from the category of finite-dimensional Grassman superalgebras into the category of the corresponding smooth manifolds (Banach or locally convex). As examples, flag supermanifolds of Banach superspaces as well as unitary supergroups of Hilbert superspaces are constructed. Second, we define ''generalized'' supermanifolds, graded by Abelian groups Z 2 sup(k), instead of the group Z 2 (Z 2 sup(k)-supermanifolds). The corresponding superfields, describing, potentially, particles with more general statistics than Bose + Fermi, generally speaking, turn out to have an infinite number of components. (author)

[Stress analysis of femoral stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer].

Science.gov (United States)

Oomori, H; Imura, S; Gesso, H

1992-04-01

To develop stem design achieving primary fixation of stems and effective load transfer to the femur, we studied stress analysis of stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer in stem-bone interface. The results of analyses of stem-bone interface stresses and von Mises stresses at the cortical bones indicated that ideal stem design features would be as follows: 1) Sufficient length, with the distal end extending beyond the isthmus region. 2) Maximum possible width, to contact the cortical bones in the isthmus region. 3) No collars but a lateral shoulder at the proximal portion. 4) A distal tip, to contact the cortical bones at the distal portion.

Two-dimensional thermofield bosonization

International Nuclear Information System (INIS)

Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.

2005-01-01

The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized

Finite-element simulation of blood perfusion in muscle tissue during compression and sustained contraction.

Science.gov (United States)

Vankan, W J; Huyghe, J M; Slaaf, D W; van Donkelaar, C C; Drost, M R; Janssen, J D; Huson, A

1997-09-01

Mechanical interaction between tissue stress and blood perfusion in skeletal muscles plays an important role in blood flow impediment during sustained contraction. The exact mechanism of this interaction is not clear, and experimental investigation of this mechanism is difficult. We developed a finite-element model of the mechanical behavior of blood-perfused muscle tissue, which accounts for mechanical blood-tissue interaction in maximally vasodilated vasculature. Verification of the model was performed by comparing finite-element results of blood pressure and flow with experimental measurements in a muscle that is subject to well-controlled mechanical loading conditions. In addition, we performed simulations of blood perfusion during tetanic, isometric contraction and maximal vasodilation in a simplified, two-dimensional finite-element model of a rat calf muscle. A vascular waterfall in the venous compartment was identified as the main cause for blood flow impediment both in the experiment and in the finite-element simulations. The validated finite-element model offers possibilities for detailed analysis of blood perfusion in three-dimensional muscle models under complicated loading conditions.

A finite element primer for beginners the basics

CERN Document Server

Zohdi, Tarek I

2014-01-01

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

Application of finite Fourier transformation for the solution of the diffusion equation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1991-01-01

The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)

Intersections of adelic groups on a surface

International Nuclear Information System (INIS)

Budylin, R Ya; Gorchinskiy, S O

2013-01-01

We solve a technical problem related to adeles on an algebraic surface. Given a finite set of natural numbers, one can associate with it an adelic group. We show that this operation commutes with taking intersections if the surface is defined over an uncountable field, and we provide a counterexample otherwise. Bibliography: 12 titles

Finite-size scaling theory and quantum hamiltonian Field theory: the transverse Ising model

International Nuclear Information System (INIS)

Hamer, C.J.; Barber, M.N.

1979-01-01

Exact results for the mass gap, specific heat and susceptibility of the one-dimensional transverse Ising model on a finite lattice are generated by constructing a finite matrix representation of the Hamiltonian using strong-coupling eigenstates. The critical behaviour of the limiting infinite chain is analysed using finite-size scaling theory. In this way, excellent estimates (to within 1/2% accuracy) are found for the critical coupling and the exponents α, ν and γ

Numerical study of effects of the beam tube on laser fields with a three-dimensional simulation code using the finite element method

CERN Document Server

Sobajima, M; Yamazaki, T; Yoshikawa, K; Ohnishi, M; Toku, H; Masuda, K; Kitagaki, J; Nakamura, T

1999-01-01

In January 1997, the Beijing FEL observed large laser amplification at 8-18 mu m. However, through the collaborative work, it was found from both experiments and numerical simulations that the laser loss on the beam tube wall was not negligible, and that the saturation was not seen in the relatively long wavelength range because of this loss. This calls for further investigation on the effects of the beam tube of finite size. In order to include such effects self-consistently, we have developed a new three-dimensional code that can solve equations with the boundary conditions of the beam tube by using the Finite Element Method. Results show that the beam tube effects are dominant in deriving higher laser modes in the tube, compared with the optical guiding effects, and consequently reduced gain especially in the longer wavelength range, where the beam tube effects are greatly emphasized. It is also found that TEM sub 0 sub 2 mode is the most dominant higher mode in the beam tube, and is also the main cause of...

Two-dimensional transient thermal analysis of a fuel rod by finite volume method

Energy Technology Data Exchange (ETDEWEB)

Costa, Rhayanne Yalle Negreiros; Silva, Mário Augusto Bezerra da; Lira, Carlos Alberto de Oliveira, E-mail: ryncosta@gmail.com, E-mail: mabs500@gmail.com, E-mail: cabol@ufpe.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Departamento de Energia Nuclear

2017-07-01

One of the greatest concerns when studying a nuclear reactor is the warranty of safe temperature limits all over the system at all time. The preservation of core structure along with the constraint of radioactive material into a controlled system are the main focus during the operation of a reactor. The purpose of this paper is to present the temperature distribution for a nominal channel of the AP1000 reactor developed by Westinghouse Co. during steady-state and transient operations. In the analysis, the system was subjected to normal operation conditions and then to blockages of the coolant flow. The time necessary to achieve a new safe stationary stage (when it was possible) was presented. The methodology applied in this analysis was based on a two-dimensional survey accomplished by the application of Finite Volume Method (FVM). A steady solution is obtained and compared with an analytical analysis that disregard axial heat transport to determine its relevance. The results show the importance of axial heat transport consideration in this type of study. A transient analysis shows the behavior of the system when submitted to coolant blockage at channel's entrance. Three blockages were simulated (10%, 20% and 30%) and the results show that, for a nominal channel, the system can still be considerate safe (there's no bubble formation until that point). (author)

The finite element response matrix method

International Nuclear Information System (INIS)

Nakata, H.; Martin, W.R.

1983-02-01

A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt

Trabecular bone strains around a dental implant and associated micromotions--a micro-CT-based three-dimensional finite element study.

Science.gov (United States)

Limbert, Georges; van Lierde, Carl; Muraru, O Luiza; Walboomers, X Frank; Frank, Milan; Hansson, Stig; Middleton, John; Jaecques, Siegfried

2010-05-07

The first objective of this computational study was to assess the strain magnitude and distribution within the three-dimensional (3D) trabecular bone structure around an osseointegrated dental implant loaded axially. The second objective was to investigate the relative micromotions between the implant and the surrounding bone. The work hypothesis adopted was that these virtual measurements would be a useful indicator of bone adaptation (resorption, homeostasis, formation). In order to reach these objectives, a microCT-based finite element model of an oral implant implanted into a Berkshire pig mandible was developed along with a robust software methodology. The finite element mesh of the 3D trabecular bone architecture was generated from the segmentation of microCT scans. The implant was meshed independently from its CAD file obtained from the manufacturer. The meshes of the implant and the bone sample were registered together in an integrated software environment. A series of non-linear contact finite element (FE) analyses considering an axial load applied to the top of the implant in combination with three sets of mechanical properties for the trabecular bone tissue was devised. Complex strain distribution patterns are reported and discussed. It was found that considering the Young's modulus of the trabecular bone tissue to be 5, 10 and 15GPa resulted in maximum peri-implant bone microstrains of about 3000, 2100 and 1400. These results indicate that, for the three sets of mechanical properties considered, the magnitude of maximum strain lies within an homeostatic range known to be sufficient to maintain/form bone. The corresponding micro-motions of the implant with respect to the bone microstructure were shown to be sufficiently low to prevent fibrous tissue formation and to favour long-term osseointegration. Copyright 2010 Elsevier Ltd. All rights reserved.

A two-dimensional analytical model for groundwater flow in a leaky aquifer extending finite distance under the estuary

Science.gov (United States)

Chuang, Mo-Hsiung; Hung, Chi-Tung; -Yen Lin, Wen; Ma, Kuo-chen

2017-04-01

In recent years, cities and industries in the vicinity of the estuarine region have developed rapidly, resulting in a sharp increase in the population concerned. The increasing demand for human activities, agriculture irrigation, and aquaculture relies on massive pumping of water in estuarine area. Since the 1950s, numerous studies have focused on the effects of tidal fluctuations on groundwater flow in the estuarine area. Tide-induced head fluctuation in a two-dimensional estuarine aquifer system is complicated and rather important in dealing with many groundwater management or remediation problems. The conceptual model of the aquifer system considered is multi-layered with estuarine bank and the leaky aquifer extend finite distance under the estuary. The solution of the model describing the groundwater head distribution in such an estuarine aquifer system and subject to the tidal fluctuation effects from estuarine river is developed based on the method of separation of variables along with river boundary. The solutions by Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour. Res. 1997; 33:1429-35) as well as Tang and Jiao (Tang Z. and J. J. Jiao, A two-dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water, Hydrological Processes, 2001; 15: 573-585) can be shown to be special cases of the present solution. On the basis of the analytical solution, the groundwater head distribution in response to estuarine boundary is examined and the influences of leakage, hydraulic parameters, and loading effect on the groundwater head fluctuation due to tide are investigated and discussed. KEYWORDS: analytical model, estuarine river, groundwater fluctuation, leaky aquifer.

Finite Element in Angle Unit Sphere Meshing for Charged Particle Transport.

Energy Technology Data Exchange (ETDEWEB)

Ortega, Mario Ivan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Drumm, Clifton R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-10-01

Finite element in angle formulations of the charged particle transport equation require the discretization of the unit sphere. In Sceptre, a three-dimensional surface mesh of a sphere is transformed into a two-dimensional mesh. Projection of a sphere onto a two-dimensional surface is well studied with map makers spending the last few centuries attempting to create maps that preserve proportion and area. Using these techniques, various meshing schemes for the unit sphere were investigated.

Study on prestressed concrete reactor vessel structures. II-5: Crack analysis by three dimensional finite elements method of 1/20 multicavity type PCRV subjected to internal pressure

Science.gov (United States)

1978-01-01

A three-dimensional finite elements analysis is reported of the nonlinear behavior of PCRV subjected to internal pressure by comparing calculated results with test results. As the first stage, an analysis considering the nonlinearity of cracking in concrete was attempted. As a result, it is found possible to make an analysis up to three times the design pressure (50 kg/sqcm), and calculated results agree well with test results.

Thermo-mechanical finite element analyses of bolted cask lid structures

International Nuclear Information System (INIS)

Wieser, G.; Qiao Linan; Eberle, A.; Voelzke, H.

2004-01-01

The analysis of complex bolted cask lid structures under mechanical or thermal accident conditions is important for the evaluation of cask integrity and leak-tightness in package design assessment according to the Transport Regulations or in aircraft crash scenarios. In this context BAM is developing methods based on Finite Elements to calculate the effects of mechanical impacts onto the bolted lid structures as well as effects caused by severe fire scenarios. I n case of fire it might be not enough to perform only a thermal heat transfer analysis. The complex cask design in connection with a severe hypothetical time-temperature-curve representing an accident fire scenario will create a strong transient heating up of the cask body and its lid system. This causes relative displacements between the seals and its counterparts that can be analyzed by a so-called thermo-mechanical calculation. Although it is currently not possible to correlate leakage rates with results from deformation analyses directly an appropriate Finite Element model of the considered type of metallic lid seal has been developed. For the present it is possible to estimate the behaviour of the seal based on the calculated relative displacements at its seating and the behaviour of the lid bolts under the impact load or the temperature field respectively. Except of the lid bolts the geometry of the cask and the mechanical loading is axial-symmetric which simplifies the analysis considerably and a two-dimensional Finite Element model with substitute lid bolts may be used. The substitute bolts are modelled as one-dimensional truss or beam elements. An advanced two-dimensional bolt submodel represents the bolts with plane stress continuum elements. This paper discusses the influence of different bolt modelling on the relative displacements at the seating of the seals. Besides this, the influence of bolt modelling, thermal properties and detail in geometry of the two-dimensional Finite Element models on

Three-dimensional finite analysis of acetabular contact pressure and contact area during normal walking.

Science.gov (United States)

Wang, Guangye; Huang, Wenjun; Song, Qi; Liang, Jinfeng

2017-11-01

This study aims to analyze the contact areas and pressure distributions between the femoral head and mortar during normal walking using a three-dimensional finite element model (3D-FEM). Computed tomography (CT) scanning technology and a computer image processing system were used to establish the 3D-FEM. The acetabular mortar model was used to simulate the pressures during 32 consecutive normal walking phases and the contact areas at different phases were calculated. The distribution of the pressure peak values during the 32 consecutive normal walking phases was bimodal, which reached the peak (4.2 Mpa) at the initial phase where the contact area was significantly higher than that at the stepping phase. The sites that always kept contact were concentrated on the acetabular top and leaned inwards, while the anterior and posterior acetabular horns had no pressure concentration. The pressure distributions of acetabular cartilage at different phases were significantly different, the zone of increased pressure at the support phase distributed at the acetabular top area, while that at the stepping phase distributed in the inside of acetabular cartilage. The zones of increased contact pressure and the distributions of acetabular contact areas had important significance towards clinical researches, and could indicate the inductive factors of acetabular osteoarthritis. Copyright © 2016. Published by Elsevier Taiwan.

Three-dimensional finite element models of the human pubic symphysis with viscohyperelastic soft tissues.

Science.gov (United States)

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.

User's manual for DYNA2D: an explicit two-dimensional hydrodynamic finite-element code with interactive rezoning

Energy Technology Data Exchange (ETDEWEB)

Hallquist, J.O.

1982-02-01

This revised report provides an updated user's manual for DYNA2D, an explicit two-dimensional axisymmetric and plane strain finite element code for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. A contact-impact algorithm permits gaps and sliding along material interfaces. By a specialization of this algorithm, such interfaces can be rigidly tied to admit variable zoning without the need of transition regions. Spatial discretization is achieved by the use of 4-node solid elements, and the equations-of motion are integrated by the central difference method. An interactive rezoner eliminates the need to terminate the calculation when the mesh becomes too distorted. Rather, the mesh can be rezoned and the calculation continued. The command structure for the rezoner is described and illustrated by an example.

In situ thermal imaging and three-dimensional finite element modeling of tungsten carbide-cobalt during laser deposition

International Nuclear Information System (INIS)

Xiong Yuhong; Hofmeister, William H.; Cheng Zhao; Smugeresky, John E.; Lavernia, Enrique J.; Schoenung, Julie M.

2009-01-01

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.

[Three dimensional finite element analysis of maxillary anterior teeth retraction with micro-implant anchorage and sliding mechanics].

Science.gov (United States)

Zhang, Yi; Zhang, Lei; Fan, Yu-bo; Song, Jin-lin; Deng, Feng

2009-10-01

To investigate the biomechanical effects of micro-implant anchorage technique with sliding mechanics on maxillary anterior teeth retraction under different implant insertion heights and different retraction hook heights. The three dimensional finite element model of maxillary anterior teeth retraction force system was constructed with CT scanning and MIMICS software and the relationships between brackets, teeth, wire and micro-implant were simulating the clinical factions. Then the initial tooth displacement was calculated when the insertion heights were 4 mm and 8 mm and the retraction hook heights were 1, 4, 7, 10 mm respectively. With retraction hook height added, the anterior teeth movement changed from lingual crown tipping to labial crown tipping and the intrusion movement was more apparent when the micro-implant was inserted in a higher location. The ideal teeth movement control could be achieved by different insertion heights of micro-implant and different retraction hook heights in straight wire retraction force system.

Finite-size effects for anisotropic bootstrap percolation : Logarithmic corrections

NARCIS (Netherlands)

van Enter, Aernout C. D.; Hulshof, Tim

In this note we analyse an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.

Finite-size effects for anisotropic bootstrap percolation: logerithmic corrections

NARCIS (Netherlands)

Enter, van A.C.D.; Hulshof, T.

2007-01-01

In this note we analyse an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.

Stress Distribution in Single Dental Implant System: Three-Dimensional Finite Element Analysis Based on an In Vitro Experimental Model.

Science.gov (United States)

Rezende, Carlos Eduardo Edwards; Chase-Diaz, Melody; Costa, Max Doria; Albarracin, Max Laurent; Paschoeto, Gabriela; Sousa, Edson Antonio Capello; Rubo, José Henrique; Borges, Ana Flávia Sanches

2015-10-01

This study aimed to analyze the stress distribution in single implant system and to evaluate the compatibility of an in vitro model with finite element (FE) model. The in vitro model consisted of Brånemark implant; multiunit set abutment of 5 mm height; metal-ceramic screw-retained crown, and polyurethane simulating the bone. Deformations were recorded in the peri-implant region in the mesial and distal aspects, after an axial 300 N load application at the center of the occlusal aspect of the crown, using strain gauges. This in vitro model was scanned with micro CT to design a three-dimensional FE model and the strains in the peri-implant bone region were registered to check the compatibility between both models. The FE model was used to evaluate stress distribution in different parts of the system. The values obtained from the in vitro model (20-587 με) and the finite element analysis (81-588 με) showed agreement among them. The highest stresses because of axial and oblique load, respectively were 5.83 and 40 MPa for the cortical bone, 55 and 1200 MPa for the implant, and 80 and 470 MPa for the abutment screw. The FE method proved to be effective for evaluating the deformation around single implant. Oblique loads lead to higher stress concentrations.

Two-dimensional isostatic meshes in the finite element method

OpenAIRE

Martínez Marín, Rubén; Samartín, Avelino

2002-01-01

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's...

Finite-size effects on multibody neutrino exchange

CERN Document Server

Abada, A; Rodríguez-Quintero, J; Abada, As

1998-01-01

The effect of multibody massless neutrino exchanges between neutrons inside a finite-size neutron star is studied. We use an effective Lagrangian, which incorporates the effect of the neutrons on the neutrinos. Following Schwinger, it is shown that the total interaction energy density is computed by comparing the zero point energy of the neutrino sea with and without the star. It has already been shown that in an infinite-size star the total energy due to neutrino exchange vanishes exactly. The opposite claim that massless neutrino exchange would produce a huge energy is due to an improper summation of an infrared-divergent quantity. The same vanishing of the total energy has been proved exactly in the case of a finite star in a one-dimensional toy model. Here we study the three-dimensional case. We first consider the effect of a sharp star border, assumed to be a plane. We find that there is a non- vanishing of the zero point energy density difference between the inside and the outside due to the refraction ...

Two dimensional finite element thermal model of laser surface glazing for H13 tool steel

Science.gov (United States)

Kabir, I. R.; Yin, D.; Naher, S.

2016-10-01

A two dimensional (2D) transient thermal model with line-heat-source was developed by Finite Element Method (FEM) for laser surface glazing of H13 tool steel using commercial software-ANSYS 15. The geometry of the model was taken as a transverse circular cross-section of cylindrical specimen. Two different power levels (300W, 200W) were used with 0.2mm width of laser beam and 0.15ms exposure time. Temperature distribution, heating and cooling rates, and the dimensions of modified surface were analysed. The maximum temperatures achieved were 2532K (2259°C) and 1592K (1319°C) for laser power 300W and 200W respectively. The maximum cooling rates were 4.2×107 K/s for 300W and 2×107 K/s for 200W. Depths of modified zone increased with increasing laser power. From this analysis, it can be predicted that for 0.2mm beam width and 0.15ms time exposer melting temperature of H13 tool steel is achieved within 200-300W power range of laser beam in laser surface glazing.

On boundary conditions in three-dimensional AdS gravity

Energy Technology Data Exchange (ETDEWEB)

Miskovic, Olivera [Instituto de Fisica, P. Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile) and Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile)]. E-mail: olivera.miskovic@ucv.cl; Olea, Rodrigo [Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile) and Centro Multidisciplinar de Astrofisica, CENTRA, Departamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal)]. E-mail: rolea@fisica.ist.utl.pt

2006-09-07

A finite action principle for three-dimensional gravity with negative cosmological constant, based on a boundary condition for the asymptotic extrinsic curvature, is considered. The bulk action appears naturally supplemented by a boundary term that is one half the Gibbons-Hawking term, that makes the Euclidean action and the Noether charges finite without additional Dirichlet counterterms. The consistency of this boundary condition with the Dirichlet problem in AdS gravity and the Chern-Simons formulation in three dimensions, and its suitability for the higher odd-dimensional case, are also discussed.

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

Energy Technology Data Exchange (ETDEWEB)

Li, K., E-mail: likai@imech.ac.cn [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100190 (China); Xun, B.; Hu, W. R. [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)

2016-05-15

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

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

International Nuclear Information System (INIS)

Li, K.; Xun, B.; Hu, W. R.

2016-01-01

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

Recursive tridiagonalization of infinite dimensional Hamiltonians

International Nuclear Information System (INIS)

Haydock, R.; Oregon Univ., Eugene, OR

1989-01-01

Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)

Advances in three-dimensional field analysis and evaluation of performance parameters of electrical machines

Science.gov (United States)

Sivasubramaniam, Kiruba

This thesis makes advances in three dimensional finite element analysis of electrical machines and the quantification of their parameters and performance. The principal objectives of the thesis are: (1)the development of a stable and accurate method of nonlinear three-dimensional field computation and application to electrical machinery and devices; and (2)improvement in the accuracy of determination of performance parameters, particularly forces and torque computed from finite elements. Contributions are made in two general areas: a more efficient formulation for three dimensional finite element analysis which saves time and improves accuracy, and new post-processing techniques to calculate flux density values from a given finite element solution. A novel three-dimensional magnetostatic solution based on a modified scalar potential method is implemented. This method has significant advantages over the traditional total scalar, reduced scalar or vector potential methods. The new method is applied to a 3D geometry of an iron core inductor and a permanent magnet motor. The results obtained are compared with those obtained from traditional methods, in terms of accuracy and speed of computation. A technique which has been observed to improve force computation in two dimensional analysis using a local solution of Laplace's equation in the airgap of machines is investigated and a similar method is implemented in the three dimensional analysis of electromagnetic devices. A new integral formulation to improve force calculation from a smoother flux-density profile is also explored and implemented. Comparisons are made and conclusions drawn as to how much improvement is obtained and at what cost. This thesis also demonstrates the use of finite element analysis to analyze torque ripples due to rotor eccentricity in permanent magnet BLDC motors. A new method for analyzing torque harmonics based on data obtained from a time stepping finite element analysis of the machine is

Finite element investigation of the prestressed jointed concrete ...

African Journals Online (AJOL)

Precast prestressed concrete pavement (PCP) technology is of recent origin, and the information on PCP performance is not available in literature. This research presents a finite-element analysis of the potential benefits of prestressing on the jointed concrete pavements (JCP). With using a 3-dimensional (3D) ...

Solution of the two-dimensional spectral factorization problem

Science.gov (United States)

Lawton, W. M.

1985-01-01

An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.

One-Dimensional Czedli-Type Islands

Science.gov (United States)

Horvath, Eszter K.; Mader, Attila; Tepavcevic, Andreja

2011-01-01

The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.

The computation of pressure waves in shock tubes by a finite difference procedure

International Nuclear Information System (INIS)

Barbaro, M.

1988-09-01

A finite difference solution of one-dimensional unsteady isentropic compressible flow equations is presented. The computer program has been tested by solving some cases of the Riemann shock tube problem. Predictions are in good agreement with those presented by other authors. Some inaccuracies may be attributed to the wave smearing consequent of the finite-difference treatment. (author)

FINITE ELEMENT ANALYSIS OF ELEMENT ANALYSIS OF A FREE ...

African Journals Online (AJOL)

eobe

the stairs and to compare the finite element ana ... tual three dimensional behavior of the stair slab system. ..... due to its close relation of output with the propo .... flights. It is best not to consider any open well when .... thermodynamics of solids.

Moment Inversion of the DPRK Nuclear Tests Using Finite-Difference Three-dimensional Strain Green's Tensors

Science.gov (United States)

Bao, X.; Shen, Y.; Wang, N.

2017-12-01

Accurate estimation of the source moment is important for discriminating underground explosions from earthquakes and other seismic sources. In this study, we invert for the full moment tensors of the recent seismic events (since 2016) at the Democratic People's Republic of Korea (PRRK) Punggye-ri test site. We use waveform data from broadband seismic stations located in China, Korea, and Japan in the inversion. Using a non-staggered-grid, finite-difference algorithm, we calculate the strain Green's tensors (SGT) based on one-dimensional (1D) and three-dimensional (3D) Earth models. Taking advantage of the source-receiver reciprocity, a SGT database pre-calculated and stored for the Punggye-ri test site is used in inversion for the source mechanism of each event. With the source locations estimated from cross-correlation using regional Pn and Pn-coda waveforms, we obtain the optimal source mechanism that best fits synthetics to the observed waveforms of both body and surface waves. The moment solutions of the first three events (2016-01-06, 2016-09-09, and 2017-09-03) show dominant isotropic components, as expected from explosions, though there are also notable non-isotropic components. The last event ( 8 minutes after the mb6.3 explosion in 2017) contained mainly implosive component, suggesting a collapse following the explosion. The solutions from the 3D model can better fit observed waveforms than the corresponding solutions from the 1D model. The uncertainty in the resulting moment solution is influenced by heterogeneities not resolved by the Earth model according to the waveform misfit. Using the moment solutions, we predict the peak ground acceleration at the Punggye-ri test site and compare the prediction with corresponding InSAR and other satellite images.

Characterization of coherent structures in three-dimensional turbulent flows using the finite-size Lyapunov exponent

International Nuclear Information System (INIS)

Bettencourt, João H; López, Cristóbal; Hernández-García, Emilio

2013-01-01

In this paper, we use the finite-size Lyapunov exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3D) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. 3D FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by the numerical solution of the primitive equations where two-dimensional (2D) turbulence dominates. In the channel flow, autocorrelations of the FSLE field show that the structure is substantially different from the near wall to the mid-channel region and relates well to the more widely studied Eulerian coherent structure of the turbulent channel flow. The ridges of the FSLE field have complex shapes due to the 3D character of the turbulent fluctuations. In the oceanic flow, strong horizontal stirring is present and the flow regime is similar to that of 2D turbulence where the domain is populated by coherent eddies that interact strongly. This in turn results in the presence of high FSLE lines throughout the domain leading to strong non-local mixing. The ridges of the FSLE field are quasi-vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, due to rotation and stratification, vertical motions in the ocean are much less intense than horizontal ones. This suppression is absent in the channel flow, as the 3D character of the FSLE ridges shows. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Time-history simulation of civil architecture earthquake disaster relief- based on the three-dimensional dynamic finite element method

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.

Tearing mode saturation with finite pressure

International Nuclear Information System (INIS)

Lee, J.K.

1988-01-01

With finite pressure, the saturation of the current-driven tearing mode is obtained in three-dimensional nonlinear resistive magnetohydrodynamic simulations for Tokamak plasmas. To effectively focus on the tearing modes, the perturbed pressure effects are excluded while the finite equilibrium pressure effects are retained. With this model, the linear growth rates of the tearing modes are found to be very insensitive to the equilibrium pressure increase. The nonlinear aspects of the tearing modes, however, are found to be very sensitive to the pressure increase in that the saturation level of the nonlinear harmonics of the tearing modes increases monotonically with the pressure rise. The increased level is associated with enhanced tearing island sizes or increased stochastic magnetic field region. (author)

Topics in quantum field theories at finite temperature

International Nuclear Information System (INIS)

Kao, Y.C.

1985-01-01

Studies on four topics in quantum field theories at finite temperature are presented in this thesis. In Chapter 1, it is shown that the chiral anomaly has no finite temperature corrections by Fujikawa's path integral approach. Chapter 2 deals with the chiral condensate in the finite temperature Schwinger model. The cluster decomposition property is employed to find . No finite critical temperature is found and the chiral condensate vanishes only at infinite temperature. In Chapter 3, the finite temperature behavior of the fermion-number breaking (Rubakov-Callan) condensate around a 't Hooft-Polyakov monopole is studied. It is found that the Rubakov-Callan condensate is suppressed exponentially from the monopole core at high temperature. The limitation of the techniques is understanding the behavior of the condensate for all temperature is also discussed. Chapter 4 is on the topological mass terms in (2 + 1)-dimensional gauge theories. The authors finds that if the gauge bosons have no topological mass at tree level, no topological mass induced radiatively up to two-loop order in either Abelian or non-Abelian theories with massive fermions. The Pauli-Villars regularization is used for fermion loops. The one-loop contributions to the topological mass terms at finite temperature are calculated and the quantization constraints in this case are discussed

A New Principle in Physics: the Principle 'Finiteness', and Some Consequences

International Nuclear Information System (INIS)

Sternlieb, Abraham

2010-01-01

In this paper I propose a new principle in physics: the principle of 'finiteness'. It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement results, including their errors, are always finite, the principle of finiteness postulates that the mathematical formulation of 'legitimate' laws of physics should prevent exactly zero or infinite solutions. Some consequences of the principle of finiteness are discussed, in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The consequences are derived independently of any other theory or principle in physics. I propose 'finiteness' as a postulate (like the constancy of the speed of light in vacuum, 'c'), as opposed to a notion whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories, or principles.

Modelling 3-D mechanical phenomena in a 1-D industrial finite element code: results and perspectives

International Nuclear Information System (INIS)

Guicheret-Retel, V.; Trivaudey, F.; Boubakar, M.L.; Masson, R.; Thevenin, Ph.

2005-01-01

Assessing fuel rod integrity in PWR reactors must enjoin two opposite goals: a one-dimensional finite element code (axial revolution symmetry) is needed to provide industrial results at the scale of the reactor core, while the main risk of cladding failure [e.g. pellet-cladding interaction (PCI)] is based on fully three-dimensional phenomena. First, parametric three-dimensional elastic calculations were performed to identify the relevant parameters (fragment number, contact pellet-cladding conditions, etc.) as regards PCI. Axial fragment number as well as friction coefficient are shown to play a major role in PCI as opposed to other parameters. Next, the main limitations of the one-dimensional hypothesis of the finite element code CYRANO3 are identified. To overcome these limitations, both two- and three-dimensional emulations of CYRANO3 were developed. These developments are shown to significantly improve the results provided by CYRANO3. (authors)

One-loop infinities in dimensionally reduced supergravities

International Nuclear Information System (INIS)

Fradkin, E.S.; Tseytlin, A.A.

1983-11-01

It is proved explicitly in the paper that d=4 theory following via reduction from N=1, d=10 supergravities is not finite at one loop while the version of N=8 supergravity directly following from N=1, d=11 theory is one-loop finite. The method used is based on quantization of initial higher dimensional theory as a first step. The results also suggest possible existence of non-standard (higher N) d>4 supergravities which reduce to d=4 theories with finite N=8 supergravity sector. (author)

A parallel finite-difference method for computational aerodynamics

International Nuclear Information System (INIS)

Swisshelm, J.M.

1989-01-01

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed. 14 refs

Flow Applications of the Least Squares Finite Element Method

Science.gov (United States)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Finite elements for non-linear analysis of pipelines

International Nuclear Information System (INIS)

Benjamim, A.C.; Ebecken, N.F.F.

1982-01-01

The application of a three-dimensional lagrangian formulation for the great dislocations analysis and great rotation of pipelines systems is studied. This formulation is derived from the soil mechanics and take into account the shear stress effects. Two finite element models are implemented. The first, of right axis, uses as interpolation functions the conventional gantry functions, defined in relation to mobile coordinates. The second, of curve axis and variable cross sections, is obtained from the degeneration of the three-dimensional isoparametric element, and uses as interpolation functions third degree polynomials. (E.G.) [pt

Finite-size effects in the three-state quantum asymmetric clock model

International Nuclear Information System (INIS)

Gehlen, G. v.; Rittenberg, V.

1983-04-01

The one-dimensional quantum Hamiltonian of the asymmetric three-state clock model is studied using finite-size scaling. Various boundary conditions are considered on chains containing up to eight sites. We calculate the boundary of the commensurate phase and the mass gap index. The model shows an interesting finite-size dependence in connexion with the presence of the incommensurate phase indicating that for the infinite system there is no Lifshitz point. (orig.)

CLASSIFICATION OF 4-DIMENSIONAL GRADED ALGEBRAS

OpenAIRE

Armour, Aaron; Chen, Hui-Xiang; ZHANG, Yinhuo

2009-01-01

Let k be an algebraically closed field. The algebraic and geometric classification of finite dimensional algebras over k with ch(k) not equal 2 was initiated by Gabriel in [6], where a complete list of nonisomorphic 4-dimensional k-algebras was given and the number of irreducible components of the variety Alg(4) was discovered to be 5. The classification of 5-dimensional k-algebras was done by Mazzola in [10]. The number of irreducible components of the variety Alg(5) is 10. With the dimensio...

Investigation of Shear Stud Performance in Flat Plate Using Finite Element Analysis

Directory of Open Access Journals (Sweden)

T.S. Viswanathan

2014-09-01

Full Text Available Three types of shear stud arrangement, respectively featuring an orthogonal, a radial and a critical perimeter pattern, were evaluated numerically. A numerical investigation was conducted using the finite element software ABAQUS to evaluate their ability to resist punching shear in a flat plate. The finite element analysis here is an application of the nonlinear analysis of reinforced concrete structures using three-dimensional solid finite elements. The nonlinear characteristics of concrete were achieved by employing the concrete damaged plasticity model in the finite element program. Transverse shear stress was evaluated using finite element analysis in terms of shear stress distribution for flat plate with and without shear stud reinforcement. The model predicted that shear studs placed along the critical perimeter are more effective compared to orthogonal and radial patterns.

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

International Nuclear Information System (INIS)

Ansanay-Alex, G.

2009-01-01

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

Creating physically-based three-dimensional microstructures: Bridging phase-field and crystal plasticity models.

Energy Technology Data Exchange (ETDEWEB)

Lim, Hojun [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Owen, Steven J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Abdeljawad, Fadi F. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hanks, Byron [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Battaile, Corbett Chandler [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-09-01

In order to better incorporate microstructures in continuum scale models, we use a novel finite element (FE) meshing technique to generate three-dimensional polycrystalline aggregates from a phase field grain growth model of grain microstructures. The proposed meshing technique creates hexahedral FE meshes that capture smooth interfaces between adjacent grains. Three dimensional realizations of grain microstructures from the phase field model are used in crystal plasticity-finite element (CP-FE) simulations of polycrystalline a -iron. We show that the interface conformal meshes significantly reduce artificial stress localizations in voxelated meshes that exhibit the so-called "wedding cake" interfaces. This framework provides a direct link between two mesoscale models - phase field and crystal plasticity - and for the first time allows mechanics simulations of polycrystalline materials using three-dimensional hexahedral finite element meshes with realistic topological features.

Synthesis of hydrocode and finite element technology for large deformation Lagrangian computation

International Nuclear Information System (INIS)

Goudreau, G.L.; Hallquist, J.O.

1979-08-01

Large deformation engineering analysis at Lawrence Livermore Laboratory has benefited from a synthesis of computational technology from the finite difference hydrocodes of the scientific weapons community and the structural finite element methodology of engineering. Two- and three-dimensional explicit and implicit Lagrangian continuum codes have been developed exploiting the strengths of each. The explicit methodology primarily exploits the primitive constant stress (or one point integration) brick element. Similarity and differences with the integral finite difference method are discussed. Choice of stress and finite strain measures, and selection of hour glass viscosity are also considered. The implicit codes also employ a Cauchy formulation, with Newton iteration and a symmetric tangent matrix. A library of finite strain material routines includes hypoelastic/plastic, hyperelastic, viscoelastic, as well as hydrodynamic behavior. Arbitrary finite element topology and a general slide-line treatment significantly extends Lagrangian hydrocode application. Computational experience spans weapons and non-weapons applications

Finite element formulation for fluid-structure interaction in three-dimensional space

International Nuclear Information System (INIS)

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

GRIZ: Visualization of finite element analysis results on unstructured grids

International Nuclear Information System (INIS)

Dovey, D.; Loomis, M.D.

1994-01-01

GRIZ is a general-purpose post-processing application that supports interactive visualization of finite element analysis results on three-dimensional unstructured grids. GRIZ includes direct-to-videodisc animation capabilities and is being used as a production tool for creating engineering animations

Finite element analysis of the Girkmann problem using the modern hp-version and the classical h-version

KAUST Repository

Niemi, Antti; Babuška, Ivo M.; Pitkä ranta, Juhani; Demkowicz, Leszek F.

2011-01-01

elasticity theory and (2) by using a dimensionally reduced shell-ring model. In the first approach the problem is solved with a fully automatic hp-adaptive finite element solver whereas the classical h-version of the finite element method is used

Analysis of competitive equilibrium in an infinite dimensional ...

African Journals Online (AJOL)

This paper considered the cost of allocated goods and attaining maximal utility with such price in the finite dimensional commodity space and observed that there exist an equilibrium price. It goes further to establish that in an infinite dimensional commodity space with subsets as consumption and production set there exist a ...

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

Science.gov (United States)

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.

Complex stiffness formulation for the finite element analysis of anisotropic axisymmetric solids subjected to nonsymmetric loads

International Nuclear Information System (INIS)

Frater, J.; Lestingi, J.; Padovan, J.

1977-01-01

This paper describes the development of an improved semi-analytical finite element for the stress analysis of anisotropic axisymmetric solids subjected to nonsymmetric loads. Orthogonal functions in the form of finite Fourier exponential transforms, which satisfy the equations of equilibrium of the theory of elasticity for an anisotropic solid of revolution, are used to expand the imposed loadings and displacement field. It is found that the orthogonality conditions for the assumed solution reduce the theta-dependency, thus reducing the three dimensional problem to an infinite series of two dimensional problems. (Auth.)

Finite-temperature second-order many-body perturbation and Hartree–Fock theories for one-dimensional solids: An application to Peierls and charge-density-wave transitions in conjugated polymers

International Nuclear Information System (INIS)

He, Xiao; Ryu, Shinsei; Hirata, So

2014-01-01

Finite-temperature extensions of ab initio Gaussian-basis-set spin-restricted Hartree–Fock (HF) and second-order many-body perturbation (MP2) theories are implemented for infinitely extended, periodic, one-dimensional solids and applied to the Peierls and charge-density-wave (CDW) transitions in polyyne and all-trans polyacetylene. The HF theory predicts insulating CDW ground states for both systems in their equidistant structures at low temperatures. In the same structures, they turn metallic at high temperatures. Starting from the “dimerized” low-temperature equilibrium structures, the systems need even higher temperatures to undergo a Peierls transition, which is accompanied by geometric as well as electronic distortions from dimerized to non-dimerized forms. The conventional finite-temperature MP2 theory shows a sign of divergence in any phase at any nonzero temperature and is useless. The renormalized finite-temperature MP2 (MP2R) theory is divergent only near metallic electronic structures, but is well behaved elsewhere. MP2R also predicts CDW and Peierls transitions occurring at two different temperatures. The effect of electron correlation is primarily to lower the Peierls transition temperature

Finite element computation of plasma equilibria

International Nuclear Information System (INIS)

Rivier, M.

1977-01-01

The applicability of the finite element method is investigated for the numerical solution of the nonlinear Grad-Shafranov equation with free boundary for the flux function of a plasma at equilibrium. This method is based on the case of variational principles and finite dimensional subspaces whose elements are piecewise polynomial functions obtained by a Lagrange type interpolation procedure over a triangulation of the domain. Two cases of plasma pressure (exponential and quadratic including a vacuum region) were examined. In both cases the nonuniqueness of the solutions was shown in exhibiting a deeper solution in the case of exponential pressure function, and a non-constant solution for a quadratic pressure function. In order to get this ''other'' solution, two linearization methods were tested with two different constraints. Different cross sections are investigated

The finite element response Matrix method

International Nuclear Information System (INIS)

Nakata, H.; Martin, W.R.

1983-01-01

A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-09-20

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

Finite elements volumes methods: applications to the Navier-Stokes equations and convergence results

International Nuclear Information System (INIS)

Emonot, P.

1992-01-01

In the first chapter are described the equations modeling incompressible fluid flow and a quick presentation of finite volumes method. The second chapter is an introduction to the finite elements volumes method. The box model is described and a method adapted to Navier-Stokes problems is proposed. The third chapter shows a fault analysis of the finite elements volumes method for the Laplacian problem and some examples in one, two, three dimensional calculations. The fourth chapter is an extension of the error analysis of the method for the Navier-Stokes problem

Finite element elastic-plastic analysis of LMFBR components

International Nuclear Information System (INIS)

Levy, A.; Pifko, A.; Armen, H. Jr.

1978-01-01

The present effort involves the development of computationally efficient finite element methods for accurately predicting the isothermal elastic-plastic three-dimensional response of thick and thin shell structures subjected to mechanical and thermal loads. This work will be used as the basis for further development of analytical tools to be used to verify the structural integrity of liquid metal fast breeder reactor (LMFBR) components. The methods presented here have been implemented into the three-dimensional solid element module (HEX) of the Grumman PLANS finite element program. These methods include the use of optimal stress points as well as a variable number of stress points within an element. This allows monitoring the stress history at many points within an element and hence provides an accurate representation of the elastic-plastic boundary using a minimum number of degrees of freedom. Also included is an improved thermal stress analysis capability in which the temperature variation and corresponding thermal strain variation are represented by the same functional form as the displacement variation. Various problems are used to demonstrate these improved capabilities. (Auth.)

On the spectral properties of random finite difference operators

International Nuclear Information System (INIS)

Kunz, H.; Souillard, B.

1980-01-01

We study a class of random finite difference operators, a typical example of which is the finite difference Schroedinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schroedinger operator with a random potential has pure point spectrum and developps no static conductivity. (orig.)

Representation theory of finite monoids

CERN Document Server

Steinberg, Benjamin

2016-01-01

This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional ...

A three-dimensional cellular automata model coupled with finite element method and thermodynamic database for alloy solidification

Science.gov (United States)

Zhao, Y.; Qin, R. S.; Chen, D. F.

2013-08-01

A three-dimensional (3D) cellular automata (CA) model has been developed for the simulation of microstructure evolution in alloy solidification. The governing rule for the CA model is associated with the phase transition driving force which is obtained via a thermodynamic database. This determines the migration rate of the non-equilibrium solid-liquid (SL) interface and is calculated according to the local temperature and chemical composition. The curvature of the interface and the anisotropic property of the surface energy are taken into consideration. A 3D finite element (FE) method is applied for the calculation of transient heat and mass transfer. Numerical calculations for the solidification of Fe-1.5 wt% C alloy have been performed. The morphological evolution of dendrites, carbon segregation and temperature distribution in both isothermal and non-isothermal conditions are studied. The parameters affecting the growth of equiaxed and columnar dendrites are discussed. The calculated results are verified using the analytical model and previous experiments. The method provides a sophisticated approach to the solidification of multi-phase and multi-component systems.

Three dimensional non-linear cracking analysis of prestressed concrete containment vessel

International Nuclear Information System (INIS)

Al-Obaid, Y.F.

2001-01-01

The paper gives full development of three-dimensional cracking matrices. These matrices are simulated in three-dimensional non-linear finite element analysis adopted for concrete containment vessels. The analysis includes a combination of conventional steel, the steel line r and prestressing tendons and the anisotropic stress-relations for concrete and concrete aggregate interlocking. The analysis is then extended and is linked to cracking analysis within the global finite element program OBAID. The analytical results compare well with those available from a model test. (author)

Finite element method for neutron diffusion problems in hexagonal geometry

International Nuclear Information System (INIS)

Wei, T.Y.C.; Hansen, K.F.

1975-06-01

The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes

The finite section method and problems in frame theory

DEFF Research Database (Denmark)

Christensen, Ole; Strohmer, T.

2005-01-01

solves related computational problems in frame theory. In the case of a frame which is localized w.r.t. an orthonormal basis we are able to estimate the rate of approximation. The results are applied to the reproducing kernel frame appearing in the theory for shift-invariant spaces generated by a Riesz......The finite section method is a convenient tool for approximation of the inverse of certain operators using finite-dimensional matrix techniques. In this paper we demonstrate that the method is very useful in frame theory: it leads to an efficient approximation of the inverse frame operator and also...

Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

Science.gov (United States)

Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

2015-04-01

The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface

From Laser Scanning to Finite Element Analysis of Complex Buildings by Using a Semi-Automatic Procedure.

Science.gov (United States)

Castellazzi, Giovanni; D'Altri, Antonio Maria; Bitelli, Gabriele; Selvaggi, Ilenia; Lambertini, Alessandro

2015-07-28

In this paper, a new semi-automatic procedure to transform three-dimensional point clouds of complex objects to three-dimensional finite element models is presented and validated. The procedure conceives of the point cloud as a stacking of point sections. The complexity of the clouds is arbitrary, since the procedure is designed for terrestrial laser scanner surveys applied to buildings with irregular geometry, such as historical buildings. The procedure aims at solving the problems connected to the generation of finite element models of these complex structures by constructing a fine discretized geometry with a reduced amount of time and ready to be used with structural analysis. If the starting clouds represent the inner and outer surfaces of the structure, the resulting finite element model will accurately capture the whole three-dimensional structure, producing a complex solid made by voxel elements. A comparison analysis with a CAD-based model is carried out on a historical building damaged by a seismic event. The results indicate that the proposed procedure is effective and obtains comparable models in a shorter time, with an increased level of automation.

Newton-sor iterative method for solving the two-dimensional porous ...

African Journals Online (AJOL)

In this paper, we consider the application of the Newton-SOR iterative method in obtaining the approximate solution of the two-dimensional porous medium equation (2D PME). The nonlinear finite difference approximation equation to the 2D PME is derived by using the implicit finite difference scheme. The developed ...

Measurement of Temperature and Soil Properties for Finite Element Model Verification

Science.gov (United States)

2012-08-01

In recent years, ADOT&PF personnel have used TEMP/W, a commercially available two-dimensional finite element program, to conduct thermal modeling of various : embankment configurations in an effort to reduce the thawing of ice-rich permafrost through...

The dilute random field Ising model by finite cluster approximation

International Nuclear Information System (INIS)

Benyoussef, A.; Saber, M.

1987-09-01

Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs

Numerical analysis of creep brittle rupture by the finite element method

International Nuclear Information System (INIS)

Goncalves, O.J.A.; Owen, D.R.J.

1983-01-01

In this work an implicit algorithm is proposed for the numerical analysis of creep brittle rupture problems by the finite element method. This kind of structural failure, typical in components operating at high temperatures for long periods of time, is modelled using either a three dimensional generalization of the Kachanov-Rabotnov equations due to Leckie and Hayhurst or the Monkman-Grant fracture criterion together with the Linear Life Fraction Rule. The finite element equations are derived by the displacement method and isoparametric elements are used for the spatial discretization. Geometric nonlinear effects (large displacements) are accounted for by an updated Lagrangian formulation. Attention is also focussed on the solution of the highly stiff differential equations that govern damage growth. Finally the numerical results of a three-dimensional analysis of a pressurized thin cylinder containing oxidised pits in its external wall are discussed. (orig.)

Influence of three-dimensional reconstruction method for building a model of the cervical spine on its biomechanical responses: A finite element analysis study

Directory of Open Access Journals (Sweden)

Iman Zafarparandeh

2016-03-01

Full Text Available In some finite element analysis studies of models of sections of the spine, the three-dimensional solid model is built by assuming symmetry about the mid-sagittal plane of the section, whereas in other studies, the model is built from the exact geometry of the section. The influence of the method used to build the solid model on model parameters, in the case of the cervical spine, has not been reported in the literature. This issue is the subject of this study, with the section being C2–C7, the applied loadings being extension, flexion, left lateral bending, and right axial rotation (each of magnitude 1 Nm, and the model parameters determined being rotation, intradiskal pressure, and facet load at each of the segments. When all the parameter results were considered, it was found that, by and large, the influence of solid model construction method used (exact geometry vs assumption of symmetry about the mid-sagittal plane of the section was marginal. As construction of a symmetric finite element model requires less time and effort, construction of an asymmetric model may be justified in special cases only.

Rare event simulation in finite-infinite dimensional space

International Nuclear Information System (INIS)

Au, Siu-Kui; Patelli, Edoardo

2016-01-01

Modern engineering systems are becoming increasingly complex. Assessing their risk by simulation is intimately related to the efficient generation of rare failure events. Subset Simulation is an advanced Monte Carlo method for risk assessment and it has been applied in different disciplines. Pivotal to its success is the efficient generation of conditional failure samples, which is generally non-trivial. Conventionally an independent-component Markov Chain Monte Carlo (MCMC) algorithm is used, which is applicable to high dimensional problems (i.e., a large number of random variables) without suffering from ‘curse of dimension’. Experience suggests that the algorithm may perform even better for high dimensional problems. Motivated by this, for any given problem we construct an equivalent problem where each random variable is represented by an arbitrary (hence possibly infinite) number of ‘hidden’ variables. We study analytically the limiting behavior of the algorithm as the number of hidden variables increases indefinitely. This leads to a new algorithm that is more generic and offers greater flexibility and control. It coincides with an algorithm recently suggested by independent researchers, where a joint Gaussian distribution is imposed between the current sample and the candidate. The present work provides theoretical reasoning and insights into the algorithm.

Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces

International Nuclear Information System (INIS)

Arai, A.

1985-01-01

We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)

Finite element analysis of the neutron transport equation in spherical geometry

International Nuclear Information System (INIS)

Kim, Yong Ill; Kim, Jong Kyung; Suk, Soo Dong

1992-01-01

The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation. (Author)

Two-dimensional model of coupled heat and moisture transport in frost-heaving soils

International Nuclear Information System (INIS)

Guymon, G.L.; Berg, R.L.; Hromadka, T.V.

1984-01-01

A two-dimensional model of coupled heat and moisture flow in frost-heaving soils is developed based upon well known equations of heat and moisture flow in soils. Numerical solution is by the nodal domain integration method which includes the integrated finite difference and the Galerkin finite element methods. Solution of the phase change process is approximated by an isothermal approach and phenomenological equations are assumed for processes occurring in freezing or thawing zones. The model has been verified against experimental one-dimensional freezing soil column data and experimental two-dimensional soil thawing tank data as well as two-dimensional soil seepage data. The model has been applied to several simple but useful field problems such as roadway embankment freezing and frost heaving

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

Science.gov (United States)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

International Nuclear Information System (INIS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-01-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix

Quantum entanglement of localized excited states at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Caputa, Paweł [Yukawa Institute for Theoretical Physics (YITP), Kyoto University,Kyoto 606-8502 (Japan); Nordita, KTH Royal Institute of Technology and Stockholm University,Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Simón, Joan; Štikonas, Andrius [School of Mathematics and Maxwell Institute for Mathematical Sciences,University of Edinburgh,King’s Buildings, Edinburgh EH9 3FD (United Kingdom); Takayanagi, Tadashi [Yukawa Institute for Theoretical Physics (YITP), Kyoto University,Kyoto 606-8502 (Japan); Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU),University of Tokyo,Kashiwa, Chiba 277-8582 (Japan)

2015-01-20

In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results.

Multi-flavor massless QED{sub 2} at finite densities via Lefschetz thimbles

Energy Technology Data Exchange (ETDEWEB)

Tanizaki, Yuya [RIKEN BNL Research Center, Brookhaven National Laboratory,Upton, NY 11973-5000 (United States); Tachibana, Motoi [Department of Physics, Saga University,Saga 840-8502 (Japan)

2017-02-15

We consider multi-flavor massless (1+1)-dimensional QED with chemical potentials at finite spatial length and the zero-temperature limit. Its sign problem is solved using the mean-field calculation with complex saddle points.

Stress distribution in delayed replanted teeth splinted with different orthodontic wires: a three-dimensional finite element analysis.

Science.gov (United States)

de Souza, Fernando Isquierdo; Poi, Wilson Roberto; da Silva, Vanessa Ferreira; Martini, Ana Paula; Melo, Regis Alexandre da Cunha; Panzarini, Sonia Regina; Rocha, Eduardo Passos

2015-06-01

The aim was to evaluate the biomechanical behavior of the supporting bony structures of replanted teeth and the periodontal ligament (PDL) of adjacent teeth when orthodontic wires with different mechanical properties are applied, with three-dimensional finite element analysis. Based on tomographic and microtomographic data, a three-dimensional model of the anterior maxilla with the corresponding teeth (tooth 13-tooth 23) was generated to simulate avulsion and replantation of the tooth 21. The teeth were splinted with orthodontic wire (Ø 0.8 mm) and composite resin. The elastic modulus of the three orthodontic wires used, that is, steel wire (FA), titanium-molybdenum wire (FTM), and nitinol wire (FN) were 200 GPa, 84 GPa, and 52 GPa, respectively. An oblique load (100 N) was applied at an angle of 45° on the incisal edge of the replanted tooth and was analyzed using Ansys Workbench software. The maximum (σmax) and minimum (σmin) principal stresses generated in the PDL, cortical and alveolar bones, and the modified von Mises (σvM) values for the orthodontic wires were obtained. With regard to the cortical bone and PDL, the highest σmin and σmax values for FTM, FN, and FA were checked. With regard to the alveolar bone, σmax and σmin values were highest for FA, followed by FTM and FN. The σvM values of the orthodontic wires followed the order of rigidity of the alloys, that is, FA > FTM > FN. The biomechanical behavior of the analyzed structures with regard to all the three patterns of flexibility was similar. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Deconfinement phase transition and finite-size scaling in SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Mogilevskij, O.A.

1988-01-01

Calculation technique for deconfinement phase transition parameters based on application of finite-size scaling theory is suggested. The essence of the technique lies in plotting of universal scaling function on the basis of numerical data obtained at different-size final lattices and discrimination of phase transition parameters for infinite lattice system. Finite-size scaling technique was developed as applied to spin system theory. β critical index for Polyakov loop and SU(2) deconfinement temperature of lattice gauge theory are calculated on the basis of finite-size scaling technique. The obtained value agrees with critical index of magnetization in Ising three-dimensional model

Five-dimensional Nernst branes from special geometry

Energy Technology Data Exchange (ETDEWEB)

Dempster, P.; Errington, D. [Department of Mathematical Sciences, University of LiverpoolPeach Street, Liverpool L69 7ZL (United Kingdom); Gutowski, J. [Department of Mathematics, University of Surrey,Guildford, GU2 7XH (United Kingdom); Mohaupt, T. [Department of Mathematical Sciences, University of LiverpoolPeach Street, Liverpool L69 7ZL (United Kingdom)

2016-11-21

We construct Nernst brane solutions, that is black branes with zero entropy density in the extremal limit, of FI-gauged minimal five-dimensional supergravity coupled to an arbitrary number of vector multiplets. While the scalars take specific constant values and dynamically determine the value of the cosmological constant in terms of the FI-parameters, the metric takes the form of a boosted AdS Schwarzschild black brane. This metric can be brought to the Carter-Novotný-Horský form that has previously been observed to occur in certain limits of boosted D3-branes. By dimensional reduction to four dimensions we recover the four-dimensional Nernst branes of arXiv:1501.07863 and show how the five-dimensional lift resolves all their UV singularities. The dynamics of the compactification circle, which expands both in the UV and in the IR, plays a crucial role. At asymptotic infinity, the curvature singularity of the four-dimensional metric and the run-away behaviour of the four-dimensional scalar combine in such a way that the lifted solution becomes asymptotic to AdS{sub 5}. Moreover, the existence of a finite chemical potential in four dimensions is related to fact that the compactification circle has a finite minimal value. While it is not clear immediately how to embed our solutions into string theory, we argue that the same type of dictionary as proposed for boosted D3-branes should apply, although with a lower amount of supersymmetry.

Three-Dimensional Finite Element Analysis on Stress Distribution of Internal Implant-Abutment Engagement Features.

Science.gov (United States)

Cho, Sung-Yong; Huh, Yun-Hyuk; Park, Chan-Jin; Cho, Lee-Ra

To investigate the stress distribution in an implant-abutment complex with a preloaded abutment screw by comparing implant-abutment engagement features using three-dimensional finite element analysis (FEA). For FEA modeling, two implants-one with a single (S) engagement system and the other with a double (D) engagement system-were placed in the human mandibular molar region. Two types of abutments (hexagonal, conical) were connected to the implants. Different implant models (a single implant, two parallel implants, and mesial and tilted distal implants with 1-mm bone loss) were assumed. A static axial force and a 45-degree oblique force of 200 N were applied as the sum of vectors to the top of the prosthetic occlusal surface with a preload of 30 Ncm in the abutment screw. The von Mises stresses at the implant-abutment and abutment-screw interfaces were measured. In the single implant model, the S-conical abutment type exhibited broader stress distribution than the S-hexagonal abutment. In the double engagement system, the stress concentration was high in the lower contact area of the implant-abutment engagement. In the tilted implant model, the stress concentration point was different from that in the parallel implant model because of the difference in the bone level. The double engagement system demonstrated a high stress concentration at the lower contact area of the implant-abutment interface. To decrease the stress concentration, the type of engagement features of the implant-abutment connection should be carefully considered.

Plantar pressure relief under the metatarsal heads: therapeutic insole design using three-dimensional finite element model of the foot.

Science.gov (United States)

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. Copyright © 2015 Elsevier Ltd. All rights reserved.

Negative dimensional integrals. Pt. 1

International Nuclear Information System (INIS)

Halliday, I.G.; Ricotta, R.M.

1987-01-01

We propose a new method of evaluating integrals based on negative dimensional integration. We compute Feynman graphs by considering analytic extensions. Propagators are raised to negative integer powers and integrated over negative integer dimensions. We are left with the problem of computing polynomial integrals and summing finite series. (orig.)

A third order accurate Lagrangian finite element scheme for the computation of generalized molecular stress function fluids

DEFF Research Database (Denmark)

Fasano, Andrea; Rasmussen, Henrik K.

2017-01-01

A third order accurate, in time and space, finite element scheme for the numerical simulation of three- dimensional time-dependent flow of the molecular stress function type of fluids in a generalized formu- lation is presented. The scheme is an extension of the K-BKZ Lagrangian finite element me...

Finite temperature approach to confinement

International Nuclear Information System (INIS)

Gave, E.; Jengo, R.; Omero, C.

1980-06-01

The finite temperature treatment of gauge theories, formulated in terms of a gauge invariant variable as in a Polyakov method, is used as a device for obtaining an effective theory where the confinement test takes the form of a correlation function. The formalism is discussed for the abelian CPsup(n-1) model in various dimensionalities and for the pure Yang-Mills theory in the limit of zero temperature. In the latter case a class of vortex like configurations of the effective theory which induce confinement correspond in particular to the instanton solutions. (author)

Hamiltonian formalism of two-dimensional Vlasov kinetic equation.

Science.gov (United States)

Pavlov, Maxim V

2014-12-08

In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

Field emission from finite barrier quantum structures

Energy Technology Data Exchange (ETDEWEB)

Biswas Sett, Shubhasree, E-mail: shubhasree24@gmail.com [The Institution of Engineers - India, 8, Gokhale Road, Kolkata 700 020 (India); Bose, Chayanika, E-mail: chayanikab@ieee.org [Electronics and Telecommunication Engg. Dept., Jadavpur University, Kolkata 700 032 (India)

2014-10-01

We study field emission from various finite barrier quasi-low dimensional structures, taking image force into account. To proceed, we first formulate an expression for field emission current density from a quantum dot. Transverse dimensions of the dot are then increased in turn, to obtain current densities respectively from quantum wire and quantum well with infinite potential energy barriers. To find out field emission from finite barrier structures, the above analysis is followed with a correction in the energy eigen values. In course, variations of field emission current density with strength of the applied electric field and structure dimensions are computed considering n-GaAs and n-GaAs/Al{sub x}Ga{sub 1−x}As as the semiconductor materials. In each case, the current density is found to increase exponentially with the applied field, while it oscillates with structure dimensions. The magnitude of the emission current is less when the image force is not considered, but retains the similar field dependence. In all cases, the field emission from infinite barrier structures exceeds those from respective finite barrier ones.

Dynamics of vortex interactions in two-dimensional flows

DEFF Research Database (Denmark)

Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.

2002-01-01

The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...... a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 ... is effectively producing small scale structures and the relation to the enstrophy "cascade" in developed 2D turbulence is discussed. The influence of finite viscosity on the merging is also investigated. Additionally, we examine vortex interactions on a finite domain, and discuss the results in connection...

Analysis of distances between inclusions in finite binary stochastic materials

International Nuclear Information System (INIS)

Griesheimer, David P.; Millman, David L.; Willis, Clarence R.

2011-01-01

A generalized probability density function (PDF) describing the distribution of inter-inclusion distances in finite, isotropic, binary stochastic materials with fixed diameter inclusions has been developed and tested. The new probability density function explicitly accounts for edge effects present in finite two- and three-dimensional stochastic materials. The generalized PDF is shown to include factors that are dependent on both the geometry of the material region as well as the statistical properties of the material. A discussion of the properties and application of this newly developed PDF is provided along with supporting numerical results for case studies in one- and two-dimensions. These numerical results demonstrate the ability of the newly derived PDF to correctly account for edge effects in finite stochastic materials, while still reproducing the expected distribution within the bulk material region.

Finite element based composite solution for neutron transport problems

International Nuclear Information System (INIS)

Mirza, A.N.; Mirza, N.M.

1995-01-01

A finite element treatment for solving neutron transport problems is presented. The employs region-wise discontinuous finite elements for the spatial representation of the neutron angular flux, while spherical harmonics are used for directional dependence. Composite solutions has been obtained by using different orders of angular approximations in different parts of a system. The method has been successfully implemented for one dimensional slab and two dimensional rectangular geometry problems. An overall reduction in the number of nodal coefficients (more than 60% in some cases as compared to conventional schemes) has been achieved without loss of accuracy with better utilization of computational resources. The method also provides an efficient way of handling physically difficult situations such as treatment of voids in duct problems and sharply changing angular flux. It is observed that a great wealth of information about the spatial and directional dependence of the angular flux is obtained much more quickly as compared to Monte Carlo method, where most of the information in restricted to the locality of immediate interest. (author)

Finite element analysis of helical flows in human aortic arch: A novel index

OpenAIRE

Lee, Cheng-Hung; Liu, Kuo-Sheng; Jhong, Guan-Heng; Liu, Shih-Jung; Hsu, Ming-Yi; Wang, Chao-Jan; Hung, Kuo-Chun

2014-01-01

This study investigates the helical secondary flows in the aortic arch using finite element analysis. The relationship between helical flow and the configuration of the aorta in patients of whose three-dimensional images constructed from computed tomography scans was examined. A finite element model of the pressurized root, arch, and supra-aortic vessels was developed to simulate the pattern of helical secondary flows. Calculations indicate that most of the helical secondary flow was formed i...

Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects

International Nuclear Information System (INIS)

Goto, R.; Hatori, T.; Miura, H.; Ito, A.; Sato, M.

2015-01-01

Two-fluid and the finite Larmor effects on linear and nonlinear growth of the Rayleigh-Taylor instability in a two-dimensional slab are studied numerically with special attention to high-wave-number dynamics and nonlinear structure formation at a low β-value. The two effects stabilize the unstable high wave number modes for a certain range of the β-value. In nonlinear simulations, the absence of the high wave number modes in the linear stage leads to the formation of the density field structure much larger than that in the single-fluid magnetohydrodynamic simulation, together with a sharp density gradient as well as a large velocity difference. The formation of the sharp velocity difference leads to a subsequent Kelvin-Helmholtz-type instability only when both the two-fluid and finite Larmor radius terms are incorporated, whereas it is not observed otherwise. It is shown that the emergence of the secondary instability can modify the outline of the turbulent structures associated with the primary Rayleigh-Taylor instability

1DFEMWATER: A one-dimensional finite element model of WATER flow through saturated-unsaturated media

International Nuclear Information System (INIS)

Yeh, G.T.

1988-08-01

This report presents the development and verification of a one- dimensional finite element model of water flow through saturated- unsaturated media. 1DFEMWATER is very flexible and capable of modeling a wide range of real-world problems. The model is designed to (1) treat heterogeneous media consisting of many geologic formations; (2) consider distributed and point sources/sinks that are spatially and temporally variable; (3) accept prescribed initial conditions or obtain them from steady state simulations; (4) deal with transient heads distributed over the Dirichlet boundary; (5) handle time-dependent fluxes caused by pressure gradient on the Neumann boundary; (6) treat time-dependent total fluxes (i.e., the sum of gravitational fluxes and pressure-gradient fluxes) on the Cauchy boundary; (7) automatically determine variable boundary conditions of evaporation, infiltration, or seepage on the soil-air interface; (8) provide two options for treating the mass matrix (consistent and lumping); (9) provide three alternatives for approximating the time derivative term (Crank-Nicolson central difference, backward difference, and mid-difference); (10) give three options (exact relaxation, underrelaxation, and overrelaxation) for estimating the nonlinear matrix; (11) automatically reset the time step size when boundary conditions or source/sinks change abruptly; and (12) check mass balance over the entire region for every time step. The model is verified with analytical solutions and other numerical models for three examples

Gluon scattering in N=4 super Yang-Mills at finite temperature

International Nuclear Information System (INIS)

Ito, Katsushi; Iwasaki, Koh; Nastase, Horatiu

2008-01-01

We extend the AdS/CFT prescription of Alday and Maldacena to finite temperature T, defining an amplitude for gluon scattering in N=4 Super Yang-Mills at strong coupling from string theory. It is defined by a lightlike 'Wilson loop' living at the horizon of the T-dual to the black hole in AdS space. Unlike the zero temperature case, this is different from the Wilson loop contour defined at the boundary of the AdS black hole metric. Thus at nonzero T there is no relation between gluon scattering amplitudes and the Wilson loop. We calculate a gauge theory observable that can be interpreted as the amplitude at strong coupling for forward scattering of a low energy gluon (E >T) in both cutoff and generalized dimensional regularization. The generalized dimensional regularization is defined in string theory as an IR modified dimensional reduction. For this calculation, the corresponding usual Wilson loop of the same boundary shape was argued to be related to the jet quenching parameter of the finite temperature N=4 SYM plasma, while the gluon scattering amplitude is related to the viscosity coefficient. (author)

Finite element reliability analysis of fatigue life

International Nuclear Information System (INIS)

Harkness, H.H.; Belytschko, T.; Liu, W.K.

1992-01-01

Fatigue reliability is addressed by the first-order reliability method combined with a finite element method. Two-dimensional finite element models of components with cracks in mode I are considered with crack growth treated by the Paris law. Probability density functions of the variables affecting fatigue are proposed to reflect a setting where nondestructive evaluation is used, and the Rosenblatt transformation is employed to treat non-Gaussian random variables. Comparisons of the first-order reliability results and Monte Carlo simulations suggest that the accuracy of the first-order reliability method is quite good in this setting. Results show that the upper portion of the initial crack length probability density function is crucial to reliability, which suggests that if nondestructive evaluation is used, the probability of detection curve plays a key role in reliability. (orig.)

Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

Directory of Open Access Journals (Sweden)

Sudi Mungkasi

2016-01-01

Full Text Available This paper presents a numerical entropy production (NEP scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

Finite

Directory of Open Access Journals (Sweden)

W.R. Azzam

2015-08-01

Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.

Reduction of infinite dimensional equations

Directory of Open Access Journals (Sweden)

Zhongding Li

2006-02-01

Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

Finite volume gauge theory partition functions in three dimensions

International Nuclear Information System (INIS)

Szabo, Richard J.

2005-01-01

We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the ε-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear σ-models. New results are given for an arbitrary number of flavours in all three cases of complex, pseudo-real and real fermions, extending some previous considerations based on random matrix theory. They are used to describe the microscopic spectral correlation functions and smallest eigenvalue distributions of the QCD 3 Dirac operator, as well as the corresponding massive spectral sum rules

Comparison of one-dimensional probabilistic finite element method with direct numerical simulation of dynamically loaded heterogeneous materials

Science.gov (United States)

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.

Probabilistic finite elements for transient analysis in nonlinear continua

Science.gov (United States)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Distribution of quantum states in enclosures of finite size I

International Nuclear Information System (INIS)

Souto, J.H.; Chaba, A.N.

1989-01-01

The expression for the density of states of a particle in a three-dimensional rectangular box of finite size can be obtained directly by Poissons's Summation formula. The expression for the case of an enclosure in the form of an infinite rectangular slab is derived. (A.C.A.S.) [pt

HYFRAC3D, 3-D Hydraulic Rock Fracture Propagation by Finite Element Method

International Nuclear Information System (INIS)

Advani, S.H.; Lee, J.K.; Lee, T.S.

2001-01-01

1 - Description of program or function: HYFRAC3D is a finite element program for simulation of three-dimensional fracture geometries with a two-dimensional planar solution. The model predicts the height, width and wing length over time for a hydraulic fracture propagating in a multi-layered system of rock with variable fluid flow and rock mechanics properties. 2 - Method of solution: The program uses the finite element Method of solution. A backward difference scheme is used by taking the weight functions on the time axis. This implicit time matching scheme requires iteration since the fracture configuration at time t+dt is not known. 3 - Restrictions on the complexity of the problem: Graphics output is not available and program is limited to fracture propagation in a single plane without proppant transport

A SIMPLE DERIVATION OF FINITE-TEMPERATURE CFT CORRELATORS FROM THE BTZ BLACK HOLE

Directory of Open Access Journals (Sweden)

Satoshi Ohya

2014-04-01

Full Text Available We present a simple Lie-algebraic approach to momentum-space two-point functions of two-dimensional conformal field theory at finite temperature dual to the BTZ black hole. Making use of the real-time prescription of AdS/CFT correspondence and ladder equations of the Lie algebra so(2,2 ∼= sl(2,RL⊕sl(2,RR, we show that the finite-temperature two-point functions in momentum space satisfy linear recurrence relations with respect to the left and right momenta. These recurrence relations are exactly solvable and completely determine the momentum-dependence of retarded and advanced two-point functions of finite-temperature conformal field theory.

From anomalies of finite symmetries to heterotic GUTs

Science.gov (United States)

Vaudrevange, Patrick K. S.

2017-11-01

We review the role of finite symmetries for particle physics with special emphasis on discrete anomalies and on their possible origin from extra dimensions. Then, we apply our knowledge on finite symmetries to the problematic proton decay operators of various mass-dimensions, focusing on ℤ4R , i.e. a special R-symmetry of order 4. We show that this ℤ4R symmetry can naturally originate from extra dimensions as a discrete remnant of higher-dimensional Lorentz symmetry. Finally, in order to obtain a unified picture from the heterotic string theory we discuss grand unified theories (GUTs) in extra dimensions compactified on ℤ2 × ℤ2 orbifolds and show how proton decay operators can be suppressed in a certain class of orbifolds.

Smooth controllability of infinite-dimensional quantum-mechanical systems

International Nuclear Information System (INIS)

Wu, Re-Bing; Tarn, Tzyh-Jong; Li, Chun-Wen

2006-01-01

Manipulation of infinite-dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite-dimensional manifolds. Recognizing that such problems are related with infinite-dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite-dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite-dimensional vector spaces to analysis over infinite-dimensional manifolds. It also opens up many interesting problems for future studies

JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

Energy Technology Data Exchange (ETDEWEB)

Biffle, J.H.

1993-02-01

JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

Energy Technology Data Exchange (ETDEWEB)

Biffle, J.H.; Blanford, M.L.

1994-05-01

JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

Conversion and comparison of the mathematical, three-dimensional, finite-difference, ground-water flow model to the modular, three-dimensional, finite-difference, ground-water flow model for the Tesuque aquifer system in northern New Mexico

Science.gov (United States)

Umari, A.M.; Szeliga, T.L.

1989-01-01

The three-dimensional finite-difference groundwater model (using a mathematical groundwater flow code) of the Tesuque aquifer system in northern New Mexico was converted to run using the U.S. Geological Survey 's modular groundwater flow code. Results from the final versions of the predevelopment and 1947 to 2080 transient simulations of the two models are compared. A correlation coefficient of 0.9905 was obtained for the match in block-by-block head-dependent fluxes for predevelopment conditions. There are, however, significant differences in at least two specific cases. In the first case, a difference is associated with the net loss from the Pojoaque River and its tributaries to the aquifer. The net loss by the river is given as 1.134 cu ft/sec using the original groundwater model, which is 38.1% less than the net loss by the river of 1.8319 cu ft/sec computed in this study. In the second case, the large difference is computed for the transient decline in the hydraulic head of a model block near Tesuque Pueblo. The hydraulic-head decline by 2080 is, using the original model, 249 ft, which is 14.7% less than the hydraulic head of 292 ft computed by this study. In general, the differences between the two sets of results are not large enough to lead to different conclusions regarding the behavior of the system at steady state or when pumped. (USGS)

Two-dimensional ferroelectrics

Energy Technology Data Exchange (ETDEWEB)

Blinov, L M; Fridkin, Vladimir M; Palto, Sergei P [A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russian Federaion (Russian Federation); Bune, A V; Dowben, P A; Ducharme, Stephen [Department of Physics and Astronomy, Behlen Laboratory of Physics, Center for Materials Research and Analysis, University of Nebraska-Linkoln, Linkoln, NE (United States)

2000-03-31

The investigation of the finite-size effect in ferroelectric crystals and films has been limited by the experimental conditions. The smallest demonstrated ferroelectric crystals had a diameter of {approx}200 A and the thinnest ferroelectric films were {approx}200 A thick, macroscopic sizes on an atomic scale. Langmuir-Blodgett deposition of films one monolayer at a time has produced high quality ferroelectric films as thin as 10 A, made from polyvinylidene fluoride and its copolymers. These ultrathin films permitted the ultimate investigation of finite-size effects on the atomic thickness scale. Langmuir-Blodgett films also revealed the fundamental two-dimensional character of ferroelectricity in these materials by demonstrating that there is no so-called critical thickness; films as thin as two monolayers (1 nm) are ferroelectric, with a transition temperature near that of the bulk material. The films exhibit all the main properties of ferroelectricity with a first-order ferroelectric-paraelectric phase transition: polarization hysteresis (switching); the jump in spontaneous polarization at the phase transition temperature; thermal hysteresis in the polarization; the increase in the transition temperature with applied field; double hysteresis above the phase transition temperature; and the existence of the ferroelectric critical point. The films also exhibit a new phase transition associated with the two-dimensional layers. (reviews of topical problems)

Finite dipolar hexagonal columns on piled layers of triangular lattice

International Nuclear Information System (INIS)

Matsushita, Katsuyoshi; Sugano, Ryoko; Kuroda, Akiyoshi; Tomita, Yusuke; Takayama, Hajime

2007-01-01

We have investigated, by the Monte Carlo simulation, spin systems which represent moments of arrayed magnetic nanoparticles interacting with each other only by the dipole-dipole interaction. In the present paper we aim the understanding of finite size effects on the magnetic nanoparticles arrayed in hexagonal columns cut out from the close-packing structures or from those with uniaxial compression. In columns with the genuine close-packing structures, we observe a single vortex state which is also observed previously in finite two-dimensional systems. On the other hand in the system with the inter-layer distance set 1/2 times of the close-packing one, we found ground states which depend on the number of layers. The dependence is induced by a finite size effect and is related to a orientation transition in the corresponding bulk system

Winding transitions at finite energy and temperature: An O(3) model

International Nuclear Information System (INIS)

Habib, S.; Mottola, E.; Tinyakov, P.

1996-01-01

Winding number transitions in the two-dimensional softly broken O(3) nonlinear σ model are studied at finite energy and temperature. New periodic instanton solutions which dominate the semiclassical transition amplitudes are found analytically at low energies, and numerically for all energies up to the sphaleron scale. The Euclidean period β of these finite energy instantons increases with energy, contrary to the behavior found in the Abelian Higgs model or simple one-dimensional systems. This results in a sharp crossover from instanton-dominated tunneling to sphaleron-dominated thermal activation at a certain critical temperature. Since this behavior is traceable to the soft breaking of conformal invariance by the mass term in the σ model, semiclassical winding number transition amplitudes in the electroweak theory in 3+1 dimensions should exhibit a similar sharp crossover. We argue that this is indeed the case in the standard model for M H W . copyright 1996 The American Physical Society

Lyapunov exponents for infinite dimensional dynamical systems

Science.gov (United States)

Mhuiris, Nessan Mac Giolla

1987-01-01

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

A three-dimensional field solutions of Halbach

International Nuclear Information System (INIS)

Chen Jizhong; Xiao Jijun; Zhang Yiming; Xu Chunyan

2008-01-01

A three-dimensional field solutions are presented for Halback cylinder magnet. Based on Ampere equivalent current methods, the permanent magnets are taken as distributing of current density. For getting the three-dimensional field solution of ideal polarized permanent magnets, the solution method entails the use of the vector potential and involves the closed-form integration of the free-space Green's function. The programmed field solution are ideal for performing rapid parametric studies of the dipole Halback cylinder magnets made from rare earth materials. The field solutions are verified by both an analytical two-dimensional algorithm and three-dimensional finite element software. A rapid method is presented for extensive analyzing and optimizing Halbach cylinder magnet. (authors)

Three-dimensional finite amplitude electroconvection in dielectric liquids

Science.gov (United States)

Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

2018-02-01

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Helix-Hopes on Finite Hyperfields

Directory of Open Access Journals (Sweden)

Thomas Vougiouklis

2016-12-01

Full Text Available Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We study the helix-hyperstructures on the representations using ordinary fields. The related theory can be faced by defining the hyperproduct on the set of non square matrices. The main tools of the Hyperstructure Theory are the fundamental relations which connect the largest class of hyperstructures, the Hv-structures, with the corresponding classical ones. We focus on finite dimensional helix-hyperstructures and on small Hv-fields, as well.

Three-dimensional parallel edge-based finite element modeling of electromagnetic data with field redatuming

DEFF Research Database (Denmark)

Cai, Hongzhu; Čuma, Martin; Zhdanov, Michael

2015-01-01

This paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom signific......This paper presents a parallelized version of the edge-based finite element method with a novel post-processing approach for numerical modeling of an electromagnetic field in complex media. The method uses an unstructured tetrahedral mesh which can reduce the number of degrees of freedom...... significantly. The linear system of finite element equations is solved using parallel direct solvers which are robust for ill-conditioned systems and efficient for multiple source electromagnetic (EM) modeling. We also introduce a novel approach to compute the scalar components of the electric field from...... the tangential components along each edge based on field redatuming. The method can produce a more accurate result as compared to conventional approach. We have applied the developed algorithm to compute the EM response for a typical 3D anisotropic geoelectrical model of the off-shore HC reservoir with complex...

ZONE: a finite element mesh generator. [In FORTRAN IV for CDC 7600

Energy Technology Data Exchange (ETDEWEB)

Burger, M. J.

1976-05-01

The ZONE computer program is a finite-element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated to describe pressure boundary conditions. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. The output from ZONE is essentially the input file to NAOS, HONDO, and other axisymmetric finite element programs. 14 figures. (RWR)

Moessbauer lineshape distortions due to finite dimensions of source and detector

International Nuclear Information System (INIS)

Flores-Llamas, H.; Zamorano-Ulloa, R.

1991-01-01

The effects of non-collimation of γ-rays and finite dimensions of source and detector upon the isomer shift, line broadening and line height of Moessbauer spectra have been determined by means of a two-dimensional angular distribution f(r, ρ) that weights a Lorentzian lineshape function. This distribution function, along with a few approximations, allow one to calculate, with ease, these Moessbauer spectral parameters. Our expressions, valid for finite dimensions, of source, detector and absorber, generalize previous calculations. As a result, we can say that when a finite source (R s = 0.4 cm) is 10 cm distance from a detector (R d = 1.4 cm), the non-collimation of the γ-rays generates distortions of the absorption line that are still within the experimental error. (orig.)

Application of the finite element groundwater model FEWA to the engineered test facility

International Nuclear Information System (INIS)

Craig, P.M.; Davis, E.C.

1985-09-01

A finite element model for water transport through porous media (FEWA) has been applied to the unconfined aquifer at the Oak Ridge National Laboratory Solid Waste Storage Area 6 Engineered Test Facility (ETF). The model was developed in 1983 as part of the Shallow Land Burial Technology - Humid Task (ONL-WL14) and was previously verified using several general hydrologic problems for which an analytic solution exists. Model application and calibration, as described in this report, consisted of modeling the ETF water table for three specialized cases: a one-dimensional steady-state simulation, a one-dimensional transient simulation, and a two-dimensional transient simulation. In the one-dimensional steady-state simulation, the FEWA output accurately predicted the water table during a long period in which there were no man-induced or natural perturbations to the system. The input parameters of most importance for this case were hydraulic conductivity and aquifer bottom elevation. In the two transient cases, the FEWA output has matched observed water table responses to a single rainfall event occurring in February 1983, yielding a calibrated finite element model that is useful for further study of additional precipitation events as well as contaminant transport at the experimental site

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional

Scattering amplitudes over finite fields and multivariate functional reconstruction

Energy Technology Data Exchange (ETDEWEB)

Peraro, Tiziano [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)

2016-12-07

Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.

Scattering amplitudes over finite fields and multivariate functional reconstruction

International Nuclear Information System (INIS)

Peraro, Tiziano

2016-01-01

Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.

Phase transitions in finite systems

Energy Technology Data Exchange (ETDEWEB)

Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), DSM-CEA / IN2P3-CNRS, 14 - Caen (France); Gulminelli, F. [Caen Univ., 14 (France). Lab. de Physique Corpusculaire

2002-07-01

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermo-statistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent. (authors)

Phase transitions in finite systems

International Nuclear Information System (INIS)

Chomaz, Ph.; Gulminelli, F.

2002-01-01

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermo-statistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent. (authors)

A study on the improvement of shape optimization associated with the modification of a finite element

International Nuclear Information System (INIS)

Sung, Jin Il; Yoo, Jeong Hoon

2002-01-01

In this paper, we investigate the effect and the importance of the accuracy of finite element analysis in the shape optimization based on the finite element method and improve the existing finite element which has inaccuracy in some cases. And then, the shape optimization is performed by using the improved finite element. One of the main stream to improve finite element is the prevention of locking phenomenon. In case of bending dominant problems, finite element solutions cannot be reliable because of shear locking phenomenon. In the process of shape optimization, the mesh distortion is large due to the change of the structure outline. So, we have to raise the accuracy of finite element analysis for the large mesh distortion. We cannot guarantee the accurate result unless the finite element itself is accurate or the finite elements are remeshed. So, we approach to more accurate shape optimization to diminish these inaccuracies by improving the existing finite element. The shape optimization using the modified finite element is applied to a two and three dimensional simple beam. Results show that the modified finite element has improved the optimization results

Chiral anomaly and anomalous finite-size conductivity in graphene

Science.gov (United States)

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

2017-09-01

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

Stress intensity factor analyses of surface cracks in three-dimensional structures

International Nuclear Information System (INIS)

Miyazaki, Noriyuki; Shibata, Katsuyuki; Watanabe, Takayuki; Tagata, Kazunori.

1983-11-01

The stress intensity factor analyses of surface cracks in various three-dimensional structures were performed using the finite element computer program EPAS-J1. The results obtained by EPAS-J1 were compared with other finite element solutions or results obtained by the simplified estimation methods. Among the simplified estimation methods, the equations proposed by Newman and Raju give the distributions of the stress intensity factor along a crack front, which were compared with the result obtained by EPAS-J1. It was confirmed by comparing the results that EPAS-J1 gives reasonable stress intensity factors of surface cracks in three-dimensional structures. (author)

Performance prediction of centrifugal compressor impellers using quasi-three-dimensional analysis

International Nuclear Information System (INIS)

Ahn, S. J.; Kim, K. Y.; Oh, H. W.

2001-01-01

This-paper presents analysis of the flows through three different types of radial compressor by using quasi-three-dimensional analysis method. The method obtains two-dimensional solution for velocity distribution on meridional plane, and then calculates approximately the static pressure distributions on blade surfaces. Finite difference method is used for the solutions of governing equations. The compressors have low level compression-ratio and 12 straight radial blades with no sweepback. The results are compared with experimental data and the results of inviscid analysis with finite element method. It can be concluded that the agreement is good for the cases where viscous effects are not dominant

Finite element analysis of multilayer coextrusion.

Energy Technology Data Exchange (ETDEWEB)

Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann

2011-09-01

Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.

Finite Unification: Theory, Models and Predictions

CERN Document Server

Heinemeyer, S; Zoupanos, G

2011-01-01

All-loop Finite Unified Theories (FUTs) are very interesting N=1 supersymmetric Grand Unified Theories (GUTs) realising an old field theory dream, and moreover have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensional couplings that guarantee the vanishing of all beta-functions in certain N=1 GUTs even to all orders. Furthermore developments in the soft supersymmetry breaking sector of N=1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory, too. Based on the above theoretical framework phenomenologically consistent FUTs have been constructed. Here we review FUT models based on the SU(5) and SU(3)^3 gauge groups and their predictions. Of particular interest is the Hig...

Application of Dynamic Analysis in Semi-Analytical Finite Element Method.

Science.gov (United States)

Liu, Pengfei; Xing, Qinyan; Wang, Dawei; Oeser, Markus

2017-08-30

Analyses of dynamic responses are significantly important for the design, maintenance and rehabilitation of asphalt pavement. In order to evaluate the dynamic responses of asphalt pavement under moving loads, a specific computational program, SAFEM, was developed based on a semi-analytical finite element method. This method is three-dimensional and only requires a two-dimensional FE discretization by incorporating Fourier series in the third dimension. In this paper, the algorithm to apply the dynamic analysis to SAFEM was introduced in detail. Asphalt pavement models under moving loads were built in the SAFEM and commercial finite element software ABAQUS to verify the accuracy and efficiency of the SAFEM. The verification shows that the computational accuracy of SAFEM is high enough and its computational time is much shorter than ABAQUS. Moreover, experimental verification was carried out and the prediction derived from SAFEM is consistent with the measurement. Therefore, the SAFEM is feasible to reliably predict the dynamic response of asphalt pavement under moving loads, thus proving beneficial to road administration in assessing the pavement's state.

Titanium versus zirconia implants supporting maxillary overdentures: three-dimensional finite element analysis.

Science.gov (United States)

Osman, Reham B; Elkhadem, Amr H; Ma, Sunyoung; Swain, Michael V

2013-01-01

The purpose of this study was to compare the stress and strain occurring in peri-implant bone and implants used to support maxillary overdentures. Three-dimensional finite element analysis (3D FEA) was used to compare one-piece zirconia and titanium implants. Two types of implants were simulated using a 3D FEA model: one-piece zirconia and titanium implants (diameter, 3.8 × 11.5 mm) with 2.25-mm diameter ball abutments. In each simulation four implants were placed bilaterally in the canine/premolar region of an edentulous maxillary model. Static loads were applied axially and 20 degrees buccolingually on the buccal slope of the lingual cusps of posterior teeth of the first quadrant. Von Mises stresses and equivalent strains generated in peri-implant bone and first principal stresses in the implants were calculated. Comparable stress and strain values were shown in the peri-implant bone for both types of implants. The maximum equivalent strain produced in the peri-implant region was mostly within the range for bone augmentation. Under oblique loading, maximum von Mises stresses and equivalent strain were more evident at the neck of the most distal implant on the loaded side. Under axial load, the stress and strain were transferred to the peri-implant bone around the apex of the implant. Maximum tensile stresses that developed for either material were well below their fracture strength. The highest stresses were mainly located at the distobuccal region of the neck for the two implant materials under both loading conditions. From a biomechanical point of view, ceramic implants made from yttrium-stabilized tetragonal polycrystalline zirconia may be a potential alternative to conventional titanium implants for the support of overdentures. This is particularly relevant for a select group of patients with a proven allergy to titanium. Prospective clinical studies are still required to confirm these in vitro results. Different simulations presenting various cortical bone

The ACR-program for automatic finite element model generation for part through cracks

International Nuclear Information System (INIS)

Leinonen, M.S.; Mikkola, T.P.J.

1989-01-01

The ACR-program (Automatic Finite Element Model Generation for Part Through Cracks) has been developed at the Technical Research Centre of Finland (VTT) for automatic finite element model generation for surface flaws using three dimensional solid elements. Circumferential or axial cracks can be generated on the inner or outer surface of a cylindrical or toroidal geometry. Several crack forms are available including the standard semi-elliptical surface crack. The program can be used in the development of automated systems for fracture mechanical analyses of structures. The tests for the accuracy of the FE-mesh have been started with two-dimensional models. The results indicate that the accuracy of the standard mesh is sufficient for practical analyses. Refinement of the standard mesh is needed in analyses with high load levels well over the limit load of the structure

A retrospective and prospective survey of three-dimensional transport calculations

International Nuclear Information System (INIS)

Nakahara, Yasuaki

1985-01-01

A retrospective survey is made on the three-dimensional radiation transport calculations. Introduction is given to computer codes based on the distinctive numerical methods such as the Monte Carlo, Direct Integration, Ssub(n) and Finite Element Methods to solve the three-dimensional transport equations. Prospective discussions are made on pros and cons of these methods. (author)

1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method

Directory of Open Access Journals (Sweden)

Szu-Hsien Peng

2012-01-01

Full Text Available The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative finite volume method, splitting is applied to manage the combination of hyperbolic term and source term of the shallow water equation and then to promote 1D to 2D. The simulations are validated by the comparison with flume experiments. Unsteady dam-break flow movement is found to be reasonably well captured by the model. The proposed concept could be further developed to the numerical calculation of non-Newtonian fluid or multilayers fluid flow.

Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

Energy Technology Data Exchange (ETDEWEB)

Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.

2014-01-01

This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.

Finite energy electroweak dyon

Energy Technology Data Exchange (ETDEWEB)

Kimm, Kyoungtae [Seoul National University, Faculty of Liberal Education, Seoul (Korea, Republic of); Yoon, J.H. [Konkuk University, Department of Physics, College of Natural Sciences, Seoul (Korea, Republic of); Cho, Y.M. [Konkuk University, Administration Building 310-4, Seoul (Korea, Republic of); Seoul National University, School of Physics and Astronomy, Seoul (Korea, Republic of)

2015-02-01

The latest MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss three different ways to estimate the mass of the electroweak monopole. We first present the dimensional and scaling arguments which indicate the monopole mass to be around 4 to 10 TeV. To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strength at short distance. Our result demonstrates that a genuine electroweak monopole whose mass scale is much smaller than the grand unification scale can exist, which can actually be detected at the present LHC. (orig.)

A three-dimensional thermal finite element analysis of AISI 304 stainless steel and copper dissimilar weldment

Science.gov (United States)

Singh, Gurdeep; Saxena, Ravindra K.; Pandey, Sunil

2018-04-01

The aim of this study to developed a 3-D thermal finite element model for dissimilar material welding of AISI-304 stainless steel and copper. Welding of similar material is widely studied using experimental and numerical methods but the problem becomes trivial for the welding of dissimilar materials especially in ferrous and nonferrous materials. Finite element analysis of dissimilar material welding is a cost-effective method for the understanding and analysis of the process. The finite element analysis has been performed to predict the heat affected zone and temperature distribution in AISI-304 stainless steel and copper dissimilar weldment using MSC Marc 2017®. Due to the difference in physical properties of these materials the behavior of heat affected zone and temperature distribution are perceived to be different. To verify the accuracy of the thermal finite element model, the welding process was simulated with butt-welded joints having same dimensions and parameters from Attarha and Far [1]. It is found from the study that the heat affected zone is larger in copper weld pads than in AISI 304 stainless steel due to large difference in thermal conductivity of these two weld pads.

First Instances of Generalized Expo-Rational Finite Elements on Triangulations

Science.gov (United States)

Dechevsky, Lubomir T.; Zanaty, Peter; Laksa˚, Arne; Bang, Børre

2011-12-01

In this communication we consider a construction of simplicial finite elements on triangulated two-dimensional polygonal domains. This construction is, in some sense, dual to the construction of generalized expo-rational B-splines (GERBS). The main result is in the obtaining of new polynomial simplicial patches of the first several lowest possible total polynomial degrees which exhibit Hermite interpolatory properties. The derivation of these results is based on the theory of piecewise polynomial GERBS called Euler Beta-function B-splines. We also provide 3-dimensional visualization of the graphs of the new polynomial simplicial patches and their control polygons.

Behavior and Three-Dimensional Finite Element Modeling of Circular Concrete Columns Partially Wrapped with FRP Strips

Directory of Open Access Journals (Sweden)

Junjie Zeng

2018-03-01

Full Text Available Fiber-reinforced polymer (FRP jacketing/wrapping has become an attractive strengthening technique for concrete columns. Wrapping an existing concrete column with continuous FRP jackets with the fiber in the jacket being oriented in the hoop direction is referred to as FRP full wrapping strengthening technique. In practice, however, strengthening concrete columns with vertically discontinuous FRP strips is also favored and this technique is referred to as FRP partial wrapping strengthening technique. Existing research has demonstrated that FRP partial wrapping strengthening technique is a promising and economical alternative to the FRP full wrapping strengthening technique. Although extensive experimental investigations have hitherto been conducted on partially FRP-confined concrete columns, the confinement mechanics of confined concrete in partially FRP-confined circular columns remains unclear. In this paper, an experimental program consisting of fifteen column specimens was conducted and the test results were presented. A reliable three-dimensional (3D finite element (FE approach for modeling of partially FRP-confined circular columns was established. In the proposed FE approach, an accurate plastic-damage model for concrete under multiaxial compression is employed. The accuracy of the proposed FE approach was verified by comparisons between the numerical results and the test results. Numerical results from the verified FE approach were then presented to gain an improved understanding of the behavior of confined concrete in partially FRP-confined concrete columns.

Imaging x-ray sources at a finite distance in coded-mask instruments

International Nuclear Information System (INIS)

Donnarumma, Immacolata; Pacciani, Luigi; Lapshov, Igor; Evangelista, Yuri

2008-01-01

We present a method for the correction of beam divergence in finite distance sources imaging through coded-mask instruments. We discuss the defocusing artifacts induced by the finite distance showing two different approaches to remove such spurious effects. We applied our method to one-dimensional (1D) coded-mask systems, although it is also applicable in two-dimensional systems. We provide a detailed mathematical description of the adopted method and of the systematics introduced in the reconstructed image (e.g., the fraction of source flux collected in the reconstructed peak counts). The accuracy of this method was tested by simulating pointlike and extended sources at a finite distance with the instrumental setup of the SuperAGILE experiment, the 1D coded-mask x-ray imager onboard the AGILE (Astro-rivelatore Gamma a Immagini Leggero) mission. We obtained reconstructed images of good quality and high source location accuracy. Finally we show the results obtained by applying this method to real data collected during the calibration campaign of SuperAGILE. Our method was demonstrated to be a powerful tool to investigate the imaging response of the experiment, particularly the absorption due to the materials intercepting the line of sight of the instrument and the conversion between detector pixel and sky direction

Comparison of finite element and influence function methods for three-dimensional elastic analysis of boiling water reactor feedwater nozzle cracks. Phase report

International Nuclear Information System (INIS)

Besuner, P.M.; Caughey, W.R.

1976-11-01

The finite element (FE) and influence function (IF) methods are compared for a three-dimensional elastic analysis of postulated circular-shaped surface cracks in the feedwater nozzle of a typical boiling water reactor (BWR). These are two of the possible methods for determining stress intensity factors for nozzle corner cracks. The FE method is incorporated in a direct manner. The IF method is used to compute stress intensity factors only when the uncracked stress field (i.e., the stress in the uncracked solid at the locus of the crack to be eventually considered) has been computed previously. Both the IF and FE methods are described in detail and are applied to several test cases chosen for their similarity to the nozzle crack problem and for the availablility of an accurate published result obtained from some recognized third method of solution

Metastability of the (φiφi)32 model at finite temperature and density

International Nuclear Information System (INIS)

Ananos, G.N.J.; Malbouisson, A.P.C.; Svaiter, N.F.

1996-11-01

Using concurrently the dimensional and analytic regularization methods we applied the Gross-Neveu model at finite temperature and density (chemical potential) in a D-dimensional spacetime. The renormalized effective potential is presented at the one-loop approximation. In the case of non-zero chemical potential we show that the effective potential acquires an imaginary part, which means that the system becomes metastable, indicating the possibility of a first phase transition. (author)

INGEN: a general-purpose mesh generator for finite element codes

International Nuclear Information System (INIS)

Cook, W.A.

1979-05-01

INGEN is a general-purpose mesh generator for two- and three-dimensional finite element codes. The basic parts of the code are surface and three-dimensional region generators that use linear-blending interpolation formulas. These generators are based on an i, j, k index scheme that is used to number nodal points, construct elements, and develop displacement and traction boundary conditions. This code can generate truss elements (2 modal points); plane stress, plane strain, and axisymmetry two-dimensional continuum elements (4 to 8 nodal points); plate elements (4 to 8 nodal points); and three-dimensional continuum elements (8 to 21 nodal points). The traction loads generated are consistent with the element generated. The expansion--contraction option is of special interest. This option makes it possible to change an existing mesh such that some regions are refined and others are made coarser than the original mesh. 9 figures

SNAP - a three dimensional neutron diffusion code

International Nuclear Information System (INIS)

McCallien, C.W.J.

1993-02-01

This report describes a one- two- three-dimensional multi-group diffusion code, SNAP, which is primarily intended for neutron diffusion calculations but can also carry out gamma calculations if the diffusion approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. SNAP can solve the multi-group neutron diffusion equations using finite difference methods. The one-dimensional slab, cylindrical and spherical geometries and the two-dimensional case are all treated as simple special cases of three-dimensional geometries. Numerous reflective and periodic symmetry options are available and may be used to reduce the number of mesh points necessary to represent the system. Extrapolation lengths can be specified at internal and external boundaries. (Author)

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

Science.gov (United States)

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Three-dimensional magnetospheric equilibrium with isotropic pressure

International Nuclear Information System (INIS)

Cheng, C.Z.

1995-05-01

In the absence of the toroidal flux, two coupled quasi two-dimensional elliptic equilibrium equations have been derived to describe self-consistent three-dimensional static magnetospheric equilibria with isotropic pressure in an optimal (Ψ,α,χ) flux coordinate system, where Ψ is the magnetic flux function, χ is a generalized poloidal angle, α is the toroidal angle, α = φ - δ(Ψ,φ,χ) is the toroidal angle, δ(Ψ,φ,χ) is periodic in φ, and the magnetic field is represented as rvec B = ∇Ψ x ∇α. A three-dimensional magnetospheric equilibrium code, the MAG-3D code, has been developed by employing an iterative metric method. The main difference between the three-dimensional and the two-dimensional axisymmetric solutions is that the field-aligned current and the toroidal magnetic field are finite for the three-dimensional case, but vanish for the two-dimensional axisymmetric case. With the same boundary flux surface shape, the two-dimensional axisymmetric results are similar to the three-dimensional magnetosphere at each local time cross section

Analytic regularization of the Yukawa model at finite temperature

International Nuclear Information System (INIS)

Malbouisson, A.P.C.; Svaiter, N.F.; Svaiter, B.F.

1996-07-01

It is analysed the one-loop fermionic contribution for the scalar effective potential in the temperature dependent Yukawa model. Ir order to regularize the model a mix between dimensional and analytic regularization procedures is used. It is found a general expression for the fermionic contribution in arbitrary spacetime dimension. It is also found that in D = 3 this contribution is finite. (author). 19 refs

Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay

Czech Academy of Sciences Publication Activity Database

Chueshov, I.; Rezunenko, Oleksandr

2015-01-01

Roč. 14, č. 5 (2015), s. 1685-1704 ISSN 1534-0392 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Parabolic evolution equations * state-dependent delay * global attractor * finite-dimension * exponential attractor Subject RIV: BC - Control Systems Theory Impact factor: 0.926, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444705.pdf

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

Directory of Open Access Journals (Sweden)

Pavel A. Akimov

2017-12-01

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

Applications of energy-release-rate techniques to part-through cracks in plates and cylinders. Volume 2. ORVIRT: a finite element program for energy release rate calculations for 2-dimensional and 3-dimensional crack models

International Nuclear Information System (INIS)

Bass, B.R.; Bryson, J.W.

1983-02-01

Certain studies of fracture phenomena, such as pressurized-thermal-shock of cracked structures, require that crack tip parameters be determined for combined thermal and mechanical loads. A method is proposed here that modifies the isothermal formulation of deLorenzi to account for thermal strains in cracked bodies. The formulation has been implemented in the virtual-crack-extension program ORVIRT (Oak Ridge VIRTual-Crack-Extension). Program ORVIRT performs energy release rate calculations for both 2- and 3-dimensional nonlinear models of crack configurations in engineering structures. Two applications of the ORVIRT program are described. In the first, semielliptical surface cracks in an experimental test vessel are analyzed under elastic-plastic conditions using the finite element method. The second application is a thick-walled test vessel subjected to combined pressure and thermal shock loading

Classification problem for exactly integrable embeddings of two-dimensional manifolds and coefficients of the third fundametal forms

International Nuclear Information System (INIS)

Saveliev, M.V.

1983-01-01

A method is proposed for classification of exactly and completely integrable embeddings of two dimensional manifoilds into Riemann or non-Riemann enveloping space, which are based on the algebraic approach to the integration of nonlinear dynamical systems.Here the grading conditions and spectral structure of the Lax-pair operators taking the values in a graded Lie algebra that pick out the integrable class of nonlinear systems are formulated 1n terms of a structure of the 3-d fundamental form tensors. Corresponding to every embedding of three-dimensional subalgebra sb(2) into a simple finite-dimensional (infinite-dimensional of finite growth) Lie algebra L is a definite class of exactly (completely) integrable embeddings of two dimensional manifold into the corresponding enveloping space supplied with the structure of L

COYOTE: a finite element computer program for nonlinear heat conduction problems

International Nuclear Information System (INIS)

Gartling, D.K.

1978-06-01

COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program

Global and Local Mechanical Responses for Necking of Rectangular Bars Using Updated and Total Lagrangian Finite Element Formulations

Directory of Open Access Journals (Sweden)

Claudio A. Careglio

2016-01-01

Full Text Available In simulations of forged and stamping processes using the finite element method, load displacement paths and three-dimensional stress and strains states should be well and reliably represented. The simple tension test is a suitable and economical tool to calibrate constitutive equations with finite strains and plasticity for those simulations. A complex three-dimensional stress and strain states are developed when this test is done on rectangular bars and the necking phenomenon appears. In this work, global and local numerical results of the mechanical response of rectangular bars subjected to simple tension test obtained from two different finite element formulations are compared and discussed. To this end, Updated and Total Lagrangian formulations are used in order to get the three-dimensional stress and strain states. Geometric changes together with strain and stress distributions at the cross section where necking occurs are assessed. In particular, a detailed analysis of the effective plastic strain, stress components in axial and transverse directions and pressure, and deviatoric stress components is presented. Specific numerical results are also validated with experimental measurements comparing, in turn, the performance of the two numerical approaches used in this study.

Blockspin transformations for finite temperature field theories with gauge fields

International Nuclear Information System (INIS)

Kerres, U.

1996-08-01

A procedure is proposed to study quantum field theories at zero or at finite temperature by a sequence of real space renormalization group (RG) or blockspin transformations. They transform to effective theories on coarser and coarser lattices. The ultimate aim is to compute constraint effective potentials, i.e. the free energy as a function of suitable order parameters. From the free energy one can read off the thermodynamic behaviour of the theory, in particular the existence and nature of phase transitions. In a finite temperature field theory one begins with either one or a sequence of transformations which transform the original theory into an effective theory on a three-dimensional lattice. Its effective action has temperature dependent coefficients. Thereafter one may proceed with further blockspin transformations of the three-dimensional theory. Assuming a finite volume, this can in principle be continued until one ends with a lattice with a single site. Its effective action is the constraint effective potential. In each RG-step, an integral over the high frequency part of the field, also called the fluctuation field, has to be performed. This is done by perturbation theory. It requires the knowledge of bare fluctuation field propagators and of interpolation operators which enter into the vertices. A detailed examination of these quantities is presented for scalar fields, abelian gauge fields and for Higgs fields, finite temperature is admitted. The lattice perturbation theory is complicated because the bare lattice propagators are complicated. This is due to a partial loss of translation invariance in each step. Therefore the use of translation invariant cutoffs in place of a lattice is also discussed. In case of gauge fields this is only possible as a continuum version of the blockspin method. (orig.)

Chiral anomaly, fermionic determinant and two dimensional models

International Nuclear Information System (INIS)

Rego Monteiro, M.A. do.

1985-01-01

The chiral anomaly in random pair dimension is analysed. This anomaly is perturbatively calculated by dimensional regularization method. A new method for non-perturbative Jacobian calculation of a general chiral transformation, 1.e., finite and non-Abelian, is developed. This method is used for non-perturbative chiral anomaly calculation, as an alternative to bosonization of two-dimensional theories for massless fermions and to study the phenomenum of fermion number fractionalization. The fermionic determinant from two-dimensional quantum chromodynamics is also studied, and calculated, exactly, as in decoupling gauge as with out reference to a particular gauge. (M.C.K.) [pt

PRIAM: A self consistent finite element code for particle simulation in electromagnetic fields

International Nuclear Information System (INIS)

Le Meur, G.; Touze, F.

1990-06-01

A 2 1/2 dimensional, relativistic particle simulation code is described. A short review of the used mixed finite element method is given. The treatment of the driving terms (charge and current densities), initial, boundary conditions are exposed. Graphical results are shown

Boundary value problems of finite elasticity local theorems on existence, uniqueness, and analytic dependence on data

CERN Document Server

Valent, Tullio

1988-01-01

In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be­ sides being quite spontaneous, allows us to consider a great many inter­ esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis­ tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b]...

Positive operator semigroups from finite to infinite dimensions

CERN Document Server

Bátkai, András; Rhandi, Abdelaziz

2017-01-01

This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate t...

Simulating Photons and Plasmons in a Three-dimensional Lattice

International Nuclear Information System (INIS)

Pletzer, A.; Shvets, G.

2002-01-01

Three-dimensional metallic photonic structures are studied using a newly developed mixed finite element-finite difference (FE-FD) code, Curly3d. The code solves the vector Helmholtz equation as an eigenvalue problem in the unit cell of a triply periodic lattice composed of conductors and/or dielectrics. The mixed FE-FD discretization scheme ensures rapid numerical convergence of the eigenvalue and allows the code to run at low resolution. Plasmon and photonic band structure calculations are presented

Influence of implant number on the biomechanical behaviour of mandibular implant-retained/supported overdentures: a three-dimensional finite element analysis.

Science.gov (United States)

Liu, Jingyin; Pan, Shaoxia; Dong, Jing; Mo, Zhongjun; Fan, Yubo; Feng, Hailan

2013-03-01

The aim of this study was to evaluate strain distribution in peri-implant bone, stress in the abutments and denture stability of mandibular overdentures anchored by different numbers of implants under different loading conditions, through three-dimensional finite element analysis (3D FEA). Four 3D finite element models of mandibular overdentures were established, using between one and four Straumann implants with Locator attachments. Three types of load were applied to the overdenture in each model: 100N vertical and inclined loads on the left first molar and a 100N vertical load on the lower incisors. The biomechanical behaviours of peri-implant bone, implants, abutments and overdentures were recorded. Under vertical load on the lower incisors, the single-implant overdenture rotated over the implant from side to side, and no obvious increase of strain was found in peri-implant bone. Under the same loading conditions, the two-implant-retained overdenture showed more apparent rotation around the fulcrum line passing through the two implants, and the maximum equivalent stress in the abutments was higher than in the other models. In the three-implant-supported overdenture, no strain concentration was found in cortical bone around the middle implant under three loading conditions. Single-implant-retained mandibular overdentures do not show damaging strain concentration in the bone around the only implant and may be a cost-effective treatment option for edentulous patients. A third implant can be placed between the original two when patients rehabilitated by two-implant overdentures report constant and obvious denture rotation around the fulcrum line. Copyright © 2012 Elsevier Ltd. All rights reserved.

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

National Research Council Canada - National Science Library

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

2000-01-01

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

NACHOS: a finite element computer program for incompressible flow problems. Part I. Theoretical background

International Nuclear Information System (INIS)

Gartling, D.K.

1978-04-01

The theoretical background for the finite element computer program, NACHOS, is presented in detail. The NACHOS code is designed for the two-dimensional analysis of viscous incompressible fluid flows, including the effects of heat transfer. A general description of the fluid/thermal boundary value problems treated by the program is described. The finite element method and the associated numerical methods used in the NACHOS code are also presented. Instructions for use of the program are documented in SAND77-1334

Finite difference methods for reducing numerical diffusion in TEACH-type calculations. [Teaching Elliptic Axisymmetric Characteristics Heuristically

Science.gov (United States)

Syed, S. A.; Chiappetta, L. M.

1985-01-01

A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.

Matrix equation decomposition and parallel solution of systems resulting from unstructured finite element problems in electromagnetics

Energy Technology Data Exchange (ETDEWEB)

Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)

1996-12-31

Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.

[Stress analysis on the acetabular side of bipolar hemiarthroplasty by the two-dimensional finite element method incorporating the boundary friction layer].

Science.gov (United States)

Ichihashi, K; Imura, S; Oomori, H; Gesso, H

1994-11-01

We compared the biomechanical characteristics of bipolar and unipolar hemiarthroplasty on the proximal migration of the outer head by determining the von Mises stress distribution and acetabular (outer head) displacement with clinical assessment of hemiarthroplasty in 75 patients. This analysis used the two-dimensional finite element method, which incorporated boundary friction layers on both the inner and outer bearings of the prosthesis. Acetabular reaming increased stress within the pelvic bone and migration of the outer head. A combination of the acetabular reaming and bone transplantation increased the stress within the pelvic bone and grafted bone, and caused outer head migration. These findings were supported by clinical results. Although the bipolar endoprosthesis was biomechanically superior to the unipolar endoprosthesis, migration of the outer head still occurred. The bipolar endoprosthesis appeared to be indicated in cases of a femoral neck fracture or of avascular necrosis in the femoral head, but its use in cases of osteoarthritis in the hip required caution.

Finite element simulations of interactions between multiple hydraulic fractures in a poroelastic rock

DEFF Research Database (Denmark)

Salimzadeh, Saeed; Usui, Tomoya; Paluszny, Adriana

2017-01-01

A fully coupled three-dimensional finite-element model for hydraulic fractures in permeable rocks is presented, and used to investigate the ranges of applicability of the classical analytical solutions that are known to be valid in limiting cases. This model simultaneously accounts for fluid flow...

Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2003-01-01

We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

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

International Nuclear Information System (INIS)

Nkemzi, Boniface

2003-10-01

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

Conduction in rectangular quasi-one-dimensional and two-dimensional random resistor networks away from the percolation threshold.

Science.gov (United States)

Kiefer, Thomas; Villanueva, Guillermo; Brugger, Jürgen

2009-08-01

In this study we investigate electrical conduction in finite rectangular random resistor networks in quasione and two dimensions far away from the percolation threshold p(c) by the use of a bond percolation model. Various topologies such as parallel linear chains in one dimension, as well as square and triangular lattices in two dimensions, are compared as a function of the geometrical aspect ratio. In particular we propose a linear approximation for conduction in two-dimensional systems far from p(c), which is useful for engineering purposes. We find that the same scaling function, which can be used for finite-size scaling of percolation thresholds, also applies to describe conduction away from p(c). This is in contrast to the quasi-one-dimensional case, which is highly nonlinear. The qualitative analysis of the range within which the linear approximation is legitimate is given. A brief link to real applications is made by taking into account a statistical distribution of the resistors in the network. Our results are of potential interest in fields such as nanostructured or composite materials and sensing applications.

Interface fracture in laminates at three-dimensional corners

Energy Technology Data Exchange (ETDEWEB)

Myhre Jensen, H.; Veluri, B. [Aarhus Univ.. Aarhus School of Engineering, Aarhus (Denmark)

2012-07-01

Interface failure close to corners has been observed in laminated layered structures. A fracture mechanics based approach focused on modelling the shape of such interface cracks and calculating the critical stress for steady-state propagation has been developed. The crack propagation is investigated by estimating the fracture mechanics parameters including the energy release rate and the three-dimensional mode-mixity along the crack front allowing determining the shape of the crack front profiles. A numerical approach is applied for coupling the far field solutions utilizing the capability of the Finite Element Method to the near field solutions at the crack front based on the J-integral. The developed two-dimensional numerical approach for the calculation of fracture mechanical properties has been validated with three-dimensional models for varying crack front shapes. In this study, a quantitative approach was formulated based on the finite element method with iterative adjustment of the crack front to estimate the critical delamination stress as a function of the fracture criterion and corner angles. The implication of the results on the delamination is discussed in terms of crack front profiles and the critical stresses. (Author)

Finite element modelling

International Nuclear Information System (INIS)

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

2015-01-01

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

High dimensional model representation method for fuzzy structural dynamics

Science.gov (United States)

Adhikari, S.; Chowdhury, R.; Friswell, M. I.

2011-03-01

Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.