Exploiting symmetries in the modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Andersen, Carl M.; Tanner, John A.

1987-01-01

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Spin-dependent μ → e conversion

DOE PAGES

Cirigliano, Vincenzo; Davidson, Sacha; Kuno, Yoshitaka

2017-05-22

The experimental sensitivity to μ→e conversion on nuclei is expected to improve by four orders of magnitude in coming years. Here, we consider the impact of μ→e flavour-changing tensor and axial-vector four-fermion operators which couple to the spin of nucleons. Such operators, which have not previously been considered, contribute to μ→e conversion in three ways: in nuclei with spin they mediate a spin-dependent transition; in all nuclei they contribute to the coherent (A 2-enhanced) spin-independent conversion via finite recoil effects and via loop mixing with dipole, scalar, and vector operators. Furthermore, we estimate the spin-dependent rate in Aluminium (the targetmore » of the upcoming COMET and Mu2e experiments), show that the loop effects give the greatest sensitivity to tensor and axial-vector operators involving first-generation quarks, and discuss the complementarity of the spin-dependent and independent contributions to μ→e conversion.« less

Spin-dependent μ → e conversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cirigliano, Vincenzo; Davidson, Sacha; Kuno, Yoshitaka

The experimental sensitivity to μ→e conversion on nuclei is expected to improve by four orders of magnitude in coming years. Here, we consider the impact of μ→e flavour-changing tensor and axial-vector four-fermion operators which couple to the spin of nucleons. Such operators, which have not previously been considered, contribute to μ→e conversion in three ways: in nuclei with spin they mediate a spin-dependent transition; in all nuclei they contribute to the coherent (A 2-enhanced) spin-independent conversion via finite recoil effects and via loop mixing with dipole, scalar, and vector operators. Furthermore, we estimate the spin-dependent rate in Aluminium (the targetmore » of the upcoming COMET and Mu2e experiments), show that the loop effects give the greatest sensitivity to tensor and axial-vector operators involving first-generation quarks, and discuss the complementarity of the spin-dependent and independent contributions to μ→e conversion.« less

Vector two-point functions in finite volume using partially quenched chiral perturbation theory at two loops

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Relefors, Johan

2017-12-01

We calculate vector-vector correlation functions at two loops using partially quenched chiral perturbation theory including finite volume effects and twisted boundary conditions. We present expressions for the flavor neutral cases and the flavor charged case with equal masses. Using these expressions we give an estimate for the ratio of disconnected to connected contributions for the strange part of the electromagnetic current. We give numerical examples for the effects of partial quenching, finite volume and twisting and suggest the use of different twists to check the size of finite volume effects. The main use of this work is expected to be for lattice QCD calculations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

Renormalizable Electrodynamics of Scalar and Vector Mesons. Part II

DOE R&D Accomplishments Database

Salam, Abdus; Delbourgo, Robert

1964-01-01

The "gauge" technique" for solving theories introduced in an earlier paper is applied to scalar and vector electrodynamics. It is shown that for scalar electrodynamics, there is no {lambda}φ*2φ2 infinity in the theory, while with conventional subtractions vector electrodynamics is completely finite. The essential ideas of the gauge technique are explained in section 3, and a preliminary set of rules for finite computation in vector electrodynamics is set out in Eqs. (7.28) - (7.34).

Vector Third Moment of Turbulent MHD Fluctuations: Theory and Interpretation

NASA Astrophysics Data System (ADS)

Forman, M. A.; MacBride, B. T.; Smith, C. W.

2006-12-01

We call attention to the fact that a certain vector third moment of turbulent MHD fluctuations, even if they are anisotropic, obeys an exact scaling relation in the inertial range. Politano and Pouquet (1998, PP) proved it from the MHD equations specifically. It is a direct analog of the long-known von Karman-Howarth-Monin (KHM) vector relation in anisotropic hydrodynamic turbulence, which follows from the Navier-Stokes equations (see Frisch, 1995). The relevant quantities in MHD are the plus and minus Elsasser vectors and their fluctuations over vector spatial differences. These are used in the mixed vector third moment S+/-(r). The mixed moment is essential, because in the MHD equations for the Elsasser variables, the z + and z- are mixed in the non-linear term. The PP relation is div (S+/-(r))= -4*(epsilon +/-) where (epsilon +/-) is the turbulent energy dissipation rate in the +/- cascade, in Joules/(kg-sec). Of the many possible vector and tensor third moments of MHD vector fluctuations, S+/-(r) is the only one known to have an exact (although vector differential) scaling valid in anisotropic MHD in the inertial range. The PP scaling of a distinctly non-zero third moment indicates that an inertial range cascade is present. The PP scaling does NOT simply result from a dimensional argument, but is derived directly from the MHD equations. A power-law power spectrum alone does not necessarily imply an inertial cascade is present. Furthermore, only the scaling of S+/-(r) gives the epsilon +/- directly. Earlier methods of determining epsilon +/-, based on the amplitude of the power spectrum, make assumptions about isotropy, Alfvenicity and scaling that are not exact. Thus, the observation of a finite S+/-(r) and its scaling with vector r, are fundamental to MHD turbulence in the solar wind, or in any magnetized plasma. We are engaged in evaluating S+/-(r )and its anisotropic scaling in the solar wind, beginning with ACE field and plasma data. For this, we are using the Taylor hypothesis that r = Vt, where t is a time lag of fluctuations seen at a single spacecraft. Because we use a forward time lag, we actually measure -S+/-(r ) which is positive in a direct cascade. We report some results in an accompanying poster. This presentation concentrates on the theory, and how the results are to be interpreted. References: Frisch, U., Turbulence, Cambridge U. Press, 1995, p. 78 Politano, H. and Pouquet, A. Geophys. Res. Lett., 25, 273, 1998

Discontinuous finite element method for vector radiative transfer

NASA Astrophysics Data System (ADS)

Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping

2017-03-01

The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.

Time-reversal and rotation symmetry breaking superconductivity in Dirac materials

NASA Astrophysics Data System (ADS)

Chirolli, Luca; de Juan, Fernando; Guinea, Francisco

2017-05-01

We consider mixed symmetry superconducting phases in Dirac materials in the odd-parity channel, where pseudoscalar and vector order parameters can coexist due to their similar critical temperatures when attractive interactions are of a finite range. We show that the coupling of these order parameters to unordered magnetic dopants favors the condensation of time-reversal symmetry breaking (TRSB) phases, characterized by a condensate magnetization, rotation symmetry breaking, and simultaneous ordering of the dopant moments. We find a rich phase diagram of mixed TRSB phases characterized by peculiar bulk quasiparticles, with Weyl nodes and nodal lines, and distinctive surface states. These findings are consistent with recent experiments on NbxBi2Se3 that report evidence of point nodes, nematicity, and TRSB superconductivity induced by Nb magnetic moments.

Flux vector splitting of the inviscid equations with application to finite difference methods

NASA Technical Reports Server (NTRS)

Steger, J. L.; Warming, R. F.

1979-01-01

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Recent advances in reduction methods for nonlinear problems. [in structural mechanics

NASA Technical Reports Server (NTRS)

Noor, A. K.

1981-01-01

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

Prediction of shear critical behavior of high-strength reinforced concrete columns using finite element methods

NASA Astrophysics Data System (ADS)

Alrasyid, Harun; Safi, Fahrudin; Iranata, Data; Chen-Ou, Yu

2017-11-01

This research shows the prediction of shear behavior of High-Strength Reinforced Concrete Columns using Finite-Element Method. The experimental data of nine half scale high-strength reinforced concrete were selected. These columns using specified concrete compressive strength of 70 MPa, specified yield strength of longitudinal and transverse reinforcement of 685 and 785 MPa, respectively. The VecTor2 finite element software was used to simulate the shear critical behavior of these columns. The combination axial compression load and monotonic loading were applied at this prediction. It is demonstrated that VecTor2 finite element software provides accurate prediction of load-deflection up to peak at applied load, but provide similar behavior at post peak load. The shear strength prediction provide by VecTor 2 are slightly conservative compare to test result.

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

PubMed

Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

2014-01-01

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Aguanno, G.; Mattiucci, N.; C. M. Bowden Facility, Building 7804, RDECOM, Redstone Arsenal, Alabama 35898

2010-01-15

We have investigated and experimentally demonstrated the applicability of the Bloch vector for one-dimensional, nonlinear, finite, dissipative systems. The case studied is the second harmonic generation from metallodielectric multilayer filters. In particular, we have applied the Bloch vector analysis to Ag/Ta{sub 2}O{sub 5} thin-film multilayer samples and shown the importance of the phase matching calculated through the Bloch vector. The nonlinear coefficients extracted from experimental results are consistent with previous studies. Nowadays, metal-based nanostructures play a fundamental role in nonlinear nanophotonics and nanoplasmonics. Our results clearly suggest that even in these forefront fields the Bloch vector continues to play anmore » essential role.« less

Mutation-selection equilibrium in games with mixed strategies.

PubMed

Tarnita, Corina E; Antal, Tibor; Nowak, Martin A

2009-11-07

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an nxn payoff matrix. Players can use mixed strategies, which are given by the vector (p(1),...,p(n)). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S(n). We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.

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

NASA Astrophysics Data System (ADS)

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.

Spin polarized phases in strongly interacting matter: Interplay between axial-vector and tensor mean fields

NASA Astrophysics Data System (ADS)

Maruyama, Tomoyuki; Nakano, Eiji; Yanase, Kota; Yoshinaga, Naotaka

2018-06-01

The spontaneous spin polarization of strongly interacting matter due to axial-vector- and tensor-type interactions is studied at zero temperature and high baryon-number densities. We start with the mean-field Lagrangian for the axial-vector and tensor interaction channels and find in the chiral limit that the spin polarization due to the tensor mean field (U ) takes place first as the density increases for sufficiently strong coupling constants, and then the spin polarization due to the axial-vector mean field (A ) emerges in the region of the finite tensor mean field. This can be understood as making the axial-vector mean-field finite requires a broken chiral symmetry somehow, which is achieved by the finite tensor mean field in the present case. It is also found from the symmetry argument that there appear the type I (II) Nambu-Goldstone modes with a linear (quadratic) dispersion in the spin polarized phase with U ≠0 and A =0 (U ≠0 and A ≠0 ), although these two phases exhibit the same symmetry breaking pattern.

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

NASA Technical Reports Server (NTRS)

Rodal, J. J. A.; Witmer, E. A.

1979-01-01

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

On the effects of grid ill-conditioning in three dimensional finite element vector potential magnetostatic field computations

NASA Technical Reports Server (NTRS)

Wang, R.; Demerdash, N. A.

1990-01-01

The effects of finite element grid geometries and associated ill-conditioning were studied in single medium and multi-media (air-iron) three dimensional magnetostatic field computation problems. The sensitivities of these 3D field computations to finite element grid geometries were investigated. It was found that in single medium applications the unconstrained magnetic vector potential curl-curl formulation in conjunction with first order finite elements produce global results which are almost totally insensitive to grid geometries. However, it was found that in multi-media (air-iron) applications first order finite element results are sensitive to grid geometries and consequent elemental shape ill-conditioning. These sensitivities were almost totally eliminated by means of the use of second order finite elements in the field computation algorithms. Practical examples are given in this paper to demonstrate these aspects mentioned above.

Recent Development of Multigrid Algorithms for Mixed and Noncomforming Methods for Second Order Elliptical Problems

NASA Technical Reports Server (NTRS)

Chen, Zhangxin; Ewing, Richard E.

1996-01-01

Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.

The limitations of staggered grid finite differences in plasticity problems

NASA Astrophysics Data System (ADS)

Pranger, Casper; Herrendörfer, Robert; Le Pourhiet, Laetitia

2017-04-01

Most crustal-scale applications operate at grid sizes much larger than those at which plasticity occurs in nature. As a consequence, plastic shear bands often localize to the scale of one grid cell, and numerical ploys — like introducing an artificial length scale — are needed to counter this. If for whatever reasons (good or bad) this is not done, we find that problems may arise due to the fact that in the staggered grid finite difference discretization, unknowns like components of the stress tensor and velocity vector are located in physically different positions. This incurs frequent interpolation, reducing the accuracy of the discretization. For purely stress-dependent plasticity problems the adverse effects might be contained because the magnitude of the stress discontinuity across a plastic shear band is limited. However, we find that when rate-dependence of friction is added in the mix, things become ugly really fast and the already hard-to-solve and highly nonlinear problem of plasticity incurs an extra penalty.

Vectorized Jiles-Atherton hysteresis model

NASA Astrophysics Data System (ADS)

Szymański, Grzegorz; Waszak, Michał

2004-01-01

This paper deals with vector hysteresis modeling. A vector model consisting of individual Jiles-Atherton components placed along principal axes is proposed. The cross-axis coupling ensures general vector model properties. Minor loops are obtained using scaling method. The model is intended for efficient finite element method computations defined in terms of magnetic vector potential. Numerical efficiency is ensured by differential susceptibility approach.

Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.

1991-01-01

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES

PubMed Central

GILLETTE, ANDREW; RAND, ALEXANDER; BAJAJ, CHANDRAJIT

2016-01-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties. PMID:28077939

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES.

PubMed

Gillette, Andrew; Rand, Alexander; Bajaj, Chandrajit

2016-10-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties.

Elastic-plastic mixed-iterative finite element analysis: Implementation and performance assessment

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

An elastic-plastic algorithm based on Von Mises and associative flow criteria is implemented in MHOST-a mixed iterative finite element analysis computer program developed by NASA Lewis Research Center. The performance of the resulting elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors of 4-node quadrilateral shell finite elements are tested for elastic-plastic performance. Generally, the membrane results are excellent, indicating the implementation of elastic-plastic mixed-iterative analysis is appropriate.

A survey of mixed finite element methods

NASA Technical Reports Server (NTRS)

Brezzi, F.

1987-01-01

This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.

Finite time synchronization of memristor-based Cohen-Grossberg neural networks with mixed delays.

PubMed

Chen, Chuan; Li, Lixiang; Peng, Haipeng; Yang, Yixian

2017-01-01

Finite time synchronization, which means synchronization can be achieved in a settling time, is desirable in some practical applications. However, most of the published results on finite time synchronization don't include delays or only include discrete delays. In view of the fact that distributed delays inevitably exist in neural networks, this paper aims to investigate the finite time synchronization of memristor-based Cohen-Grossberg neural networks (MCGNNs) with both discrete delay and distributed delay (mixed delays). By means of a simple feedback controller and novel finite time synchronization analysis methods, several new criteria are derived to ensure the finite time synchronization of MCGNNs with mixed delays. The obtained criteria are very concise and easy to verify. Numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

NASA Astrophysics Data System (ADS)

Bause, Markus

2008-02-01

In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is observed, which however is less significant for the accompanying solute transport.

Wave-vector and polarization dependent impedance model for a hexagonal periodic metasurface exemplified through finite-difference time-domain simulations.

PubMed

Ding, Yi S; He, Yang

2017-08-21

An isotropic impedance sheet model is proposed for a loop-type hexagonal periodic metasurface. Both frequency and wave-vector dispersion are considered near the resonance frequency. Therefore both the angle and polarization dependences of the metasurface impedance can be properly and simultaneously described in our model. The constitutive relation of this model is transformed into auxiliary differential equations which are integrated into the finite-difference time-domain algorithm. Finally, a finite large metasurface sample under oblique illumination is used to test the model and the algorithm. Our model and algorithm can significantly increase the accuracy of the homogenization methods for modeling periodic metasurfaces.

A hybrid LBG/lattice vector quantizer for high quality image coding

NASA Technical Reports Server (NTRS)

Ramamoorthy, V.; Sayood, K.; Arikan, E. (Editor)

1991-01-01

It is well known that a vector quantizer is an efficient coder offering a good trade-off between quantization distortion and bit rate. The performance of a vector quantizer asymptotically approaches the optimum bound with increasing dimensionality. A vector quantized image suffers from the following types of degradations: (1) edge regions in the coded image contain staircase effects, (2) quasi-constant or slowly varying regions suffer from contouring effects, and (3) textured regions lose details and suffer from granular noise. All three of these degradations are due to the finite size of the code book, the distortion measures used in the design, and due to the finite training procedure involved in the construction of the code book. In this paper, we present an adaptive technique which attempts to ameliorate the edge distortion and contouring effects.

Nucleon form factors with 2+1 flavor dynamical domain-wall fermions

NASA Astrophysics Data System (ADS)

Yamazaki, Takeshi; Aoki, Yasumichi; Blum, Tom; Lin, Huey-Wen; Ohta, Shigemi; Sasaki, Shoichi; Tweedie, Robert; Zanotti, James

2009-06-01

We report our numerical lattice QCD calculations of the isovector nucleon form factors for the vector and axial-vector currents: the vector, induced tensor, axial-vector, and induced pseudoscalar form factors. The calculation is carried out with the gauge configurations generated with Nf=2+1 dynamical domain-wall fermions and Iwasaki gauge actions at β=2.13, corresponding to a cutoff a-1=1.73GeV, and a spatial volume of (2.7fm)3. The up and down-quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange quark mass is about 12% heavier than the physical one. We calculate the form factors in the range of momentum transfers, 0.26 is required to ensure that finite-volume effects are below 1%.

αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Ambra, P.; Vassilevski, P. S.

2014-05-30

Adaptive Algebraic Multigrid (or Multilevel) Methods (αAMG) are introduced to improve robustness and efficiency of classical algebraic multigrid methods in dealing with problems where no a-priori knowledge or assumptions on the near-null kernel of the underlined matrix are available. Recently we proposed an adaptive (bootstrap) AMG method, αAMG, aimed to obtain a composite solver with a desired convergence rate. Each new multigrid component relies on a current (general) smooth vector and exploits pairwise aggregation based on weighted matching in a matrix graph to define a new automatic, general-purpose coarsening process, which we refer to as “the compatible weighted matching”. Inmore » this work, we present results that broaden the applicability of our method to different finite element discretizations of elliptic PDEs. In particular, we consider systems arising from displacement methods in linear elasticity problems and saddle-point systems that appear in the application of the mixed method to Darcy problems.« less

Application of the control volume mixed finite element method to a triangular discretization

USGS Publications Warehouse

Naff, R.L.

2012-01-01

A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

NASA Technical Reports Server (NTRS)

Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.

1990-01-01

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

A Mixed Finite Volume Element Method for Flow Calculations in Porous Media

NASA Technical Reports Server (NTRS)

Jones, Jim E.

1996-01-01

A key ingredient in the simulation of flow in porous media is the accurate determination of the velocities that drive the flow. The large scale irregularities of the geology, such as faults, fractures, and layers suggest the use of irregular grids in the simulation. Work has been done in applying the finite volume element (FVE) methodology as developed by McCormick in conjunction with mixed methods which were developed by Raviart and Thomas. The resulting mixed finite volume element discretization scheme has the potential to generate more accurate solutions than standard approaches. The focus of this paper is on a multilevel algorithm for solving the discrete mixed FVE equations. The algorithm uses a standard cell centered finite difference scheme as the 'coarse' level and the more accurate mixed FVE scheme as the 'fine' level. The algorithm appears to have potential as a fast solver for large size simulations of flow in porous media.

Full Wave Analysis of RF Signal Attenuation in a Lossy Cave using a High Order Time Domain Vector Finite Element Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pingenot, J; Rieben, R; White, D

2004-12-06

We present a computational study of signal propagation and attenuation of a 200 MHz dipole antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The simulation is performed for a series of random meshes in order to generate statistical data for the propagation and attenuation properties of the cave environment. Results for the power spectral density and phase ofmore » the electric field vector components are presented and discussed.« less

Multigrid Equation Solvers for Large Scale Nonlinear Finite Element Simulations

DTIC Science & Technology

1999-01-01

purpose of the second partitioning phase , on each SMP, is to minimize the communication within the SMP; even if a multi - threaded matrix vector product...8.7 Comparison of model with experimental data for send phase of matrix vector product on ne grid...140 8.4 Matrix vector product phase times : : : : : : : : : : : : : : : : : : : : : : : 145 9.1 Flat and

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Finite element modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, A. K.; Andersen, C. M.

1983-01-01

Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Reynolds number effects on mixing due to topological chaos.

PubMed

Smith, Spencer A; Warrier, Sangeeta

2016-03-01

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for three different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finite-order protocols, they actually exhibit non-monotonic behavior for the pseudo-Anosov protocol.

Gradients estimation from random points with volumetric tensor in turbulence

NASA Astrophysics Data System (ADS)

Watanabe, Tomoaki; Nagata, Koji

2017-12-01

We present an estimation method of fully-resolved/coarse-grained gradients from randomly distributed points in turbulence. The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3 × 3 matrix determined by a geometric distribution of the points. The coarse grained gradient can be considered as a low pass filtered gradient, whose cutoff is estimated with the eigenvalues of the volumetric tensor. The present method, the volumetric tensor approximation, is tested for velocity and passive scalar gradients in incompressible planar jet and mixing layer. Comparison with a finite difference approximation on a Cartesian grid shows that the volumetric tensor approximation computes the coarse grained gradients fairly well at a moderate computational cost under various conditions of spatial distributions of points. We also show that imposing the solenoidal condition improves the accuracy of the present method for solenoidal vectors, such as a velocity vector in incompressible flows, especially when the number of the points is not large. The volumetric tensor approximation with 4 points poorly estimates the gradient because of anisotropic distribution of the points. Increasing the number of points from 4 significantly improves the accuracy. Although the coarse grained gradient changes with the cutoff length, the volumetric tensor approximation yields the coarse grained gradient whose magnitude is close to the one obtained by the finite difference. We also show that the velocity gradient estimated with the present method well captures the turbulence characteristics such as local flow topology, amplification of enstrophy and strain, and energy transfer across scales.

Navier-Stokes solution on the CYBER-203 by a pseudospectral technique

NASA Technical Reports Server (NTRS)

Lambiotte, J. J.; Hussaini, M. Y.; Bokhari, S.; Orszag, S. A.

1983-01-01

A three-level, time-split, mixed spectral/finite difference method for the numerical solution of the three-dimensional, compressible Navier-Stokes equations has been developed and implemented on the Control Data Corporation (CDC) CYBER-203. This method uses a spectral representation for the flow variables in the streamwise and spanwise coordinates, and central differences in the normal direction. The five dependent variables are interleaved one horizontal plane at a time and the array of their values at the grid points of each horizontal plane is a typical vector in the computation. The code is organized so as to require, per time step, a single forward-backward pass through the entire data base. The one-and two-dimensional Fast Fourier Transforms are performed using software especially developed for the CYBER-203.

Dynamic analysis of suspension cable based on vector form intrinsic finite element method

NASA Astrophysics Data System (ADS)

Qin, Jian; Qiao, Liang; Wan, Jiancheng; Jiang, Ming; Xia, Yongjun

2017-10-01

A vector finite element method is presented for the dynamic analysis of cable structures based on the vector form intrinsic finite element (VFIFE) and mechanical properties of suspension cable. Firstly, the suspension cable is discretized into different elements by space points, the mass and external forces of suspension cable are transformed into space points. The structural form of cable is described by the space points at different time. The equations of motion for the space points are established according to the Newton’s second law. Then, the element internal forces between the space points are derived from the flexible truss structure. Finally, the motion equations of space points are solved by the central difference method with reasonable time integration step. The tangential tension of the bearing rope in a test ropeway with the moving concentrated loads is calculated and compared with the experimental data. The results show that the tangential tension of suspension cable with moving loads is consistent with the experimental data. This method has high calculated precision and meets the requirements of engineering application.

Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

New vector-like fermions and flavor physics

DOE PAGES

Ishiwata, Koji; Ligeti, Zoltan; Wise, Mark B.

2015-10-06

We study renormalizable extensions of the standard model that contain vector-like fermions in a (single) complex representation of the standard model gauge group. There are 11 models where the vector-like fermions Yukawa couple to the standard model fermions via the Higgs field. These models do not introduce additional fine-tunings. They can lead to, and are constrained by, a number of different flavor-changing processes involving leptons and quarks, as well as direct searches. An interesting feature of the models with strongly interacting vector-like fermions is that constraints from neutral meson mixings (apart from CP violation inmore » $$ {K}^0-{\\overline{K}}^0 $$ mixing) are not sensitive to higher scales than other flavor-changing neutral-current processes. We identify order 1/(4πM) 2 (where M is the vector-like fermion mass) one-loop contributions to the coefficients of the four-quark operators for meson mixing, that are not suppressed by standard model quark masses and/or mixing angles.« less

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

NASA Astrophysics Data System (ADS)

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-10-01

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.

Cranking of Nuclei at Finite Temperature:

NASA Astrophysics Data System (ADS)

Bartel, J.; Bencheikh, K.; Quentin, P.

We present a generalization of the Extended Thomas Fermi (ETF) theory to fermionic systems at finite temperature and finite angular momentum. In fact the present approach is more general in the sense that it is able to treat an excited system of fermions subject to an external vector field which in the case of nuclear rotations, developed more extensively here, is simply ěc{r}×ěc{ω }.

Lattice study of finite volume effect in HVP for muon g-2

NASA Astrophysics Data System (ADS)

Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo

2018-03-01

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brito, K. D.; Sprague, M. A.

2012-10-01

Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for amore » given model size or total computation time.« less

Effects of Crimped Fiber Paths on Mixed Mode Delamination Behaviors in Woven Fabric Composites

DTIC Science & Technology

2016-09-01

continuum finite - element models. Three variations of a plain-woven fabric architecture—each of which had different crimped fiber paths—were considered... Finite - Element Analysis Fracture Mechanics Fracture Toughness Mixed Modes Strain Energy Release Rate 16. SECURITY...polymer FB Fully balanced laminate FEA Finite - element analysis FTCM Fracture toughness conversion mechanism G Shear modulus GI, GII, GIII Mode

Numerical simulation using vorticity-vector potential formulation

NASA Technical Reports Server (NTRS)

Tokunaga, Hiroshi

1993-01-01

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Explicit time integration of finite element models on a vectorized, concurrent computer with shared memory

NASA Technical Reports Server (NTRS)

Gilbertsen, Noreen D.; Belytschko, Ted

1990-01-01

The implementation of a nonlinear explicit program on a vectorized, concurrent computer with shared memory is described and studied. The conflict between vectorization and concurrency is described and some guidelines are given for optimal block sizes. Several example problems are summarized to illustrate the types of speed-ups which can be achieved by reprogramming as compared to compiler optimization.

Electric and magnetic superlattices in trilayer graphene

NASA Astrophysics Data System (ADS)

Uddin, Salah; Chan, K. S.

2016-01-01

The properties of one dimensional Kronig-Penney type of periodic electric and vector potential on ABC-trilayer graphene superlattices are investigated. The energy spectra obtained with periodic vector potentials shows the emergence of extra Dirac points in the energy spectrum with finite energies. For identical barrier and well widths, the original as well as the extra Dirac points are located in the ky = 0 plane. An asymmetry between the barrier and well widths causes a shift in the extra Dirac points away from the ky = 0 plane. Extra Dirac points having same electron hole crossing energy as that of the original Dirac point as well as finite energy Dirac points are generated in the energy spectrum when periodic electric potential is applied to the system. By applying electric and vector potential together, the symmetry of the energy spectrum about the Fermi level is broken. A tunable band gap is induced in the energy spectrum by applying both electric and vector potential simultaneously with different barrier and well widths.

Lie-Hamilton systems on the plane: Properties, classification and applications

NASA Astrophysics Data System (ADS)

Ballesteros, A.; Blasco, A.; Herranz, F. J.; de Lucas, J.; Sardón, C.

2015-04-01

We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian vector fields with respect to a Poisson structure. We start with the local classification of finite-dimensional real Lie algebras of vector fields on the plane obtained in González-López, Kamran, and Olver (1992) [23] and we interpret their results as a local classification of Lie systems. By determining which of these real Lie algebras consist of Hamiltonian vector fields relative to a Poisson structure, we provide the complete local classification of Lie-Hamilton systems on the plane. We present and study through our results new Lie-Hamilton systems of interest which are used to investigate relevant non-autonomous differential equations, e.g. we get explicit local diffeomorphisms between such systems. We also analyse biomathematical models, the Milne-Pinney equations, second-order Kummer-Schwarz equations, complex Riccati equations and Buchdahl equations.

Mixed time integration methods for transient thermal analysis of structures, appendix 5

NASA Technical Reports Server (NTRS)

Liu, W. K.

1982-01-01

Mixed time integration methods for transient thermal analysis of structures are studied. An efficient solution procedure for predicting the thermal behavior of aerospace vehicle structures was developed. A 2D finite element computer program incorporating these methodologies is being implemented. The performance of these mixed time finite element algorithms can then be evaluated employing the proposed example problem.

Material nonlinear analysis via mixed-iterative finite element method

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1992-01-01

The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.

Model-Independent Bounds on Kinetic Mixing

DOE PAGES

Hook, Anson; Izaguirre, Eder; Wacker, Jay G.

2011-01-01

New Abelimore » an vector bosons can kinetically mix with the hypercharge gauge boson of the Standard Model. This letter computes the model-independent limits on vector bosons with masses from 1 GeV to 1 TeV. The limits arise from the numerous e + e − experiments that have been performed in this energy range and bound the kinetic mixing by ϵ ≲ 0.03 for most of the mass range studied, regardless of any additional interactions that the new vector boson may have.« less

Reynolds number effects on mixing due to topological chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Spencer A.; Warrier, Sangeeta

2016-03-15

Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for threemore » different stirring protocols, one topologically complex (pseudo-Anosov) and two simple (finite-order), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudo-Anosov protocol over the finite-order protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finite-order protocols, they actually exhibit non-monotonic behavior for the pseudo-Anosov protocol.« less

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

Nilpotent representations of classical quantum groups at roots of unity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abe, Yuuki; Nakashima, Toshiki

2005-11-01

Properly specializing the parameters in 'Schnizer modules', for types A,B,C, and D, we get its unique primitive vector. Then we show that the module generated by the primitive vector is an irreducible highest weight module of finite dimensional classical quantum groups at roots of unity.

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

An analysis of cross-coupling of a multicomponent jet engine test stand using finite element modeling techniques

NASA Technical Reports Server (NTRS)

Schweikhard, W. G.; Singnoi, W. N.

1985-01-01

A two axis thrust measuring system was analyzed by using a finite a element computer program to determine the sensitivities of the thrust vectoring nozzle system to misalignment of the load cells and applied loads, and the stiffness of the structural members. Three models were evaluated: (1) the basic measuring element and its internal calibration load cells; (2) the basic measuring element and its external load calibration equipment; and (3) the basic measuring element, external calibration load frame and the altitude facility support structure. Alignment of calibration loads was the greatest source of error for multiaxis thrust measuring systems. Uniform increases or decreases in stiffness of the members, which might be caused by the selection of the materials, have little effect on the accuracy of the measurements. It is found that the POLO-FINITE program is a viable tool for designing and analyzing multiaxis thrust measurement systems. The response of the test stand to step inputs that might be encountered with thrust vectoring tests was determined. The dynamic analysis show a potential problem for measuring the dynamic response characteristics of thrust vectoring systems because of the inherently light damping of the test stand.

A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation

NASA Technical Reports Server (NTRS)

Crivelli, Luis A.; Felippa, Carlos A.

1992-01-01

A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.

Analysis of Flexible Bars and Frames with Large Displacements of Nodes By Finite Element Method in the Form of Classical Mixed Method

NASA Astrophysics Data System (ADS)

Ignatyev, A. V.; Ignatyev, V. A.; Onischenko, E. V.

2017-11-01

This article is the continuation of the work made bt the authors on the development of the algorithms that implement the finite element method in the form of a classical mixed method for the analysis of geometrically nonlinear bar systems [1-3]. The paper describes an improved algorithm of the formation of the nonlinear governing equations system for flexible plane frames and bars with large displacements of nodes based on the finite element method in a mixed classical form and the use of the procedure of step-by-step loading. An example of the analysis is given.

Estimating finite-population reproductive numbers in heterogeneous populations.

PubMed

Keegan, Lindsay T; Dushoff, Jonathan

2016-05-21

The basic reproductive number, R0, is one of the most important epidemiological quantities. R0 provides a threshold for elimination and determines when a disease can spread or when a disease will die out. Classically, R0 is calculated assuming an infinite population of identical hosts. Previous work has shown that heterogeneity in the host mixing rate increases R0 in an infinite population. However, it has been suggested that in a finite population, heterogeneity in the mixing rate may actually decrease the finite-population reproductive numbers. Here, we outline a framework for discussing different types of heterogeneity in disease parameters, and how these affect disease spread and control. We calculate "finite-population reproductive numbers" with different types of heterogeneity, and show that in a finite population, heterogeneity has complicated effects on the reproductive number. We find that simple heterogeneity decreases the finite-population reproductive number, whereas heterogeneity in the intrinsic mixing rate (which affects both infectiousness and susceptibility) increases the finite-population reproductive number when R0 is small relative to the size of the population and decreases the finite-population reproductive number when R0 is large relative to the size of the population. Although heterogeneity has complicated effects on the finite-population reproductive numbers, its implications for control are straightforward: when R0 is large relative to the size of the population, heterogeneity decreases the finite-population reproductive numbers, making disease control or elimination easier than predicted by R0. Copyright © 2016 Elsevier Ltd. All rights reserved.

SAPNEW: Parallel finite element code for thin shell structures on the Alliant FX/80

NASA Astrophysics Data System (ADS)

Kamat, Manohar P.; Watson, Brian C.

1992-02-01

The results of a research activity aimed at providing a finite element capability for analyzing turbo-machinery bladed-disk assemblies in a vector/parallel processing environment are summarized. Analysis of aircraft turbofan engines is very computationally intensive. The performance limit of modern day computers with a single processing unit was estimated at 3 billions of floating point operations per second (3 gigaflops). In view of this limit of a sequential unit, performance rates higher than 3 gigaflops can be achieved only through vectorization and/or parallelization as on Alliant FX/80. Accordingly, the efforts of this critically needed research were geared towards developing and evaluating parallel finite element methods for static and vibration analysis. A special purpose code, named with the acronym SAPNEW, performs static and eigen analysis of multi-degree-of-freedom blade models built-up from flat thin shell elements.

SAPNEW: Parallel finite element code for thin shell structures on the Alliant FX/80

NASA Technical Reports Server (NTRS)

Kamat, Manohar P.; Watson, Brian C.

1992-01-01

The results of a research activity aimed at providing a finite element capability for analyzing turbo-machinery bladed-disk assemblies in a vector/parallel processing environment are summarized. Analysis of aircraft turbofan engines is very computationally intensive. The performance limit of modern day computers with a single processing unit was estimated at 3 billions of floating point operations per second (3 gigaflops). In view of this limit of a sequential unit, performance rates higher than 3 gigaflops can be achieved only through vectorization and/or parallelization as on Alliant FX/80. Accordingly, the efforts of this critically needed research were geared towards developing and evaluating parallel finite element methods for static and vibration analysis. A special purpose code, named with the acronym SAPNEW, performs static and eigen analysis of multi-degree-of-freedom blade models built-up from flat thin shell elements.

Impacts of Ocean Waves on the Atmospheric Surface Layer: Simulations and Observations

DTIC Science & Technology

2008-06-06

energy and pressure described in § 4 are solved using a mixed finite - difference pseudospectral scheme with a third-order Runge-Kutta time stepping with a...to that in our DNS code (Sullivan and McWilliams 2002; Sullivan et al. 2000). For our mixed finite - difference pseudospec- tral differencing scheme a...Poisson equation. The spatial discretization is pseu- dospectral along lines of constant or and second- order finite difference in the vertical

Energy-exchange collisions of dark-bright-bright vector solitons.

PubMed

Radhakrishnan, R; Manikandan, N; Aravinthan, K

2015-12-01

We find a dark component guiding the practically interesting bright-bright vector one-soliton to two different parametric domains giving rise to different physical situations by constructing a more general form of three-component dark-bright-bright mixed vector one-soliton solution of the generalized Manakov model with nine free real parameters. Moreover our main investigation of the collision dynamics of such mixed vector solitons by constructing the multisoliton solution of the generalized Manakov model with the help of Hirota technique reveals that the dark-bright-bright vector two-soliton supports energy-exchange collision dynamics. In particular the dark component preserves its initial form and the energy-exchange collision property of the bright-bright vector two-soliton solution of the Manakov model during collision. In addition the interactions between bound state dark-bright-bright vector solitons reveal oscillations in their amplitudes. A similar kind of breathing effect was also experimentally observed in the Bose-Einstein condensates. Some possible ways are theoretically suggested not only to control this breathing effect but also to manage the beating, bouncing, jumping, and attraction effects in the collision dynamics of dark-bright-bright vector solitons. The role of multiple free parameters in our solution is examined to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation of our solution. It is interesting to note that the polarization vector of our mixed vector one-soliton evolves in sphere or hyperboloid depending upon the initial parametric choices.

Eigenvalues of Rectangular Waveguide Using FEM With Hybrid Elements

NASA Technical Reports Server (NTRS)

Deshpande, Manohar D.; Hall, John M.

2002-01-01

A finite element analysis using hybrid triangular-rectangular elements is developed to estimate eigenvalues of a rectangular waveguide. Use of rectangular vector-edge finite elements in the vicinity of the PEC boundary and triangular elements in the interior region more accurately models the physical nature of the electromagnetic field, and consequently quicken the convergence.

A Ring Construction Using Finite Directed Graphs

ERIC Educational Resources Information Center

Bardzell, Michael

2012-01-01

In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…

A detailed analysis of inviscid flux splitting algorithms for real gases with equilibrium or finite-rate chemistry

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Liou, Meng-Sing; Van Leer, Bram

1989-01-01

The extension of the known flux-vector and flux-difference splittings to real gases via rigorous mathematical procedures is demonstrated. Formulations of both equilibrium and finite-rate chemistry for real-gas flows are described, with emphasis on derivations of finite-rate chemistry. Split-flux formulas from other authors are examined. A second-order upwind-based TVD scheme is adopted to eliminate oscillations and to obtain a sharp representation of discontinuities.

Improved methods of vibration analysis of pretwisted, airfoil blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1984-01-01

Vibration analysis of pretwisted blades of asymmetric airfoil cross section is performed by using two mixed variational approaches. Numerical results obtained from these two methods are compared to those obtained from an improved finite difference method and also to those given by the ordinary finite difference method. The relative merits, convergence properties and accuracies of all four methods are studied and discussed. The effects of asymmetry and pretwist on natural frequencies and mode shapes are investigated. The improved finite difference method is shown to be far superior to the conventional finite difference method in several respects. Close lower bound solutions are provided by the improved finite difference method for untwisted blades with a relatively coarse mesh while the mixed methods have not indicated any specific bound.

Separable decompositions of bipartite mixed states

NASA Astrophysics Data System (ADS)

Li, Jun-Li; Qiao, Cong-Feng

2018-04-01

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8:1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then, we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.

Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1986-01-01

A mixed shear flexible finite element, with relaxed continuity, is developed for the geometrically linear and nonlinear analysis of layered anisotropic plates. The element formulation is based on a refined higher order theory which satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate and requires no shear correction coefficients. The mixed finite element developed herein consists of eleven degrees of freedom per node which include three displacements, two rotations and six moment resultants. The element is evaluated for its accuracy in the analysis of the stability and vibration of anisotropic rectangular plates with different lamination schemes and boundary conditions. The mixed finite element described here for the higher order theory gives very accurate results for buckling loads and natural frequencies.

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

NASA Technical Reports Server (NTRS)

Deng, Qingping

1996-01-01

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds.

PubMed

Lu, Haishu; Wang, Zhihua

2017-01-01

This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a scalar equilibrium problem, and a perturbed saddle point problem. Finally, as an application of the existence of solutions to the generalized scalar equilibrium problem, we obtain a weakly mixed variational inequality and two mixed variational inequalities. The results presented in this paper unify and generalize many known results in the literature.

Comparison of Computational-Model and Experimental-Example Trained Neural Networks for Processing Speckled Fringe Patterns

NASA Technical Reports Server (NTRS)

Decker, A. J.; Fite, E. B.; Thorp, S. A.; Mehmed, O.

1998-01-01

The responses of artificial neural networks to experimental and model-generated inputs are compared for detection of damage in twisted fan blades using electronic holography. The training-set inputs, for this work, are experimentally generated characteristic patterns of the vibrating blades. The outputs are damage-flag indicators or second derivatives of the sensitivity-vector-projected displacement vectors from a finite element model. Artificial neural networks have been trained in the past with computational-model-generated training sets. This approach avoids the difficult inverse calculations traditionally used to compare interference fringes with the models. But the high modeling standards are hard to achieve, even with fan-blade finite-element models.

Comparison of Computational, Model and Experimental, Example Trained Neural Networks for Processing Speckled Fringe Patterns

NASA Technical Reports Server (NTRS)

Decker, A. J.; Fite, E. B.; Thorp, S. A.; Mehmed, O.

1998-01-01

The responses of artificial neural networks to experimental and model-generated inputs are compared for detection of damage in twisted fan blades using electronic holography. The training-set inputs, for this work, are experimentally generated characteristic patterns of the vibrating blades. The outputs are damage-flag indicators or second derivatives of the sensitivity-vector-projected displacement vectors from a finite element model. Artificial neural networks have been trained in the past with computational-model- generated training sets. This approach avoids the difficult inverse calculations traditionally used to compare interference fringes with the models. But the high modeling standards are hard to achieve, even with fan-blade finite-element models.

Interframe vector wavelet coding technique

NASA Astrophysics Data System (ADS)

Wus, John P.; Li, Weiping

1997-01-01

Wavelet coding is often used to divide an image into multi- resolution wavelet coefficients which are quantized and coded. By 'vectorizing' scalar wavelet coding and combining this with vector quantization (VQ), vector wavelet coding (VWC) can be implemented. Using a finite number of states, finite-state vector quantization (FSVQ) takes advantage of the similarity between frames by incorporating memory into the video coding system. Lattice VQ eliminates the potential mismatch that could occur using pre-trained VQ codebooks. It also eliminates the need for codebook storage in the VQ process, thereby creating a more robust coding system. Therefore, by using the VWC coding method in conjunction with the FSVQ system and lattice VQ, the formulation of a high quality very low bit rate coding systems is proposed. A coding system using a simple FSVQ system where the current state is determined by the previous channel symbol only is developed. To achieve a higher degree of compression, a tree-like FSVQ system is implemented. The groupings are done in this tree-like structure from the lower subbands to the higher subbands in order to exploit the nature of subband analysis in terms of the parent-child relationship. Class A and Class B video sequences from the MPEG-IV testing evaluations are used in the evaluation of this coding method.

Crossover in growth laws for phase-separating binary fluids: molecular dynamics simulations.

PubMed

Ahmad, Shaista; Das, Subir K; Puri, Sanjay

2012-03-01

Pattern and dynamics during phase separation in a symmetrical binary (A+B) Lennard-Jones fluid are studied via molecular dynamics simulations after quenching homogeneously mixed critical (50:50) systems to temperatures below the critical one. The morphology of the domains, rich in A or B particles, is observed to be bicontinuous. The early-time growth of the average domain size is found to be consistent with the Lifshitz-Slyozov law for diffusive domain coarsening. After a characteristic time, dependent on the temperature, we find a clear crossover to an extended viscous hydrodynamic regime where the domains grow linearly with time. Pattern formation in the present system is compared with that in solid binary mixtures, as a function of temperature. Important results for the finite-size and temperature effects on the small-wave-vector behavior of the scattering function are also presented.

A study of the response of nonlinear springs

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Knott, T. W.; Johnson, E. R.

1991-01-01

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

A mixed shear flexible finite element for the analysis of laminated plates

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1984-01-01

A mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated. The element consists of three displacements, two rotations, and three moments as the generalized degrees of freedom per node. The numerical convergence and accuracy characteristics of the element are investigated by comparing the finite element solutions with the exact solutions. The present study shows that reduced-order integration of the stiffness coefficients due to shear is necessary to obtain accurate results for thin plates.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

A high-accuracy optical linear algebra processor for finite element applications

NASA Technical Reports Server (NTRS)

Casasent, D.; Taylor, B. K.

1984-01-01

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

Guidelines for developing vectorizable computer programs

NASA Technical Reports Server (NTRS)

Miner, E. W.

1982-01-01

Some fundamental principles for developing computer programs which are compatible with array-oriented computers are presented. The emphasis is on basic techniques for structuring computer codes which are applicable in FORTRAN and do not require a special programming language or exact a significant penalty on a scalar computer. Researchers who are using numerical techniques to solve problems in engineering can apply these basic principles and thus develop transportable computer programs (in FORTRAN) which contain much vectorizable code. The vector architecture of the ASC is discussed so that the requirements of array processing can be better appreciated. The "vectorization" of a finite-difference viscous shock-layer code is used as an example to illustrate the benefits and some of the difficulties involved. Increases in computing speed with vectorization are illustrated with results from the viscous shock-layer code and from a finite-element shock tube code. The applicability of these principles was substantiated through running programs on other computers with array-associated computing characteristics, such as the Hewlett-Packard (H-P) 1000-F.

Multitasking 3-D forward modeling using high-order finite difference methods on the Cray X-MP/416

DOE Office of Scientific and Technical Information (OSTI.GOV)

Terki-Hassaine, O.; Leiss, E.L.

1988-01-01

The CRAY X-MP/416 was used to multitask 3-D forward modeling by the high-order finite difference method. Flowtrace analysis reveals that the most expensive operation in the unitasked program is a matrix vector multiplication. The in-core and out-of-core versions of a reentrant subroutine can perform any fraction of the matrix vector multiplication independently, a pattern compatible with multitasking. The matrix vector multiplication routine can be distributed over two to four processors. The rest of the program utilizes the microtasking feature that lets the system treat independent iterations of DO-loops as subtasks to be performed by any available processor. The availability ofmore » the Solid-State Storage Device (SSD) meant the I/O wait time was virtually zero. A performance study determined a theoretical speedup, taking into account the multitasking overhead. Multitasking programs utilizing both macrotasking and microtasking features obtained actual speedups that were approximately 80% of the ideal speedup.« less

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

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.

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Three dimensional magnetic fields in extra high speed modified Lundell alternators computed by a combined vector-scalar magnetic potential finite element method

NASA Technical Reports Server (NTRS)

Demerdash, N. A.; Wang, R.; Secunde, R.

1992-01-01

A 3D finite element (FE) approach was developed and implemented for computation of global magnetic fields in a 14.3 kVA modified Lundell alternator. The essence of the new method is the combined use of magnetic vector and scalar potential formulations in 3D FEs. This approach makes it practical, using state of the art supercomputer resources, to globally analyze magnetic fields and operating performances of rotating machines which have truly 3D magnetic flux patterns. The 3D FE-computed fields and machine inductances as well as various machine performance simulations of the 14.3 kVA machine are presented in this paper and its two companion papers.

Visualizing turbulent mixing of gases and particles

NASA Technical Reports Server (NTRS)

Ma, Kwan-Liu; Smith, Philip J.; Jain, Sandeep

1995-01-01

A physical model and interactive computer graphics techniques have been developed for the visualization of the basic physical process of stochastic dispersion and mixing from steady-state CFD calculations. The mixing of massless particles and inertial particles is visualized by transforming the vector field from a traditionally Eulerian reference frame into a Lagrangian reference frame. Groups of particles are traced through the vector field for the mean path as well as their statistical dispersion about the mean position by using added scalar information about the root mean square value of the vector field and its Lagrangian time scale. In this way, clouds of particles in a turbulent environment are traced, not just mean paths. In combustion simulations of many industrial processes, good mixing is required to achieve a sufficient degree of combustion efficiency. The ability to visualize this multiphase mixing can not only help identify poor mixing but also explain the mechanism for poor mixing. The information gained from the visualization can be used to improve the overall combustion efficiency in utility boilers or propulsion devices. We have used this technique to visualize steady-state simulations of the combustion performance in several furnace designs.

Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

2000-01-01

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Spatial Convergence of Three Dimensional Turbulent Flows

NASA Technical Reports Server (NTRS)

Park, Michael A.; Anderson, W. Kyle

2016-01-01

Finite-volume and finite-element schemes, both implemented within the FUN3D flow solver, are evaluated for several test cases described on the Turbulence-Modeling Resource (TMR) web site. The cases include subsonic flow over a hemisphere cylinder, subsonic flow over a swept bump configuration, and supersonic flow in a square duct. The finite- volume and finite-element schemes are both used to obtain solutions for the first two cases, whereas only the finite-volume scheme is used for the supersonic duct. For the hemisphere cylinder, finite-element solutions obtained on tetrahedral meshes are compared with finite- volume solutions on mixed-element meshes. For the swept bump, finite-volume solutions have been obtained for both hexahedral and tetrahedral meshes and are compared with finite-element solutions obtained on tetrahedral meshes. For the hemisphere cylinder and the swept bump, solutions are obtained on a series of meshes with varying grid density and comparisons are made between drag coefficients, pressure distributions, velocity profiles, and profiles of the turbulence working variable. The square duct shows small variation due to element type or the spatial accuracy of turbulence model convection. It is demonstrated that the finite-element scheme on tetrahedral meshes yields similar accuracy as the finite- volume scheme on mixed-element and hexahedral grids, and demonstrates less sensitivity to the mesh topology (biased tetrahedral grids) than the finite-volume scheme.

An integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin

NASA Astrophysics Data System (ADS)

Chang, Chien-Chieh; Chen, Chia-Shyun

2002-06-01

A flowing partially penetrating well with infinitesimal well skin is a mixed boundary because a Cauchy condition is prescribed along the screen length and a Neumann condition of no flux is stipulated over the remaining unscreened part. An analytical approach based on the integral transform technique is developed to determine the Laplace domain solution for such a mixed boundary problem in a confined aquifer of finite thickness. First, the mixed boundary is changed into a homogeneous Neumann boundary by substituting the Cauchy condition with a Neumann condition in terms of well bore flux that varies along the screen length and is time dependent. Despite the well bore flux being unknown a priori, the modified model containing this homogeneous Neumann boundary can be solved with the Laplace and the finite Fourier cosine transforms. To determine well bore flux, screen length is discretized into a finite number of segments, to which the Cauchy condition is reinstated. This reinstatement also restores the relation between the original model and the solutions obtained. For a given time, the numerical inversion of the Laplace domain solution yields the drawdown distributions, well bore flux, and the well discharge. This analytical approach provides an alternative for dealing with the mixed boundary problems, especially when aquifer thickness is assumed to be finite.

The parallel-antiparallel signal difference in double-wave-vector diffusion-weighted MR at short mixing times: A phase evolution perspective

NASA Astrophysics Data System (ADS)

Finsterbusch, Jürgen

2011-01-01

Experiments with two diffusion weightings applied in direct succession in a single acquisition, so-called double- or two-wave-vector diffusion-weighting (DWV) experiments at short mixing times, have been shown to be a promising tool to estimate cell or compartment sizes, e.g. in living tissue. The basic theory for such experiments predicts that the signal decays for parallel and antiparallel wave vector orientations differ by a factor of three for small wave vectors. This seems to be surprising because in standard, single-wave-vector experiments the polarity of the diffusion weighting has no influence on the signal attenuation. Thus, the question how this difference can be understood more pictorially is often raised. In this rather educational manuscript, the phase evolution during a DWV experiment for simple geometries, e.g. diffusion between parallel, impermeable planes oriented perpendicular to the wave vectors, is considered step-by-step and demonstrates how the signal difference develops. Considering the populations of the phase distributions obtained, the factor of three between the signal decays which is predicted by the theory can be reproduced. Furthermore, the intermediate signal decay for orthogonal wave vector orientations can be derived when investigating diffusion in a box. Thus, the presented “phase gymnastics” approach may help to understand the signal modulation observed in DWV experiments at short mixing times.

Energy Dissipation of Rayleigh Waves due to Absorption Along the Path by the Use of Finite Element Method

DTIC Science & Technology

1979-07-31

3 x 3 t Strain vector a ij,j Space derivative of the stress tensor Fi Force vector per unit volume o Density x CHAPTER III F Total force K Stiffness...matrix 6Vector displacements M Mass matrix B Space operating matrix DO Matrix moduli 2 x 3 DZ Operating matrix in Z direction N Matrix of shape...dissipating medium the deformation of a solid is a function of time, temperature and space . Creep phenomenon is a deformation process in which there is

Analysis of superconducting electromagnetic finite elements based on a magnetic vector potential variational principle

NASA Technical Reports Server (NTRS)

Schuler, James J.; Felippa, Carlos A.

1991-01-01

Electromagnetic finite elements are extended based on a variational principle that uses the electromagnetic four potential as primary variable. The variational principle is extended to include the ability to predict a nonlinear current distribution within a conductor. The extension of this theory is first done on a normal conductor and tested on two different problems. In both problems, the geometry remains the same, but the material properties are different. The geometry is that of a 1-D infinite wire. The first problem is merely a linear control case used to validate the new theory. The second problem is made up of linear conductors with varying conductivities. Both problems perform well and predict current densities that are accurate to within a few ten thousandths of a percent of the exact values. The fourth potential is then removed, leaving only the magnetic vector potential, and the variational principle is further extended to predict magnetic potentials, magnetic fields, the number of charge carriers, and the current densities within a superconductor. The new element produces good results for the mean magnetic field, the vector potential, and the number of superconducting charge carriers despite a relatively high system condition number. The element did not perform well in predicting the current density. Numerical problems inherent to this formulation are explored and possible remedies to produce better current predicting finite elements are presented.

Finite-time mixed outer synchronization of complex networks with coupling time-varying delay.

PubMed

He, Ping; Ma, Shu-Hua; Fan, Tao

2012-12-01

This article is concerned with the problem of finite-time mixed outer synchronization (FMOS) of complex networks with coupling time-varying delay. FMOS is a recently developed generalized synchronization concept, i.e., in which different state variables of the corresponding nodes can evolve into finite-time complete synchronization, finite-time anti-synchronization, and even amplitude finite-time death simultaneously for an appropriate choice of the controller gain matrix. Some novel stability criteria for the synchronization between drive and response complex networks with coupling time-varying delay are derived using the Lyapunov stability theory and linear matrix inequalities. And a simple linear state feedback synchronization controller is designed as a result. Numerical simulations for two coupled networks of modified Chua's circuits are then provided to demonstrate the effectiveness and feasibility of the proposed complex networks control and synchronization schemes and then compared with the proposed results and the previous schemes for accuracy.

Periodic trim solutions with hp-version finite elements in time

NASA Technical Reports Server (NTRS)

Peters, David A.; Hou, Lin-Jun

1990-01-01

Finite elements in time as an alternative strategy for rotorcraft trim problems are studied. The research treats linear flap and linearized flap-lag response both for quasi-trim and trim cases. The connection between Fourier series analysis and hp-finite elements for periodic a problem is also examined. It is proved that Fourier series is a special case of space-time finite elements in which one element is used with a strong displacement formulation. Comparisons are made with respect to accuracy among Fourier analysis, displacement methods, and mixed methods over a variety parameters. The hp trade-off is studied for the periodic trim problem to provide an optimum step size and order of polynomial for a given error criteria. It is found that finite elements in time can outperform Fourier analysis for periodic problems, and for some given error criteria. The mixed method provides better results than does the displacement method.

Generalized dark-bright vector soliton solution to the mixed coupled nonlinear Schrödinger equations.

PubMed

Manikandan, N; Radhakrishnan, R; Aravinthan, K

2014-08-01

We have constructed a dark-bright N-soliton solution with 4N+3 real parameters for the physically interesting system of mixed coupled nonlinear Schrödinger equations. Using this as well as an asymptotic analysis we have investigated the interaction between dark-bright vector solitons. Each colliding dark-bright one-soliton at the asymptotic limits includes more coupling parameters not only in the polarization vector but also in the amplitude part. Our present solution generalizes the dark-bright soliton in the literature with parametric constraints. By exploiting the role of such coupling parameters we are able to control certain interaction effects, namely beating, breathing, bouncing, attraction, jumping, etc., without affecting other soliton parameters. Particularly, the results of the interactions between the bound state dark-bright vector solitons reveal oscillations in their amplitudes under certain parametric choices. A similar kind of effect was also observed experimentally in the BECs. We have also characterized the solutions with complicated structure and nonobvious wrinkle to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation. It is interesting to identify that the polarization vector of the dark-bright one-soliton evolves on a spherical surface instead of a hyperboloid surface as in the bright-bright case of the mixed coupled nonlinear Schrödinger equations.

Stretching Diagnostics and Mixing Properties In The Stratosphere

NASA Astrophysics Data System (ADS)

Legras, B.; Shuckburgh, E.

The "finite size Lyapunov exponent" and the "effective diffusivity" are two diagnos- tics of mixing which have been recently introduced to investigate atmospheric flows. Both have been used to successfully identify the barriers to transport, for instance at the edge of the stratospheric polar vortex. Here we compare the two diagnostics in detail. The equivalent length has the advantage of arising as a mixing quantification from a rigid theoretical framework, however it has the disadvantage of being an aver- age quantity (the average around a tracer contour). The finite size Lyapunov exponent may be defined at any point in the flow, and quantifies the stretching properties expe- rienced by a fluid parcel both in its past and future evolution. In particular, the lines of maximum stretching at any time delineate the building blocks of the chaotic stirring. However the interpretation of the finite size Lyapunov exponent as a mixing time is less direct and depends on the alignment of tracer contours with the stretching lines.

The canonical quantization of chaotic maps on the torus

NASA Astrophysics Data System (ADS)

Rubin, Ron Shai

In this thesis, a quantization method for classical maps on the torus is presented. The quantum algebra of observables is defined as the quantization of measurable functions on the torus with generators exp (2/pi ix) and exp (2/pi ip). The Hilbert space we use remains the infinite-dimensional L2/ (/IR, dx). The dynamics is given by a unitary quantum propagator such that as /hbar /to 0, the classical dynamics is returned. We construct such a quantization for the Kronecker map, the cat map, the baker's map, the kick map, and the Harper map. For the cat map, we find the same for the propagator on the plane the same integral kernel conjectured in (HB) using semiclassical methods. We also define a quantum 'integral over phase space' as a trace over the quantum algebra. Using this definition, we proceed to define quantum ergodicity and mixing for maps on the torus. We prove that the quantum cat map and Kronecker map are both ergodic, but only the cat map is mixing, true to its classical origins. For Planck's constant satisfying the integrality condition h = 1/N, with N/in doubz+, we construct an explicit isomorphism between L2/ (/IR, dx) and the Hilbert space of sections of an N-dimensional vector bundle over a θ-torus T2 of boundary conditions. The basis functions are distributions in L2/ (/IR, dx), given by an infinite comb of Dirac δ-functions. In Bargmann space these distributions take on the form of Jacobi ϑ-functions. Transformations from position to momentum representation can be implemented via a finite N-dimensional discrete Fourier transform. With the θ-torus, we provide a connection between the finite-dimensional quantum maps given in the physics literature and the canonical quantization presented here and found in the language of pseudo-differential operators elsewhere in mathematics circles. Specifically, at a fixed point of the dynamics on the θ-torus, we return a finite-dimensional matrix propagator. We present this connection explicitly for several examples.

An algorithm for targeting finite burn maneuvers

NASA Technical Reports Server (NTRS)

Barbieri, R. W.; Wyatt, G. H.

1972-01-01

An algorithm was developed to solve the following problem: given the characteristics of the engine to be used to make a finite burn maneuver and given the desired orbit, when must the engine be ignited and what must be the orientation of the thrust vector so as to obtain the desired orbit? The desired orbit is characterized by classical elements and functions of these elements whereas the control parameters are characterized by the time to initiate the maneuver and three direction cosines which locate the thrust vector. The algorithm was built with a Monte Carlo capability whereby samples are taken from the distribution of errors associated with the estimate of the state and from the distribution of errors associated with the engine to be used to make the maneuver.

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

NASA Technical Reports Server (NTRS)

Tsiveriotis, K.; Brown, R. A.

1993-01-01

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Possible microplate generation at RRR triple junctions due to the non-circular finite motion of plates relative to each other

NASA Astrophysics Data System (ADS)

Cronin, V. S.

2012-12-01

First generation ideas of the kinematic stability of triple junctions lead to the common belief that the geometry of ridge-ridge-ridge (RRR) triple junctions remains constant over time under conditions of symmetric spreading. Given constant relative motion between each plate pair -- that is, the pole of plate relative motion is fixed to both plates in each pair during finite motion, as assumed in many accounts of plate kinematics -- there would be no boundary mismatch at the triple junction and no apparent kinematic reason why a microplate might develop there. But if, in a given RRR triple junction, the finite motion of one plate as observed from the other plate is not circular (as is generally the case, given the three-plate problem of plate kinematics), the geometry of the ridges and the triple junction will vary with time (Cronin, 1992, Tectonophys 207, 287-301). To explore the possible consequences of non-circular finite motion between plates at an RRR triple junction, a simple model was coded based on the cycloid finite-motion model (e.g., Cronin, 1987, Geology 15, 1006-1009) using NNR-MORVEL56 velocities for individual plates (Argus et al., 2011, G3 12, doi: 10.1029/2011GC003751). Initial assumptions include a spherical Earth, symmetric spreading, and constant angular velocities during the modeled finite time interval. The assumed-constant angular velocity vectors constitute a reference frame for observing finite plate motion. Typical results are [1] that the triple junction migrates relative to a coordinate system fixed to the angular-velocity vectors, [2] ridge axes rotates relative to each other, and [3] a boundary mismatch develops at the synthetic triple junction that might result in microplate nucleation. In a model simulating the Galapagos triple junction between the Cocos, Nazca and Pacific plates whose initial state did not include the Galapagos microplate, the mismatch gap was as much as ~3.4 km during 3 Myr of model displacement (see figure). The centroid of the synthetic triple junction translates ~81 km toward azimuth ~352° in 3 Myr. Of course, the details will vary as different angular velocity vectors are used; however, modeling indicates that non-circular finite relative motion between adjacent plates generally results in boundary mismatches and rotation of ridge segments relative to each other at RRR triple junctions. Left: synthetic Galapagos triple junction at initial model time, without a microplate. Right: synthetic triple junction after 3 Myr displacement, illustrating the resulting boundary mismatch (gap) and rotated ridge axes.

Clouding tracing: Visualization of the mixing of fluid elements in convection-diffusion systems

NASA Technical Reports Server (NTRS)

Ma, Kwan-Liu; Smith, Philip J.

1993-01-01

This paper describes a highly interactive method for computer visualization of the basic physical process of dispersion and mixing of fluid elements in convection-diffusion systems. It is based on transforming the vector field from a traditionally Eulerian reference frame into a Lagrangian reference frame. Fluid elements are traced through the vector field for the mean path as well as the statistical dispersion of the fluid elements about the mean position by using added scalar information about the root mean square value of the vector field and its Lagrangian time scale. In this way, clouds of fluid elements are traced and are not just mean paths. We have used this method to visualize the simulation of an industrial incinerator to help identify mechanisms for poor mixing.

Finite element based electric motor design optimization

NASA Technical Reports Server (NTRS)

Campbell, C. Warren

1993-01-01

The purpose of this effort was to develop a finite element code for the analysis and design of permanent magnet electric motors. These motors would drive electromechanical actuators in advanced rocket engines. The actuators would control fuel valves and thrust vector control systems. Refurbishing the hydraulic systems of the Space Shuttle after each flight is costly and time consuming. Electromechanical actuators could replace hydraulics, improve system reliability, and reduce down time.

Bombus terrestris as pollinator-and-vector to suppress Botrytis cinerea in greenhouse strawberry.

PubMed

Mommaerts, Veerle; Put, Kurt; Smagghe, Guy

2011-09-01

Bombus terrestris L. bumblebees are widely used as commercial pollinators, but they might also be of help in the battle against economically important crop diseases. This alternative control strategy is referred to as pollinator-and-vector technology. The present study was designed to investigate the capacity of B. terrestris to fulfil this role in greenhouse strawberry flowers, which were manually inoculated with a major plant pathogen, the grey mould Botrytis cinerea Pers.: Fr. A model microbiological control agent (MCA) product Prestop-Mix was loaded in a newly developed two-way bumblebee dispenser, and, in addition, the use of the diluent Maizena-Plus (corn starch) was tested. Importantly, loading of the MCA caused no adverse effects on bumblebee workers, with no loss of survival or impairment of flight activity of the workers during the 4 week flowering period. Secondly, vectoring of Prestop-Mix by bumblebees resulted in a higher crop production, as 71% of the flowers developed into healthy red strawberries at picking (preharvest yield) as compared with 54% in the controls. In addition, these strawberries were better protected, as 79% of the picked berries remained free of B. cinerea after a 2 day incubation (post-harvest yield), while this percentage was only 43% in the control. Overall, the total yield (preharvest × post-harvest) was 2-2.5 times higher than the total yield in the controls (24%) in plants exposed to bumblebees vectoring Prestop-Mix. Thirdly, the addition of the diluent Maizena-Plus to Prestop-Mix at 1:1 (w/w) resulted in a similar yield to that of Prestop-Mix used alone, and in no negative effects on the bumblebees, flowers and berries. This greenhouse study provides strong evidence that B. terrestris bumblebees can vector a MCA to reduce B. cinerea incidence in greenhouse strawberries, resulting in higher yields. Similar yields obtained in the treatments with Prestop-Mix and Prestop-Mix + Maizena-Plus suggest an equally efficient dissemination of the biocontrol agent into the flowers with only half the initial concentration of Prestop-Mix, which illustrates the importance of the diluent. Copyright © 2011 Society of Chemical Industry.

On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle

NASA Technical Reports Server (NTRS)

Karlovitz, L. A.; Atluri, S. N.; Xue, W.-M.

1985-01-01

The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.

Reconstruction of interatomic vectors by principle component analysis of nuclear magnetic resonance data in multiple alignments

NASA Astrophysics Data System (ADS)

Hus, Jean-Christophe; Bruschweiler, Rafael

2002-07-01

A general method is presented for the reconstruction of interatomic vector orientations from nuclear magnetic resonance (NMR) spectroscopic data of tensor interactions of rank 2, such as dipolar coupling and chemical shielding anisotropy interactions, in solids and partially aligned liquid-state systems. The method, called PRIMA, is based on a principal component analysis of the covariance matrix of the NMR parameters collected for multiple alignments. The five nonzero eigenvalues and their eigenvectors efficiently allow the approximate reconstruction of the vector orientations of the underlying interactions. The method is demonstrated for an isotropic distribution of sample orientations as well as for finite sets of orientations and internuclear vectors encountered in protein systems.

Computational mechanics analysis tools for parallel-vector supercomputers

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.; Nguyen, Duc T.; Baddourah, Majdi; Qin, Jiangning

1993-01-01

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigensolution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization search analysis and domain decomposition. The source code for many of these algorithms is available.

Vector Potential Generation for Numerical Relativity Simulations

NASA Astrophysics Data System (ADS)

Silberman, Zachary; Faber, Joshua; Adams, Thomas; Etienne, Zachariah; Ruchlin, Ian

2017-01-01

Many different numerical codes are employed in studies of highly relativistic magnetized accretion flows around black holes. Based on the formalisms each uses, some codes evolve the magnetic field vector B, while others evolve the magnetic vector potential A, the two being related by the curl: B=curl(A). Here, we discuss how to generate vector potentials corresponding to specified magnetic fields on staggered grids, a surprisingly difficult task on finite cubic domains. The code we have developed solves this problem in two ways: a brute-force method, whose scaling is nearly linear in the number of grid cells, and a direct linear algebra approach. We discuss the success both algorithms have in generating smooth vector potential configurations and how both may be extended to more complicated cases involving multiple mesh-refinement levels. NSF ACI-1550436

On mixed and displacement finite element models of a refined shear deformation theory for laminated anisotropic plates

NASA Technical Reports Server (NTRS)

Reddy, J. N.

1986-01-01

An improved plate theory that accounts for the transverse shear deformation is presented, and mixed and displacement finite element models of the theory are developed. The theory is based on an assumed displacement field in which the inplane displacements are expanded in terms of the thickness coordinate up to the cubic term and the transverse deflection is assumed to be independent of the thickness coordinate. The governing equations of motion for the theory are derived from the Hamilton's principle. The theory eliminates the need for shear correction factors because the transverse shear stresses are represented parabolically. A mixed finite element model that uses independent approximations of the displacements and moments, and a displacement model that uses only displacements as degrees of freedom are developed. A comparison of the numerical results for bending with the exact solutions of the new theory and the three-dimensional elasticity theory shows that the present theory (and hence the finite element models) is more accurate than other plate-theories of the same order.

Finite element model for MOI applications using A-V formulation

NASA Astrophysics Data System (ADS)

Xuan, L.; Shanker, B.; Udpa, L.; Shih, W.; Fitzpatrick, G.

2001-04-01

Magneto-optic imaging (MOI) is a relatively new sensor application of an extension of bubble memory technology to NDT and produce easy-to-interpret, real time analog images. MOI systems use a magneto-optic (MO) sensor to produce analog images of magnetic flux leakage from surface and subsurface defects. The instrument's capability in detecting the relatively weak magnetic fields associated with subsurface defects depends on the sensitivity of the magneto-optic sensor. The availability of a theoretical model that can simulate the MOI system performance is extremely important for optimization of the MOI sensor and hardware system. A nodal finite element model based on magnetic vector potential formulation has been developed for simulating MOI phenomenon. This model has been used for predicting the magnetic fields in simple test geometry with corrosion dome defects. In the case of test samples with multiple discontinuities, a more robust model using the magnetic vector potential Ā and electrical scalar potential V is required. In this paper, a finite element model based on A-V formulation is developed to model complex circumferential crack under aluminum rivets in dimpled countersink.

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

NASA Technical Reports Server (NTRS)

Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro

1989-01-01

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

SutraPlot, a graphical post-processor for SUTRA, a model for ground-water flow with solute or energy transport

USGS Publications Warehouse

Souza, W.R.

1999-01-01

This report documents a graphical display post-processor (SutraPlot) for the U.S. Geological Survey Saturated-Unsaturated flow and solute or energy TRAnsport simulation model SUTRA, Version 2D3D.1. This version of SutraPlot is an upgrade to SutraPlot for the 2D-only SUTRA model (Souza, 1987). It has been modified to add 3D functionality, a graphical user interface (GUI), and enhanced graphic output options. Graphical options for 2D SUTRA (2-dimension) simulations include: drawing the 2D finite-element mesh, mesh boundary, and velocity vectors; plots of contours for pressure, saturation, concentration, and temperature within the model region; 2D finite-element based gridding and interpolation; and 2D gridded data export files. Graphical options for 3D SUTRA (3-dimension) simulations include: drawing the 3D finite-element mesh; plots of contours for pressure, saturation, concentration, and temperature in 2D sections of the 3D model region; 3D finite-element based gridding and interpolation; drawing selected regions of velocity vectors (projected on principal coordinate planes); and 3D gridded data export files. Installation instructions and a description of all graphic options are presented. A sample SUTRA problem is described and three step-by-step SutraPlot applications are provided. In addition, the methodology and numerical algorithms for the 2D and 3D finite-element based gridding and interpolation, developed for SutraPlot, are described. 1

HFEM3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weiss, Chester J

Software solves the three-dimensional Poisson equation div(k(grad(u)) = f, by the finite element method for the case when material properties, k, are distributed over hierarchy of edges, facets and tetrahedra in the finite element mesh. Method is described in Weiss, CJ, Finite element analysis for model parameters distributed on a hierarchy of geometric simplices, Geophysics, v82, E155-167, doi:10.1190/GEO2017-0058.1 (2017). A standard finite element method for solving Poisson’s equation is augmented by including in the 3D stiffness matrix additional 2D and 1D stiffness matrices representing the contributions from material properties associated with mesh faces and edges, respectively. The resulting linear systemmore » is solved iteratively using the conjugate gradient method with Jacobi preconditioning. To minimize computer storage for program execution, the linear solver computes matrix-vector contractions element-by-element over the mesh, without explicit storage of the global stiffness matrix. Program output vtk compliant for visualization and rendering by 3rd party software. Program uses dynamic memory allocation and as such there are no hard limits on problem size outside of those imposed by the operating system and configuration on which the software is run. Dimension, N, of the finite element solution vector is constrained by the the addressable space in 32-vs-64 bit operating systems. Total storage requirements for the problem. Total working space required for the program is approximately 13*N double precision words.« less

Delocalized SYZ mirrors and confronting top-down SU(3)-structure holographic meson masses at finite g and N_c with P(article) D(ata) G(roup) values

NASA Astrophysics Data System (ADS)

Yadav, Vikas; Misra, Aalok; Sil, Karunava

2017-10-01

Meson spectroscopy at finite gauge coupling - whereat any perturbative QCD computation would break down - and finite number of colors, from a top-down holographic string model, has thus far been entirely missing in the literature. This paper fills this gap. Using the delocalized type IIA SYZ mirror (with SU(3) structure) of the holographic type IIB dual of large- N thermal QCD of Mia et al. (Nucl Phys B 839:187. arXiv:0902.1540 [hep-th], 2010) as constructed in Dhuria and Misra (JHEP 1311:001. arXiv:1306.4339 [hep-th], 2013) at finite coupling and number of colors (N_c = number of D5(\\overline{D5})-branes wrapping a vanishing two-cycle in the top-down holographic construct of Mia et al. (Nucl Phys B 839:187. arXiv:0902.1540 [hep-th], 2010) = O(1) in the IR in the MQGP limit of Dhuria and Misra (JHEP 1311:001. arXiv:1306.4339 [hep-th], 2013) at the end of a Seiberg-duality cascade), we obtain analytical (not just numerical) expressions for the vector and scalar meson spectra and compare our results with previous calculations of Sakai and Sugimoto (Prog Theor Phys 113:843. doi: 10.1143/PTP.113.843 arXiv:hep-th/0412141, 2005) and Dasgupta et al. (JHEP 1507:122. doi: 10.1007/JHEP07(2015)122 arXiv:1409.0559 [hep-th], 2015), and we obtain a closer match with the Particle Data Group (PDG) results of Olive et al. (Particle Data Group) (Chin Phys C 38:090001, 2014). Through explicit computations, we verify that the vector and scalar meson spectra obtained by the gravity dual with a black hole for all temperatures (small and large) are nearly isospectral with the spectra obtained by a thermal gravity dual valid for only low temperatures; the isospectrality is much closer for vector mesons than scalar mesons. The black-hole gravity dual (with a horizon radius smaller than the deconfinement scale) also provides the expected large- N suppressed decrease in vector meson mass with increase of temperature.

Cost-Effectiveness of Chagas Disease Vector Control Strategies in Northwestern Argentina

PubMed Central

Vazquez-Prokopec, Gonzalo M.; Spillmann, Cynthia; Zaidenberg, Mario; Kitron, Uriel; Gürtler, Ricardo E.

2009-01-01

Background Control and prevention of Chagas disease rely mostly on residual spraying of insecticides. In Argentina, vector control shifted from a vertical to a fully horizontal strategy based on community participation between 1992 and 2004. The effects of such strategy on Triatoma infestans, the main domestic vector, and on disease transmission have not been assessed. Methods and Findings Based on retrospective (1993–2004) records from the Argentinean Ministry of Health for the Moreno Department, Northwestern Argentina, we performed a cost-effectiveness (CE) analysis and compared the observed CE of the fully horizontal vector control strategy with the expected CE for a vertical or a mixed (i.e., vertical attack phase followed by horizontal surveillance) strategy. Total direct costs (in 2004 US$) of the horizontal and mixed strategies were, respectively, 3.3 and 1.7 times lower than the costs of the vertical strategy, due to reductions in personnel costs. The estimated CE ratios for the vertical, mixed and horizontal strategies were US$132, US$82 and US$45 per averted human case, respectively. When per diems were excluded from the costs (i.e., simulating the decentralization of control activities), the CE of vertical, mixed and horizontal strategies was reduced to US$60, US$42 and US$32 per averted case, respectively. Conclusions and Significance The mixed strategy would have averted between 1.6 and 4.0 times more human cases than the fully horizontal strategy, and would have been the most cost-effective option to interrupt parasite transmission in the Department. In rural and dispersed areas where waning vertical vector programs cannot accomplish full insecticide coverage, alternative strategies need to be developed. If properly implemented, community participation represents not only the most appealing but also the most cost-effective alternative to accomplish such objectives. PMID:19156190

A weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1989-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

A weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1990-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Weak Hamiltonian finite element method for optimal control problems

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.

1991-01-01

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Flow Applications of the Least Squares Finite Element Method

NASA Technical Reports Server (NTRS)

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.

Existence and stability, and discrete BB and rank conditions, for general mixed-hybrid finite elements in elasticity

NASA Technical Reports Server (NTRS)

Xue, W.-M.; Atluri, S. N.

1985-01-01

In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.

Computational mechanics analysis tools for parallel-vector supercomputers

NASA Technical Reports Server (NTRS)

Storaasli, O. O.; Nguyen, D. T.; Baddourah, M. A.; Qin, J.

1993-01-01

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigen-solution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization algorithm and domain decomposition. The source code for many of these algorithms is available from NASA Langley.

Automatic differentiation for design sensitivity analysis of structural systems using multiple processors

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Storaasli, Olaf O.; Qin, Jiangning; Qamar, Ramzi

1994-01-01

An automatic differentiation tool (ADIFOR) is incorporated into a finite element based structural analysis program for shape and non-shape design sensitivity analysis of structural systems. The entire analysis and sensitivity procedures are parallelized and vectorized for high performance computation. Small scale examples to verify the accuracy of the proposed program and a medium scale example to demonstrate the parallel vector performance on multiple CRAY C90 processors are included.

Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-05-01

We study the evolution of finite perturbations in the Lorenz ‘96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.

Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-01-01

We study the evolution of finite perturbations in the Lorenz `96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.

Weaving Knotted Vector Fields with Tunable Helicity.

PubMed

Kedia, Hridesh; Foster, David; Dennis, Mark R; Irvine, William T M

2016-12-30

We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot, and its generalizations. As finite-energy physical fields, they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly, we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.

A description of rotations for DEM models of particle systems

NASA Astrophysics Data System (ADS)

Campello, Eduardo M. B.

2015-06-01

In this work, we show how a vector parameterization of rotations can be adopted to describe the rotational motion of particles within the framework of the discrete element method (DEM). It is based on the use of a special rotation vector, called Rodrigues rotation vector, and accounts for finite rotations in a fully exact manner. The use of fictitious entities such as quaternions or complicated structures such as Euler angles is thereby circumvented. As an additional advantage, stick-slip friction models with inter-particle rolling motion are made possible in a consistent and elegant way. A few examples are provided to illustrate the applicability of the scheme. We believe that simple vector descriptions of rotations are very useful for DEM models of particle systems.

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data

NASA Astrophysics Data System (ADS)

Koltai, Péter; Renger, D. R. Michiel

2018-06-01

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.

Non-perturbative calculation of orbital and spin effects in molecules subject to non-uniform magnetic fields

NASA Astrophysics Data System (ADS)

Sen, Sangita; Tellgren, Erik I.

2018-05-01

External non-uniform magnetic fields acting on molecules induce non-collinear spin densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a general Hartree-Fock method, without any spin constraints, for non-perturbative calculations with finite non-uniform fields. London atomic orbitals are used to ensure faster basis convergence as well as invariance under constant gauge shifts of the magnetic vector potential. The implementation has been applied to investigate the joint orbital and spin response to a field gradient—quantified through the anapole moments—of a set of small molecules. The relative contributions of orbital and spin-Zeeman interaction terms have been studied both theoretically and computationally. Spin effects are stronger and show a general paramagnetic behavior for closed shell molecules while orbital effects can have either direction. Basis set convergence and size effects of anapole susceptibility tensors have been reported. The relation of the mixed anapole susceptibility tensor to chirality is also demonstrated.

Are Bred Vectors The Same As Lyapunov Vectors?

NASA Astrophysics Data System (ADS)

Kalnay, E.; Corazza, M.; Cai, M.

Regional loss of predictability is an indication of the instability of the underlying flow, where small errors in the initial conditions (or imperfections in the model) grow to large amplitudes in finite times. The stability properties of evolving flows have been studied using Lyapunov vectors (e.g., Alligood et al, 1996, Ott, 1993, Kalnay, 2002), singular vectors (e.g., Lorenz, 1965, Farrell, 1988, Molteni and Palmer, 1993), and, more recently, with bred vectors (e.g., Szunyogh et al, 1997, Cai et al, 2001). Bred vectors (BVs) are, by construction, closely related to Lyapunov vectors (LVs). In fact, after an infinitely long breeding time, and with the use of infinitesimal ampli- tudes, bred vectors are identical to leading Lyapunov vectors. In practical applications, however, bred vectors are different from Lyapunov vectors in two important ways: a) bred vectors are never globally orthogonalized and are intrinsically local in space and time, and b) they are finite-amplitude, finite-time vectors. These two differences are very significant in a dynamical system whose size is very large. For example, the at- mosphere is large enough to have "room" for several synoptic scale instabilities (e.g., storms) to develop independently in different regions (say, North America and Aus- tralia), and it is complex enough to have several different possible types of instabilities (such as barotropic, baroclinic, convective, and even Brownian motion). Bred vectors share some of their properties with leading LVs (Corazza et al, 2001a, 2001b, Toth and Kalnay, 1993, 1997, Cai et al, 2001). For example, 1) Bred vectors are independent of the norm used to define the size of the perturba- tion. Corazza et al. (2001) showed that bred vectors obtained using a potential enstro- phy norm were indistinguishable from bred vectors obtained using a streamfunction squared norm, in contrast with singular vectors. 2) Bred vectors are independent of the length of the rescaling period as long as the perturbations remain approximately linear (for example, for atmospheric models the interval for rescaling could be varied between a single time step and 1 day without affecting qualitatively the characteristics of the bred vectors. However, the finite-amplitude, finite-time, and lack of orthogonalization of the BVs introduces important differences with LVs: 1) In regions that undergo strong instabilities, the bred vectors tend to be locally domi- 1 nated by simple, low-dimensional structures. Patil et al (2001) showed that the BV-dim (appendix) gives a good estimate of the number of dominant directions (shapes) of the local k bred vectors. For example, if half of them are aligned in one direction, and half in a different direction, the BV-dim is about two. If the majority of the bred vectors are aligned predominantly in one direction and only a few are aligned in a second direction, then the BV-dim is between 1 and 2. Patil et al., (2001) showed that the regions with low dimensionality cover about 20% of the atmosphere. They also found that these low-dimensionality regions have a very well defined vertical structure, and a typical lifetime of 3-7 days. The low dimensionality identifies regions where the in- stability of the basic flow has manifested itself in a low number of preferred directions of perturbation growth. 2) Using a Quasi-Geostrophic simulation system of data assimilation developed by Morss (1999), Corazza et al (2001a, b) found that bred vectors have structures that closely resemble the background (short forecasts used as first guess) errors, which in turn dominate the local analysis errors. This is especially true in regions of low dimensionality, which is not surprising if these are unstable regions where errors grow in preferred shapes. 3) The number of bred vectors needed to represent the unstable subspace in the QG system is small (about 6-10). This was shown by computing the local BV-dim as a function of the number of independent bred vectors. Convergence in the local dimen- sion starts to occur at about 6 BVs, and is essentially complete when the number of vectors is about 10-15 (Corazza et al, 2001a). This should be contrasted with the re- sults of Snyder and Joly (1998) and Palmer et al (1998) who showed that hundreds of Lyapunov vectors with positive Lyapunov exponents are needed to represent the attractor of the system in quasi-geostrophic models. 4) Since only a few bred vectors are needed, and background errors project strongly in the subspace of bred vectors, Corazza et al (2001b) were able to develop cost-efficient methods to improve the 3D-Var data assimilation by adding to the background error covariance terms proportional to the outer product of the bred vectors, thus represent- ing the "errors of the day". This approach led to a reduction of analysis error variance of about 40% at very low cost. 5) The fact that BVs have finite amplitude provides a natural way to filter out instabil- ities present in the system that have fast growth, but saturate nonlinearly at such small amplitudes that they are irrelevant for ensemble perturbations. As shown by Lorenz (1996) Lyapunov vectors (and singular vectors) of models including these physical phenomena would be dominated by the fast but small amplitude instabilities, unless they are explicitly excluded from the linearized models. Bred vectors, on the other 2 hand, through the choice of an appropriate size for the perturbation, provide a natural filter based on nonlinear saturation of fast but irrelevant instabilities. 6) Every bred vector is qualitatively similar to the *leading* LV. LVs beyond the leading LV are obtained by orthogonalization after each time step with respect to the previous LVs subspace. The orthogonalization requires the introduction of a norm. With an enstrophy norm, the successive LVs have larger and larger horizontal scales, and a choice of a stream function norm would lead to successively smaller scales in the LVs. Beyond the first few LVs, there is little qualitative similarity between the background errors and the LVs. In summary, in a system like the atmosphere with enough physical space for several independent local instabilities, BVs and LVs share some properties but they also have significant differences. BV are finite-amplitude, finite-time, and because they are not globally orthogonalized, they have local properties in space. Bred vectors are akin to the leading LV, but bred vectors derived from different arbitrary initial perturba- tions remain distinct from each other, instead of collapsing into a single leading vec- tor, presumably because the nonlinear terms and physical parameterizations introduce sufficient stochastic forcing to avoid such convergence. As a result, there is no need for global orthogonalization, and the number of bred vectors required to describe the natural instabilities in an atmospheric system (from a local point of view) is much smaller than the number of Lyapunov vectors with positive Lyapunov exponents. The BVs are independent of the norm, whereas the LVs beyond the first one do depend on the choice of norm: for example, they become larger in scale with a vorticity norm, and smaller with a stream function norm. These properties of BVs result in significant advantages for data assimilation and en- semble forecasting for the atmosphere. Errors in the analysis have structures very similar to bred vectors, and it is found that they project very strongly on the subspace of a few bred vectors. This is not true for either Lyapunov vectors beyond the lead- ing LVs, or for singular vectors unless they are constructed with a norm based on the analysis error covariance matrix (or a bred vector covariance). The similarity between bred vectors and analysis errors leads to the ability to include "errors of the day" in the background error covariance and a significant improvement of the analysis beyond 3D-Var at a very low cost (Corazza, 2001b). References Alligood K. T., T. D. Sauer and J. A. Yorke, 1996: Chaos: an introduction to dynamical systems. Springer-Verlag, New York. Buizza R., J. Tribbia, F. Molteni and T. Palmer, 1993: Computation of optimal unstable 3 structures for numerical weather prediction models. Tellus, 45A, 388-407. Cai, M., E. Kalnay and Z. Toth, 2001: Potential impact of bred vectors on ensemble forecasting and data assimilation in the Zebiak-Cane model. Submitted to J of Climate. Corazza, M., E. Kalnay, D. J. Patil, R. Morss, M. Cai, I. Szunyogh, B. R. Hunt, E. Ott and J. Yorke, 2001: Use of the breeding technique to determine the structure of the "errors of the day". Submitted to Nonlinear Processes in Geophysics. Corazza, M., E. Kalnay, DJ Patil, E. Ott, J. Yorke, I Szunyogh and M. Cai, 2001: Use of the breeding technique in the estimation of the background error covariance matrix for a quasigeostrophic model. AMS Symposium on Observations, Data Assimilation and Predictability, Preprints volume, Orlando, FA, 14-17 January 2002. Farrell, B., 1988: Small error dynamics and the predictability of atmospheric flow, J. Atmos. Sciences, 45, 163-172. Kalnay, E 2002: Atmospheric modeling, data assimilation and predictability. Chapter 6. Cambridge University Press, UK. In press. Kalnay E and Z Toth 1994: Removing growing errors in the analysis. Preprints, Tenth Conference on Numerical Weather Prediction, pp 212-215. Amer. Meteor. Soc., July 18-22, 1994. Lorenz, E.N., 1965: A study of the predictability of a 28-variable atmospheric model. Tellus, 21, 289-307. Lorenz, E.N., 1996: Predictability- A problem partly solved. Proceedings of the ECMWF Seminar on Predictability, Reading, England, Vol. 1 1-18. Molteni F. and TN Palmer, 1993: Predictability and finite-time instability of the north- ern winter circulation. Q. J. Roy. Meteorol. Soc. 119, 269-298. Morss, R.E.: 1999: Adaptive observations: Idealized sampling strategies for improving numerical weather prediction. Ph.D. Thesis, Massachussetts Institute of Technology, 225pp. Ott, E., 1993: Chaos in Dynamical Systems. Cambridge University Press. New York. Palmer, TN, R. Gelaro, J. Barkmeijer and R. Buizza, 1998: Singular vectors, metrics and adaptive observations. J. Atmos Sciences, 55, 633-653. Patil, DJ, BR Hunt, E Kalnay, J. Yorke, and E. Ott, 2001: Local low dimensionality of atmospheric dynamics. Phys. Rev. Lett., 86, 5878. Patil, DJ, I. Szunyogh, BR Hunt, E Kalnay, E Ott, and J. Yorke, 2001: Using large 4 member ensembles to isolate local low dimensionality of atmospheric dynamics. AMS Symposium on Observations, Data Assimilation and Predictability, Preprints volume, Orlando, FA, 14-17 January 2002. Snyder, C. and A. Joly, 1998: Development of perturbations within growing baroclinic waves. Q. J. Roy. Meteor. Soc., 124, pp 1961. Szunyogh, I, E. Kalnay and Z. Toth, 1997: A comparison of Lyapunov and Singular vectors in a low resolution GCM. Tellus, 49A, 200-227. Toth, Z and E Kalnay 1993: Ensemble forecasting at NMC - the generation of pertur- bations. Bull. Amer. Meteorol. Soc., 74, 2317-2330. Toth, Z and E Kalnay 1997: Ensemble forecasting at NCEP and the breeding method. Mon Wea Rev, 125, 3297-3319. * Corresponding author address: Eugenia Kalnay, Meteorology Depart- ment, University of Maryland, College Park, MD 20742-2425, USA; email: ekalnay@atmos.umd.edu Appendix: BV-dimension Patil et al., (2001) defined local bred vectors around a point in the 3-dimensional grid of the model by taking the 24 closest horizontal neighbors. If there are k bred vectors available, and N model variables for each grid point, the k local bred vectors form the columns of a 25Nxk matrix B. The kxk covariance matrix is C=B^T B. Its eigen- values are positive, and its eigenvectors v(i) are the singular vectors of the local bred vector subspace. The Bred Vector dimension (BV-dim) measures the local effective dimension: BV-dim[s,s,...,s(k)]={SUM[s(i)]}^2/SUM[s(i)]^2 where s(i) are the square roots of the eigenvalues of the covariance matrix. 5

Dual Formulations of Mixed Finite Element Methods with Applications

PubMed Central

Gillette, Andrew; Bajaj, Chandrajit

2011-01-01

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail. PMID:21984841

Automotive applications of superconductors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ginsberg, M.

1987-01-01

These proceedings compile papers on supercomputers in the automobile industry. Titles include: An automotive engineer's guide to the effective use of scalar, vector, and parallel computers; fluid mechanics, finite elements, and supercomputers; and Automotive crashworthiness performance on a supercomputer.

Dual and mixed nonsymmetric stress-based variational formulations for coupled thermoelastodynamics with second sound effect

NASA Astrophysics Data System (ADS)

Tóth, Balázs

2018-03-01

Some new dual and mixed variational formulations based on a priori nonsymmetric stresses will be developed for linearly coupled irreversible thermoelastodynamic problems associated with second sound effect according to the Lord-Shulman theory. Having introduced the entropy flux vector instead of the entropy field and defining the dissipation and the relaxation potential as the function of the entropy flux, a seven-field dual and mixed variational formulation will be derived from the complementary Biot-Hamilton-type variational principle, using the Lagrange multiplier method. The momentum-, the displacement- and the infinitesimal rotation vector, and the a priori nonsymmetric stress tensor, the temperature change, the entropy field and its flux vector are considered as the independent field variables of this formulation. In order to handle appropriately the six different groups of temporal prescriptions in the relaxed- and/or the strong form, two variational integrals will be incorporated into the seven-field functional. Then, eliminating the entropy from this formulation through the strong fulfillment of the constitutive relation for the temperature change with the use of the Legendre transformation between the enthalpy and Gibbs potential, a six-field dual and mixed action functional is obtained. As a further development, the elimination of the momentum- and the velocity vector from the six-field principle through the a priori satisfaction of the kinematic equation and the constitutive relation for the momentum vector leads to a five-field variational formulation. These principles are suitable for the transient analyses of the structures exposed to a thermal shock of short temporal domain or a large heat flux.

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Angles-Only Navigation: Position and Velocity Solution from Absolute Triangulation

DTIC Science & Technology

2011-01-01

geocentric position vectors. Using two vectors derived from each such observation (see next section), a solution for a portion of the boat’s track was...t)x0 describes the curvature of the path in the direction x 0, which, for a geocentric coordinate system and /(t) < 0, will be toward the center of...finite distances, with geocentric coordinates known to a meter or better (readily available on the Internet) a straightfor- ward triangulation method

Vector 33: A reduce program for vector algebra and calculus in orthogonal curvilinear coordinates

NASA Astrophysics Data System (ADS)

Harper, David

1989-06-01

This paper describes a package with enables REDUCE 3.3 to perform algebra and calculus operations upon vectors. Basic algebraic operations between vectors and between scalars and vectors are provided, including scalar (dot) product and vector (cross) product. The vector differential operators curl, divergence, gradient and Laplacian are also defined, and are valid in any orthogonal curvilinear coordinate system. The package is written in RLISP to allow algebra and calculus to be performed using notation identical to that for operations. Scalars and vectors can be mixed quite freely in the same expression. The package will be of interest to mathematicians, engineers and scientists who need to perform vector calculations in orthogonal curvilinear coordinates.

The Vector-Ballot Approach for Online Voting Procedures

NASA Astrophysics Data System (ADS)

Kiayias, Aggelos; Yung, Moti

Looking at current cryptographic-based e-voting protocols, one can distinguish three basic design paradigms (or approaches): (a) Mix-Networks based, (b) Homomorphic Encryption based, and (c) Blind Signatures based. Each of the three possesses different advantages and disadvantages w.r.t. the basic properties of (i) efficient tallying, (ii) universal verifiability, and (iii) allowing write-in ballot capability (in addition to predetermined candidates). In fact, none of the approaches results in a scheme that simultaneously achieves all three. This is unfortunate, since the three basic properties are crucial for efficiency, integrity and versatility (flexibility), respectively. Further, one can argue that a serious business offering of voting technology should offer a flexible technology that achieves various election goals with a single user interface. This motivates our goal, which is to suggest a new "vector-ballot" based approach for secret-ballot e-voting that is based on three new notions: Provably Consistent Vector Ballot Encodings, Shrink-and-Mix Networks and Punch-Hole-Vector-Ballots. At the heart of our approach is the combination of mix networks and homomorphic encryption under a single user interface; given this, it is rather surprising that it achieves much more than any of the previous approaches for e-voting achieved in terms of the basic properties. Our approach is presented in two generic designs called "homomorphic vector-ballots with write-in votes" and "multi-candidate punch-hole vector-ballots"; both of our designs can be instantiated over any homomorphic encryption function.

Estimation of proportions in mixed pixels through their region characterization

NASA Technical Reports Server (NTRS)

Chittineni, C. B. (Principal Investigator)

1981-01-01

A region of mixed pixels can be characterized through the probability density function of proportions of classes in the pixels. Using information from the spectral vectors of a given set of pixels from the mixed pixel region, expressions are developed for obtaining the maximum likelihood estimates of the parameters of probability density functions of proportions. The proportions of classes in the mixed pixels can then be estimated. If the mixed pixels contain objects of two classes, the computation can be reduced by transforming the spectral vectors using a transformation matrix that simultaneously diagonalizes the covariance matrices of the two classes. If the proportions of the classes of a set of mixed pixels from the region are given, then expressions are developed for obtaining the estmates of the parameters of the probability density function of the proportions of mixed pixels. Development of these expressions is based on the criterion of the minimum sum of squares of errors. Experimental results from the processing of remotely sensed agricultural multispectral imagery data are presented.

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

Stabilization of lower hybrid drift modes by finite parallel wavenumber and electron temperature gradients in field-reversed configurations

NASA Astrophysics Data System (ADS)

Farengo, R.; Guzdar, P. N.; Lee, Y. C.

1989-08-01

The effect of finite parallel wavenumber and electron temperature gradients on the lower hybrid drift instability is studied in the parameter regime corresponding to the TRX-2 device [Fusion Technol. 9, 48 (1986)]. Perturbations in the electrostatic potential and all three components of the vector potential are considered and finite beta electron orbit modifications are included. The electron temperature gradient decreases the growth rate of the instability but, for kz=0, unstable modes exist for ηe(=T'en0/Ten0)>6. Since finite kz effects completely stabilize the mode at small values of kz/ky(≂5×10-3), magnetic shear could be responsible for stabilizing the lower hybrid drift instability in field-reversed configurations.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

Radiation and scattering from printed antennas on cylindrically conformal platforms

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.; Bindiganavale, Sunil

1994-01-01

The goal was to develop suitable methods and software for the analysis of antennas on cylindrical coated and uncoated platforms. Specifically, the finite element boundary integral and finite element ABC methods were employed successfully and associated software were developed for the analysis and design of wraparound and discrete cavity-backed arrays situated on cylindrical platforms. This work led to the successful implementation of analysis software for such antennas. Developments which played a role in this respect are the efficient implementation of the 3D Green's function for a metallic cylinder, the incorporation of the fast Fourier transform in computing the matrix-vector products executed in the solver of the finite element-boundary integral system, and the development of a new absorbing boundary condition for terminating the finite element mesh on cylindrical surfaces.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

The MUSIC algorithm for impedance tomography of small inclusions from discrete data

NASA Astrophysics Data System (ADS)

Lechleiter, A.

2015-09-01

We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm’s images.

Full Wave Analysis of RF Signal Attenuation in a Lossy Rough Surface Cave using a High Order Time Domain Vector Finite Element Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pingenot, J; Rieben, R; White, D

2005-10-31

We present a computational study of signal propagation and attenuation of a 200 MHz planar loop antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The numerical technique is first verified against theoretical results for a planar loop antenna in a smooth lossy cave. The simulation is then performed for a series of random rough surface meshes in ordermore » to generate statistical data for the propagation and attenuation properties of the antenna in a cave environment. Results for the mean and variance of the power spectral density of the electric field are presented and discussed.« less

Nonreciprocal dispersion of spin waves in ferromagnetic thin films covered with a finite-conductivity metal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mruczkiewicz, M.; Krawczyk, M.

2014-03-21

We study the effect of one-side metallization of a uniform ferromagnetic thin film on its spin-wave dispersion relation in the Damon–Eshbach geometry. Due to the finite conductivity of the metallic cover layer on the ferromagnetic film, the spin-wave dispersion relation may be nonreciprocal only in a limited wave-vector range. We provide an approximate analytical solution for the spin-wave frequency, discuss its validity, and compare it with numerical results. The dispersion is analyzed systematically by varying the parameters of the ferromagnetic film, the metal cover layer and the value of the external magnetic field. The conclusions drawn from this analysis allowmore » us to define a structure based on a 30 nm thick CoFeB film with an experimentally accessible nonreciprocal dispersion relation in a relatively wide wave-vector range.« less

Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

NASA Astrophysics Data System (ADS)

Voznyuk, I.; Litman, A.; Tortel, H.

2015-08-01

A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.

A combined registration and finite element analysis method for fast estimation of intraoperative brain shift; phantom and animal model study.

PubMed

Mohammadi, Amrollah; Ahmadian, Alireza; Rabbani, Shahram; Fattahi, Ehsan; Shirani, Shapour

2017-12-01

Finite element models for estimation of intraoperative brain shift suffer from huge computational cost. In these models, image registration and finite element analysis are two time-consuming processes. The proposed method is an improved version of our previously developed Finite Element Drift (FED) registration algorithm. In this work the registration process is combined with the finite element analysis. In the Combined FED (CFED), the deformation of whole brain mesh is iteratively calculated by geometrical extension of a local load vector which is computed by FED. While the processing time of the FED-based method including registration and finite element analysis was about 70 s, the computation time of the CFED was about 3.2 s. The computational cost of CFED is almost 50% less than similar state of the art brain shift estimators based on finite element models. The proposed combination of registration and structural analysis can make the calculation of brain deformation much faster. Copyright © 2016 John Wiley & Sons, Ltd.

Modeling the purging of dense fluid from a street canyon driven by an interfacial mixing flow and skimming flow

NASA Astrophysics Data System (ADS)

Baratian-Ghorghi, Z.; Kaye, N. B.

2013-07-01

An experimental study is presented to investigate the mechanism of flushing a trapped dense contaminant from a canyon by turbulent boundary layer flow. The results of a series of steady-state experiments are used to parameterize the flushing mechanisms. The steady-state experimental results for a canyon with aspect ratio one indicate that dense fluid is removed from the canyon by two different processes, skimming of dense fluid from the top of the dense layer; and by an interfacial mixing flow that mixes fresh fluid down into the dense lower layer (entrainment) while mixing dense fluid into the flow above the canyon (detrainment). A model is developed for the time varying buoyancy profile within the canyon as a function of the Richardson number which parameterizes both the interfacial mixing and skimming processes observed. The continuous release steady-state experiments allowed for the direct measurement of the skimming and interfacial mixing flow rates for any layer depth and Richardson number. Both the skimming rate and the interfacial mixing rate were found to be power-law functions of the Richardson number of the layer. The model results were compared to the results of previously published finite release experiments [Z. Baratian-Ghorghi and N. B. Kaye, Atmos. Environ. 60, 392-402 (2012)], 10.1016/j.atmosenv.2012.06.077. A high degree of consistency was found between the finite release data and the continuous release data. This agreement acts as an excellent check on the measurement techniques used, as the finite release data was based on curve fitting through buoyancy versus time data, while the continuous release data was calculated directly by measuring the rate of addition of volume and buoyancy once a steady-state was established. Finally, a system of ordinary differential equations is presented to model the removal of dense fluid from the canyon based on empirical correlations of the skimming and interfacial mixing taken form the steady-state experiments. The ODE model predicts well the time taken for a finite volume of dense fluid to be flushed from a canyon.

Improved accuracy for finite element structural analysis via an integrated force method

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Aiello, R. A.; Berke, L.

1992-01-01

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

Spectral functions at small energies and the electrical conductivity in hot quenched lattice QCD.

PubMed

Aarts, Gert; Allton, Chris; Foley, Justin; Hands, Simon; Kim, Seyong

2007-07-13

In lattice QCD, the maximum entropy method can be used to reconstruct spectral functions from Euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and gives a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.

Explicit Finite Element Techniques Used to Characterize Splashdown of the Space Shuttle Solid Rocket Booster Aft Skirt

NASA Technical Reports Server (NTRS)

Melis, Matthew E.

2003-01-01

NASA Glenn Research Center s Structural Mechanics Branch has years of expertise in using explicit finite element methods to predict the outcome of ballistic impact events. Shuttle engineers from the NASA Marshall Space Flight Center and NASA Kennedy Space Flight Center required assistance in assessing the structural loads that a newly proposed thrust vector control system for the space shuttle solid rocket booster (SRB) aft skirt would expect to see during its recovery splashdown.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Assessing uncertainty in the turbulent upper-ocean mixed layer using an unstructured finite-element solver

NASA Astrophysics Data System (ADS)

Pacheco, Luz; Smith, Katherine; Hamlington, Peter; Niemeyer, Kyle

2017-11-01

Vertical transport flux in the ocean upper mixed layer has recently been attributed to submesoscale currents, which occur at scales on the order of kilometers in the horizontal direction. These phenomena, which include fronts and mixed-layer instabilities, have been of particular interest due to the effect of turbulent mixing on nutrient transport, facilitating phytoplankton blooms. We study these phenomena using a non-hydrostatic, large eddy simulation for submesoscale currents in the ocean, developed using the extensible, open-source finite element platform FEniCs. Our model solves the standard Boussinesq Euler equations in variational form using the finite element method. FEniCs enables the use of parallel computing on modern systems for efficient computing time, and is suitable for unstructured grids where irregular topography can be considered in the future. The solver will be verified against the well-established NCAR-LES model and validated against observational data. For the verification with NCAR-LES, the velocity, pressure, and buoyancy fields are compared through a surface-wind-driven, open-ocean case. We use this model to study the impacts of uncertainties in the model parameters, such as near-surface buoyancy flux and secondary circulation, and discuss implications.

Vortical susceptibility of finite-density QCD matter

DOE PAGES

Aristova, A.; Frenklakh, D.; Gorsky, A.; ...

2016-10-07

Here, the susceptibility of finite-density QCD matter to vorticity is introduced, as an analog of magnetic susceptibility. It describes the spin polarization of quarks and antiquarks in finite-density QCD matter induced by rotation. We estimate this quantity in the chirally broken phase using the mixed gauge-gravity anomaly at finite baryon density. It is proposed that the vortical susceptibility of QCD matter is responsible for the polarization of Λ and Λ¯ hyperons observed recently in heavy ion collisions at RHIC by the STAR collaboration.

Parallel-Vector Algorithm For Rapid Structural Anlysis

NASA Technical Reports Server (NTRS)

Agarwal, Tarun R.; Nguyen, Duc T.; Storaasli, Olaf O.

1993-01-01

New algorithm developed to overcome deficiency of skyline storage scheme by use of variable-band storage scheme. Exploits both parallel and vector capabilities of modern high-performance computers. Gives engineers and designers opportunity to include more design variables and constraints during optimization of structures. Enables use of more refined finite-element meshes to obtain improved understanding of complex behaviors of aerospace structures leading to better, safer designs. Not only attractive for current supercomputers but also for next generation of shared-memory supercomputers.

Lie theory and control systems defined on spheres

NASA Technical Reports Server (NTRS)

Brockett, R. W.

1972-01-01

It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case.

Exploring and Making Sense of Large Graphs

DTIC Science & Technology

2015-08-01

and bold) are n × n ; vectors (lower-case bold) are n × 1 column vectors, and scalars (in lower-case plain font) typically correspond to strength of...graph is often denoted as |V| or n . Edges or Links: A finite set E of lines between objects in a graph. The edges represent relationships between the...Adjacency matrix of a simple, unweighted and undirected graph. Adjacency matrix: The adjacency matrix of a graph G is an n × n matrix A, whose element aij

Implementation details of the coupled QMR algorithm

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1992-01-01

The original quasi-minimal residual method (QMR) relies on the three-term look-ahead Lanczos process, to generate basis vectors for the underlying Krylov subspaces. However, empirical observations indicate that, in finite precision arithmetic, three-term vector recurrences are less robust than mathematically equivalent coupled two-term recurrences. Therefore, we recently proposed a new implementation of the QMR method based on a coupled two-term look-ahead Lanczos procedure. In this paper, we describe implementation details of this coupled QMR algorithm, and we present results of numerical experiments.

Using trees to compute approximate solutions to ordinary differential equations exactly

NASA Technical Reports Server (NTRS)

Grossman, Robert

1991-01-01

Some recent work is reviewed which relates families of trees to symbolic algorithms for the exact computation of series which approximate solutions of ordinary differential equations. It turns out that the vector space whose basis is the set of finite, rooted trees carries a natural multiplication related to the composition of differential operators, making the space of trees an algebra. This algebraic structure can be exploited to yield a variety of algorithms for manipulating vector fields and the series and algebras they generate.

An Evaluation of an Algorithm for Linear Inequalities and Its Applications

NASA Technical Reports Server (NTRS)

Jurgensen, J.

1973-01-01

An algorithm is presented for obtaining a solution alpha to a set of inequalities (A alpha) 0 where A is an N x m-matrix and alpha is an m-vector. If the set of inequalities is consistant, then the algorithm is guaranteed to arrive at a solution in a finite number of steps. Also, if in the iteration, a negative vector is obtained, then the initial set of inequalities is inconsistant, and the iteration is terminated.

Differential Calculus on h-Deformed Spaces

NASA Astrophysics Data System (ADS)

Herlemont, Basile; Ogievetsky, Oleg

2017-10-01

We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators {Diff}_{h},σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings {Diff}_{h},σ(n).

Outcomes of co-infection by two potyviruses: implications for the evolution of manipulative strategies

PubMed Central

Salvaudon, Lucie; De Moraes, Consuelo M.; Mescher, Mark C.

2013-01-01

Recent studies have documented effects of plant viruses on host plants that appear to enhance transmission by insect vectors. But, almost no empirical work has explored the implications of such apparent manipulation for interactions among co-infecting pathogens. We examined single and mixed infections of two potyviruses, watermelon mosaic virus (WMV) and zucchini yellow mosaic virus (ZYMV), that frequently co-occur in cucurbitaceae populations and share the same aphid vectors. We found that ZYMV isolates replicated at similar rates in single and mixed infections, whereas WMV strains accumulated to significantly lower levels in the presence of ZYMV. Furthermore, ZYMV induced changes in leaf colour and volatile emissions that enhanced aphid (Aphis gossypii) recruitment to infected plants. By contrast, WMV did not elicit strong effects on plant–aphid interactions. Nevertheless, WMV was still readily transmitted from mixed infections, despite fairing poorly in in-plant competition. These findings suggest that pathogen effects on host–vector interactions may well influence competition among co-infecting pathogens. For example, if non-manipulative pathogens benefit from the increased vector traffic elicited by manipulative competitors, their costs of competition may be mitigated to some extent. Conversely, the benefits of manipulation may be limited by free-rider effects in systems where there is strong competition among pathogens for host resources and/or access to vectors. PMID:23407835

Identification of DNA-Binding Proteins Using Mixed Feature Representation Methods.

PubMed

Qu, Kaiyang; Han, Ke; Wu, Song; Wang, Guohua; Wei, Leyi

2017-09-22

DNA-binding proteins play vital roles in cellular processes, such as DNA packaging, replication, transcription, regulation, and other DNA-associated activities. The current main prediction method is based on machine learning, and its accuracy mainly depends on the features extraction method. Therefore, using an efficient feature representation method is important to enhance the classification accuracy. However, existing feature representation methods cannot efficiently distinguish DNA-binding proteins from non-DNA-binding proteins. In this paper, a multi-feature representation method, which combines three feature representation methods, namely, K-Skip-N-Grams, Information theory, and Sequential and structural features (SSF), is used to represent the protein sequences and improve feature representation ability. In addition, the classifier is a support vector machine. The mixed-feature representation method is evaluated using 10-fold cross-validation and a test set. Feature vectors, which are obtained from a combination of three feature extractions, show the best performance in 10-fold cross-validation both under non-dimensional reduction and dimensional reduction by max-relevance-max-distance. Moreover, the reduced mixed feature method performs better than the non-reduced mixed feature technique. The feature vectors, which are a combination of SSF and K-Skip-N-Grams, show the best performance in the test set. Among these methods, mixed features exhibit superiority over the single features.

Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials

NASA Technical Reports Server (NTRS)

Camanho, Pedro P.; Davila, Carlos G.

2002-01-01

A new decohesion element with mixed-mode capability is proposed and demonstrated. The element is used at the interface between solid finite elements to model the initiation and non-self-similar growth of delaminations. A single relative displacement-based damage parameter is applied in a softening law to track the damage state of the interface and to prevent the restoration of the cohesive state during unloading. The softening law for mixed-mode delamination propagation can be applied to any mode interaction criterion such as the two-parameter power law or the three-parameter Benzeggagh-Kenane criterion. To demonstrate the accuracy of the predictions and the irreversibility capability of the constitutive law, steady-state delamination growth is simulated for quasistatic loading-unloading cycles of various single mode and mixed-mode delamination test specimens.

An improved flux-split algorithm applied to hypersonic flows in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1988-01-01

An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.

Accurate solutions for transonic viscous flow over finite wings

NASA Technical Reports Server (NTRS)

Vatsa, V. N.

1986-01-01

An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.

Finite-time consensus for controlled dynamical systems in network

NASA Astrophysics Data System (ADS)

Zoghlami, Naim; Mlayeh, Rhouma; Beji, Lotfi; Abichou, Azgal

2018-04-01

The key challenges in networked dynamical systems are the component heterogeneities, nonlinearities, and the high dimension of the formulated vector of state variables. In this paper, the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift. For each model structure that defines homogeneous and heterogeneous multi-system behaviour, we derive protocols leading to finite-time consensus. For each model evolving in networks forming a homogeneous or heterogeneous multi-system, protocols integrating sufficient conditions are derived leading to finite-time consensus. Likewise, for the networking topology, we make use of fixed directed and undirected graphs. To prove our approaches, finite-time stability theory and Lyapunov methods are considered. As illustrative examples, the homogeneous multi-unicycle kinematics and the homogeneous/heterogeneous multi-second order dynamics in networks are studied.

Shallow-trap-induced positive absorptive two-beam coupling 'gain' and light-induced transparency in nominally undoped barium titanate

NASA Technical Reports Server (NTRS)

Garrett, M. H.; Tayebati, P.; Chang, J. Y.; Jenssen, H. P.; Warde, C.

1992-01-01

The asymmetry of beam coupling with respect to the orientation of the polar axis in a nominally undoped barium titanate crystal is used to determine the electro-optic and absorptive 'gain' in the usual beam-coupling geometry. For small grating wave vectors, the electrooptic coupling vanishes but the absorptive coupling remains finite and positive. Positive absorptive coupling at small grating wave vectors is correlated with the light-induced transparency of the crystal described herein. The intensity and grating wave vector dependence of the electrooptic and absorptive coupling, and the light-induced transparency are consistent with a model incorporating deep and shallow levels.

Mixed-mode stress intensity factors for kink cracks with finite kink length loaded in tension and bending: application to dentin and enamel.

PubMed

Bechtle, Sabine; Fett, Theo; Rizzi, Gabriele; Habelitz, Stefan; Schneider, Gerold A

2010-05-01

Fracture toughness resistance curves describe a material's resistance against crack propagation. These curves are often used to characterize biomaterials like bone, nacre or dentin as these materials commonly exhibit a pronounced increase in fracture toughness with crack extension due to co-acting mechanisms such as crack bridging, crack deflection and microcracking. The knowledge of appropriate stress intensity factors which depend on the sample and crack geometry is essential for determining these curves. For the dental biomaterials enamel and dentin it was observed that, under bending and tensile loading, crack propagation occurs under certain constant angles to the initial notch direction during testing procedures used for fracture resistance curve determination. For this special crack geometry (a kink crack of finite length in a finite body) appropriate geometric function solutions are missing. Hence, we present in this study new mixed-mode stress intensity factors for kink cracks with finite kink length within samples of finite dimensions for two loading cases (tension and bending) which were derived from a combination of mixed-mode stress intensity factors of kink cracks with infinitely small kinks and of slant cracks. These results were further applied to determine the fracture resistance curves of enamel and dentin by testing single edge notched bending (SENB) specimens. It was found that kink cracks with finite kink length exhibit identical stress fields to slant cracks as soon as the kink length exceeds 0.15 times the initial straight crack or notch length. The use of stress intensity factor solutions for infinitely small kink cracks for the determination of dentin fracture resistance curves (as was done by other researchers) leads to an overestimation of dentin's fracture resistance of up to 30%. Copyright 2010 Elsevier Ltd. All rights reserved.

Effects of mixing in threshold models of social behavior

NASA Astrophysics Data System (ADS)

Akhmetzhanov, Andrei R.; Worden, Lee; Dushoff, Jonathan

2013-07-01

We consider the dynamics of an extension of the influential Granovetter model of social behavior, where individuals are affected by their personal preferences and observation of the neighbors’ behavior. Individuals are arranged in a network (usually the square lattice), and each has a state and a fixed threshold for behavior changes. We simulate the system asynchronously by picking a random individual and we either update its state or exchange it with another randomly chosen individual (mixing). We describe the dynamics analytically in the fast-mixing limit by using the mean-field approximation and investigate it mainly numerically in the case of finite mixing. We show that the dynamics converge to a manifold in state space, which determines the possible equilibria, and show how to estimate the projection of this manifold by using simulated trajectories, emitted from different initial points. We show that the effects of considering the network can be decomposed into finite-neighborhood effects, and finite-mixing-rate effects, which have qualitatively similar effects. Both of these effects increase the tendency of the system to move from a less-desired equilibrium to the “ground state.” Our findings can be used to probe shifts in behavioral norms and have implications for the role of information flow in determining when social norms that have become unpopular in particular communities (such as foot binding or female genital cutting) persist or vanish.

DOMAIN DECOMPOSITION METHOD APPLIED TO A FLOW PROBLEM Norberto C. Vera Guzmán Institute of Geophysics, UNAM

NASA Astrophysics Data System (ADS)

Vera, N. C.; GMMC

2013-05-01

In this paper we present the results of macrohybrid mixed Darcian flow in porous media in a general three-dimensional domain. The global problem is solved as a set of local subproblems which are posed using a domain decomposition method. Unknown fields of local problems, velocity and pressure are approximated using mixed finite elements. For this application, a general three-dimensional domain is considered which is discretized using tetrahedra. The discrete domain is decomposed into subdomains and reformulated the original problem as a set of subproblems, communicated through their interfaces. To solve this set of subproblems, we use finite element mixed and parallel computing. The parallelization of a problem using this methodology can, in principle, to fully exploit a computer equipment and also provides results in less time, two very important elements in modeling. Referencias G.Alduncin and N.Vera-Guzmán Parallel proximal-point algorithms for mixed _nite element models of _ow in the subsurface, Commun. Numer. Meth. Engng 2004; 20:83-104 (DOI: 10.1002/cnm.647) Z. Chen, G.Huan and Y. Ma Computational Methods for Multiphase Flows in Porous Media, SIAM, Society for Industrial and Applied Mathematics, Philadelphia, 2006. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer-Verlag, Berlin, 1994. Brezzi F, Fortin M. Mixed and Hybrid Finite Element Methods. Springer: New York, 1991.

Fuzzy interval Finite Element/Statistical Energy Analysis for mid-frequency analysis of built-up systems with mixed fuzzy and interval parameters

NASA Astrophysics Data System (ADS)

Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan

2016-10-01

This paper introduces mixed fuzzy and interval parametric uncertainties into the FE components of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model for mid-frequency analysis of built-up systems, thus an uncertain ensemble combining non-parametric with mixed fuzzy and interval parametric uncertainties comes into being. A fuzzy interval Finite Element/Statistical Energy Analysis (FIFE/SEA) framework is proposed to obtain the uncertain responses of built-up systems, which are described as intervals with fuzzy bounds, termed as fuzzy-bounded intervals (FBIs) in this paper. Based on the level-cut technique, a first-order fuzzy interval perturbation FE/SEA (FFIPFE/SEA) and a second-order fuzzy interval perturbation FE/SEA method (SFIPFE/SEA) are developed to handle the mixed parametric uncertainties efficiently. FFIPFE/SEA approximates the response functions by the first-order Taylor series, while SFIPFE/SEA improves the accuracy by considering the second-order items of Taylor series, in which all the mixed second-order items are neglected. To further improve the accuracy, a Chebyshev fuzzy interval method (CFIM) is proposed, in which the Chebyshev polynomials is used to approximate the response functions. The FBIs are eventually reconstructed by assembling the extrema solutions at all cut levels. Numerical results on two built-up systems verify the effectiveness of the proposed methods.

Liquid-gas phase transition in asymmetric nuclear matter at finite temperature

NASA Astrophysics Data System (ADS)

Maruyama, Toshiki; Tatsumi, Toshitaka; Chiba, Satoshi

2010-03-01

Liquid-gas phase transition is discussed in warm asymmetric nuclear matter. Some peculiar features are figured out from the viewpoint of the basic thermodynamics about the phase equilibrium. We treat the mixed phase of the binary system based on the Gibbs conditions. When the Coulomb interaction is included, the mixed phase is no more uniform and the sequence of the pasta structures appears. Comparing the results with those given by the simple bulk calculation without the Coulomb interaction, we extract specific features of the pasta structures at finite temperature.

On the Use of a Mixed Gaussian/Finite-Element Basis Set for the Calculation of Rydberg States

NASA Technical Reports Server (NTRS)

Thuemmel, Helmar T.; Langhoff, Stephen (Technical Monitor)

1996-01-01

Configuration-interaction studies are reported for the Rydberg states of the helium atom using mixed Gaussian/finite-element (GTO/FE) one particle basis sets. Standard Gaussian valence basis sets are employed, like those, used extensively in quantum chemistry calculations. It is shown that the term values for high-lying Rydberg states of the helium atom can be obtained accurately (within 1 cm -1), even for a small GTO set, by augmenting the n-particle space with configurations, where orthonormalized interpolation polynomials are singly occupied.

The finite state projection algorithm for the solution of the chemical master equation.

PubMed

Munsky, Brian; Khammash, Mustafa

2006-01-28

This article introduces the finite state projection (FSP) method for use in the stochastic analysis of chemically reacting systems. One can describe the chemical populations of such systems with probability density vectors that evolve according to a set of linear ordinary differential equations known as the chemical master equation (CME). Unlike Monte Carlo methods such as the stochastic simulation algorithm (SSA) or tau leaping, the FSP directly solves or approximates the solution of the CME. If the CME describes a system that has a finite number of distinct population vectors, the FSP method provides an exact analytical solution. When an infinite or extremely large number of population variations is possible, the state space can be truncated, and the FSP method provides a certificate of accuracy for how closely the truncated space approximation matches the true solution. The proposed FSP algorithm systematically increases the projection space in order to meet prespecified tolerance in the total probability density error. For any system in which a sufficiently accurate FSP exists, the FSP algorithm is shown to converge in a finite number of steps. The FSP is utilized to solve two examples taken from the field of systems biology, and comparisons are made between the FSP, the SSA, and tau leaping algorithms. In both examples, the FSP outperforms the SSA in terms of accuracy as well as computational efficiency. Furthermore, due to very small molecular counts in these particular examples, the FSP also performs far more effectively than tau leaping methods.

Finite Geometries in Quantum Theory:. from Galois (fields) to Hjelmslev (rings)

NASA Astrophysics Data System (ADS)

Saniga, Metod; Planat, Michel

Geometries over Galois fields (and related finite combinatorial structures/algebras) have recently been recognized to play an ever-increasing role in quantum theory, especially when addressing properties of mutually unbiased bases (MUBs). The purpose of this contribution is to show that completely new vistas open up if we consider a generalized class of finite (projective) geometries, viz. those defined over Galois rings and/or other finite Hjelmslev rings. The case is illustrated by demonstrating that the basic combinatorial properties of a complete set of MUBs of a q-dimensional Hilbert space { H}q, q = pr with p being a prime and r a positive integer, are qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p2 and rank r. The q vectors of a basis of { H}q correspond to the q points of a (so-called) neighbour class and the q + 1 MUBs answer to the total number of (pairwise disjoint) neighbour classes on the conic. Although this remarkable analogy is still established at the level of cardinalities only, we currently work on constructing an explicit mapping by associating a MUB to each neighbour class of the points of the conic and a state vector of this MUB to a particular point of the class. Further research in this direction may prove to be of great relevance for many areas of quantum information theory, in particular for quantum information processing.

Scaling laws and reduced-order models for mixing and reactive-transport in heterogeneous anisotropic porous media

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Karra, S.; Nakshatrala, K. B.

2016-12-01

Fundamental to enhancement and control of the macroscopic spreading, mixing, and dilution of solute plumes in porous media structures is the topology of flow field and underlying heterogeneity and anisotropy contrast of porous media. Traditionally, in literature, the main focus was limited to the shearing effects of flow field (i.e., flow has zero helical density, meaning that flow is always perpendicular to vorticity vector) on scalar mixing [2]. However, the combined effect of anisotropy of the porous media and the helical structure (or chaotic nature) of the flow field on the species reactive-transport and mixing has been rarely studied. Recently, it has been experimentally shown that there is an irrefutable evidence that chaotic advection and helical flows are inherent in porous media flows [1,2]. In this poster presentation, we present a non-intrusive physics-based model-order reduction framework to quantify the effects of species mixing in-terms of reduced-order models (ROMs) and scaling laws. The ROM framework is constructed based on the recent advancements in non-negative formulations for reactive-transport in heterogeneous anisotropic porous media [3] and non-intrusive ROM methods [4]. The objective is to generate computationally efficient and accurate ROMs for species mixing for different values of input data and reactive-transport model parameters. This is achieved by using multiple ROMs, which is a way to determine the robustness of the proposed framework. Sensitivity analysis is performed to identify the important parameters. Representative numerical examples from reactive-transport are presented to illustrate the importance of the proposed ROMs to accurately describe mixing process in porous media. [1] Lester, Metcalfe, and Trefry, "Is chaotic advection inherent to porous media flow?," PRL, 2013. [2] Ye, Chiogna, Cirpka, Grathwohl, and Rolle, "Experimental evidence of helical flow in porous media," PRL, 2015. [3] Mudunuru, and Nakshatrala, "On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method," JCP, 2016. [4] Quarteroni, Manzoni, and Negri. "Reduced Basis Methods for Partial Differential Equations: An Introduction," Springer, 2016.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

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

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

In vitro fatigue tests and in silico finite element analysis of dental implants with different fixture/abutment joint types using computer-aided design models.

PubMed

Yamaguchi, Satoshi; Yamanishi, Yasufumi; Machado, Lucas S; Matsumoto, Shuji; Tovar, Nick; Coelho, Paulo G; Thompson, Van P; Imazato, Satoshi

2018-01-01

The aim of this study was to evaluate fatigue resistance of dental fixtures with two different fixture-abutment connections by in vitro fatigue testing and in silico three-dimensional finite element analysis (3D FEA) using original computer-aided design (CAD) models. Dental implant fixtures with external connection (EX) or internal connection (IN) abutments were fabricated from original CAD models using grade IV titanium and step-stress accelerated life testing was performed. Fatigue cycles and loads were assessed by Weibull analysis, and fatigue cracking was observed by micro-computed tomography and a stereomicroscope with high dynamic range software. Using the same CAD models, displacement vectors of implant components were also analyzed by 3D FEA. Angles of the fractured line occurring at fixture platforms in vitro and of displacement vectors corresponding to the fractured line in silico were compared by two-way ANOVA. Fatigue testing showed significantly greater reliability for IN than EX (p<0.001). Fatigue crack initiation was primarily observed at implant fixture platforms. FEA demonstrated that crack lines of both implant systems in vitro were observed in the same direction as displacement vectors of the implant fixtures in silico. In silico displacement vectors in the implant fixture are insightful for geometric development of dental implants to reduce complex interactions leading to fatigue failure. Copyright © 2017 Japan Prosthodontic Society. Published by Elsevier Ltd. All rights reserved.

3-D Magnetotelluric Forward Modeling And Inversion Incorporating Topography By Using Vector Finite-Element Method Combined With Divergence Corrections Based On The Magnetic Field (VFEH++)

NASA Astrophysics Data System (ADS)

Shi, X.; Utada, H.; Jiaying, W.

2009-12-01

The vector finite-element method combined with divergence corrections based on the magnetic field H, referred to as VFEH++ method, is developed to simulate the magnetotelluric (MT) responses of 3-D conductivity models. The advantages of the new VFEH++ method are the use of edge-elements to eliminate the vector parasites and the divergence corrections to explicitly guarantee the divergence-free conditions in the whole modeling domain. 3-D MT topographic responses are modeling using the new VFEH++ method, and are compared with those calculated by other numerical methods. The results show that MT responses can be modeled highly accurate using the VFEH+ +method. The VFEH++ algorithm is also employed for the 3-D MT data inversion incorporating topography. The 3-D MT inverse problem is formulated as a minimization problem of the regularized misfit function. In order to avoid the huge memory requirement and very long time for computing the Jacobian sensitivity matrix for Gauss-Newton method, we employ the conjugate gradient (CG) approach to solve the inversion equation. In each iteration of CG algorithm, the cost computation is the product of the Jacobian sensitivity matrix with a model vector x or its transpose with a data vector y, which can be transformed into two pseudo-forwarding modeling. This avoids the full explicitly Jacobian matrix calculation and storage which leads to considerable savings in the memory required by the inversion program in PC computer. The performance of CG algorithm will be illustrated by several typical 3-D models with horizontal earth surface and topographic surfaces. The results show that the VFEH++ and CG algorithms can be effectively employed to 3-D MT field data inversion.

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Numerical model of glulam beam delamination in dependence on cohesive strength

NASA Astrophysics Data System (ADS)

Kawecki, Bartosz; Podgórski, Jerzy

2018-01-01

This paper presents an attempt of using a finite element method for predicting delamination of a glue laminated timber beam through a cohesive layer. There were used cohesive finite elements, quadratic stress damage initiation criterion and mixed mode energy release rate failure model. Finite element damage was equal to its complete stiffness degradation. Timber material was considered to be an orthotropic with plastic behaviour after reaching bending limit.

An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment.

PubMed

Gültekin, Osman; Sommer, Gerhard; Holzapfel, Gerhard A

2016-11-01

This study deals with the viscoelastic constitutive modeling and the respective computational analysis of the human passive myocardium. We start by recapitulating the locally orthotropic inner structure of the human myocardial tissue and model the mechanical response through invariants and structure tensors associated with three orthonormal basis vectors. In accordance with recent experimental findings the ventricular myocardial tissue is assumed to be incompressible, thick-walled, orthotropic and viscoelastic. In particular, one spring element coupled with Maxwell elements in parallel endows the model with viscoelastic features such that four dashpots describe the viscous response due to matrix, fiber, sheet and fiber-sheet fragments. In order to alleviate the numerical obstacles, the strictly incompressible model is altered by decomposing the free-energy function into volumetric-isochoric elastic and isochoric-viscoelastic parts along with the multiplicative split of the deformation gradient which enables the three-field mixed finite element method. The crucial aspect of the viscoelastic formulation is linked to the rate equations of the viscous overstresses resulting from a 3-D analogy of a generalized 1-D Maxwell model. We provide algorithmic updates for second Piola-Kirchhoff stress and elasticity tensors. In the sequel, we address some numerical aspects of the constitutive model by applying it to elastic, cyclic and relaxation test data obtained from biaxial extension and triaxial shear tests whereby we assess the fitting capacity of the model. With the tissue parameters identified, we conduct (elastic and viscoelastic) finite element simulations for an ellipsoidal geometry retrieved from a human specimen.

Topography-Guided Transepithelial Surface Ablation in the Treatment of Moderate to High Astigmatism.

PubMed

Chen, Xiangjun; Stojanovic, Aleksandar; Simonsen, David; Wang, Xiaorui; Liu, Yanhua; Utheim, Tor Paaske

2016-06-01

To analyze the outcomes of treatment of astigmatism of 2.00 diopters (D) or greater with topography-guided transepithelial surface ablation. Retrospective analysis of a series of 206 eyes divided into two groups: myopic astigmatism (153 eyes) and mixed astigmatism (53 eyes). All cases were treated with topography-guided transepithelial surface ablation. Efficacy, safety, and predictability were evaluated, and vector analysis of cylindrical correction was performed. The median preoperative spherical equivalent was -2.63 and -0.63 D for the myopic and mixed astigmatism groups, respectively, with median cylinder of -2.50 D. Postoperative uncorrected distance visual acuity was 20/20 or better in 92% and 83% of eyes in the myopic and mixed astigmatism groups, respectively; the corresponding efficacy indices were 1.00 and 0.96 and residual astigmatism of 0.50 D or less was present in 82.4% and 56.7% of eyes in the myopic and mixed astigmatism groups, respectively. The arithmetic mean magnitude of the difference vector was 0.38 (myopic) and 0.65 (mixed) D. Difference vector magnitude was positively correlated with the magnitude of target induced astigmatism in both groups. The geometric mean coefficient of adjustment index was 1.04 and 1.19, representing undercorrection of 4% and 19% in the myopic and mixed astigmatism groups, respectively. Topography-guided transepithelial ablation is a safe, effective, and predictable treatment for moderate to high astigmatism. [J Refract Surg. 2016;32(6):418-425.]. Copyright 2016, SLACK Incorporated.

On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations

NASA Astrophysics Data System (ADS)

Schröder, Jörg; Viebahn, Nils; Wriggers, Peter; Auricchio, Ferdinando; Steeger, Karl

2017-09-01

In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075-1092, 2005, Comput Mech 52:1153-1167, 2013).

An extension of the finite cell method using boolean operations

NASA Astrophysics Data System (ADS)

Abedian, Alireza; Düster, Alexander

2017-05-01

In the finite cell method, the fictitious domain approach is combined with high-order finite elements. The geometry of the problem is taken into account by integrating the finite cell formulation over the physical domain to obtain the corresponding stiffness matrix and load vector. In this contribution, an extension of the FCM is presented wherein both the physical and fictitious domain of an element are simultaneously evaluated during the integration. In the proposed extension of the finite cell method, the contribution of the stiffness matrix over the fictitious domain is subtracted from the cell, resulting in the desired stiffness matrix which reflects the contribution of the physical domain only. This method results in an exponential rate of convergence for porous domain problems with a smooth solution and accurate integration. In addition, it reduces the computational cost, especially when applying adaptive integration schemes based on the quadtree/octree. Based on 2D and 3D problems of linear elastostatics, numerical examples serve to demonstrate the efficiency and accuracy of the proposed method.

A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS

NASA Technical Reports Server (NTRS)

Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.

1993-01-01

Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).

Generalization of mixed multiscale finite element methods with applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, C S

Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixedmore » multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii« less

Modeling dam-break flows using finite volume method on unstructured grid

USDA-ARS?s Scientific Manuscript database

Two-dimensional shallow water models based on unstructured finite volume method and approximate Riemann solvers for computing the intercell fluxes have drawn growing attention because of their robustness, high adaptivity to complicated geometry and ability to simulate flows with mixed regimes and di...

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

NASA Astrophysics Data System (ADS)

Li, Xiaomin; Guo, Xueli; Guo, Haiyan

2018-06-01

Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element (VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton's second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method (FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.

Understanding the power reflection and transmission coefficients of a plane wave at a planar interface

NASA Astrophysics Data System (ADS)

Ye, Qian; Jiang, Yikun; Lin, Haoze

2017-03-01

In most textbooks, after discussing the partial transmission and reflection of a plane wave at a planar interface, the power (energy) reflection and transmission coefficients are introduced by calculating the normal-to-interface components of the Poynting vectors for the incident, reflected and transmitted waves, separately. Ambiguity arises among students since, for the Poynting vector to be interpreted as the energy flux density, on the incident (reflected) side, the electric and magnetic fields involved must be the total fields, namely, the sum of incident and reflected fields, instead of the partial fields which are just the incident (reflected) fields. The interpretation of the cross product of partial fields as energy flux has not been obviously justified in most textbooks. Besides, the plane wave is actually an idealisation that is only ever found in textbooks, then what do the reflection and transmission coefficients evaluated for a plane wave really mean for a real beam of limited extent? To provide a clearer physical picture, we exemplify a light beam of finite transverse extent by a fundamental Gaussian beam and simulate its reflection and transmission at a planar interface. Due to its finite transverse extent, we can then insert the incident fields or reflected fields as total fields into the expression of the Poynting vector to evaluate the energy flux and then power reflection and transmission coefficients. We demonstrate that the power reflection and transmission coefficients of a beam of finite extent turn out to be the weighted sum of the corresponding coefficients for all constituent plane wave components that form the beam. The power reflection and transmission coefficients of a single plane wave serve, in turn, as the asymptotes for the corresponding coefficients of a light beam as its width expands infinitely.

Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-10-01

In this work we study the generalization of the problem considered in [Phys. Rev. E 91, 013002 (2015), 10.1103/PhysRevE.91.013002] to the case of finite correlation time of the environment (velocity) field. The model describes a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow. Inertial-range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and preassigned pair correlation function. Due to the presence of distinguished direction n , all the multiloop diagrams in this model vanish, so that the results obtained are exact. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to the two nontrivial fixed points of the RG equations. Their stability depends on the relation between the exponents in the energy spectrum E ∝k⊥1 -ξ and the dispersion law ω ∝k⊥2 -η . In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the corrections to ordinary scaling are polynomials of logarithms of the integral turbulence scale L .

A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brinkman, D., E-mail: Daniel.Brinkman@asu.edu; School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287; Heitzinger, C., E-mail: Clemens.Heitzinger@asu.edu

2014-01-15

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses.

Determination of stress intensity factors for interface cracks under mixed-mode loading

NASA Technical Reports Server (NTRS)

Naik, Rajiv A.; Crews, John H., Jr.

1992-01-01

A simple technique was developed using conventional finite element analysis to determine stress intensity factors, K1 and K2, for interface cracks under mixed-mode loading. This technique involves the calculation of crack tip stresses using non-singular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating three different bimaterial combinations. For the normal loading case, the K's were within 2.6 percent of an exact solution. The normalized K's under shear loading were shown to be related to the normalized K's under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from knowledge of the K's under normal loading. The equation was verified by computing the K's for a mixed-mode case with equal and normal shear loading. The correlation between exact and finite element solutions is within 3.7 percent. This study provides a simple procedure to compute K2/K1 ratio which has been used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/K1 ratios could be used to fully characterize interface fracture toughness.

Improved accuracy for finite element structural analysis via a new integrated force method

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.; Aiello, Robert A.; Berke, Laszlo

1992-01-01

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

The development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements

NASA Technical Reports Server (NTRS)

Truman, W. M.; Balanis, C. A.; Holmes, J. J.

1977-01-01

In this paper, a three-dimensional Fourier transform inversion method describing the interaction between water surface emitted radiation from a flat finite wave tank and antenna radiation characteristics is reported. The transform technique represents the scanning of the antenna mathematically as a correlation. Computation time is reduced by using the efficient and economical fast Fourier transform algorithm. To verify the inversion method, computations have been made and compared with known data and other available results. The technique has been used to restore data of the finite wave tank system and other available antenna temperature measurements made at the Cape Cod Canal. The restored brightness temperatures serve as better representations of the emitted radiation than the measured antenna temperatures.

A Design of Finite Memory Residual Generation Filter for Sensor Fault Detection

NASA Astrophysics Data System (ADS)

Kim, Pyung Soo

2017-04-01

In the current paper, a residual generation filter with finite memory structure is proposed for sensor fault detection. The proposed finite memory residual generation filter provides the residual by real-time filtering of fault vector using only the most recent finite measurements and inputs on the window. It is shown that the residual given by the proposed residual generation filter provides the exact fault for noisefree systems. The proposed residual generation filter is specified to the digital filter structure for the amenability to hardware implementation. Finally, to illustrate the capability of the proposed residual generation filter, extensive simulations are performed for the discretized DC motor system with two types of sensor faults, incipient soft bias-type fault and abrupt bias-type fault. In particular, according to diverse noise levels and windows lengths, meaningful simulation results are given for the abrupt bias-type fault.

Transcranial Magnetic Stimulation: An Automated Procedure to Obtain Coil-specific Models for Field Calculations.

PubMed

Madsen, Kristoffer H; Ewald, Lars; Siebner, Hartwig R; Thielscher, Axel

2015-01-01

Field calculations for transcranial magnetic stimulation (TMS) are increasingly implemented online in neuronavigation systems and in more realistic offline approaches based on finite-element methods. They are often based on simplified and/or non-validated models of the magnetic vector potential of the TMS coils. To develop an approach to reconstruct the magnetic vector potential based on automated measurements. We implemented a setup that simultaneously measures the three components of the magnetic field with high spatial resolution. This is complemented by a novel approach to determine the magnetic vector potential via volume integration of the measured field. The integration approach reproduces the vector potential with very good accuracy. The vector potential distribution of a standard figure-of-eight shaped coil determined with our setup corresponds well with that calculated using a model reconstructed from x-ray images. The setup can supply validated models for existing and newly appearing TMS coils. Copyright © 2015 Elsevier Inc. All rights reserved.

Navier-Stokes dynamics on a differential one-form

NASA Astrophysics Data System (ADS)

Story, Troy L.

2006-11-01

After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x^k and the conjugate to the position bk as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as | x^k | ->,, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained.

Classical stability of sudden and big rip singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barrow, John D.; Lip, Sean Z. W.

2009-08-15

We introduce a general characterization of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar, vector, and tensor perturbations using gauge-invariant perturbation theory. We establish that sudden singularities at which the scale factor, expansion rate, and density are finite are stable except for a set of special parameter values. We also apply our analysis to the stability of Big Rip singularities and find the conditions for their stability against small scalar, vector, and tensor perturbations.

A fast direct solver for a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. Wayne

1992-01-01

An efficient, direct, second-order solver for the discrete solution of two-dimensional separable elliptic equations on the sphere is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wavenumber and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

LFSPMC: Linear feature selection program using the probability of misclassification

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr.; Marion, B. P.

1975-01-01

The computational procedure and associated computer program for a linear feature selection technique are presented. The technique assumes that: a finite number, m, of classes exists; each class is described by an n-dimensional multivariate normal density function of its measurement vectors; the mean vector and covariance matrix for each density function are known (or can be estimated); and the a priori probability for each class is known. The technique produces a single linear combination of the original measurements which minimizes the one-dimensional probability of misclassification defined by the transformed densities.

Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements

NASA Technical Reports Server (NTRS)

Truman, W. M.; Balanis, C. A.

1977-01-01

The three-dimensional vector interaction between a microwave radiometer and a wave tank was modeled. Computer programs for predicting the response of the radiometer to the brightness temperature characteristics of the surroundings were developed along with a computer program that can invert (restore) the radiometer measurements. It is shown that the computer programs can be used to simulate the viewing of large bodies of water, and is applicable to radiometer measurements received from satellites monitoring the ocean. The water temperature, salinity, and wind speed can be determined.

A path model for Whittaker vectors

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Kedem, Rinat; Turmunkh, Bolor

2017-06-01

In this paper we construct weighted path models to compute Whittaker vectors in the completion of Verma modules, as well as Whittaker functions of fundamental type, for all finite-dimensional simple Lie algebras, affine Lie algebras, and the quantum algebra U_q(slr+1) . This leads to series expressions for the Whittaker functions. We show how this construction leads directly to the quantum Toda equations satisfied by these functions, and to the q-difference equations in the quantum case. We investigate the critical limit of affine Whittaker functions computed in this way.

A Unified Development of Basis Reduction Methods for Rotor Blade Analysis

NASA Technical Reports Server (NTRS)

Ruzicka, Gene C.; Hodges, Dewey H.; Rutkowski, Michael (Technical Monitor)

2001-01-01

The axial foreshortening effect plays a key role in rotor blade dynamics, but approximating it accurately in reduced basis models has long posed a difficult problem for analysts. Recently, though, several methods have been shown to be effective in obtaining accurate,reduced basis models for rotor blades. These methods are the axial elongation method,the mixed finite element method, and the nonlinear normal mode method. The main objective of this paper is to demonstrate the close relationships among these methods, which are seemingly disparate at first glance. First, the difficulties inherent in obtaining reduced basis models of rotor blades are illustrated by examining the modal reduction accuracy of several blade analysis formulations. It is shown that classical, displacement-based finite elements are ill-suited for rotor blade analysis because they can't accurately represent the axial strain in modal space, and that this problem may be solved by employing the axial force as a variable in the analysis. It is shown that the mixed finite element method is a convenient means for accomplishing this, and the derivation of a mixed finite element for rotor blade analysis is outlined. A shortcoming of the mixed finite element method is that is that it increases the number of variables in the analysis. It is demonstrated that this problem may be rectified by solving for the axial displacements in terms of the axial forces and the bending displacements. Effectively, this procedure constitutes a generalization of the widely used axial elongation method to blades of arbitrary topology. The procedure is developed first for a single element, and then extended to an arbitrary assemblage of elements of arbitrary type. Finally, it is shown that the generalized axial elongation method is essentially an approximate solution for an invariant manifold that can be used as the basis for a nonlinear normal mode.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dupertuis, M.A.; Proctor, M.; Acklin, B.

Energy balance and reciprocity relations are studied for harmonic inhomogeneous plane waves that are incident upon a stack of continuous absorbing dielectric media that are macroscopically characterized by their electric and magnetic permittivities and their conductivities. New cross terms between parallel electric and parallel magnetic modes are identified in the fully generalized Poynting vector. The symmetry and the relations between the general Fresnel coefficients are investigated in the context of energy balance at the interface. The contributions of the so-called mixed Poynting vector are discussed in detail. In particular a new transfer matrix is introduced for energy fluxes in thin-filmmore » optics based on the Poynting and mixed Poynting vectors. Finally, the study of reciprocity relations leads to a generalization of a theorem of reversibility for conducting and dielectric media. 16 refs.« less

Flipping Undergraduate Finite Mathematics: Findings and Implications

ERIC Educational Resources Information Center

Guerrero, Shannon; Beal, Melissa; Lamb, Chris; Sonderegger, Derek; Baumgartel, Drew

2015-01-01

This paper reports on a research project that investigated the effects of a flipped instructional approach on student attitudes and achievement in a lower division university-level Finite Mathematics course. The project employed a mixed-methods design that included content exams, an attitude survey, open-ended student responses, observations, and…

Development of design parameters for mass concrete using finite element analysis : final report, February 2010.

DOT National Transportation Integrated Search

2010-02-01

A finite element model for analysis of mass concrete was developed in this study. To validate the developed model, large concrete blocks made with four different mixes of concrete, typical of use in mass concrete applications in Florida, were made an...

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

NASA Astrophysics Data System (ADS)

Wu, Jiang; Liao, Fucheng; Tomizuka, Masayoshi

2017-01-01

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Moorthi, S.; Higgins, R. W.

1993-01-01

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations

NASA Technical Reports Server (NTRS)

Gerritsen, Margot; Olsson, Pelle

1996-01-01

We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently.

The Method of Fundamental Solutions using the Vector Magnetic Dipoles for Calculation of the Magnetic Fields in the Diagnostic Problems Based on Full-Scale Modelling Experiment

NASA Astrophysics Data System (ADS)

Bakhvalov, Yu A.; Grechikhin, V. V.; Yufanova, A. L.

2016-04-01

The article describes the calculation of the magnetic fields in the problems diagnostic of technical systems based on the full-scale modeling experiment. Use of gridless fundamental solution method and its variants in combination with grid methods (finite differences and finite elements) are allowed to considerably reduce the dimensionality task of the field calculation and hence to reduce calculation time. When implementing the method are used fictitious magnetic charges. In addition, much attention is given to the calculation accuracy. Error occurs when wrong choice of the distance between the charges. The authors are proposing to use vector magnetic dipoles to improve the accuracy of magnetic fields calculation. Examples of this approacharegiven. The article shows the results of research. They are allowed to recommend the use of this approach in the method of fundamental solutions for the full-scale modeling tests of technical systems.

A study of reacting free and ducted hydrogen/air jets

NASA Technical Reports Server (NTRS)

Beach, H. L., Jr.

1975-01-01

The mixing and reaction of a supersonic jet of hydrogen in coaxial free and ducted high temperature test gases were investigated. The importance of chemical kinetics on computed results, and the utilization of free-jet theoretical approaches to compute enclosed flow fields were studied. Measured pitot pressure profiles were correlated by use of a parabolic mixing analysis employing an eddy viscosity model. All computations, including free, ducted, reacting, and nonreacting cases, use the same value of the empirical constant in the viscosity model. Equilibrium and finite rate chemistry models were utilized. The finite rate assumption allowed prediction of observed ignition delay, but the equilibrium model gave the best correlations downstream from the ignition location. Ducted calculations were made with finite rate chemistry; correlations were, in general, as good as the free-jet results until problems with the boundary conditions were encountered.

A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Calise, Anthony J.; Bless, Robert R.; Leung, Martin

1989-01-01

A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.

A real-time TaqMan polymerase chain reaction for the identification of Culex vectors of West Nile and Saint Louis encephalitis viruses in North America.

PubMed

Sanogo, Yibayiri O; Kim, Chang-Hyun; Lampman, Richard; Novak, Robert J

2007-07-01

In North America, West Nile and St. Louis encephalitis viruses have been detected in a wide range of vector species, but the majority of isolations continue to be from pools of mixed mosquitoes in the Culex subgenus Culex. Unfortunately, the morphologic identification of these important disease vectors is often difficult, particularly in regions of sympatry. We developed a sensitive real-time TaqMan polymerase chain reaction assay that allows reliable identification of Culex mosquitoes including Culex pipiens pipiens, Cx. p. quinquefasciatus, Cx. restuans, Cx. salinarius, Cx. nigripalpus, and Cx. tarsalis. Primers and fluorogenic probes specific to each species were designed based on sequences of the acetylcholinesterase gene (Ace2). Both immature and adult mosquitoes were successfully identified as individuals and as mixed species pools. This identification technique provides the basis for a rapid, sensitive, and high-throughput method for expounding the species-specific contribution of vectors to various phases of arbovirus transmission.

Ignition and structure of a laminar diffusion flame in a compressible mixing layer with finite rate chemistry

NASA Technical Reports Server (NTRS)

Grosch, C. E.; Jackson, T. L.

1991-01-01

The ignition and structure of a reacting compressible mixing layer is considered using finite rate chemistry lying between two streams of reactants with different freestream speeds and temperatures. Numerical integration of the governing equations show that the structure of the reacting flow can be quite complicated depending on the magnitude of the Zeldovich number. An analysis of both the ignition a diffusion flame regimes is presented using a combination of large Zeldovich number asymptotics and numerics. This allows to analyze the behavior of these regimes as a function of the parameters of the problem.

Domain decomposition for a mixed finite element method in three dimensions

USGS Publications Warehouse

Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.

2003-01-01

We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.

A combined vector potential-scalar potential method for FE computation of 3D magnetic fields in electrical devices with iron cores

NASA Technical Reports Server (NTRS)

Wang, R.; Demerdash, N. A.

1991-01-01

A method of combined use of magnetic vector potential based finite-element (FE) formulations and magnetic scalar potential (MSP) based formulations for computation of three-dimensional magnetostatic fields is introduced. In this method, the curl-component of the magnetic field intensity is computed by a reduced magnetic vector potential. This field intensity forms the basic of a forcing function for a global magnetic scalar potential solution over the entire volume of the region. This method allows one to include iron portions sandwiched in between conductors within partitioned current-carrying subregions. The method is most suited for large-scale global-type 3-D magnetostatic field computations in electrical devices, and in particular rotating electric machinery.

The vector homology problem in diagnostic nucleic acid hybridization of clinical specimens.

PubMed Central

Ambinder, R F; Charache, P; Staal, S; Wright, P; Forman, M; Hayward, S D; Hayward, G S

1986-01-01

Nucleic acid hybridization techniques using cloned probes are finding application in assays of clinical specimens in research and diagnostic laboratories. The probes that we and others have used are recombinant plasmids composed of viral inserts and bacterial plasmid vectors such as pBR322. We suspected that there was material homologous to pBR322 present in many clinical samples. because hybridization occurred in samples which lacked evidence of virus by other techniques. If the presence of this vector-homologous material was unrecognized, hybridization in the test sample might erroneously be interpreted as indicating the presence of viral sequences. In this paper we demonstrate specific hybridization of labeled pBR322 DNA with DNA from various clinical samples. Evidence is presented that nonspecific probe trapping could not account for this phenomenon. In mixing experiments, it is shown that contamination of clinical samples with bacteria would explain such a result. Approaches tested to circumvent this problem included the use of isolated insert probes, alternate cloning vectors, and cold competitor pBR322 DNA in prehybridization and hybridization mixes. None proved entirely satisfactory. We therefore emphasize that it is essential that all hybridization detection systems use a control probe of the vector alone in order to demonstrate the absence of material with vector homology in the specimen tested. Images PMID:3013928

Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures

NASA Astrophysics Data System (ADS)

Lello, Louis; Boyanovsky, Daniel; Pisarski, Robert D.

2017-02-01

In the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at temperatures near the masses of the electroweak bosons. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles, which is applicable over a wide range of temperature, to all orders in interactions of the standard model and to leading order in a small mixing angle for the neutrinos. We emphasize the relation between the production rate and Landau damping at one-loop order and show that production rates and effective mixing angles depend sensitively upon the neutrino's helicity. Sterile neutrinos with positive helicity interact more weakly with the medium than those with negative helicity, and their effective mixing angle is not modified significantly. Negative helicity states couple more strongly to the vector bosons, but their mixing angle is strongly suppressed by the medium. Consequently, if the mass of the sterile neutrino is ≲8.35 MeV , there are fewer states with negative helicity produced than those with positive helicity. There is an Mikheyev-Smirnov-Wolfenstein-type resonance in the absence of lepton asymmetry, but due to screening by the damping rate, the production rate is not enhanced. Sterile neutrinos with negative helicity freeze out at Tf-≃5 GeV , whereas positive helicity neutrinos freeze out at Tf+≃8 GeV , with both distributions far from thermal. As the temperature decreases, due to competition between a decreasing production rate and an increasing mixing angle, the distribution function for states with negative helicity is broader in momentum and hotter than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime, and cosmological constraints to be the sole dark matter component in the Universe. Massive sterile neutrinos produced via vector boson decay might solve the 7Li problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. We argue that heavy sterile neutrinos with lifetime ≤1 /H0 reach local thermodynamic equilibrium.

Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures

DOE PAGES

Lello, Louis; Boyanovsky, Daniel; Pisarski, Robert D.

2017-02-22

Here, in the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at temperatures near the masses of the electroweak bosons. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles, which is applicable over a wide range of temperature, to all orders in interactions of the standard model and to leading order in a small mixing angle for the neutrinos. We emphasize the relation between the production rate and Landau damping at one-loop order and show that production rates and effective mixing angles depend sensitively upon the neutrino’s helicity. Sterile neutrinos with positive helicity interact more weakly with the medium than those with negative helicity, and their effective mixing angle is not modified significantly. Negative helicity states couple more strongly to the vector bosons, but their mixing angle is strongly suppressed by the medium. Consequently, if the mass of the sterile neutrino is ≲ 8.35 MeV , there are fewer states with negative helicity produced than those with positive helicity. There is an Mikheyev-Smirnov-Wolfenstein-type resonance in the absence of lepton asymmetry, but due to screening by the damping rate, the production rate is not enhanced. Sterile neutrinos with negative helicity freeze out at Tmore » $$-\\atop{f}$$ ≃ 5 GeV , whereas positive helicity neutrinos freeze out at T$$+\\atop{f}$$≃ 8 GeV , with both distributions far from thermal. As the temperature decreases, due to competition between a decreasing production rate and an increasing mixing angle, the distribution function for states with negative helicity is broader in momentum and hotter than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime, and cosmological constraints to be the sole dark matter component in the Universe. Massive sterile neutrinos produced via vector boson decay might solve the 7Li problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. In conclusion, we argue that heavy sterile neutrinos with lifetime ≤1/H 0 reach local thermodynamic equilibrium.« less

On load paths and load bearing topology from finite element analysis

NASA Astrophysics Data System (ADS)

Kelly, D.; Reidsema, C.; Lee, M.

2010-06-01

Load paths can be mapped from vector plots of 'pointing stress vectors'. They define a path along which a component of load remains constant as it traverses the solution domain. In this paper the theory for the paths is first defined. Properties of the plots that enable a designer to interpret the structural behavior from the contours are then identified. Because stress is a second order tensor defined on an orthogonal set of axes, the vector plots define separate paths for load transfer in each direction of the set of axes. An algorithm is therefore presented that combines the vectors to define a topology to carry the loads. The algorithm is shown to straighten the paths reducing bending moments and removing stress concentration. Application to a bolted joint, a racing car body and a yacht hull demonstrate the usefulness of the plots.

Conditional Entropy-Constrained Residual VQ with Application to Image Coding

NASA Technical Reports Server (NTRS)

Kossentini, Faouzi; Chung, Wilson C.; Smith, Mark J. T.

1996-01-01

This paper introduces an extension of entropy-constrained residual vector quantization (VQ) where intervector dependencies are exploited. The method, which we call conditional entropy-constrained residual VQ, employs a high-order entropy conditioning strategy that captures local information in the neighboring vectors. When applied to coding images, the proposed method is shown to achieve better rate-distortion performance than that of entropy-constrained residual vector quantization with less computational complexity and lower memory requirements. Moreover, it can be designed to support progressive transmission in a natural way. It is also shown to outperform some of the best predictive and finite-state VQ techniques reported in the literature. This is due partly to the joint optimization between the residual vector quantizer and a high-order conditional entropy coder as well as the efficiency of the multistage residual VQ structure and the dynamic nature of the prediction.

Comparison of SOM point densities based on different criteria.

PubMed

Kohonen, T

1999-11-15

Point densities of model (codebook) vectors in self-organizing maps (SOMs) are evaluated in this article. For a few one-dimensional SOMs with finite grid lengths and a given probability density function of the input, the numerically exact point densities have been computed. The point density derived from the SOM algorithm turned out to be different from that minimizing the SOM distortion measure, showing that the model vectors produced by the basic SOM algorithm in general do not exactly coincide with the optimum of the distortion measure. A new computing technique based on the calculus of variations has been introduced. It was applied to the computation of point densities derived from the distortion measure for both the classical vector quantization and the SOM with general but equal dimensionality of the input vectors and the grid, respectively. The power laws in the continuum limit obtained in these cases were found to be identical.

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

A Calculation Method for Convective Heat and Mass Transfer in Multiply-Slotted Film-Cooling Applications.

DTIC Science & Technology

1980-01-01

Transport of Heat ..... .......... 8 3. THE SOLUTION PROCEDURE ..... .. ................. 8 3.1 The Finite-Difference Grid Network ... .......... 8 3.2...The Finite-Difference Grid Network. Figure 4: The Iterative Solution Procedure used at each Streamwise Station. Figure 5: Velocity Profiles in the...the finite-difference grid in the y-direction. I is the mixing length. L is the distance in the x-direction from the injection slot entrance to the

Nonlocal and Mixed-Locality Multiscale Finite Element Methods

DOE PAGES

Costa, Timothy B.; Bond, Stephen D.; Littlewood, David J.

2018-03-27

In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale finite element method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, inmore » this study, we present the first work toward application of the multiscale finite element method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale finite element method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale finite element methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale finite element method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.« less

Influence of Finite Element Software on Energy Release Rates Computed Using the Virtual Crack Closure Technique

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Goetze, Dirk; Ransom, Jonathon (Technical Monitor)

2006-01-01

Strain energy release rates were computed along straight delamination fronts of Double Cantilever Beam, End-Notched Flexure and Single Leg Bending specimens using the Virtual Crack Closure Technique (VCCT). Th e results were based on finite element analyses using ABAQUS# and ANSYS# and were calculated from the finite element results using the same post-processing routine to assure a consistent procedure. Mixed-mode strain energy release rates obtained from post-processing finite elem ent results were in good agreement for all element types used and all specimens modeled. Compared to previous studies, the models made of s olid twenty-node hexahedral elements and solid eight-node incompatible mode elements yielded excellent results. For both codes, models made of standard brick elements and elements with reduced integration did not correctly capture the distribution of the energy release rate acr oss the width of the specimens for the models chosen. The results suggested that element types with similar formulation yield matching results independent of the finite element software used. For comparison, m ixed-mode strain energy release rates were also calculated within ABAQUS#/Standard using the VCCT for ABAQUS# add on. For all specimens mod eled, mixed-mode strain energy release rates obtained from ABAQUS# finite element results using post-processing were almost identical to re sults calculated using the VCCT for ABAQUS# add on.

Nonlocal and Mixed-Locality Multiscale Finite Element Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costa, Timothy B.; Bond, Stephen D.; Littlewood, David J.

In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale finite element method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, inmore » this study, we present the first work toward application of the multiscale finite element method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale finite element method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale finite element methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale finite element method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.« less

Direct model-based predictive control scheme without cost function for voltage source inverters with reduced common-mode voltage

NASA Astrophysics Data System (ADS)

Kim, Jae-Chang; Moon, Sung-Ki; Kwak, Sangshin

2018-04-01

This paper presents a direct model-based predictive control scheme for voltage source inverters (VSIs) with reduced common-mode voltages (CMVs). The developed method directly finds optimal vectors without using repetitive calculation of a cost function. To adjust output currents with the CMVs in the range of -Vdc/6 to +Vdc/6, the developed method uses voltage vectors, as finite control resources, excluding zero voltage vectors which produce the CMVs in the VSI within ±Vdc/2. In a model-based predictive control (MPC), not using zero voltage vectors increases the output current ripples and the current errors. To alleviate these problems, the developed method uses two non-zero voltage vectors in one sampling step. In addition, the voltage vectors scheduled to be used are directly selected at every sampling step once the developed method calculates the future reference voltage vector, saving the efforts of repeatedly calculating the cost function. And the two non-zero voltage vectors are optimally allocated to make the output current approach the reference current as close as possible. Thus, low CMV, rapid current-following capability and sufficient output current ripple performance are attained by the developed method. The results of a simulation and an experiment verify the effectiveness of the developed method.

Method of orbit sums in the theory of modular vector invariants

NASA Astrophysics Data System (ADS)

Stepanov, S. A.

2006-12-01

Let F be a field, V a finite-dimensional F-vector space, G\\leqslant \\operatorname{GL}_F(V) a finite group, and V^m=V\\oplus\\dots\\oplus V the m-fold direct sum with the diagonal action of G. The group G acts naturally on the symmetric graded algebra A_m=F \\lbrack V^m \\rbrack as a group of non-degenerate linear transformations of the variables. Let A_m^G be the subalgebra of invariants of the polynomial algebra A_m with respect to G. A classical result of Noether [1] says that if \\operatorname{char}F=0, then A_m^G is generated as an F-algebra by homogeneous polynomials of degree at most \\vert G\\vert, no matter how large m can be. On the other hand, it was proved by Richman [2], [3] that this result does not hold when the characteristic of F is positive and divides the order \\vert G\\vert of G. Let p, p>2, be a prime number, F=F_p a finite field of p elements, V a linear F_p-vector space of dimension n, and H\\leqslant \\operatorname{GL}_{F_p}(V) a cyclic group of order p generated by a matrix \\gamma of a certain special form. In this paper we describe explicitly (Theorem 1) one complete set of generators of A_m^H. After that, for an arbitrary complete set of generators of this algebra we find a lower bound for the highest degree of the generating elements of this algebra. This is a significant extension of the corresponding result of Campbell and Hughes [4] for the particular case of n=2. As a consequence we show (Theorem 3) that if m>n and G\\ge H is an arbitrary finite group, then each complete set of generators of A_m^G contains an element of degree at least 2(m-n+2r)(p-1)/r, where r=r(H) is a positive integer dependent on the structure of the generating matrix \\gamma of the group H. This result refines considerably the earlier lower bound obtained by Richman [3].

Exponential Mixing of the 3D Stochastic Navier-Stokes Equations Driven by Mildly Degenerate Noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albeverio, Sergio; Debussche, Arnaud, E-mail: arnaud.debussche@bretagne.ens-cachan.fr; Xu Lihu, E-mail: Lihu.Xu@brunel.ac.uk

2012-10-15

We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes being forced) via a Kolmogorov equation approach.

Optical computing and image processing using photorefractive gallium arsenide

NASA Technical Reports Server (NTRS)

Cheng, Li-Jen; Liu, Duncan T. H.

1990-01-01

Recent experimental results on matrix-vector multiplication and multiple four-wave mixing using GaAs are presented. Attention is given to a simple concept of using two overlapping holograms in GaAs to do two matrix-vector multiplication processes operating in parallel with a common input vector. This concept can be used to construct high-speed, high-capacity, reconfigurable interconnection and multiplexing modules, important for optical computing and neural-network applications.

40 CFR 503.33 - Vector attraction reduction.

Code of Federal Regulations, 2013 CFR

2013-07-01

... less than 15 percent, vector attraction reduction is achieved. (4) The specific oxygen uptake rate... shall be equal to or greater than 75 percent based on the moisture content and total solids prior to... the moisture content and total solids prior to mixing with other materials. (9)(i) Sewage sludge shall...

40 CFR 503.33 - Vector attraction reduction.

Code of Federal Regulations, 2014 CFR

2014-07-01

... less than 15 percent, vector attraction reduction is achieved. (4) The specific oxygen uptake rate... shall be equal to or greater than 75 percent based on the moisture content and total solids prior to... the moisture content and total solids prior to mixing with other materials. (9)(i) Sewage sludge shall...

40 CFR 503.33 - Vector attraction reduction.

Code of Federal Regulations, 2010 CFR

2010-07-01

... less than 15 percent, vector attraction reduction is achieved. (4) The specific oxygen uptake rate... shall be equal to or greater than 75 percent based on the moisture content and total solids prior to... the moisture content and total solids prior to mixing with other materials. (9)(i) Sewage sludge shall...

40 CFR 503.33 - Vector attraction reduction.

Code of Federal Regulations, 2011 CFR

2011-07-01

... less than 15 percent, vector attraction reduction is achieved. (4) The specific oxygen uptake rate... shall be equal to or greater than 75 percent based on the moisture content and total solids prior to... the moisture content and total solids prior to mixing with other materials. (9)(i) Sewage sludge shall...

40 CFR 503.33 - Vector attraction reduction.

Code of Federal Regulations, 2012 CFR

2012-07-01

... less than 15 percent, vector attraction reduction is achieved. (4) The specific oxygen uptake rate... shall be equal to or greater than 75 percent based on the moisture content and total solids prior to... the moisture content and total solids prior to mixing with other materials. (9)(i) Sewage sludge shall...

Developments in the Gung Ho dynamical core

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2017-04-01

Gung Ho is the new dynamical core being developed for the next generation Met Office weather and climate model, suitable for meeting the exascale challenge on emerging computer architectures. It builds upon the earlier collaborative project between the Met Office, NERC and STFC Daresbury of the same name to investigate suitable numerical methods for dynamical cores. A mixed-finite element approach is used, where different finite element spaces are used to represent various fields. This method provides a number of beneficial improvements over the current model, such a compatibility and inherent conservation on quasi-uniform unstructured meshes, whilst maintaining the accuracy and good dispersion properties of the staggered grid currently used. Furthermore, the mixed finite element approach allows a large degree of flexibility in the type of mesh, order of approximation and discretisation, providing a simple way to test alternative options to obtain the best model possible.

A hybridized formulation for the weak Galerkin mixed finite element method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

A hybridized formulation for the weak Galerkin mixed finite element method

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2016-01-14

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations.

PubMed

Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman

2015-04-01

The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.

Exploiting symmetries in the modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Andersen, C. M.; Tanner, John A.

1989-01-01

A computational procedure is presented for reducing the size of the analysis models of tires having unsymmetric material, geometry and/or loading. The two key elements of the procedure when applied to anisotropic tires are: (1) decomposition of the stiffness matrix into the sum of an orthotropic and nonorthotropic parts; and (2) successive application of the finite-element method and the classical Rayleigh-Ritz technique. The finite-element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The proposed technique has high potential for handling practical tire problems with anisotropic materials, unsymmetric imperfections and asymmetric loading. It is also particularly useful for use with three-dimensional finite-element models of tires.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giunta, G.; Belouettar, S.

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigationsmore » show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.« less

A comparative study of an ABC and an artificial absorber for truncating finite element meshes

NASA Technical Reports Server (NTRS)

Oezdemir, T.; Volakis, John L.

1993-01-01

The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.

Simulation of thin slot spirals and dual circular patch antennas using the finite element method with mixed elements

NASA Technical Reports Server (NTRS)

Gong, Jian; Volakis, John L.; Nurnberger, Michael W.

1995-01-01

This semi-annual report describes progress up to mid-January 1995. The report contains five sections all dealing with the modeling of spiral and patch antennas recessed in metallic platforms. Of significance is the development of decomposition schemes which separate the different regions of the antenna volume. Substantial effort was devoted to improving the feed model in the context of the finite element method (FEM). Finally, an innovative scheme for truncating finite element meshes is presented.

A mixed-penalty biphasic finite element formulation incorporating viscous fluids and material interfaces.

PubMed

Chan, B; Donzelli, P S; Spilker, R L

2000-06-01

The fluid viscosity term of the fluid phase constitutive equation and the interface boundary conditions between biphasic, solid and fluid domains have been incorporated into a mixed-penalty finite element formulation of the linear biphasic theory for hydrated soft tissue. The finite element code can now model a single-phase viscous incompressible fluid, or a single-phase elastic solid, as limiting cases of a biphasic material. Interface boundary conditions allow the solution of problems involving combinations of biphasic, fluid and solid regions. To incorporate these conditions, the volume-weighted mixture velocity is introduced as a degree of freedom at interface nodes so that the kinematic continuity conditions are satisfied by conventional finite element assembly techniques. Results comparing our numerical method with an independent, analytic solution for the problem of Couette flow over rigid and deformable porous biphasic layers show that the finite element code accurately predicts the viscous fluid flows and deformation in the porous biphasic region. Thus, the analysis can be used to model the interface between synovial fluid and articular cartilage in diarthrodial joints. This is an important step toward modeling and understanding the mechanisms of joint lubrication and another step toward fully modeling the in vivo behavior of a diarthrodial joint.

Rapid magnetic reconnection caused by finite amplitude fluctuations

NASA Technical Reports Server (NTRS)

Matthaeus, W. H.; Lamkin, S. L.

1985-01-01

The nonlinear dynamics of the magnetohydrodynamic sheet pinch have been investigated as an unforced initial value problem for large scale Reynolds numbers up to 1000. Reconnection is triggered by adding to the sheet pinch a small but finite level of broadband random perturbations. Effects of turbulence in the solutions include the production of reconnected magnetic islands at rates that are insensitive to resistivity at early times. This is explained by noting that electric field fluctuations near the X point produce irregularities in the vector potential, sometimes taking the form of 'magnetic bubbles', which allow rapid change of field topology.

Charmonium ground and excited states at finite temperature from complex Borel sum rules

NASA Astrophysics Data System (ADS)

Araki, Ken-Ji; Suzuki, Kei; Gubler, Philipp; Oka, Makoto

2018-05-01

Charmonium spectral functions in vector and pseudoscalar channels at finite temperature are investigated through the complex Borel sum rules and the maximum entropy method. Our approach enables us to extract the peaks corresponding to the excited charmonia, ψ‧ and ηc‧ , as well as those of the ground states, J / ψ and ηc, which has never been achieved in usual QCD sum rule analyses. We show the spectral functions in vacuum and their thermal modification around the critical temperature, which leads to the almost simultaneous melting (or peak disappearance) of the ground and excited states.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Raju, I. S.

1991-01-01

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program.

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Raju, I. S.

1992-01-01

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1991-01-01

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iaroshenko, Oleksandr; Gyrya, Vitaliy; Manzini, Gianmarco

2016-09-01

In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

Divergence preserving discrete surface integral methods for Maxwell's curl equations using non-orthogonal unstructured grids

NASA Technical Reports Server (NTRS)

Madsen, Niel K.

1992-01-01

Several new discrete surface integral (DSI) methods for solving Maxwell's equations in the time-domain are presented. These methods, which allow the use of general nonorthogonal mixed-polyhedral unstructured grids, are direct generalizations of the canonical staggered-grid finite difference method. These methods are conservative in that they locally preserve divergence or charge. Employing mixed polyhedral cells, (hexahedral, tetrahedral, etc.) these methods allow more accurate modeling of non-rectangular structures and objects because the traditional stair-stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided. Numerical results demonstrating the accuracy of these new methods are presented.

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

NASA Astrophysics Data System (ADS)

Nestler, M.; Nitschke, I.; Praetorius, S.; Voigt, A.

2018-02-01

We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hayami, Satoru; Lin, Shi -Zeng; Kamiya, Yoshitomo

Finite-Q magnetic instabilities are rather common in frustrated magnets. When the magnetic susceptibility is maximized at multiple-Q vectors related through lattice symmetry operations, exotic magnetic orderings such as vortex and skyrmion crystals may follow. Here, we show that a periodic array of nonmagnetic impurities, which can be realized through charge density wave ordering, leads to a rich phase diagram featuring a plethora of chiral magnetic phases, especially when there is a simple relation between the reciprocal vectors of the impurity superlattice and the magnetic Q vectors. We also investigate the effect of changing the impurity concentration or disturbing the impuritymore » array with small quenched randomness. Lastly, alternative realizations of impurity superlattices are briefly discussed.« less

Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities

DOE PAGES

Hayami, Satoru; Lin, Shi -Zeng; Kamiya, Yoshitomo; ...

2016-11-10

Finite-Q magnetic instabilities are rather common in frustrated magnets. When the magnetic susceptibility is maximized at multiple-Q vectors related through lattice symmetry operations, exotic magnetic orderings such as vortex and skyrmion crystals may follow. Here, we show that a periodic array of nonmagnetic impurities, which can be realized through charge density wave ordering, leads to a rich phase diagram featuring a plethora of chiral magnetic phases, especially when there is a simple relation between the reciprocal vectors of the impurity superlattice and the magnetic Q vectors. We also investigate the effect of changing the impurity concentration or disturbing the impuritymore » array with small quenched randomness. Lastly, alternative realizations of impurity superlattices are briefly discussed.« less

Tribal and Locality Dynamics in Afghanistan: A View from the National Military Academy of Afghanistan

DTIC Science & Technology

2009-01-01

CD VVV ∪= with DV countable and nCV ℜ∈ ; XInit ⊆ is a set of initial states; CXVXf →×: is a vector field, assumed to be 4 globally...DV countable and nCV ℜ∈ ; XInit ⊆ is a set of initial states; CXVXf →×: is a vector field, assumed to be globally Lipschitz in CX and...8217 ; V is a finite collection of input variables. We assume ( )CD VVV ∪= with DV countable and nCV ℜ∈ ; XInit ⊆ is a set of initial states

User's and test case manual for FEMATS

NASA Technical Reports Server (NTRS)

Chatterjee, Arindam; Volakis, John; Nurnberger, Mike; Natzke, John

1995-01-01

The FEMATS program incorporates first-order edge-based finite elements and vector absorbing boundary conditions into the scattered field formulation for computation of the scattering from three-dimensional geometries. The code has been validated extensively for a large class of geometries containing inhomogeneities and satisfying transition conditions. For geometries that are too large for the workstation environment, the FEMATS code has been optimized to run on various supercomputers. Currently, FEMATS has been configured to run on the HP 9000 workstation, vectorized for the Cray Y-MP, and parallelized to run on the Kendall Square Research (KSR) architecture and the Intel Paragon.

On diagrammatic technique for nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Semenyakin, Mykola

2014-11-01

In this paper, we investigate phase flows over ℂn and ℝn generated by vector fields V = ∑ Pi∂i where Pi are finite degree polynomials. With the convenient diagrammatic technique, we get expressions for evolution operators ev{V|t} : x(0) ↦ x(t) through the series in powers of x(0) and t, represented as sum over all trees of a particular type. Estimates are made for the radius of convergence in some particular cases. The phase flows behavior in the neighborhood of vector field fixed points are examined. Resonance cases are considered separately.

A proposed method for enhanced eigen-pair extraction using finite element methods: Theory and application

NASA Technical Reports Server (NTRS)

Jara-Almonte, J.; Mitchell, L. D.

1988-01-01

The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.

Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy

NASA Astrophysics Data System (ADS)

Meng, Qingping; Wu, Lijun; Welch, David O.; Zhu, Yimei

2015-06-01

We studied the lattice vibrations of two interpenetrating atomic sublattices via the Frenkel-Kontorova (FK) model of a linear chain of harmonically interacting atoms subjected to an on-site potential using the technique of thermodynamic Green's functions based on quantum field-theoretical methods. General expressions were deduced for the phonon frequency-wave-vector dispersion relations, number density, and energy of the FK model system. As the application of the theory, we investigated in detail cases of linear chains with various periods of the on-site potential of the FK model. Some unusual but interesting features for different amplitudes of the on-site potential of the FK model are discussed. In the commensurate structure, the phonon spectrum always starts at a finite frequency, and the gaps of the spectrum are true ones with a zero density of modes. In the incommensurate structure, the phonon spectrum starts from zero frequency, but at a nonzero wave vector; there are some modes inside these gap regions, but their density is very low. In our approximation, the energy of a higher-order commensurate state of the one-dimensional system at a finite temperature may become indefinitely close to the energy of an incommensurate state. This finding implies that the higher-order incommensurate-commensurate transitions are continuous ones and that the phase transition may exhibit a "devil's staircase" behavior at a finite temperature.

Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays

NASA Astrophysics Data System (ADS)

Meier, Joachim; Hudock, Jared; Christodoulides, Demetrios; Stegeman, George; Silberberg, Y.; Morandotti, R.; Aitchison, J. S.

2003-10-01

We report the first experimental observation of discrete vector solitons in AlGaAs nonlinear waveguide arrays. These self-trapped states are possible through the coexistence of two orthogonally polarized fields and are stable in spite of the presence of four-wave mixing effects. We demonstrate that at sufficiently high power levels the two polarizations lock into a highly localized vector discrete soliton that would have been otherwise impossible in the absence of either one of these two components.

Efficient modeling of photonic crystals with local Hermite polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boucher, C. R.; Li, Zehao; Albrecht, J. D.

2014-04-21

Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (planemore » wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This general method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits.« less

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Accelerating 4D flow MRI by exploiting vector field divergence regularization.

PubMed

Santelli, Claudio; Loecher, Michael; Busch, Julia; Wieben, Oliver; Schaeffter, Tobias; Kozerke, Sebastian

2016-01-01

To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field. Iterative image reconstruction in which magnitude and phase are regularized separately in alternating iterations was implemented. The approach allows incorporating prior knowledge of the flow field being imaged. In the present work, velocity data were regularized to reduce divergence, using either divergence-free wavelets (DFW) or a finite difference (FD) method using the ℓ1-norm of divergence and curl. The reconstruction methods were tested on a numerical phantom and in vivo data. Results of the DFW and FD approaches were compared with data obtained with standard compressed sensing (CS) reconstruction. Relative to standard CS, directional errors of vector fields and divergence were reduced by 55-60% and 38-48% for three- and six-fold undersampled data with the DFW and FD methods. Velocity vector displays of the numerical phantom and in vivo data were found to be improved upon DFW or FD reconstruction. Regularization of vector field divergence in image reconstruction from undersampled 4D flow data is a valuable approach to improve reconstruction accuracy of velocity vector fields. © 2014 Wiley Periodicals, Inc.

Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

NASA Astrophysics Data System (ADS)

Kaus, B.; Popov, A.

2015-12-01

The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results with those obtained with a finite difference approximation of the Jacobian. This project is funded by ERC Starting Grant 258830 and computer facilities were provided by Jülich supercomputer center (Germany).

Shear-flexible finite-element models of laminated composite plates and shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Mathers, M. D.

1975-01-01

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

QCD sum-rules analysis of vector (1-) heavy quarkonium meson-hybrid mixing

NASA Astrophysics Data System (ADS)

Palameta, A.; Ho, J.; Harnett, D.; Steele, T. G.

2018-02-01

We use QCD Laplace sum rules to study meson-hybrid mixing in vector (1-) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multiresonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compared to single resonance models that include only the ground state, we find that models that also include excited states lead to significantly improved agreement between QCD and experiment. In the charmonium sector, we find that meson-hybrid mixing is consistent with a two-resonance model consisting of the J /ψ and a 4.3 GeV resonance. In the bottomonium sector, we find evidence for meson-hybrid mixing in the ϒ (1 S ) , ϒ (2 S ), ϒ (3 S ), and ϒ (4 S ).

An implementation of the QMR method based on coupled two-term recurrences

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noeel M.

1992-01-01

The authors have proposed a new Krylov subspace iteration, the quasi-minimal residual algorithm (QMR), for solving non-Hermitian linear systems. In the original implementation of the QMR method, the Lanczos process with look-ahead is used to generate basis vectors for the underlying Krylov subspaces. In the Lanczos algorithm, these basis vectors are computed by means of three-term recurrences. It has been observed that, in finite precision arithmetic, vector iterations based on three-term recursions are usually less robust than mathematically equivalent coupled two-term vector recurrences. This paper presents a look-ahead algorithm that constructs the Lanczos basis vectors by means of coupled two-term recursions. Implementation details are given, and the look-ahead strategy is described. A new implementation of the QMR method, based on this coupled two-term algorithm, is described. A simplified version of the QMR algorithm without look-ahead is also presented, and the special case of QMR for complex symmetric linear systems is considered. Results of numerical experiments comparing the original and the new implementations of the QMR method are reported.

Fourier transform inequalities for phylogenetic trees.

PubMed

Matsen, Frederick A

2009-01-01

Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.

Hájek-Rényi inequality for m-asymptotically almost negatively associated random vectors in Hilbert space and applications.

PubMed

Ko, Mi-Hwa

2018-01-01

In this paper, we obtain the Hájek-Rényi inequality and, as an application, we study the strong law of large numbers for H -valued m -asymptotically almost negatively associated random vectors with mixing coefficients [Formula: see text] such that [Formula: see text].

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiegelmann, T.; Solanki, S. K.; Barthol, P.

Magneto-static models may overcome some of the issues facing force-free magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quiet-Sun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the Sunrise balloon-borne solar observatory in 2013 June as boundary conditions for a magneto-static model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO /HMI. This work continues our magneto-static extrapolation approach,more » which was applied earlier to a quiet-Sun region observed with Sunrise I. In an active region the signal-to-noise-ratio in the measured Stokes parameters is considerably higher than in the quiet-Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magneto-static equilibria. The high spatial resolution of IMaX (110–130 km, pixel size 40 km) enables us to model the non-force-free layer between the photosphere and the mid-chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower-resolution photospheric measurements in the past. The linear model does not, however, permit us to model intrinsic nonlinear structures like strongly localized electric currents.« less

Synergy between repellents and organophosphates on bed nets: efficacy and behavioural response of natural free-flying An. gambiae mosquitoes.

PubMed

Pennetier, Cédric; Costantini, Carlo; Corbel, Vincent; Licciardi, Séverine; Dabiré, Roch K; Lapied, Bruno; Chandre, Fabrice; Hougard, Jean-Marc

2009-11-19

Chemicals are used on bed nets in order to prevent infected bites and to kill aggressive malaria vectors. Because pyrethroid resistance has become widespread in the main malaria vectors, research for alternative active ingredients becomes urgent. Mixing a repellent and a non-pyrethroid insecticide seemed to be a promising tool as mixtures in the laboratory showed the same features as pyrethroids. We present here the results of two trials run against free-flying Anopheles gambiae populations comparing the effects of two insect repellents (either DEET or KBR 3023, also known as icaridin) and an organophosphate insecticide at low-doses (pirimiphos-methyl, PM) used alone and in combination on bed nets. We showed that mixtures of PM and the repellents induced higher exophily, blood feeding inhibition and mortality among wild susceptible and resistant malaria vectors than compounds used alone. Nevertheless the synergistic interactions are only involved in the high mortality induced by the two mixtures. These field trials argue in favour of the strategy of mixing repellent and organophosphate on bed nets to better control resistant malaria vectors.

Characterization of Hadamard vector classes in terms of least deviations of their elements from vectors of finite degree

DOE Office of Scientific and Technical Information (OSTI.GOV)

Radzievski, G V

2001-12-31

Let A be a linear operator with domain D(A) in a complex Banach space X. An element g element of D{sub {infinity}}(A):=intersection{sub j=1}{sup {infinity}}D(A{sup j}) is called a vector of degree at most {xi} (>0) relative to A if ||A{sup j}g||{<=}c(g){xi}{sup j}, j=0,1,.... The set of vectors of degree at most {xi} is denoted by G{sub {xi}}(A) and the least deviation of an element f of X from the set G{sub {xi}}(A) is denoted by E{sub {xi}}(f,A). For a fixed sequence of positive numbers ({psi}{sub j}){sub j=1}{sup {infinity}} consider a function {gamma}({xi}):=min{sub j=1,2,...}({xi}{psi}{sub j}){sup 1/j}. Conditions for the sequence ({psi}{submore » j}){sub j=1}{sup {infinity}} and the operator A are found that ensure the equality lim sup{sub j{yields}}{sub {infinity}}((||A{sup j}f||)/({psi}{sub j})){sup 1/j} = lim sup{sub {xi}}{sub {yields}}{sub {infinity}}{xi}/({gamma}(E{sub {xi}}(f,A){sup -1})) for f element of D{sub {infinity}}(A). If the quantity on the left-hand side of this formula is finite, then f belongs to the Hadamard class determined by the operator A and the sequence {l_brace}{psi}{sub j}{r_brace}{sub j=1}{sup {infinity}}. One consequence of the above formula is an expression in terms of E{sub {xi}}(f,A) for the radius of holomorphy of the vector-valued function F(zA)f, where f element of D{sub {infinity}}(A), and F(z):={sigma}{sub j=1}{sup {infinity}}z{sup j}/{psi}{sub j} is an entire function.« less

Stationary states of fermions in a sign potential with a mixed vector–scalar coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castilho, W.M., E-mail: castilho.w@gmail.com; Castro, A.S. de, E-mail: castro@pq.cnpq.br

2014-01-15

The scattering of a fermion in the background of a sign potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling under the Sturm–Liouville perspective. When the vector coupling and the scalar coupling have different magnitudes, an isolated solution shows that the fermion under a strong potential can be trapped in a highly localized region without manifestation of Klein’s paradox. It is also shown that the lonely bound-state solution disappears asymptotically as one approaches the conditions for the realization of spin and pseudospin symmetries. --more » Highlights: •Scattering of fermions in a sign potential assessed under a Sturm–Liouville perspective. •An isolated bounded solution. •No pair production despite the high localization. •No bounded solution under exact spin and pseudospin symmetries.« less

Documentation of a graphical display program for the saturated- unsaturated transport (SUTRA) finite-element simulation model

USGS Publications Warehouse

Souza, W.R.

1987-01-01

This report documents a graphical display program for the U. S. Geological Survey finite-element groundwater flow and solute transport model. Graphic features of the program, SUTRA-PLOT (SUTRA-PLOT = saturated/unsaturated transport), include: (1) plots of the finite-element mesh, (2) velocity vector plots, (3) contour plots of pressure, solute concentration, temperature, or saturation, and (4) a finite-element interpolator for gridding data prior to contouring. SUTRA-PLOT is written in FORTRAN 77 on a PRIME 750 computer system, and requires Version 9.0 or higher of the DISSPLA graphics library. The program requires two input files: the SUTRA input data list and the SUTRA simulation output listing. The program is menu driven and specifications for individual types of plots are entered and may be edited interactively. Installation instruction, a source code listing, and a description of the computer code are given. Six examples of plotting applications are used to demonstrate various features of the plotting program. (Author 's abstract)

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

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

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo; Lunati, Ivan

2016-10-01

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

Implicit, nonswitching, vector-oriented algorithm for steady transonic flow

NASA Technical Reports Server (NTRS)

Lottati, I.

1983-01-01

A rapid computation of a sequence of transonic flow solutions has to be performed in many areas of aerodynamic technology. The employment of low-cost vector array processors makes the conduction of such calculations economically feasible. However, for a full utilization of the new hardware, the developed algorithms must take advantage of the special characteristics of the vector array processor. The present investigation has the objective to develop an efficient algorithm for solving transonic flow problems governed by mixed partial differential equations on an array processor.

Easily Testable PLA-Based Finite State Machines

DTIC Science & Technology

1989-03-01

PLATYPUS (20]. Then, justifi- type 1, 4 and 5 can be guaranteed to be testable via cation paths are obtained from the STG using simple logic...next state lines is found, if such a vector par that is gnrt d y the trupt eexists, using PLATYPUS [20]. pair that is generated by the first corrupted

Numerical study of comparison of vorticity and passive vectors in turbulence and inviscid flows

NASA Astrophysics Data System (ADS)

Ohkitani, Koji

2002-04-01

The nonlinear vortex stretching in incompressible Navier-Stokes turbulence is compared with a linear stretching process of passive vectors (PVs). In particular, we pay special attention to the difference of these processes under long and short time evolutions. For finite time evolution, we confirm our previous finding that the stretching effect of vorticity is weaker than that of general passive vectors for a majority of the initial conditions with the same energy spectra. The above difference can be explained qualitatively by examining the Biot-Savart formula. In order to see to what extent infinitesimal time development explains the above difference, we examine the probability density functions (PDFs) of the stretching rates of the passive vectors in the vicinity of a solution of Navier-Stokes equations. It is found that the PDFs are found to have a Gaussian distribution, suggesting that there are equally many PVs that stretched less and more than the vorticity. This suggests the importance of the vorticity-strain correlation built up over finite time in turbulence. We also discuss the case of Euler equations, where the dynamics of the Jacobian matrix relating the physical and material coordinates is examined numerically. A kind of alignment problem associated with the Cauchy-Green tensor is proposed and studied using the results of numerical simulations. It is found that vorticity tends to align itself with the most compressing eigenvector of the Cauchy-Green tensor. A two-dimensional counterpart of active-passive comparison is briefly studied. There is no essential difference between stretching of vorticity gradients and that of passive scalar gradients and a physical interpretation is given to it.

Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM

NASA Astrophysics Data System (ADS)

Beckstein, Pascal; Galindo, Vladimir; Vukčević, Vuko

2017-09-01

Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential A and the electric scalar potential ϕ. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.

von Kármán–Howarth and Corrsin equations closure based on Lagrangian description of the fluid motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com

A new approach to obtain the closure formulas for the von Kármán–Howarth and Corrsin equations is presented, which is based on the Lagrangian representation of the fluid motion, and on the Liouville theorem associated to the kinematics of a pair of fluid particles. This kinematics is characterized by the finite scale separation vector which is assumed to be statistically independent from the velocity field. Such assumption is justified by the hypothesis of fully developed turbulence and by the property that this vector varies much more rapidly than the velocity field. This formulation leads to the closure formulas of von Kármán–Howarthmore » and Corrsin equations in terms of longitudinal velocity and temperature correlations following a demonstration completely different with respect to the previous works. Some of the properties and the limitations of the closed equations are discussed. In particular, we show that the times of evolution of the developed kinetic energy and temperature spectra are finite quantities which depend on the initial conditions.« less

Decays of the vector glueball

NASA Astrophysics Data System (ADS)

Giacosa, Francesco; Sammet, Julia; Janowski, Stanislaus

2017-06-01

We calculate two- and three-body decays of the (lightest) vector glueball into (pseudo)scalar, (axial-)vector, as well as pseudovector and excited vector mesons in the framework of a model of QCD. While absolute values of widths cannot be predicted because the corresponding coupling constants are unknown, some interesting branching ratios can be evaluated by setting the mass of the yet hypothetical vector glueball to 3.8 GeV as predicted by quenched lattice QCD. We find that the decay mode ω π π should be one of the largest (both through the decay chain O →b1π →ω π π and through the direct coupling O →ω π π ). Similarly, the (direct and indirect) decay into π K K*(892 ) is sizable. Moreover, the decays into ρ π and K*(892 )K are, although subleading, possible and could play a role in explaining the ρ π puzzle of the charmonium state ψ (2 S ) thanks to a (small) mixing with the vector glueball. The vector glueball can be directly formed at the ongoing BESIII experiment as well as at the future PANDA experiment at the FAIR facility. If the width is sufficiently small (≲100 MeV ) it should not escape future detection. It should be stressed that the employed model is based on some inputs and simplifying assumptions: the value of glueball mass (at present, the quenched lattice value is used), the lack of mixing of the glueball with other quarkonium states, and the use of few interaction terms. It then represents a first step toward the identification of the main decay channels of the vector glueball, but shall be improved when corresponding experimental candidates and/or new lattice results will be available.

Comparison of two computer programs by predicting turbulent mixing of helium in a ducted supersonic airstream

NASA Technical Reports Server (NTRS)

Pan, Y. S.; Drummond, J. P.; Mcclinton, C. R.

1978-01-01

Two parabolic flow computer programs, SHIP (a finite-difference program) and COMOC (a finite-element program), are used for predicting three-dimensional turbulent reacting flow fields in supersonic combustors. The theoretical foundation of the two computer programs are described, and then the programs are applied to a three-dimensional turbulent mixing experiment. The cold (nonreacting) flow experiment was performed to study the mixing of helium jets with a supersonic airstream in a rectangular duct. Surveys of the flow field at an upstream were used as the initial data by programs; surveys at a downstream station provided comparison to assess program accuracy. Both computer programs predicted the experimental results and data trends reasonably well. However, the comparison between the computations from the two programs indicated that SHIP was more accurate in computation and more efficient in both computer storage and computing time than COMOC.

A semi-implicit finite difference model for three-dimensional tidal circulation,

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1992-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.

Coupled Aerodynamic and Structural Sensitivity Analysis of a High-Speed Civil Transport

NASA Technical Reports Server (NTRS)

Mason, B. H.; Walsh, J. L.

2001-01-01

An objective of the High Performance Computing and Communication Program at the NASA Langley Research Center is to demonstrate multidisciplinary shape and sizing optimization of a complete aerospace vehicle configuration by using high-fidelity, finite-element structural analysis and computational fluid dynamics aerodynamic analysis. In a previous study, a multi-disciplinary analysis system for a high-speed civil transport was formulated to integrate a set of existing discipline analysis codes, some of them computationally intensive, This paper is an extension of the previous study, in which the sensitivity analysis for the coupled aerodynamic and structural analysis problem is formulated and implemented. Uncoupled stress sensitivities computed with a constant load vector in a commercial finite element analysis code are compared to coupled aeroelastic sensitivities computed by finite differences. The computational expense of these sensitivity calculation methods is discussed.

Critical behavior in a stochastic model of vector mediated epidemics

NASA Astrophysics Data System (ADS)

Alfinito, E.; Beccaria, M.; Macorini, G.

2016-06-01

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

Critical behavior in a stochastic model of vector mediated epidemics.

PubMed

Alfinito, E; Beccaria, M; Macorini, G

2016-06-06

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

Stable Local Volatility Calibration Using Kernel Splines

NASA Astrophysics Data System (ADS)

Coleman, Thomas F.; Li, Yuying; Wang, Cheng

2010-09-01

We propose an optimization formulation using L1 norm to ensure accuracy and stability in calibrating a local volatility function for option pricing. Using a regularization parameter, the proposed objective function balances the calibration accuracy with the model complexity. Motivated by the support vector machine learning, the unknown local volatility function is represented by a kernel function generating splines and the model complexity is controlled by minimizing the 1-norm of the kernel coefficient vector. In the context of the support vector regression for function estimation based on a finite set of observations, this corresponds to minimizing the number of support vectors for predictability. We illustrate the ability of the proposed approach to reconstruct the local volatility function in a synthetic market. In addition, based on S&P 500 market index option data, we demonstrate that the calibrated local volatility surface is simple and resembles the observed implied volatility surface in shape. Stability is illustrated by calibrating local volatility functions using market option data from different dates.

A finite element based method for solution of optimal control problems

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.; Calise, Anthony J.

1989-01-01

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

The gamma decay of the giant dipole resonance: from zero to finite temperature

NASA Astrophysics Data System (ADS)

Bracco, Angela; Camera, Franco

2016-08-01

This paper is intended to give a selected and rather brief overview of the work made in the last thirty years to study the properties of the giant dipole resonance focusing in particular on nuclei formed at finite temperatures using heavy ion reactions. The physical problems that are discussed (using examples of particular results) in this paper can be grouped into 3 major topics: (i) the temperature dependence of the GDR width; (ii) the dipole oscillation in reaction dynamics; (iii) the isospin mixing at finite temperature.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 3: Systems' manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1989-01-01

The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.

Adaptive finite element method for turbulent flow near a propeller

NASA Astrophysics Data System (ADS)

Pelletier, Dominique; Ilinca, Florin; Hetu, Jean-Francois

1994-11-01

This paper presents an adaptive finite element method based on remeshing to solve incompressible turbulent free shear flow near a propeller. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Turbulence is modeled by a mixing length formulation. Two general purpose error estimators, which take into account swirl and the variation of the eddy viscosity, are presented and applied to the turbulent wake of a propeller. Predictions compare well with experimental measurements. The proposed adaptive scheme is robust, reliable and cost effective.

A Simple Method to Increase the Transduction Efficiency of Single-Stranded Adeno-Associated Virus Vectors In Vitro and In Vivo

PubMed Central

Ma, Wenqin; Li, Baozheng; Ling, Chen; Jayandharan, Giridhara R.; Byrne, Barry J.

2011-01-01

Abstract We have recently shown that co-administration of conventional single-stranded adeno-associated virus 2 (ssAAV2) vectors with self-complementary (sc) AAV2-protein phosphatase 5 (PP5) vectors leads to a significant increase in the transduction efficiency of ssAAV2 vectors in human cells in vitro as well as in murine hepatocytes in vivo. In the present study, this strategy has been further optimized by generating a mixed population of ssAAV2-EGFP and scAAV2-PP5 vectors at a 10:1 ratio to achieve enhanced green fluorescent protein (EGFP) transgene expression at approximately 5- to 10-fold higher efficiency, both in vitro and in vivo. This simple coproduction method should be adaptable to any ssAAV serotype vector containing transgene cassettes that are too large to be encapsidated in scAAV vectors. PMID:21219084

The Mixed Effects Trend Vector Model

ERIC Educational Resources Information Center

de Rooij, Mark; Schouteden, Martijn

2012-01-01

Maximum likelihood estimation of mixed effect baseline category logit models for multinomial longitudinal data can be prohibitive due to the integral dimension of the random effects distribution. We propose to use multidimensional unfolding methodology to reduce the dimensionality of the problem. As a by-product, readily interpretable graphical…

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Gain in computational efficiency by vectorization in the dynamic simulation of multi-body systems

NASA Technical Reports Server (NTRS)

Amirouche, F. M. L.; Shareef, N. H.

1991-01-01

An improved technique for the identification and extraction of the exact quantities associated with the degrees of freedom at the element as well as the flexible body level is presented. It is implemented in the dynamic equations of motions based on the recursive formulation of Kane et al. (1987) and presented in a matrix form, integrating the concepts of strain energy, the finite-element approach, modal analysis, and reduction of equations. This technique eliminates the CPU intensive matrix multiplication operations in the code's hot spots for the dynamic simulation of the interconnected rigid and flexible bodies. A study of a simple robot with flexible links is presented by comparing the execution times on a scalar machine and a vector-processor with and without vector options. Performance figures demonstrating the substantial gains achieved by the technique are plotted.

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

[Three-dimensional finite analysis of the stress in first mandibular molar with composite class I restoration when various mixing ratios of bases were used].

PubMed

Zhou, Lan; Yang, Jin-Bo; Liu, Dan; Liu, Zhan; Chen, Ying; Gao, Bo

2008-06-01

To analyze the possible damage to the remaining tooth and composite restorations when various mixing ratios of bases were used. Testing elastic modulus and poission's ratio of glass-ionomer Vitrebond and self-cured calcium hydroxide Dycal with mixing ratios of 1:1, 3:4, 4:3. Micro-CT was used to scan the first mandibular molar, and the three-dimensional finite element model of the first permanent mandibular molar with class I cavity was established. Analyzing the stress of tooth structure, composite and base cement under physical load when different mixing ratios of base cement were used. The elastic modulus of base cement in various mixing ratios was different, which had the statistic significance. The magnitude and location of stress in restored tooth made no differences when the mixing ratios of Vitrebond and Dycal were changed. The peak stress and spreading area in the model with Dycal was more than that with Vitrebond. Changing the best mixing ratio of base cement can partially influence the mechanistic character, but make no differences on the magnitude and location of stress in restored tooth. During the treatment of deep caries, the base cement of the elastic modulus which is proximal to the dentin and restoration should be chosen to avoid the fracture of tooth or restoration.

Two Dimensional Finite Element Based Magnetotelluric Inversion using Singular Value Decomposition Method on Transverse Electric Mode

NASA Astrophysics Data System (ADS)

Tjong, Tiffany; Yihaa’ Roodhiyah, Lisa; Nurhasan; Sutarno, Doddy

2018-04-01

In this work, an inversion scheme was performed using a vector finite element (VFE) based 2-D magnetotelluric (MT) forward modelling. We use an inversion scheme with Singular value decomposition (SVD) method toimprove the accuracy of MT inversion.The inversion scheme was applied to transverse electric (TE) mode of MT. SVD method was used in this inversion to decompose the Jacobian matrices. Singular values which obtained from the decomposition process were analyzed. This enabled us to determine the importance of data and therefore to define a threshold for truncation process. The truncation of singular value in inversion processcould improve the resulted model.

Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains.

PubMed

Reich, W; Scheuermann, G

2012-12-01

Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In our paper we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov-Chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies.

Calculation of gravity and magnetic anomalies of finite-length right polygonal prisms.

USGS Publications Warehouse

Cady, J.W.

1980-01-01

An equation is derived for the vertical gravity field due to a homogeneous body with polygonal cross‐section and finite strike‐length. The equation can be separated into the two‐dimensional (2-D) terms of Talwani et al. (1959) and exact terms for the contributions of the ends of the prism. Equations for the magnetic field due to a similar body were derived by Shuey and Pasquale (1973), who coined the term “two‐and‐a‐half dimensional” (2 1/2-D) to describe the geometry. Magnetic intensities are expressed as a vector sum, from which the common dot product formulation can be obtained by binomial expansion.

Optical laboratory solution and error model simulation of a linear time-varying finite element equation

NASA Technical Reports Server (NTRS)

Taylor, B. K.; Casasent, D. P.

1989-01-01

The use of simplified error models to accurately simulate and evaluate the performance of an optical linear-algebra processor is described. The optical architecture used to perform banded matrix-vector products is reviewed, along with a linear dynamic finite-element case study. The laboratory hardware and ac-modulation technique used are presented. The individual processor error-source models and their simulator implementation are detailed. Several significant simplifications are introduced to ease the computational requirements and complexity of the simulations. The error models are verified with a laboratory implementation of the processor, and are used to evaluate its potential performance.

Singular perturbation, state aggregation and nonlinear filtering

NASA Technical Reports Server (NTRS)

Hijab, O.; Sastry, S.

1981-01-01

Consideration is given to a state process evolving in R(n), whose motion is that of a pure jump process in R(n) in the 0(1) time scale, upon which is superimposed a continuous motion along the orbits of a gradient-like vector field g in R(n) in the 0(1/epsilon) time scale. The infinitesimal generator of the state process is, in other words, of the form L + (1/epsilon)g. It follows from the main results presented that the projected filters converge to the finite state Wonham filter corresponding to the problem of estimating the finite state process in the presence of additive white noise.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 2: User's manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1989-01-01

The user options available for running the MHOST finite element analysis package is described. MHOST is a solid and structural analysis program based on the mixed finite element technology, and is specifically designed for 3-D inelastic analysis. A family of 2- and 3-D continuum elements along with beam and shell structural elements can be utilized, many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. The outline of solution algorithms is discussed along with the data input and output, analysis options including the user subroutines and the definition of the finite elements implemented in the program package.

New perspectives in tracing vector-borne interaction networks.

PubMed

Gómez-Díaz, Elena; Figuerola, Jordi

2010-10-01

Disentangling trophic interaction networks in vector-borne systems has important implications in epidemiological and evolutionary studies. Molecular methods based on bloodmeal typing in vectors have been increasingly used to identify hosts. Although most molecular approaches benefit from good specificity and sensitivity, their temporal resolution is limited by the often rapid digestion of blood, and mixed bloodmeals still remain a challenge for bloodmeal identification in multi-host vector systems. Stable isotope analyses represent a novel complementary tool that can overcome some of these problems. The utility of these methods using examples from different vector-borne systems are discussed and the extents to which they are complementary and versatile are highlighted. There are excellent opportunities for progress in the study of vector-borne transmission networks resulting from the integration of both molecular and stable isotope approaches. Copyright © 2010 Elsevier Ltd. All rights reserved.

A mixed parallel strategy for the solution of coupled multi-scale problems at finite strains

NASA Astrophysics Data System (ADS)

Lopes, I. A. Rodrigues; Pires, F. M. Andrade; Reis, F. J. P.

2018-02-01

A mixed parallel strategy for the solution of homogenization-based multi-scale constitutive problems undergoing finite strains is proposed. The approach aims to reduce the computational time and memory requirements of non-linear coupled simulations that use finite element discretization at both scales (FE^2). In the first level of the algorithm, a non-conforming domain decomposition technique, based on the FETI method combined with a mortar discretization at the interface of macroscopic subdomains, is employed. A master-slave scheme, which distributes tasks by macroscopic element and adopts dynamic scheduling, is then used for each macroscopic subdomain composing the second level of the algorithm. This strategy allows the parallelization of FE^2 simulations in computers with either shared memory or distributed memory architectures. The proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the Newton-Raphson scheme. Several examples are presented to demonstrate the robustness and efficiency of the proposed parallel strategy.

A Mixed Multi-Field Finite Element Formulation for Thermopiezoelectric Composite Shells

NASA Technical Reports Server (NTRS)

Lee, Ho-Jun; Saravanos, Dimitris A.

1999-01-01

Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite shell structures. A new mixed multi-field laminate theory is developed which combines "single layer" assumptions for the displacements along with layerwise fields for the electric potential and temperature. This laminate theory is formulated using curvilinear coordinates and is based on the principles of linear thermopiezoelectricity. The mechanics have the inherent capability to explicitly model both the active and sensory responses of piezoelectric composite shells in thermal environment. Finite element equations are derived and implemented for an eight-noded shell element. Numerical studies are conducted to investigate both the sensory and active responses of piezoelectric composite shell structures subjected to thermal loads. Results for a cantilevered plate with an attached piezoelectric layer are com- pared with corresponding results from a commercial finite element code and a previously developed program. Additional studies are conducted on a cylindrical shell with an attached piezoelectric layer to demonstrate capabilities to achieve thermal shape control on curved piezoelectric structures.

Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation

DOE PAGES

Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; ...

1995-01-01

In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

A linear shock cell model for jets of arbitrary exit geometry

NASA Technical Reports Server (NTRS)

Morris, P. J.; Bhat, T. R. S.; Chen, G.

1989-01-01

The shock cell structures of single supersonic non-ideally expanded jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. This formulation enables the calculations to be performed only on the vortex sheet. This permits the efficient and convenient study of complicated jet geometries. Results are given for circular, elliptic and rectangular jets and the results are compared with analysis and experiment. The agreement between the predictions and measurements is very good but depends on the assumptions made to predict the geometry of the fully expanded jet. A finite diffference technique is used to examine the effect of finite mixing layer thickness for a single jet. The finite thickness of the mixing layer is found to decrease the shock spacing by approximately 20 percent over the length of the jet potential core.

On the computer analysis of structures and mechanical systems

NASA Technical Reports Server (NTRS)

Bennett, B. E.

1984-01-01

The governing equations for the analysis of open branch-chain mechanical systems are developed in a form suitable for implementation in a general purpose finite element computer program. Lagrange's form of d'Alembert's principle is used to derive the system mass matrix and force vector. The generalized coordinates are selected as the unconstrained relative degrees of freedom giving the position and orientation of each slave link with respect to their master link. Each slave link may have from zero to six degrees of freedom relative to the reference frames of its master link. A strategy for automatic generation of the system mass matrix and force vector is described.

Dynamic current-current susceptibility in three-dimensional Dirac and Weyl semimetals

NASA Astrophysics Data System (ADS)

Thakur, Anmol; Sadhukhan, Krishanu; Agarwal, Amit

2018-01-01

We study the linear response of doped three-dimensional Dirac and Weyl semimetals to vector potentials, by calculating the wave-vector- and frequency-dependent current-current response function analytically. The longitudinal part of the dynamic current-current response function is then used to study the plasmon dispersion and the optical conductivity. The transverse response in the static limit yields the orbital magnetic susceptibility. In a Weyl semimetal, along with the current-current response function, all these quantities are significantly impacted by the presence of parallel electric and magnetic fields (a finite E .B term) and can be used to experimentally explore the chiral anomaly.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

A mixed finite-element method for solving the poroelastic Biot equations with electrokinetic coupling

NASA Astrophysics Data System (ADS)

Pain, C. C.; Saunders, J. H.; Worthington, M. H.; Singer, J. M.; Stuart-Bruges, W.; Mason, G.; Goddard, A.

2005-02-01

In this paper, a numerical method for solving the Biot poroelastic equations is developed. These equations comprise acoustic (typically water) and elastic (porous medium frame) equations, which are coupled mainly through fluid/solid drag terms. This wave solution is coupled to a simplified form of Maxwell's equations, which is solved for the streaming potential resulting from electrokinesis. The ultimate aim is to use the generated electrical signals to provide porosity, permeability and other information about the formation surrounding a borehole. The electrical signals are generated through electrokinesis by seismic waves causing movement of the fluid through pores or fractures of a porous medium. The focus of this paper is the numerical solution of the Biot equations in displacement form, which is achieved using a mixed finite-element formulation with a different finite-element representation for displacements and stresses. The mixed formulation is used in order to reduce spurious displacement modes and fluid shear waves in the numerical solutions. These equations are solved in the time domain using an implicit unconditionally stable time-stepping method using iterative solution methods amenable to solving large systems of equations. The resulting model is embodied in the MODELLING OF ACOUSTICS, POROELASTICS AND ELECTROKINETICS (MAPEK) computer model for electroseismic analysis.

Effects of finite volume on the K L – K S mass difference

DOE PAGES

Christ, N.  H.; Feng, X.; Martinelli, G.; ...

2015-06-24

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the Kmore » L – K S mass difference ΔM K and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less

A Locally Modal B-Spline Based Full-Vector Finite-Element Method with PML for Nonlinear and Lossy Plasmonic Waveguide

NASA Astrophysics Data System (ADS)

Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan

2016-09-01

In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.

Finite element area and line integral transforms for generalization of aperture function and geometry in Kirchhoff scalar diffraction theory

NASA Astrophysics Data System (ADS)

Kraus, Hal G.

1993-02-01

Two finite element-based methods for calculating Fresnel region and near-field region intensities resulting from diffraction of light by two-dimensional apertures are presented. The first is derived using the Kirchhoff area diffraction integral and the second is derived using a displaced vector potential to achieve a line integral transformation. The specific form of each of these formulations is presented for incident spherical waves and for Gaussian laser beams. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define apertures of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s), which may be of continuous or discontinuous form. The finite element transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is illustrated in several examples which include secondary obstructions, secondary spider supports, multiple mirror arrays, synthetic aperture arrays, apertures covered by screens, apodization, phase plates, and off-axis apertures. Typically, the finite element line integral transform results in significant gains in computational efficiency over the finite element Kirchhoff transform method, but is also subject to some loss in generality.

A continuous mixing model for pdf simulations and its applications to combusting shear flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Chen, J.-Y.

1991-01-01

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in this work. A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Qingping; Wu, Lijun; Welch, David O.

2015-06-17

We studied the lattice vibrations of two inter-penetrating atomic sublattices via the Frenkel-Kontorova (FK) model of a linear chain of harmonically interacting atoms subjected to an on-site potential, using the technique of thermodynamic Green's functions based on quantum field-theoretical methods. General expressions were deduced for the phonon frequency-wave-vector dispersion relations, number density, and energy of the FK model system. In addition, as the application of the theory, we investigated in detail cases of linear chains with various periods of the on-site potential of the FK model. Some unusual but interesting features for different amplitudes of the on-site potential of themore » FK model are discussed. In the commensurate structure, the phonon spectrum always starts at a finite frequency, and the gaps of the spectrum are true ones with a zero density of modes. In the incommensurate structure, the phonon spectrum starts from zero frequency, but at a non-zero wave vector; there are some modes inside these gap regions, but their density is very low. In our approximation, the energy of a higher-order commensurate state of the one-dimensional system at a finite temperature may become indefinitely close to the energy of an incommensurate state. This finding implies that the higher-order incommensurate-commensurate transitions are continuous ones and that the phase transition may exhibit a “devil's staircase” behavior at a finite temperature.« less

An M-step preconditioned conjugate gradient method for parallel computation

NASA Technical Reports Server (NTRS)

Adams, L.

1983-01-01

This paper describes a preconditioned conjugate gradient method that can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systems of linear equations. The implementation on the CYBER 203/205 and on the Finite Element Machine is discussed and results obtained using the method on these machines are given.

Evaluation of a Nonlinear Finite Element Program - ABAQUS.

DTIC Science & Technology

1983-03-15

anisotropic properties. * MATEXP - Linearly elastic thermal expansions with isotropic, orthotropic and anisotropic properties. * MATELG - Linearly...elastic materials for general sections (options available for beam and shell elements). • MATEXG - Linearly elastic thermal expansions for general...decomposition of a matrix. * Q-R algorithm • Vector normalization, etc. Obviously, by consolidating all the utility subroutines in a library, ABAQUS has

The infinum principle

NASA Technical Reports Server (NTRS)

Geering, H. P.; Athans, M.

1973-01-01

A complete theory of necessary and sufficient conditions is discussed for a control to be superior with respect to a nonscalar-valued performance criterion. The latter maps into a finite dimensional, integrally closed directed, partially ordered linear space. The applicability of the theory to the analysis of dynamic vector estimation problems and to a class of uncertain optimal control problems is demonstrated.

Problems with heterogeneous and non-isotropic media or distorted grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hyman, J.; Shashkov, M.; Steinberg, S.

1996-08-01

This paper defines discretizations of the divergence and flux operators that produce symmetric, positive-definite, and accurate approximations to steady-state diffusion problems. Because discontinuous material properties and highly distorted grids are allowed, the flux operator, rather than the gradient, is used as a fundamental operator to be discretized. Resulting finite-difference scheme is similar to those obtained from the mixed finite-element method.

Parallel processors and nonlinear structural dynamics algorithms and software

NASA Technical Reports Server (NTRS)

Belytschko, Ted

1990-01-01

Techniques are discussed for the implementation and improvement of vectorization and concurrency in nonlinear explicit structural finite element codes. In explicit integration methods, the computation of the element internal force vector consumes the bulk of the computer time. The program can be efficiently vectorized by subdividing the elements into blocks and executing all computations in vector mode. The structuring of elements into blocks also provides a convenient way to implement concurrency by creating tasks which can be assigned to available processors for evaluation. The techniques were implemented in a 3-D nonlinear program with one-point quadrature shell elements. Concurrency and vectorization were first implemented in a single time step version of the program. Techniques were developed to minimize processor idle time and to select the optimal vector length. A comparison of run times between the program executed in scalar, serial mode and the fully vectorized code executed concurrently using eight processors shows speed-ups of over 25. Conjugate gradient methods for solving nonlinear algebraic equations are also readily adapted to a parallel environment. A new technique for improving convergence properties of conjugate gradients in nonlinear problems is developed in conjunction with other techniques such as diagonal scaling. A significant reduction in the number of iterations required for convergence is shown for a statically loaded rigid bar suspended by three equally spaced springs.

Phase mismatched optical parametric generation in semiconductor magnetoplasma

NASA Astrophysics Data System (ADS)

Dubey, Swati; Ghosh, S.; Jain, Kamal

2017-05-01

Optical parametric generation involves the interaction of pump, signal, and idler waves satisfying law of conservation of energy. Phase mismatch parameter plays important role for the spatial distribution of the field along the medium. In this paper instead of exactly matching wave vector, a small mismatch is admitted with a degree of phase velocity mismatch between these waves. Hence the medium must possess certain finite coherence length. This wave mixing process is well explained by coupled mode theory and one dimensional hydrodynamic model. Based on this scheme, expressions for threshold pump field and transmitted intensity have been derived. It is observed that the threshold pump intensity and transmitted intensity can be manipulated by varying doping concentration and magnetic field under phase mismatched condition. A compound semiconductor crystal of n-InSb is assumed to be shined at 77 K by a 10.6μm CO2 laser with photon energy well below band gap energy of the crystal, so that only free charge carrier influence the optical properties of the medium for the I.R. parametric generation in a semiconductor plasma medium. Favorable parameters were explored to incite the said process keeping in mind the cost effectiveness and conversion efficiency of the process.

Learning With Mixed Hard/Soft Pointwise Constraints.

PubMed

Gnecco, Giorgio; Gori, Marco; Melacci, Stefano; Sanguineti, Marcello

2015-09-01

A learning paradigm is proposed and investigated, in which the classical framework of learning from examples is enhanced by the introduction of hard pointwise constraints, i.e., constraints imposed on a finite set of examples that cannot be violated. Such constraints arise, e.g., when requiring coherent decisions of classifiers acting on different views of the same pattern. The classical examples of supervised learning, which can be violated at the cost of some penalization (quantified by the choice of a suitable loss function) play the role of soft pointwise constraints. Constrained variational calculus is exploited to derive a representer theorem that provides a description of the functional structure of the optimal solution to the proposed learning paradigm. It is shown that such an optimal solution can be represented in terms of a set of support constraints, which generalize the concept of support vectors and open the doors to a novel learning paradigm, called support constraint machines. The general theory is applied to derive the representation of the optimal solution to the problem of learning from hard linear pointwise constraints combined with soft pointwise constraints induced by supervised examples. In some cases, closed-form optimal solutions are obtained.

Continuous-wave THz vector imaging system utilizing two-tone signal generation and self-mixing detection.

PubMed

Song, Hajun; Hwang, Sejin; An, Hongsung; Song, Ho-Jin; Song, Jong-In

2017-08-21

We propose and demonstrate a continuous-wave vector THz imaging system utilizing a photonic generation of two-tone THz signals and self-mixing detection. The proposed system measures amplitude and phase information simultaneously without the local oscillator reference or phase rotation scheme that is required for heterodyne or homodyne detection. In addition, 2π phase ambiguity that occurs when the sample is thicker than the wavelength of THz radiation can be avoided. In this work, THz signal having two frequency components was generated with a uni-traveling-carrier photodiode and electro-optic modulator on the emitter side and detected with a Schottky barrier diode detector used as a self-mixer on the receiver side. The proposed THz vector imaging system exhibited a 50-dB signal to noise ratio and 0.012-rad phase fluctuation with 100-μs integration time at 325-GHz. With the system, we demonstrate two-dimensional THz phase contrast imaging. Considering the recent use of two-dimensional arrays of Schottky barrier diodes as a THz image sensor, the proposed system is greatly advantageous for realizing a real-time THz vector imaging system due to its simple receiver configuration.

Synergy between Repellents and Organophosphates on Bed Nets: Efficacy and Behavioural Response of Natural Free-Flying An. gambiae Mosquitoes

PubMed Central

Pennetier, Cédric; Costantini, Carlo; Corbel, Vincent; Licciardi, Séverine; Dabiré, Roch K.; Lapied, Bruno; Chandre, Fabrice; Hougard, Jean-Marc

2009-01-01

Background Chemicals are used on bed nets in order to prevent infected bites and to kill aggressive malaria vectors. Because pyrethroid resistance has become widespread in the main malaria vectors, research for alternative active ingredients becomes urgent. Mixing a repellent and a non-pyrethroid insecticide seemed to be a promising tool as mixtures in the laboratory showed the same features as pyrethroids. Methodology/Principal Findings We present here the results of two trials run against free-flying Anopheles gambiae populations comparing the effects of two insect repellents (either DEET or KBR 3023, also known as icaridin) and an organophosphate insecticide at low-doses (pirimiphos-methyl, PM) used alone and in combination on bed nets. We showed that mixtures of PM and the repellents induced higher exophily, blood feeding inhibition and mortality among wild susceptible and resistant malaria vectors than compounds used alone. Nevertheless the synergistic interactions are only involved in the high mortality induced by the two mixtures. Conclusion These field trials argue in favour of the strategy of mixing repellent and organophosphate on bed nets to better control resistant malaria vectors. PMID:19936249

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

On Multifunctional Collaborative Methods in Engineering Science

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2001-01-01

Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.

Anomalous group velocity at the high energy range of real 3D photonic nanostructures

NASA Astrophysics Data System (ADS)

Botey, Muriel; Martorell, Jordi; Lozano, Gabriel; Míguez, Hernán; Dorado, Luis A.; Depine, Ricardo A.

2010-05-01

We perform a theoretical study on the group velocity for finite thin artificial opal slabs made of a reduced number of layers in the spectral range where the light wavelength is on the order of the lattice parameter. The vector KKR method including extinction allows us to evaluate the finite-size effects on light propagation in the ΓL and ΓX directions of fcc close-packed opal films made of dielectric spheres. The group is index determined from the phase delay introduced by the structure to the forwardly transmitted electric field. We show that for certain frequencies, light propagation can either be superluminal -positive or negative- or approach zero depending on the crystal size and absorption. Such anomalous behavior can be attributed to the finite character of the structure and provides confirmation of recently emerged experimental results.

A 2D Daubechies finite wavelet domain method for transient wave response analysis in shear deformable laminated composite plates

NASA Astrophysics Data System (ADS)

Nastos, C. V.; Theodosiou, T. C.; Rekatsinas, C. S.; Saravanos, D. A.

2018-03-01

An efficient numerical method is developed for the simulation of dynamic response and the prediction of the wave propagation in composite plate structures. The method is termed finite wavelet domain method and takes advantage of the outstanding properties of compactly supported 2D Daubechies wavelet scaling functions for the spatial interpolation of displacements in a finite domain of a plate structure. The development of the 2D wavelet element, based on the first order shear deformation laminated plate theory is described and equivalent stiffness, mass matrices and force vectors are calculated and synthesized in the wavelet domain. The transient response is predicted using the explicit central difference time integration scheme. Numerical results for the simulation of wave propagation in isotropic, quasi-isotropic and cross-ply laminated plates are presented and demonstrate the high spatial convergence and problem size reduction obtained by the present method.

Numerical studies in geophysics

NASA Astrophysics Data System (ADS)

Hier Majumder, Catherine Anne

2003-10-01

This thesis focuses on the use of modern numerical techniques in the geo- and environmental sciences. Four topics are discussed in this thesis: finite Prandtl number convection, wavelet analysis, inverse methods and data assimilation, and nuclear waste tank mixing. The finite Prandtl number convection studies examine how convection behavior changes as Prandtl numbers are increased to as high as 2 x 104, on the order of Prandtl numbers expected in very hot magmas or mushy ice diapirs. I found that there are significant differences in the convection style between finite Prandtl number convection and the infinite Prandtl number approximation even for Prandtl numbers on the order of 104. This indicates that the infinite Prandtl convection approximation might not accurately model behavior in fluids with large, but finite Prandtl numbers. The section on inverse methods and data assimilation used the technique of four dimensional variational data assimilation (4D-VAR) developed by meteorologists to integrate observations into forecasts. It was useful in studying the predictability and dependence on initial conditions of finite Prandtl simulations. This technique promises to be useful in a wide range of geological and geophysical fields, including mantle convection, hydrogeology, and sedimentology. Wavelet analysis was used to help image and scrutinize at small-scales both temperature and vorticity fields from convection simulations and the geoid. It was found to be extremely helpful in both cases. It allowed us to separate the information in the data into various spatial scales without losing the locations of the signals in space. This proved to be essential in understanding the processes producing the total signal in the datasets. The nuclear waste study showed that techniques developed in geology and geophysics can be used to solve scientific problems in other fields. I applied state-of-the-art techniques currently employed in geochemistry, sedimentology, and mantle mixing to simulate dynamical processes occurring in the course of mixing nuclear waste tanks.

Decohesion Elements using Two and Three-Parameter Mixed-Mode Criteria

NASA Technical Reports Server (NTRS)

Davila, Carlos G.; Camanho, Pedro P.

2001-01-01

An eight-node decohesion element implementing different criteria to predict delamination growth under mixed-mode loading is proposed. The element is used at the interface between solid finite elements to model the initiation and propagation of delamination. A single displacement-based damage parameter is used in a softening law to track the damage state of the interface. The power law criterion and a three-parameter mixed-mode criterion are used to predict delamination growth. The accuracy of the predictions is evaluated in single mode delamination and in the mixed-mode bending tests.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lello, Louis; Boyanovsky, Daniel; Pisarski, Robert D.

Here, in the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at temperatures near the masses of the electroweak bosons. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles, which is applicable over a wide range of temperature, to all orders in interactions of the standard model and to leading order in a small mixing angle for the neutrinos. We emphasize the relation between the production rate and Landau damping at one-loop order and show that production rates and effective mixing angles depend sensitively upon the neutrino’s helicity. Sterile neutrinos with positive helicity interact more weakly with the medium than those with negative helicity, and their effective mixing angle is not modified significantly. Negative helicity states couple more strongly to the vector bosons, but their mixing angle is strongly suppressed by the medium. Consequently, if the mass of the sterile neutrino is ≲ 8.35 MeV , there are fewer states with negative helicity produced than those with positive helicity. There is an Mikheyev-Smirnov-Wolfenstein-type resonance in the absence of lepton asymmetry, but due to screening by the damping rate, the production rate is not enhanced. Sterile neutrinos with negative helicity freeze out at Tmore » $$-\\atop{f}$$ ≃ 5 GeV , whereas positive helicity neutrinos freeze out at T$$+\\atop{f}$$≃ 8 GeV , with both distributions far from thermal. As the temperature decreases, due to competition between a decreasing production rate and an increasing mixing angle, the distribution function for states with negative helicity is broader in momentum and hotter than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime, and cosmological constraints to be the sole dark matter component in the Universe. Massive sterile neutrinos produced via vector boson decay might solve the 7Li problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. In conclusion, we argue that heavy sterile neutrinos with lifetime ≤1/H 0 reach local thermodynamic equilibrium.« less

Simulation of 3-D viscous compressible flow in multistage turbomachinery by finite element methods

NASA Astrophysics Data System (ADS)

Sleiman, Mohamad

1999-11-01

The flow in a multistage turbomachinery blade row is compressible, viscous, and unsteady. Complex flow features such as boundary layers, wake migration from upstream blade rows, shocks, tip leakage jets, and vortices interact together as the flow convects through the stages. These interactions contribute significantly to the aerodynamic losses of the system and degrade the performance of the machine. The unsteadiness also leads to blade vibration and a shortening of its life. It is therefore difficult to optimize the design of a blade row, whether aerodynamically or structurally, in isolation, without accounting for the effects of the upstream and downstream rows. The effects of axial spacing, blade count, clocking (relative position of follow-up rotors with respect to wakes shed by upstream ones), and levels of unsteadiness may have a significance on performance and durability. In this Thesis, finite element formulations for the simulation of multistage turbomachinery are presented in terms of the Reynolds-averaged Navier-Stokes equations for three-dimensional steady or unsteady, viscous, compressible, turbulent flows. Three methodologies are presented and compared. First, a steady multistage analysis using a a-mixing- plane model has been implemented and has been validated against engine data. For axial machines, it has been found that the mixing plane simulation methods match very well the experimental data. However, the results for a centrifugal stage, consisting of an impeller followed by a vane diffuser of equal pitch, show flagrant inconsistency with engine performance data, indicating that the mixing plane method has been found to be inappropriate for centrifugal machines. Following these findings, a more complete unsteady multistage model has been devised for a configuration with equal number of rotor and stator blades (equal pitches). Non-matching grids are used at the rotor-stator interface and an implicit interpolation procedure devised to ensure continuity of fluxes across. This permits the rotor and stator equations to be solved in a fully- coupled manner, allowing larger time steps in attaining a time-periodic solution. This equal pitch approach has been validated on the complex geometry of a centrifugal stage. Finally, for a stage configuration with unequal pitches, the time-inclined method, developed by Giles (1991) for 2-D viscous compressible flow, has been extended to 3-D and formulated in terms of the physical solution vector U, rather than Q, a non-physical one. The method has been evaluated for unsteady flow through a rotor blade passage of the power turbine of a turboprop.

A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1986-01-01

The present study is concerned with the development of a mixed shear flexible finite element with relaxed continuity for the geometrically linear and nonlinear analysis of laminated anisotropic plates. The formulation of the element is based on a refined higher-order theory. This theory satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate. Shear correction coefficients are not needed. The developed element consists of 11 degrees-of-freedom per node, taking into account three displacements, two rotations, and six moment resultants. An evaluation of the element is conducted with respect to the accuracy obtained in the bending of laminated anistropic rectangular plates with different lamination schemes, loadings, and boundary conditions.

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Noisy bases in Hilbert space: A new class of thermal coherent states and their properties

NASA Technical Reports Server (NTRS)

Vourdas, A.; Bishop, R. F.

1995-01-01

Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.

INTERIM ANALYSIS OF THE CONTRIBUTION OF HIGH-LEVEL EVIDENCE FOR DENGUE VECTOR CONTROL.

PubMed

Horstick, Olaf; Ranzinger, Silvia Runge

2015-01-01

This interim analysis reviews the available systematic literature for dengue vector control on three levels: 1) single and combined vector control methods, with existing work on peridomestic space spraying and on Bacillus thuringiensis israelensis; further work is available soon on the use of Temephos, Copepods and larvivorous fish; 2) or for a specific purpose, like outbreak control, and 3) on a strategic level, as for example decentralization vs centralization, with a systematic review on vector control organization. Clear best practice guidelines for methodology of entomological studies are needed. There is a need to include measuring dengue transmission data. The following recommendations emerge: Although vector control can be effective, implementation remains an issue; Single interventions are probably not useful; Combinations of interventions have mixed results; Careful implementation of vector control measures may be most important; Outbreak interventions are often applied with questionable effectiveness.

Separating Internal Waves and Vortical Motions: Analysis of LatMix -EM-APEX Float Measurements

DTIC Science & Technology

2015-09-30

vortical motions and internal waves and quantify their effects on horizontal dispersion and diapycnal mixing. WORK COMPLETED...defined as Π = ( + ∇×)⋅∇( − η) (e.g., Kunze and Sanford 1993), where f is the Coriolis frequency, U the velocity vector, z the vertical coordinate

User's guide for NASCRIN: A vectorized code for calculating two-dimensional supersonic internal flow fields

NASA Technical Reports Server (NTRS)

Kumar, A.

1984-01-01

A computer program NASCRIN has been developed for analyzing two-dimensional flow fields in high-speed inlets. It solves the two-dimensional Euler or Navier-Stokes equations in conservation form by an explicit, two-step finite-difference method. An explicit-implicit method can also be used at the user's discretion for viscous flow calculations. For turbulent flow, an algebraic, two-layer eddy-viscosity model is used. The code is operational on the CDC CYBER 203 computer system and is highly vectorized to take full advantage of the vector-processing capability of the system. It is highly user oriented and is structured in such a way that for most supersonic flow problems, the user has to make only a few changes. Although the code is primarily written for supersonic internal flow, it can be used with suitable changes in the boundary conditions for a variety of other problems.

Magnetoacoustic Tomography with Magnetic Induction: Bioimepedance reconstruction through vector source imaging

PubMed Central

Mariappan, Leo; He, Bin

2013-01-01

Magneto acoustic tomography with magnetic induction (MAT-MI) is a technique proposed to reconstruct the conductivity distribution in biological tissue at ultrasound imaging resolution. A magnetic pulse is used to generate eddy currents in the object, which in the presence of a static magnetic field induces Lorentz force based acoustic waves in the medium. This time resolved acoustic waves are collected with ultrasound transducers and, in the present work, these are used to reconstruct the current source which gives rise to the MAT-MI acoustic signal using vector imaging point spread functions. The reconstructed source is then used to estimate the conductivity distribution of the object. Computer simulations and phantom experiments are performed to demonstrate conductivity reconstruction through vector source imaging in a circular scanning geometry with a limited bandwidth finite size piston transducer. The results demonstrate that the MAT-MI approach is capable of conductivity reconstruction in a physical setting. PMID:23322761

States that are far from being stabilizer states

NASA Astrophysics Data System (ADS)

Andersson, David; Bengtsson, Ingemar; Blanchfield, Kate; Bui Dang, Hoan

2015-08-01

Stabilizer states are eigenvectors of maximal commuting sets of operators in a finite Heisenberg group. States that are far from being stabilizer states include magic states in quantum computation, MUB-balanced states, and SIC vectors. In prime dimensions the latter two fall under the umbrella of minimum uncertainty states (MUSs) in the sense of Wootters and Sussman. We study the correlation between two ways in which the notion of ‘far from being a stabilizer state’ can be quantified. Two theorems valid for all prime dimensions are given, as well as detailed results for low dimensions. In dimension 7 we identify the MUB-balanced states as being antipodal to the SIC vectors within the set of MUS, in a sense that we make definite. In dimension 4 we show that the states that come closest to being MUS with respect to all of the six stabilizer MUBs are the fiducial vectors for Alltop MUBs.

Precomputed state dependent digital control of a nuclear rocket engine

NASA Technical Reports Server (NTRS)

Johnson, M. R.

1972-01-01

A control method applicable to multiple-input multiple-output nonlinear time-invariant systems in which desired behavior can be expressed explicitly as a trajectory in system state space is developed. The precomputed state dependent control method is basically a synthesis technique in which a suboptimal control law is developed off-line, prior to system operation. This law is obtained by conducting searches at a finite number of points in state space, in the vicinity of some desired trajectory, to obtain a set of constant control vectors which tend to return the system to the desired trajectory. These vectors are used to evaluate the unknown coefficients in a control law having an assumed hyperellipsoidal form. The resulting coefficients constitute the heart of the controller and are used in the on-line computation of control vectors. Two examples of PSDC are given prior to the more detailed description of the NERVA control system development.

Multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2017-04-01

As the fourth stage of the project multi-indexed orthogonal polynomials, we present the multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials in the framework of ‘discrete quantum mechanics’ with real shifts defined on the semi-infinite lattice in one dimension. They are obtained, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier, from the quantum mechanical systems corresponding to the original orthogonal polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of virtual state vectors. The virtual state vectors are the solutions of the matrix Schrödinger equation on all the lattice points having negative energies and infinite norm. This is in good contrast to the (q-)Racah systems defined on a finite lattice, in which the ‘virtual state’ vectors satisfy the matrix Schrödinger equation except for one of the two boundary points.

Fully synchronous solutions and the synchronization phase transition for the finite-N Kuramoto model

NASA Astrophysics Data System (ADS)

Bronski, Jared C.; DeVille, Lee; Jip Park, Moon

2012-09-01

We present a detailed analysis of the stability of phase-locked solutions to the Kuramoto system of oscillators. We derive an analytical expression counting the dimension of the unstable manifold associated to a given stationary solution. From this we are able to derive a number of consequences, including analytic expressions for the first and last frequency vectors to phase-lock, upper and lower bounds on the probability that a randomly chosen frequency vector will phase-lock, and very sharp results on the large N limit of this model. One of the surprises in this calculation is that for frequencies that are Gaussian distributed, the correct scaling for full synchrony is not the one commonly studied in the literature; rather, there is a logarithmic correction to the scaling which is related to the extremal value statistics of the random frequency vector.

Status of quarkonia-like negative and positive parity states in a relativistic confinement scheme

NASA Astrophysics Data System (ADS)

Bhavsar, Tanvi; Shah, Manan; Vinodkumar, P. C.

2018-03-01

Properties of quarkonia-like states in the charm and bottom sector have been studied in the frame work of relativistic Dirac formalism with a linear confinement potential. We have computed the mass spectroscopy and decay properties (vector decay constant and leptonic decay width) of several quarkonia-like states. The present study is also intended to identify some of the unexplained states as mixed P-wave and mixed S-D-wave states of charmonia and bottomonia. The results indicate that the X(4140) state can be an admixture of two P states of charmonium. And the charmonium-like states X(4630) and X(4660) are the admixed state of S-D-waves. Similarly, the X(10610) state recently reported by Belle II can be mixed P-states of bottomonium. In the relativistic framework we have computed the vector decay constant and the leptonic decay width for S wave charmonium and bottomonium. The leptonic decay widths for the J^{PC} = 1^{-} mixed states are also predicted. Further, both the masses and the leptonic decay width are considered for the identification of the quarkonia-like states.

The effects of vector leptoquark on the ℬb(ℬ = Λ,Σ) →ℬμ+μ- decays

NASA Astrophysics Data System (ADS)

Wang, Shuai-Wei; Huang, Jin-Shu

2016-07-01

In this paper, we have studied the baryonic semileptonic ℬb(ℬ = Λ, Σ) →ℬμ+μ- decays in the vector leptoquark model with U = (3, 3, 2/3) state. Using the parameters’ space constrained through some well-measured decay modes, such as Bs → μ+μ-, Bs -B¯s mixing and B → K∗μ+μ- decays, we show the effects of vector leptoquark state on the double lepton polarization asymmetries of ℬb(ℬ = Λ, Σ) →ℬμ+μ- decays, and find that the double lepton polarization asymmetries, except for PLL, PLN and PNL, are sensitive to the contributions of vector leptoquark model.

A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

PubMed

Zhang, Xian-Ming; Han, Qing-Long; Ge, Xiaohua

2017-09-22

This paper is concerned with the problem of robust H∞ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust H∞ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Multi-perspective views of students’ difficulties with one-dimensional vector and two-dimensional vector

NASA Astrophysics Data System (ADS)

Fauzi, Ahmad; Ratna Kawuri, Kunthi; Pratiwi, Retno

2017-01-01

Researchers of students’ conceptual change usually collects data from written tests and interviews. Moreover, reports of conceptual change often simply refer to changes in concepts, such as on a test, without any identification of the learning processes that have taken place. Research has shown that students have difficulties with vectors in university introductory physics courses and high school physics courses. In this study, we intended to explore students’ understanding of one-dimensional and two-dimensional vector in multi perspective views. In this research, we explore students’ understanding through test perspective and interviews perspective. Our research study adopted the mixed-methodology design. The participants of this research were sixty students of third semester of physics education department. The data of this research were collected by testand interviews. In this study, we divided the students’ understanding of one-dimensional vector and two-dimensional vector in two categories, namely vector skills of the addition of one-dimensionaland two-dimensional vector and the relation between vector skills and conceptual understanding. From the investigation, only 44% of students provided correct answer for vector skills of the addition of one-dimensional and two-dimensional vector and only 27% students provided correct answer for the relation between vector skills and conceptual understanding.

Optimization Based Efficiencies in First Order Reliability Analysis

NASA Technical Reports Server (NTRS)

Peck, Jeffrey A.; Mahadevan, Sankaran

2003-01-01

This paper develops a method for updating the gradient vector of the limit state function in reliability analysis using Broyden's rank one updating technique. In problems that use commercial code as a black box, the gradient calculations are usually done using a finite difference approach, which becomes very expensive for large system models. The proposed method replaces the finite difference gradient calculations in a standard first order reliability method (FORM) with Broyden's Quasi-Newton technique. The resulting algorithm of Broyden updates within a FORM framework (BFORM) is used to run several example problems, and the results compared to standard FORM results. It is found that BFORM typically requires fewer functional evaluations that FORM to converge to the same answer.

A finite element beam propagation method for simulation of liquid crystal devices.

PubMed

Vanbrabant, Pieter J M; Beeckman, Jeroen; Neyts, Kristiaan; James, Richard; Fernandez, F Anibal

2009-06-22

An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell's equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

A parallel finite-difference method for computational aerodynamics

NASA Technical Reports Server (NTRS)

Swisshelm, Julie 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.

Free stream capturing in fluid conservation law for moving coordinates in three dimensions

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

The free-stream capturing technique for both the finite-volume (FV) and finite-difference (FD) framework is summarized. For an arbitrary motion of the grid, the FV analysis shows that volumes swept by all six surfaces of the cell have to be computed correctly. This means that the free-stream capturing time-metric terms should be calculated not only from a surface vector of a cell at a single time level, but also from a volume swept by the cell surface in space and time. The FV free-stream capturing formulation is applicable to the FD formulation by proper translation from an FV cell to an FD mesh.

Direct coordinate-free derivation of the compatibility equation for finite strains

NASA Astrophysics Data System (ADS)

Ryzhak, E. I.

2014-07-01

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness.

Finite-element solutions for geothermal systems

NASA Technical Reports Server (NTRS)

Chen, J. C.; Conel, J. E.

1977-01-01

Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.

Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Ogilvie, P. L.

1978-01-01

The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.

Solutal Marangoni flows of miscible liquids drive transport without surface contamination

NASA Astrophysics Data System (ADS)

Kim, Hyoungsoo; Muller, Koen; Shardt, Orest; Afkhami, Shahriar; Stone, Howard A.

2017-11-01

Mixing and spreading of different liquids are omnipresent in nature, life and technology, such as oil pollution on the sea, estuaries, food processing, cosmetic and beverage industries, lab-on-a-chip devices, and polymer processing. However, the mixing and spreading mechanisms for miscible liquids remain poorly characterized. Here, we show that a fully soluble liquid drop deposited on a liquid surface remains as a static lens without immediately spreading and mixing, and simultaneously a Marangoni-driven convective flow is generated, which are counterintuitive results when two liquids have different surface tensions. To understand the dynamics, we develop a theoretical model to predict the finite spreading time and length scales, the Marangoni-driven convection flow speed, and the finite timescale to establish the quasi-steady state for the Marangoni flow. The fundamental understanding of this solutal Marangoni flow may enable driving bulk flows and constructing an effective drug delivery and surface cleaning approach without causing surface contamination by immiscible chemical species.

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Godfrey, Andrew G.

1993-01-01

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Scalability, Complexity and Reliability in Quantum Information Processing

DTIC Science & Technology

2007-03-01

hidden subgroup framework to abelian groups which are not finitely generated. An extension of the basic algorithm breaks the Buchmann-Williams...finding short lattice vectors . In [2], we showed that the generalization of the standard method --- random coset state preparation followed by fourier...sampling --- required exponential time for sufficiently non-abelian groups including the symmetric group , at least when the fourier transforms are

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Domination Problem for Vector Measures and Applications to Nonstationary Processes.

DTIC Science & Technology

1981-09-23

meas- ures, which have p-semi-variation finite, I a p a 2 . The work here do- pieda in part on an inequality of Grothendieck- Pietsch . The rest of the...7], Corol. 2 to Thi. 4.3 and Prop. 3.1, the Latter is the Grothendieck- Pietsch inequality alluded to in the Introduction), the space I - C(S) being

On the breakdown of asymptotic Poincare invariance in D = 3 Einstein gravity

NASA Technical Reports Server (NTRS)

Deser, S.

1985-01-01

It is shown through a series of calculations that neither momentum nor boosts are definable for finite energy solutions of Einstein gravity in D = 3. The contrast between the effects of Lorentz transformations on the corresponding metrics for D = 3 and D = 4 gravity is demonstrated, and some comparisons with the vector gauge treatment of the problem are offered.

BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oh, Duk -Soon; Widlund, Olof B.; Zampini, Stefano

Here, a BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are introduced. The methods are based on a new type of weighted average an adaptive selection of primal constraints developed to deal with coefficients with high contrast even inside individual subdomains. For problems with very many subdomains, a third level of the preconditioner is introduced. Assuming that the subdomains aremore » all built from elements of a coarse triangulation of the given domain, and that in each subdomain the material parameters are consistent, one obtains a bound for the preconditioned linear system's condition number which is independent of the values and jumps of these parameters across the subdomains' interface. Numerical experiments, using the PETSc library, are also presented which support the theory and show the algorithms' effectiveness even for problems not covered by the theory. Also included are experiments with Brezzi-Douglas-Marini finite-element approximations.« less

BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields

DOE PAGES

Oh, Duk -Soon; Widlund, Olof B.; Zampini, Stefano; ...

2017-06-21

Here, a BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are introduced. The methods are based on a new type of weighted average an adaptive selection of primal constraints developed to deal with coefficients with high contrast even inside individual subdomains. For problems with very many subdomains, a third level of the preconditioner is introduced. Assuming that the subdomains aremore » all built from elements of a coarse triangulation of the given domain, and that in each subdomain the material parameters are consistent, one obtains a bound for the preconditioned linear system's condition number which is independent of the values and jumps of these parameters across the subdomains' interface. Numerical experiments, using the PETSc library, are also presented which support the theory and show the algorithms' effectiveness even for problems not covered by the theory. Also included are experiments with Brezzi-Douglas-Marini finite-element approximations.« less

Finite mixture models for the computation of isotope ratios in mixed isotopic samples

NASA Astrophysics Data System (ADS)

Koffler, Daniel; Laaha, Gregor; Leisch, Friedrich; Kappel, Stefanie; Prohaska, Thomas

2013-04-01

Finite mixture models have been used for more than 100 years, but have seen a real boost in popularity over the last two decades due to the tremendous increase in available computing power. The areas of application of mixture models range from biology and medicine to physics, economics and marketing. These models can be applied to data where observations originate from various groups and where group affiliations are not known, as is the case for multiple isotope ratios present in mixed isotopic samples. Recently, the potential of finite mixture models for the computation of 235U/238U isotope ratios from transient signals measured in individual (sub-)µm-sized particles by laser ablation - multi-collector - inductively coupled plasma mass spectrometry (LA-MC-ICPMS) was demonstrated by Kappel et al. [1]. The particles, which were deposited on the same substrate, were certified with respect to their isotopic compositions. Here, we focus on the statistical model and its application to isotope data in ecogeochemistry. Commonly applied evaluation approaches for mixed isotopic samples are time-consuming and are dependent on the judgement of the analyst. Thus, isotopic compositions may be overlooked due to the presence of more dominant constituents. Evaluation using finite mixture models can be accomplished unsupervised and automatically. The models try to fit several linear models (regression lines) to subgroups of data taking the respective slope as estimation for the isotope ratio. The finite mixture models are parameterised by: • The number of different ratios. • Number of points belonging to each ratio-group. • The ratios (i.e. slopes) of each group. Fitting of the parameters is done by maximising the log-likelihood function using an iterative expectation-maximisation (EM) algorithm. In each iteration step, groups of size smaller than a control parameter are dropped; thereby the number of different ratios is determined. The analyst only influences some control parameters of the algorithm, i.e. the maximum count of ratios, the minimum relative group-size of data points belonging to each ratio has to be defined. Computation of the models can be done with statistical software. In this study Leisch and Grün's flexmix package [2] for the statistical open-source software R was applied. A code example is available in the electronic supplementary material of Kappel et al. [1]. In order to demonstrate the usefulness of finite mixture models in fields dealing with the computation of multiple isotope ratios in mixed samples, a transparent example based on simulated data is presented and problems regarding small group-sizes are illustrated. In addition, the application of finite mixture models to isotope ratio data measured in uranium oxide particles is shown. The results indicate that finite mixture models perform well in computing isotope ratios relative to traditional estimation procedures and can be recommended for more objective and straightforward calculation of isotope ratios in geochemistry than it is current practice. [1] S. Kappel, S. Boulyga, L. Dorta, D. Günther, B. Hattendorf, D. Koffler, G. Laaha, F. Leisch and T. Prohaska: Evaluation Strategies for Isotope Ratio Measurements of Single Particles by LA-MC-ICPMS, Analytical and Bioanalytical Chemistry, 2013, accepted for publication on 2012-12-18 (doi: 10.1007/s00216-012-6674-3) [2] B. Grün and F. Leisch: Fitting finite mixtures of generalized linear regressions in R. Computational Statistics & Data Analysis, 51(11), 5247-5252, 2007. (doi:10.1016/j.csda.2006.08.014)

Critical behavior in a stochastic model of vector mediated epidemics

PubMed Central

Alfinito, E.; Beccaria, M.; Macorini, G.

2016-01-01

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation. PMID:27264105

Full-field drift Hamiltonian particle orbits in 3D geometry

NASA Astrophysics Data System (ADS)

Cooper, W. A.; Graves, J. P.; Brunner, S.; Isaev, M. Yu

2011-02-01

A Hamiltonian/Lagrangian theory to describe guiding centre orbit drift motion which is canonical in the Boozer coordinate frame has been extended to include full electromagnetic perturbed fields in anisotropic pressure 3D equilibria with nested magnetic flux surfaces. A redefinition of the guiding centre velocity to eliminate the motion due to finite equilibrium radial magnetic fields and the choice of a gauge condition that sets the radial component of the electromagnetic vector potential to zero are invoked to guarantee that the Boozer angular coordinates retain the canonical structure. The canonical momenta are identified and the guiding centre particle radial drift motion and parallel gyroradius evolution are derived. The particle coordinate position is linearly modified by wave-particle interactions. All the nonlinear wave-wave interactions appear explicitly only in the evolution of the parallel gyroradius. The radial variation of the electrostatic potential is related to the binormal component of the displacement vector for MHD-type perturbations. The electromagnetic vector potential projections can then be determined from the electrostatic potential and the radial component of the MHD displacement vector.

Phase definition to assess synchronization quality of nonlinear oscillators

NASA Astrophysics Data System (ADS)

Freitas, Leandro; Torres, Leonardo A. B.; Aguirre, Luis A.

2018-05-01

This paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.

Wick Product for Commutation Relations Connected with Yang-Baxter Operators and New Constructions of Factors

NASA Astrophysics Data System (ADS)

Krsolarlak, Ilona

We analyze a certain class of von Neumann algebras generated by selfadjoint elements , for satisfying the general commutation relations: Such algebras can be continuously embedded into some closure of the set of finite linear combinations of vectors , where is an orthonormal basis of a Hilbert space . The operator which represents the vector is denoted by and called the ``Wick product'' of the operators . We describe explicitly the form of this product. Also, we estimate the operator norm of for . Finally we apply these two results and prove that under the assumption all the von Neumann algebras considered are II1 factors.

Dynamic tailoring of surface plasmon polaritons through incident angle modulation.

PubMed

Qiu, Peizhen; Zhang, Dawei; Jing, Ming; Lu, Taiguo; Yu, Binbin; Zhan, Qiwen; Zhuang, Songlin

2018-04-16

Dynamic tailoring of the propagating surface plasmon polaritons (SPPs) through incident angle modulation is proposed and numerically demonstrated. The generation and tailoring mechanism of the SPPs are discussed. The relationship formula between the incident angle and the generated SPP wave vector direction is theoretically derived. The correctness of the formula is verified with three different approaches using finite difference time domain method. Using this formula, the generated SPP wave vector direction can be precisely modulated by changing the incident angle. The precise modulation results of two dimensional Bessel-like SPP beam and SPP bottle beam array are given. The results can deepen the understanding of the generation and modulation mechanism of the SPPs.

Supercomputers for engineering analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

1986-07-01

The Cray-1 and Cray X-MP/48 experience in engineering computations at the Lawrence Livermore National Laboratory is surveyed. The fully vectorized explicit DYNA and implicit NIKE finite element codes are discussed with respect to solid and structural mechanics. The main efficiencies for production analyses are currently obtained by simple CFT compiler exploitation of pipeline architecture for inner do-loop optimization. Current developmet of outer-loop multitasking is also discussed. Applications emphasis will be on 3D examples spanning earth penetrator loads analysis, target lethality assessment, and crashworthiness. The use of a vectorized large deformation shell element in both DYNA and NIKE has substantially expandedmore » 3D nonlinear capability. 25 refs., 7 figs.« less

Phase definition to assess synchronization quality of nonlinear oscillators.

PubMed

Freitas, Leandro; Torres, Leonardo A B; Aguirre, Luis A

2018-05-01

This paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.

Design of single-polarization wavelength splitter based on photonic crystal fiber.

PubMed

Zhang, Shanshan; Zhang, Weigang; Geng, Pengcheng; Li, Xiaolan; Ruan, Juan

2011-12-20

A new single-polarization wavelength splitter based on the photonic crystal fiber (PCF) has been proposed. The full-vector finite-element method (FEM) is applied to analyze the single-polarization single-mode guiding properties. Splitting of two different wavelengths is realized by adjusting the structural parameters. The semi-vector three-dimensional beam propagation method is employed to confirm the wavelength splitting characteristics of the PCF. Numerical simulations show that the wavelengths of 1.3 μm and 1.55 μm are split for a fiber length of 10.7 mm with single-polarization guiding in each core. The crosstalk between the two cores is low over appreciable optical bandwidths.

Analysis of Discontinuities in a Rectangular Waveguide Using Dyadic Green's Function Approach in Conjunction with Method of Moments

NASA Technical Reports Server (NTRS)

Deshpande, M. D.

1997-01-01

The dyadic Green's function for an electric current source placed in a rectangular waveguide is derived using a magnetic vector potential approach. A complete solution for the electric and magnetic fields including the source location is obtained by simple differentiation of the vector potential around the source location. The simple differentiation approach which gives electric and magnetic fields identical to an earlier derivation is overlooked by the earlier workers in the derivation of the dyadic Green's function particularly around the source location. Numerical results obtained using the Green's function approach are compared with the results obtained using the Finite Element Method (FEM).

The inference of vector magnetic fields from polarization measurements with limited spectral resolution

NASA Technical Reports Server (NTRS)

Lites, B. W.; Skumanich, A.

1985-01-01

A method is presented for recovery of the vector magnetic field and thermodynamic parameters from polarization measurement of photospheric line profiles measured with filtergraphs. The method includes magneto-optic effects and may be utilized on data sampled at arbitrary wavelengths within the line profile. The accuracy of this method is explored through inversion of synthetic Stokes profiles subjected to varying levels of random noise, instrumental wave-length resolution, and line profile sampling. The level of error introduced by the systematic effect of profile sampling over a finite fraction of the 5 minute oscillation cycle is also investigated. The results presented here are intended to guide instrumental design and observational procedure.

A feasibility study of a 3-D finite element solution scheme for aeroengine duct acoustics

NASA Technical Reports Server (NTRS)

Abrahamson, A. L.

1980-01-01

The advantage from development of a 3-D model of aeroengine duct acoustics is the ability to analyze axial and circumferential liner segmentation simultaneously. The feasibility of a 3-D duct acoustics model was investigated using Galerkin or least squares element formulations combined with Gaussian elimination, successive over-relaxation, or conjugate gradient solution algorithms on conventional scalar computers and on a vector machine. A least squares element formulation combined with a conjugate gradient solver on a CDC Star vector computer initially appeared to have great promise, but severe difficulties were encountered with matrix ill-conditioning. These difficulties in conditioning rendered this technique impractical for realistic problems.

Chiral Magnetic Effect and Anomalous Transport from Real-Time Lattice Simulations

DOE PAGES

Müller, Niklas; Schlichting, Sören; Sharma, Sayantan

2016-09-30

Here, we present a first-principles study of anomaly induced transport phenomena by performing real-time lattice simulations with dynamical fermions coupled simultaneously to non-Abelian S U ( N c ) and Abelian U ( 1 ) gauge fields. By investigating the behavior of vector and axial currents during a sphaleron transition in the presence of an external magnetic field, we demonstrate how the interplay of the chiral magnetic and chiral separation effect leads to the formation of a propagating wave. Furthermore, we analyze the dependence of the magnitude of the induced vector current and the propagation of the wave on themore » amount of explicit chiral symmetry breaking due to finite quark masses.« less

Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation.

PubMed

Selvaraj, P; Sakthivel, R; Kwon, O M

2018-06-07

This paper addresses the problem of finite-time synchronization of stochastic coupled neural networks (SCNNs) subject to Markovian switching, mixed time delay, and actuator saturation. In addition, coupling strengths of the SCNNs are characterized by mutually independent random variables. By utilizing a simple linear transformation, the problem of stochastic finite-time synchronization of SCNNs is converted into a mean-square finite-time stabilization problem of an error system. By choosing a suitable mode dependent switched Lyapunov-Krasovskii functional, a new set of sufficient conditions is derived to guarantee the finite-time stability of the error system. Subsequently, with the help of anti-windup control scheme, the actuator saturation risks could be mitigated. Moreover, the derived conditions help to optimize estimation of the domain of attraction by enlarging the contractively invariant set. Furthermore, simulations are conducted to exhibit the efficiency of proposed control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Doppler Lidar Vector Retrievals and Atmospheric Data Visualization in Mixed/Augmented Reality

NASA Astrophysics Data System (ADS)

Cherukuru, Nihanth Wagmi

Environmental remote sensing has seen rapid growth in the recent years and Doppler wind lidars have gained popularity primarily due to their non-intrusive, high spatial and temporal measurement capabilities. While lidar applications early on, relied on the radial velocity measurements alone, most of the practical applications in wind farm control and short term wind prediction require knowledge of the vector wind field. Over the past couple of years, multiple works on lidars have explored three primary methods of retrieving wind vectors viz., using homogeneous windfield assumption, computationally extensive variational methods and the use of multiple Doppler lidars. Building on prior research, the current three-part study, first demonstrates the capabilities of single and dual Doppler lidar retrievals in capturing downslope windstorm-type flows occurring at Arizona's Barringer Meteor Crater as a part of the METCRAX II field experiment. Next, to address the need for a reliable and computationally efficient vector retrieval for adaptive wind farm control applications, a novel 2D vector retrieval based on a variational formulation was developed and applied on lidar scans from an offshore wind farm and validated with data from a cup and vane anemometer installed on a nearby research platform. Finally, a novel data visualization technique using Mixed Reality (MR)/ Augmented Reality (AR) technology is presented to visualize data from atmospheric sensors. MR is an environment in which the user's visual perception of the real world is enhanced with live, interactive, computer generated sensory input (in this case, data from atmospheric sensors like Doppler lidars). A methodology using modern game development platforms is presented and demonstrated with lidar retrieved wind fields. In the current study, the possibility of using this technology to visualize data from atmospheric sensors in mixed reality is explored and demonstrated with lidar retrieved wind fields as well as a few earth science datasets for education and outreach activities.

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE PAGES

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.; ...

2016-09-22

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, M.G.; Castro, A.S. de

2009-11-15

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schroedinger-like equation with an effective Rosen-Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and moremore » efficient problem of solving an irrational algebraic equation.« less

Few-mode fiber, splice and SDM component characterization by spatially-diverse optical vector network analysis.

PubMed

Rommel, Simon; Mendinueta, José Manuel Delgado; Klaus, Werner; Sakaguchi, Jun; Olmos, Juan José Vegas; Awaji, Yoshinari; Monroy, Idelfonso Tafur; Wada, Naoya

2017-09-18

This paper discusses spatially diverse optical vector network analysis for space division multiplexing (SDM) component and system characterization, which is becoming essential as SDM is widely considered to increase the capacity of optical communication systems. Characterization of a 108-channel photonic lantern spatial multiplexer, coupled to a 36-core 3-mode fiber, is experimentally demonstrated, extracting the full impulse response and complex transfer function matrices as well as insertion loss (IL) and mode-dependent loss (MDL) data. Moreover, the mode-mixing behavior of fiber splices in the few-mode multi-core fiber and their impact on system IL and MDL are analyzed, finding splices to cause significant mode-mixing and to be non-negligible in system capacity analysis.

Exclusive vector meson production with leading neutrons in a saturation model for the dipole amplitude in mixed space

NASA Astrophysics Data System (ADS)

Amaral, J. T.; Becker, V. M.

2018-05-01

We investigate ρ vector meson production in e p collisions at HERA with leading neutrons in the dipole formalism. The interaction of the dipole and the pion is described in a mixed-space approach, in which the dipole-pion scattering amplitude is given by the Marquet-Peschanski-Soyez saturation model, which is based on the traveling wave solutions of the nonlinear Balitsky-Kovchegov equation. We estimate the magnitude of the absorption effects and compare our results with a previous analysis of the same process in full coordinate space. In contrast with this approach, the present study leads to absorption K factors in the range of those predicted by previous theoretical studies on semi-inclusive processes.

Mixed-Mode Bending Method for Delamination Testing

NASA Technical Reports Server (NTRS)

Reeder, James R.; Crews, John R., Jr.

1990-01-01

A mixed mode delamination test procedure was developed combining double cantilever beam (DCB) mode I loading and end-notch fixture (ENF) mode II loading on a split unidirectional laminate. By loading with a lever, a single applied load simultaneously produces mode I and mode II bending loads on the specimen. This mixed-mode bending (MMB) test was analyzed using both finite-element procedures and beam theory to calculate the mode I and mode II components of strain-energy release rate G(sub I) and G(sub II), respectively. A wide range of G(sub I)/G(sub II) ratios can be produced by varying the load position on the lever. As the delamination extended, the G(sub I)/G(sub II) ratios varied by less than 5%. Beam theory equations agreed closely with the finite-element results and provide a basis for selection of G(sub I)/G(sub II) test ratios and a basis for computing the mode I and mode II components of measured delamination toughness. The MMB test was demonstrated using AS4/PEEK (APC2) unidirectional laminates. The MMB test introduced in this paper is rather simple and is believed to offer several advantages over most current mixed-mode test.

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

Declining Prevalence of Disease Vectors Under Climate Change

NASA Astrophysics Data System (ADS)

Escobar, Luis E.; Romero-Alvarez, Daniel; Leon, Renato; Lepe-Lopez, Manuel A.; Craft, Meggan E.; Borbor-Cordova, Mercy J.; Svenning, Jens-Christian

2016-12-01

More than half of the world population is at risk of vector-borne diseases including dengue fever, chikungunya, zika, yellow fever, leishmaniasis, chagas disease, and malaria, with highest incidences in tropical regions. In Ecuador, vector-borne diseases are present from coastal and Amazonian regions to the Andes Mountains; however, a detailed characterization of the distribution of their vectors has never been carried out. We estimate the distribution of 14 vectors of the above vector-borne diseases under present-day and future climates. Our results consistently suggest that climate warming is likely threatening some vector species with extinction, locally or completely. These results suggest that climate change could reduce the burden of specific vector species. Other vector species are likely to shift and constrain their geographic range to the highlands in Ecuador potentially affecting novel areas and populations. These forecasts show the need for development of early prevention strategies for vector species currently absent in areas projected as suitable under future climate conditions. Informed interventions could reduce the risk of human exposure to vector species with distributional shifts, in response to current and future climate changes. Based on the mixed effects of future climate on human exposure to disease vectors, we argue that research on vector-borne diseases should be cross-scale and include climatic, demographic, and landscape factors, as well as forces facilitating disease transmission at fine scales.

Ice Shape Characterization Using Self-Organizing Maps

NASA Technical Reports Server (NTRS)

McClain, Stephen T.; Tino, Peter; Kreeger, Richard E.

2011-01-01

A method for characterizing ice shapes using a self-organizing map (SOM) technique is presented. Self-organizing maps are neural-network techniques for representing noisy, multi-dimensional data aligned along a lower-dimensional and possibly nonlinear manifold. For a large set of noisy data, each element of a finite set of codebook vectors is iteratively moved in the direction of the data closest to the winner codebook vector. Through successive iterations, the codebook vectors begin to align with the trends of the higher-dimensional data. In information processing, the intent of SOM methods is to transmit the codebook vectors, which contains far fewer elements and requires much less memory or bandwidth, than the original noisy data set. When applied to airfoil ice accretion shapes, the properties of the codebook vectors and the statistical nature of the SOM methods allows for a quantitative comparison of experimentally measured mean or average ice shapes to ice shapes predicted using computer codes such as LEWICE. The nature of the codebook vectors also enables grid generation and surface roughness descriptions for use with the discrete-element roughness approach. In the present study, SOM characterizations are applied to a rime ice shape, a glaze ice shape at an angle of attack, a bi-modal glaze ice shape, and a multi-horn glaze ice shape. Improvements and future explorations will be discussed.

Mixing Single Scattering Properties in Vector Radiative Transfer for Deterministic and Stochastic Solutions

NASA Astrophysics Data System (ADS)

Mukherjee, L.; Zhai, P.; Hu, Y.; Winker, D. M.

2016-12-01

Among the primary factors, which determine the polarized radiation, field of a turbid medium are the single scattering properties of the medium. When multiple types of scatterers are present, the single scattering properties of the scatterers need to be properly mixed in order to find the solutions to the vector radiative transfer theory (VRT). The VRT solvers can be divided into two types: deterministic and stochastic. The deterministic solver can only accept one set of single scattering property in its smallest discretized spatial volume. When the medium contains more than one kind of scatterer, their single scattering properties are averaged, and then used as input for the deterministic solver. The stochastic solver, can work with different kinds of scatterers explicitly. In this work, two different mixing schemes are studied using the Successive Order of Scattering (SOS) method and Monte Carlo (MC) methods. One scheme is used for deterministic and the other is used for the stochastic Monte Carlo method. It is found that the solutions from the two VRT solvers using two different mixing schemes agree with each other extremely well. This confirms the equivalence to the two mixing schemes and also provides a benchmark for the VRT solution for the medium studied.

Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty

NASA Technical Reports Server (NTRS)

Lai, Chen-Yao G.

1996-01-01

The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.

Coupled mixed-field laminate theory and finite element for smart piezoelectric composite shell structures

NASA Technical Reports Server (NTRS)

Saravanos, Dimitris A.

1996-01-01

Mechanics for the analysis of laminated composite shells with piezoelectric actuators and sensors are presented. A new mixed-field laminate theory for piezoelectric shells is formulated in curvilinear coordinates which combines single-layer assumptions for the displacements and a layerwise representation for the electric potential. The resultant coupled governing equations for curvilinear piezoelectric laminates are described. Structural mechanics are subsequently developed and an 8-node finite-element is formulated for the static and dynamic analysis of adaptive composite structures of general laminations containing piezoelectric layers. Evaluations of the method and comparisons with reported results are presented for laminated piezoelectric-composite plates, a closed cylindrical shell with a continuous piezoceramic layer and a laminated composite semi-circular cantilever shell with discrete cylindrical piezoelectric actuators and/or sensors.

Scalable algorithms for three-field mixed finite element coupled poromechanics

NASA Astrophysics Data System (ADS)

Castelletto, Nicola; White, Joshua A.; Ferronato, Massimiliano

2016-12-01

We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 × 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. The performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.

A mathematical model of diffusion from a steady source of short duration in a finite mixing layer

NASA Astrophysics Data System (ADS)

Bianconi, Roberto; Tamponi, Matteo

This paper presents an analytical unsteady-state solution to the atmospheric dispersion equation for substances subject to chemical-physical decay in a finite mixing layer for releases of short duration. This solution is suitable for describing critical events relative to accidental release of toxic, flammable or explosive substances. To implement the solution, the Modello per Rilasci a Breve Termine (MRBT) code has been developed, for some characteristics parameters of which the results of the sensitivity analysis are presented. Moreover some examples of application to the calculation of exposure to toxic substances and to the determination of the ignition field of flammable substances are described. Finally, the mathematical model described can be used to interpret the phenomenon of pollutant accumulation.

Towards a unified solution of localization failure with mixed finite elements

NASA Astrophysics Data System (ADS)

Benedetti, Lorenzo; Cervera, Miguel; Chiumenti, Michele; Zeidler, Antonia; Fischer, Jan-Thomas

2015-04-01

Notwithstanding computational scientists made significant steps in the numerical simulation of failure in last three decades, the strain localization problem is still an open question. Especially in a geotechnical setting, when dealing with stability analysis of slopes, it is necessary to provide correct distribution of displacements, to evaluate the stresses in the ground and, therefore, to be able to identify the slip lines that brings to progressive collapse of the slope. Finite elements are an attractive method of solution thanks to profound mathematical foundations and the possibility of describing generic geometries. In order to account for the onset of localization band, the smeared crack approach [1] is introduced, that is the strain localization is assumed to occur in a band of finite width where the displacements are continuous and the strains are discontinuous but bounded. It is well known that this kind of approach poses some challenges. The standard irreducible formulation of FEM is known to be heavily affected by spurious mesh dependence when softening behavior occurs and, consequently, slip lines evolution is biased by the orientation of the mesh. Moreover, in the case of isochoric behavior, unbounded pressure oscillations arise and the consequent locking of the stresses pollutes the numerical solution. Both problems can be shown not to be related to the mathematical statement of the continuous problem but instead to its discrete (FEM) counterpart. Mixed finite element formulations represent a suitable alternative to mitigate these drawbacks. As it has been shown in previous works by Cervera [2], a mixed formulation in terms of displacements and pressure not only provides a propitious solution to the problem of incompressibility, but also it was found to possess the needed robustness in case of strain concentration. This presentation introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement interpolations. As a fundamental enhancement of the displacement-pressure formulation above mentioned, this kind of formulation benefits of the following advantages: it provides enhanced rate of convergence for the strain (and stress) and it is able to deal with incompressible situations. The method is completed with constitutive laws from Von Mises and Drucker-Prager local plasticity models with nonlinear strain softening. Moreover, global and local error norms are discussed to support the advantages of the proposed method. Then, numerical examples of stability analysis of slopes are presented to demonstrate the capability of the method. It will be shown that not only soil slopes can be modeled but also snow avalanche release and their weak layer fracture can be similarly treated. Consequently, this formulation appears to be a general and accurate tool for the solution of mechanical problem involving failure with localization bands [3,4]. References [1] Y.R. Rashid, 'Ultimate strength analysis of prestressed concrete pressure vessels', Nuclear Engineering and Design, Volume 7, Issue 4, April, Pages 334-344, 1968. [2] M. Cervera, M. Chiumenti, D. Di Capua. 'Benchmarking on bifurcation and localization in J 2 plasticity for plane stress and plane strain conditions.' Computer Methods in Applied Mechanics and Engineering, Vol. 241-244, Pages 206-224, 2012. [3] L. Benedetti, M. Cervera, M. Chiumenti. 'Stress-accurate mixed FEM for soil failure under shallow foundations involving strain localization in plasticity' Computers and Geotechnics, Vol. 64, pp. 32-47, 2015. [4] Cervera, M., Chiumenti, M., Benedetti, L., Codina, R. 'Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity' Computer Methods in Applied Mechanics and Engineering, to appear, 2015.

Drekar v.2.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seefeldt, Ben; Sondak, David; Hensinger, David M.

Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary Lagrangian Eulerian (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less

Numerical simulations of short-mixing-time double-wave-vector diffusion-weighting experiments with multiple concatenations on whole-body MR systems

NASA Astrophysics Data System (ADS)

Finsterbusch, Jürgen

2010-12-01

Double- or two-wave-vector diffusion-weighting experiments with short mixing times in which two diffusion-weighting periods are applied in direct succession, are a promising tool to estimate cell sizes in the living tissue. However, the underlying effect, a signal difference between parallel and antiparallel wave vector orientations, is considerably reduced for the long gradient pulses required on whole-body MR systems. Recently, it has been shown that multiple concatenations of the two wave vectors in a single acquisition can double the modulation amplitude if short gradient pulses are used. In this study, numerical simulations of such experiments were performed with parameters achievable with whole-body MR systems. It is shown that the theoretical model yields a good approximation of the signal behavior if an additional term describing free diffusion is included. More importantly, it is demonstrated that the shorter gradient pulses sufficient to achieve the desired diffusion weighting for multiple concatenations, increase the signal modulation considerably, e.g. by a factor of about five for five concatenations. Even at identical echo times, achieved by a shortened diffusion time, a moderate number of concatenations significantly improves the signal modulation. Thus, experiments on whole-body MR systems may benefit from multiple concatenations.

3D Visualization of Global Ocean Circulation

NASA Astrophysics Data System (ADS)

Nelson, V. G.; Sharma, R.; Zhang, E.; Schmittner, A.; Jenny, B.

2015-12-01

Advanced 3D visualization techniques are seldom used to explore the dynamic behavior of ocean circulation. Streamlines are an effective method for visualization of flow, and they can be designed to clearly show the dynamic behavior of a fluidic system. We employ vector field editing and extraction software to examine the topology of velocity vector fields generated by a 3D global circulation model coupled to a one-layer atmosphere model simulating preindustrial and last glacial maximum (LGM) conditions. This results in a streamline-based visualization along multiple density isosurfaces on which we visualize points of vertical exchange and the distribution of properties such as temperature and biogeochemical tracers. Previous work involving this model examined the change in the energetics driving overturning circulation and mixing between simulations of LGM and preindustrial conditions. This visualization elucidates the relationship between locations of vertical exchange and mixing, as well as demonstrates the effects of circulation and mixing on the distribution of tracers such as carbon isotopes.

High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices

NASA Astrophysics Data System (ADS)

Dunham, Benjamin Z.

This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of finding the Hessian-vector product. All variants are implemented on a stochastic diffusion problem and compared in-depth with various cost and accuracy metrics.

An ultrashort mixing length micromixer: the shear superposition micromixer.

PubMed

Bottausci, Frédéric; Cardonne, Caroline; Meinhart, Carl; Mezić, Igor

2007-03-01

We report for the first time a laminar high-performance continuous micromixing process of two fluids over a length of 200 microns in under 10 milliseconds achieved by an optimization of the control parameters amplitude and frequency in the mixing device denoted as 'Shear Superposition Micromixer'. We improve mixing time by approximately 5 orders of magnitude over diffusion-limited mixing. The data indicate that rapid mixing is a result of the combined action of Taylor-Aris dispersion in the main and secondary microchannels and unsteady vortex motion that occurs at finite Reynolds number, which occurs above a threshold amplitude and frequency. The mixing performance is quantified using micron-resolution particle image velocimetry (micro-PIV) and computational fluid dynamics (CFD) simulations.

Study Guide for a Beginning Course in Ground-Water Hydrology: Part 1 -- Course Participants

DTIC Science & Technology

1990-01-01

and Lonnquist, 1971 , fig. 7.) . . . . . . . . . . . . . . . . . . . . . . 99 Vector areas associated with branches in a square-mesh finite...water reservoir. (From Bennett and Giusti, 1971 .). 112 Location and general geographic features of Long Island, New York. (From Franke and...Techniques of Water- Resources Investigations of the U.S. Geological Survey, Book 2, Chapter Fl, 97 p. Stallman, R. W., 1971 , Aquifer-test design

On orthogonal projectors induced by compact groups and Haar measures

NASA Astrophysics Data System (ADS)

Niezgoda, Marek

2008-02-01

We study the difference of two orthogonal projectors induced by compact groups of linear operators acting on a vector space. An upper bound for the difference is derived using the Haar measures of the groups. A particular attention is paid to finite groups. Some applications are given for complex matrices and unitarily invariant norms. Majorization inequalities of Fan and Hoffmann and of Causey are rediscovered.

Preface

DTIC Science & Technology

2016-09-13

lems arising, for example, after discretization of optimal control problems. Lucien developed a general framework for quantifying near-optimality...Polak, E., Da Cunha, N.O.: Constrainedminimization under vector valued-criteria in finite dimensional spaces. J. Math . Anal. Appl. 19(1), 103–124...1969) 12. Pironneau, O., Polak, E.: On the rate of convergence of certain methods of centers. Math . Program. 2(2), 230–258 (1972) 13. Polak, E., Sargent

Process for computing geometric perturbations for probabilistic analysis

DOEpatents

Fitch, Simeon H. K. [Charlottesville, VA; Riha, David S [San Antonio, TX; Thacker, Ben H [San Antonio, TX

2012-04-10

A method for computing geometric perturbations for probabilistic analysis. The probabilistic analysis is based on finite element modeling, in which uncertainties in the modeled system are represented by changes in the nominal geometry of the model, referred to as "perturbations". These changes are accomplished using displacement vectors, which are computed for each node of a region of interest and are based on mean-value coordinate calculations.

Domain Derivatives in Dielectric Rough Surface Scattering

DTIC Science & Technology

2015-01-01

and require the gradient of the objective function in the unknown model parameter vector at each stage of iteration. For large N, finite...differencing becomes numerically intensive, and an efficient alternative is domain differentiation in which the full gradient is obtained by solving a single...derivative calculation of the gradient for a locally perturbed dielectric interface. The method is non-variational, and algebraic in nature in that it

Another elementary proof of the Jordan form of a matrix

NASA Astrophysics Data System (ADS)

Budhi, Wono Setya

2012-05-01

In this paper we establish the Jordan Form for a matrix using the elementary concepts of vector differentiation and partial fractions. The idea comes from the resolvent of the operator. For the matrix, the Laurent series is finite and easy to compute through rational representation. We also give a proof of some famous theorems in matrix analysis as consequences from the result.

Analysis and Experimentation of Control Strategies for Underactuated Spacecraft

DTIC Science & Technology

2009-09-01

control techniques that provide time -invariant global asymptotic stability of the fully actuated spacecraft system of equations. Although these control ...momentum wheel actuators in finite time under the restriction that the total angular momentum vector of the system is zero. This control methodology...can be stabilizable to an arbitrarily small region about the equilibrium of the system via time -invariant smooth state feedback control

Three-dimensional Hybrid Simulation Study of Anisotropic Turbulence in the Proton Kinetic Regime

NASA Astrophysics Data System (ADS)

Vasquez, Bernard J.; Markovskii, Sergei A.; Chandran, Benjamin D. G.

2014-06-01

Three-dimensional numerical hybrid simulations with particle protons and quasi-neutralizing fluid electrons are conducted for a freely decaying turbulence that is anisotropic with respect to the background magnetic field. The turbulence evolution is determined by both the combined root-mean-square (rms) amplitude for fluctuating proton bulk velocity and magnetic field and by the ratio of perpendicular to parallel wavenumbers. This kind of relationship had been considered in the past with regard to interplanetary turbulence. The fluctuations nonlinearly evolve to a turbulent phase whose net wave vector anisotropy is usually more perpendicular than the initial one, irrespective of the initial ratio of perpendicular to parallel wavenumbers. Self-similar anisotropy evolution is found as a function of the rms amplitude and parallel wavenumber. Proton heating rates in the turbulent phase vary strongly with the rms amplitude but only weakly with the initial wave vector anisotropy. Even in the limit where wave vectors are confined to the plane perpendicular to the background magnetic field, the heating rate remains close to the corresponding case with finite parallel wave vector components. Simulation results obtained as a function of proton plasma to background magnetic pressure ratio β p in the range 0.1-0.5 show that the wave vector anisotropy also weakly depends on β p .

The numerical modelling of mixing phenomena of nanofluids in passive micromixers

NASA Astrophysics Data System (ADS)

Milotin, R.; Lelea, D.

2018-01-01

The paper deals with the rapid mixing phenomena in micro-mixing devices with four tangential injections and converging tube, considering nanoparticles and water as the base fluid. Several parameters like Reynolds number (Re = 6 - 284) or fluid temperature are considered in order to optimize the process and obtain fundamental insight in mixing phenomena. The set of partial differential equations is considered based on conservation of momentum and species. Commercial package software Ansys-Fluent is used for solution of differential equations, based on a finite volume method. The results reveal that mixing index and mixing process is strongly dependent both on Reynolds number and heat flux. Moreover there is a certain Reynolds number when flow instabilities are generated that intensify the mixing process due to the tangential injections of the fluids.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amariti, Antonio; Toldo, Chiara

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0; 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c 2d, similarly to the 4d picture, where the exact R-current maximizes the central charge a 4d. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T 1,1 with one Betti vector multiplet,more » dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS 5 to AdS 3 vacua in the supergravity picture. We verify the existence of the flow to AdS 3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.« less

Betti multiplets, flows across dimensions and c-extremization

DOE PAGES

Amariti, Antonio; Toldo, Chiara

2017-07-10

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0; 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c 2d, similarly to the 4d picture, where the exact R-current maximizes the central charge a 4d. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T 1,1 with one Betti vector multiplet,more » dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS 5 to AdS 3 vacua in the supergravity picture. We verify the existence of the flow to AdS 3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.« less

Betti multiplets, flows across dimensions and c-extremization

NASA Astrophysics Data System (ADS)

Amariti, Antonio; Toldo, Chiara

2017-07-01

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0, 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c 2 d , similarly to the 4d picture, where the exact R-current maximizes the central charge a 4 d . There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T 1,1 with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS5 to AdS3 vacua in the supergravity picture. We verify the existence of the flow to AdS3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.

The evolution of plant virus transmission pathways.

PubMed

Hamelin, Frédéric M; Allen, Linda J S; Prendeville, Holly R; Hajimorad, M Reza; Jeger, Michael J

2016-05-07

The evolution of plant virus transmission pathways is studied through transmission via seed, pollen, or a vector. We address the questions: under what circumstances does vector transmission make pollen transmission redundant? Can evolution lead to the coexistence of multiple virus transmission pathways? We restrict the analysis to an annual plant population in which reproduction through seed is obligatory. A semi-discrete model with pollen, seed, and vector transmission is formulated to investigate these questions. We assume vector and pollen transmission rates are frequency-dependent and density-dependent, respectively. An ecological stability analysis is performed for the semi-discrete model and used to inform an evolutionary study of trade-offs between pollen and seed versus vector transmission. Evolutionary dynamics critically depend on the shape of the trade-off functions. Assuming a trade-off between pollen and vector transmission, evolution either leads to an evolutionarily stable mix of pollen and vector transmission (concave trade-off) or there is evolutionary bi-stability (convex trade-off); the presence of pollen transmission may prevent evolution of vector transmission. Considering a trade-off between seed and vector transmission, evolutionary branching and the subsequent coexistence of pollen-borne and vector-borne strains is possible. This study contributes to the theory behind the diversity of plant-virus transmission patterns observed in nature. Copyright © 2016 Elsevier Ltd. All rights reserved.

Feeding profile of Mepraia spinolai, a sylvatic vector of Chagas disease in Chile.

PubMed

Chacón, F; Bacigalupo, A; Quiroga, J F; Ferreira, A; Cattan, P E; Ramírez-Toloza, G

2016-10-01

American trypanosomiasis is a chronic disease transmitted mainly by vectors. The hematophagous triatomine vectors transmit Trypanosoma cruzi to a wide variety of mammals, which usually are their food source. This study determined the feeding profile of Mepraia spinolai, a sylvatic triatomine vector, present in endemic areas of Chile. Vectors were captured in the north-central area of Chile. Samples of intestinal contents were analyzed by an Enzyme-linked immunosorbent assay (ELISA) that identifies and discriminates the presence of serum antigens from Homo sapiens and nine animal species (Canis familiaris, Felis catus, Capra hircus, Mus musculus, Gallus gallus, Octodon degus, Thylamys elegans, Phyllotis darwini and Oryctolagus cuniculus). Our data indicate the most frequent feeding source in this area was P. darwini, followed by O. degus, O. cuniculus, M. musculus, G. gallus, T. elegans, C. familiaris, F. catus and C. hircus. Mixed food sources were also identified. Copyright © 2016 Elsevier B.V. All rights reserved.

Predicting surface fuel models and fuel metrics using lidar and CIR imagery in a dense mixed conifer forest

Treesearch

Marek K. Jakubowksi; Qinghua Guo; Brandon Collins; Scott Stephens; Maggi Kelly

2013-01-01

We compared the ability of several classification and regression algorithms to predict forest stand structure metrics and standard surface fuel models. Our study area spans a dense, topographically complex Sierra Nevada mixed-conifer forest. We used clustering, regression trees, and support vector machine algorithms to analyze high density (average 9 pulses/m

DYNA3D: A computer code for crashworthiness engineering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hallquist, J.O.; Benson, D.J.

1986-09-01

A finite element program with crashworthiness applications has been developed at LLNL. DYNA3D, an explicit, fully vectorized, finite deformation structural dynamics program, has four capabilities that are critical for the efficient and realistic modeling crash phenomena: (1) fully optimized nonlinear solid, shell, and beam elements for representing a structure; (2) a broad range of constitutive models for simulating material behavior; (3) sophisticated contact algorithms for impact interactions; (4) a rigid body capability to represent the bodies away from the impact region at a greatly reduced cost without sacrificing accuracy in the momentum calculations. Basic methodologies of the program are brieflymore » presented along with several crashworthiness calculations. Efficiencies of the Hughes-Liu and Belytschko-Tsay shell formulations are considered.« less

A finite element approach for solution of the 3D Euler equations

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.; Dechaumphai, P.

1986-01-01

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

Magnetic fields end-face effect investigation of HTS bulk over PMG with 3D-modeling numerical method

NASA Astrophysics Data System (ADS)

Qin, Yujie; Lu, Yiyun

2015-09-01

In this paper, the magnetic fields end-face effect of high temperature superconducting (HTS) bulk over a permanent magnetic guideway (PMG) is researched with 3D-modeling numerical method. The electromagnetic behavior of the bulk is simulated using finite element method (FEM). The framework is formulated by the magnetic field vector method (H-method). A superconducting levitation system composed of one rectangular HTS bulk and one infinite long PMG is successfully investigated using the proposed method. The simulation results show that for finite geometrical HTS bulk, even the applied magnetic field is only distributed in x-y plane, the magnetic field component Hz which is along the z-axis can be observed interior the HTS bulk.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1990-01-01

A new computer code was developed for predicting the turbulent and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1989-01-01

A new computer code was developed for predicting the turbulent, and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, 3-D Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

Predict the fatigue life of crack based on extended finite element method and SVR

NASA Astrophysics Data System (ADS)

Song, Weizhen; Jiang, Zhansi; Jiang, Hui

2018-05-01

Using extended finite element method (XFEM) and support vector regression (SVR) to predict the fatigue life of plate crack. Firstly, the XFEM is employed to calculate the stress intensity factors (SIFs) with given crack sizes. Then predicetion model can be built based on the function relationship of the SIFs with the fatigue life or crack length. Finally, according to the prediction model predict the SIFs at different crack sizes or different cycles. Because of the accuracy of the forward Euler method only ensured by the small step size, a new prediction method is presented to resolve the issue. The numerical examples were studied to demonstrate the proposed method allow a larger step size and have a high accuracy.

Adiabatic and nonadiabatic perturbation theory for coherence vector description of neutrino oscillations

NASA Astrophysics Data System (ADS)

Hollenberg, Sebastian; Päs, Heinrich

2012-01-01

The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and nonadiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g., matter) potentials. Neglecting effects of ensemble decoherence for now, we study the evolution of a neutrino ensemble governed by the associated quantum kinetic equations, which apply to systems with finite temperature. The quantum kinetic equations are solved formally using the Magnus expansion and it is shown that a convenient choice of the quantum mechanical picture (e.g., the interaction picture) reveals suitable parameters to characterize the physics of the underlying system (e.g., an effective oscillation length). It is understood that this method also provides a promising starting point for the treatment of the more general case in which decoherence is taken into account.

IR properties of chiral effects in pionic matter

NASA Astrophysics Data System (ADS)

Avdoshkin, A.; Sadofyev, A. V.; Zakharov, V. I.

2018-04-01

Chiral effects exhibit peculiar universality in idealized theoretical limits. However, they are known to be infrared sensitive and get modified in more realistic settings. In this work we study how the corresponding conductivities vary with the constituent mass. We concentrate on a pionic realization of chiral effects which provides a better control over infrared properties of the theory. The pionic medium is considered at finite vector and axial isospin chemical potentials in the presence of an external magnetic field. This system supports electric and axial isospin currents along the magnetic field which correspond to chiral magnetic and chiral separation effects. We show that these currents are sensitive to the finite mass of the constituents but the conductivities follow a simple scaling with the corresponding charge densities as one would expect for polarization effects. It is argued that this relation can capture the dependence of chiral effects on other infrared parameters. Finally, we briefly comment on the realization of the 't Hooft matching condition in pionic media at finite densities.

Computation of transonic potential flow about 3 dimensional inlets, ducts, and bodies

NASA Technical Reports Server (NTRS)

Reyhner, T. A.

1982-01-01

An analysis was developed and a computer code, P465 Version A, written for the prediction of transonic potential flow about three dimensional objects including inlet, duct, and body geometries. Finite differences and line relaxation are used to solve the complete potential flow equation. The coordinate system used for the calculations is independent of body geometry. Cylindrical coordinates are used for the computer code. The analysis is programmed in extended FORTRAN 4 for the CYBER 203 vector computer. The programming of the analysis is oriented toward taking advantage of the vector processing capabilities of this computer. Comparisons of computed results with experimental measurements are presented to verify the analysis. Descriptions of program input and output formats are also presented.

A combined representation method for use in band structure calculations. 1: Method

NASA Technical Reports Server (NTRS)

Friedli, C.; Ashcroft, N. W.

1975-01-01

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.

Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States

NASA Astrophysics Data System (ADS)

Cao, Huai-Xin; Long, Gui-Lu; Guo, Zhi-Hua; Chen, Zheng-Li

2013-06-01

Following the idea of duality quantum computation, a generalized duality quantum computer (GDQC) acting on vector-states is defined as a tuple consisting of a generalized quantum wave divider (GQWD) and a finite number of unitary operators as well as a generalized quantum wave combiner (GQWC). It is proved that the GQWD and GQWC of a GDQC are an isometry and a co-isometry, respectively, and mutually dual. It is also proved that every GDQC gives a contraction, called a generalized duality quantum gate (GDQG). A classification of GDQCs is given and the properties of GDQGs are discussed. Some applications are obtained, including two orthogonal duality quantum computer algorithms for unsorted database search and an understanding of the Mach-Zehnder interferometer.

Effective-medium theory of elastic waves in random networks of rods.

PubMed

Katz, J I; Hoffman, J J; Conradi, M S; Miller, J G

2012-06-01

We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining wavelength-dependent effective elastic moduli, we calculate both the static moduli and the dispersion relations of ultrasonic longitudinal and transverse elastic waves. At finite wave vector k the waves are dispersive, with phase and group velocities decreasing with increasing wave vector. These results are directly applicable to networks with empty pore space. They also describe the solid matrix in two-component (Biot) theories of fluid-filled porous media. We suggest the possibility of low density materials with higher ratios of stiffness and strength to density than those of foams, aerogels, or trabecular bone.

Computation of output feedback gains for linear stochastic systems using the Zangwill-Powell method

NASA Technical Reports Server (NTRS)

Kaufman, H.

1977-01-01

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell.

Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing

DOE PAGES

Martin, James E.; Solis, Kyle Jameson

2015-11-09

It has recently been reported that two types of triaxial electric or magnetic fields can drive vorticity in dielectric or magnetic particle suspensions, respectively. The first type-symmetry -- breaking rational fields -- consists of three mutually orthogonal fields, two alternating and one dc, and the second type -- rational triads -- consists of three mutually orthogonal alternating fields. In each case it can be shown through experiment and theory that the fluid vorticity vector is parallel to one of the three field components. For any given set of field frequencies this axis is invariant, but the sign and magnitude ofmore » the vorticity (at constant field strength) can be controlled by the phase angles of the alternating components and, at least for some symmetry-breaking rational fields, the direction of the dc field. In short, the locus of possible vorticity vectors is a 1-d set that is symmetric about zero and is along a field direction. In this paper we show that continuous, 3-d control of the vorticity vector is possible by progressively transitioning the field symmetry by applying a dc bias along one of the principal axes. Such biased rational triads are a combination of symmetry-breaking rational fields and rational triads. A surprising aspect of these transitions is that the locus of possible vorticity vectors for any given field bias is extremely complex, encompassing all three spatial dimensions. As a result, the evolution of a vorticity vector as the dc bias is increased is complex, with large components occurring along unexpected directions. More remarkable are the elaborate vorticity vector orbits that occur when one or more of the field frequencies are detuned. As a result, these orbits provide the basis for highly effective mixing strategies wherein the vorticity axis periodically explores a range of orientations and magnitudes.« less

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

Finite element method for optimal guidance of an advanced launch vehicle

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin

1992-01-01

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Serendipity in dark photon searches

NASA Astrophysics Data System (ADS)

Ilten, Philip; Soreq, Yotam; Williams, Mike; Xue, Wei

2018-06-01

Searches for dark photons provide serendipitous discovery potential for other types of vector particles. We develop a framework for recasting dark photon searches to obtain constraints on more general theories, which includes a data-driven method for determining hadronic decay rates. We demonstrate our approach by deriving constraints on a vector that couples to the B-L current, a leptophobic B boson that couples directly to baryon number and to leptons via B- γ kinetic mixing, and on a vector that mediates a protophobic force. Our approach can easily be generalized to any massive gauge boson with vector couplings to the Standard Model fermions, and software to perform any such recasting is provided at https://gitlab.com/philten/darkcast .

Approximate degeneracy of J =1 spatial correlators in high temperature QCD

NASA Astrophysics Data System (ADS)

Rohrhofer, C.; Aoki, Y.; Cossu, G.; Fukaya, H.; Glozman, L. Ya.; Hashimoto, S.; Lang, C. B.; Prelovsek, S.

2017-11-01

We study spatial isovector meson correlators in Nf=2 QCD with dynamical domain-wall fermions on 3 23×8 lattices at temperatures T =220 - 380 MeV . We measure the correlators of spin-one (J =1 ) operators including vector, axial-vector, tensor and axial-tensor. Restoration of chiral U (1 )A and S U (2 )L×S U (2 )R symmetries of QCD implies degeneracies in vector-axial-vector (S U (2 )L×S U (2 )R) and tensor-axial-tensor (U (1 )A) pairs, which are indeed observed at temperatures above Tc. Moreover, we observe an approximate degeneracy of all J =1 correlators with increasing temperature. This approximate degeneracy suggests emergent S U (2 )CS and S U (4 ) symmetries at high temperatures, that mix left- and right-handed quarks.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Nonlinear absorption of short intense laser pulse in multispecies plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kargarian, A.; Hajisharifi, K.; Mehdian, H.

In the present paper, the detailed investigation concerning the effect of inclusion of heavy negative ions into the finite background plasma on the laser absorption has been carried out by employing particle-in-cell simulation method. For this purpose, in this configuration, the laser energy absorption relying on the nonlinear phenomena such as phase-mixing, wave-breaking, and scattering has been studied in the Raman-Brillouin regime. It is shown that the inclusion of heavy negative ions suppresses the scattering while increases the phase-mixing time. Moreover, it is illustrated that this inclusion can increase the laser absorption in finite plasma environment, after saturation. The obtainedmore » results are expected to be relevant to the experiments on the mass spectrometry with laser desorption techniques as well as on the laser-plasma interaction with application to particles acceleration.« less

Vectorized and multitasked solution of the few-group neutron diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zee, S.K.; Turinsky, P.J.; Shayer, Z.

1989-03-01

A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. Formore » the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model.« less

Application of Bred Vectors To Data Assimilation

NASA Astrophysics Data System (ADS)

Corazza, M.; Kalnay, E.; Patil, Dj

We introduced a statistic, the BV-dimension, to measure the effective local finite-time dimensionality of the atmosphere. We show that this dimension is often quite low, and suggest that this finding has important implications for data assimilation and the accuracy of weather forecasting (Patil et al, 2001). The original database for this study was the forecasts of the NCEP global ensemble forecasting system. The initial differences between the control forecast and the per- turbed forecasts are called bred vectors. The control and perturbed initial conditions valid at time t=n(t are evolved using the forecast model until time t=(n+1) (t. The differences between the perturbed and the control forecasts are scaled down to their initial amplitude, and constitute the bred vectors valid at (n+1) (t. Their growth rate is typically about 1.5/day. The bred vectors are similar by construction to leading Lya- punov vectors except that they have small but finite amplitude, and they are valid at finite times. The original NCEP ensemble data set has 5 independent bred vectors. We define a local bred vector at each grid point by choosing the 5 by 5 grid points centered at the grid point (a region of about 1100km by 1100km), and using the north-south and east- west velocity components at 500mb pressure level to form a 50 dimensional column vector. Since we have k=5 global bred vectors, we also have k local bred vectors at each grid point. We estimate the effective dimensionality of the subspace spanned by the local bred vectors by performing a singular value decomposition (EOF analysis). The k local bred vector columns form a 50xk matrix M. The singular values s(i) of M measure the extent to which the k column unit vectors making up the matrix M point in the direction of v(i). We define the bred vector dimension as BVDIM={Sum[s(i)]}^2/{Sum[s(i)]^2} For example, if 4 out of the 5 vectors lie along v, and one lies along v, the BV- dimension would be BVDIM[sqrt(4), 1, 0,0,0]=1.8, less than 2 because one direction is more dominant than the other in representing the original data. The results (Patil et al, 2001) show that there are large regions where the bred vectors span a subspace of substantially lower dimension than that of the full space. These low dimensionality regions are dominant in the baroclinic extratropics, typically have a lifetime of 3-7 days, have a well-defined horizontal and vertical structure that spans 1 most of the atmosphere, and tend to move eastward. New results with a large number of ensemble members confirm these results and indicate that the low dimensionality regions are quite robust, and depend only on the verification time (i.e., the underlying flow). Corazza et al (2001) have performed experiments with a data assimilation system based on a quasi-geostrophic model and simulated observations (Morss, 1999, Hamill et al, 2000). A 3D-variational data assimilation scheme for a quasi-geostrophic chan- nel model is used to study the structure of the background error and its relationship to the corresponding bred vectors. The "true" evolution of the model atmosphere is defined by an integration of the model and "rawinsonde observations" are simulated by randomly perturbing the true state at fixed locations. It is found that after 3-5 days the bred vectors develop well organized structures which are very similar for the two different norms considered in this paper (potential vorticity norm and streamfunction norm). The results show that the bred vectors do indeed represent well the characteristics of the data assimilation forecast errors, and that the subspace of bred vectors contains most of the forecast error, except in areas where the forecast errors are small. For example, the angle between the 6hr forecast error and the subspace spanned by 10 bred vectors is less than 10o over 90% of the domain, indicating a pattern correlation of more than 98.5% between the forecast error and its projection onto the bred vector subspace. The presence of low-dimensional regions in the perturbations of the basic flow has important implications for data assimilation. At any given time, there is a difference between the true atmospheric state and the model forecast. Assuming that model er- rors are not the dominant source of errors, in a region of low BV-dimensionality the difference between the true state and the forecast should lie substantially in the low dimensional unstable subspace of the few bred vectors that contribute most strongly to the low BV-dimension. This information should yield a substantial improvement in the forecast: the data assimilation algorithm should correct the model state by moving it closer to the observations along the unstable subspace, since this is where the true state most likely lies. Preliminary experiments have been conducted with the quasi-geostrophic data assim- ilation system testing whether it is possible to add "errors of the day" based on bred vectors to the standard (constant) 3D-Var background error covariance in order to capture these important errors. The results are extremely encouraging, indicating a significant reduction (about 40%) in the analysis errors at a very low computational cost. References: 2 Corazza, M., E. Kalnay, DJ Patil, R. Morss, M Cai, I. Szunyogh, BR Hunt, E Ott and JA Yorke, 2001: Use of the breeding technique to estimate the structure of the analysis "errors of the day". Submitted to Nonlinear Processes in Geophysics. Hamill, T.M., Snyder, C., and Morss, R.E., 2000: A Comparison of Probabilistic Fore- casts from Bred, Singular-Vector and Perturbed Observation Ensembles, Mon. Wea. Rev., 128, 1835­1851. Kalnay, E., and Z. Toth, 1994: Removing growing errors in the analysis cycle. Preprints of the Tenth Conference on Numerical Weather Prediction, Amer. Meteor. Soc., 1994, 212-215. Morss, R. E., 1999: Adaptive observations: Idealized sampling strategies for improv- ing numerical weather prediction. PHD thesis, Massachussetts Institute of technology, 225pp. Patil, D. J. S., B. R. Hunt, E. Kalnay, J. A. Yorke, and E. Ott., 2001: Local Low Dimensionality of Atmospheric Dynamics. Phys. Rev. Lett., 86, 5878. 3

Nonnormal operators in physics, a singular-vectors approach: illustration in polarization optics.

PubMed

Tudor, Tiberiu

2016-04-20

The singular-vectors analysis of a general nonnormal operator defined on a finite-dimensional complex vector space is given in the frame of a pure operatorial ("nonmatrix," "coordinate-free") approach, performed in a Dirac language. The general results are applied in the field of polarization optics, where the nonnormal operators are widespread as operators of various polarization devices. Two nonnormal polarization devices representative for the class of nonnormal and even pathological operators-the standard two-layer elliptical ideal polarizer (singular operator) and the three-layer ambidextrous ideal polarizer (singular and defective operator)-are analyzed in detail. It is pointed out that the unitary polar component of the operator exists and preserves, in such pathological case too, its role of converting the input singular basis of the operator in its output singular basis. It is shown that for any nonnormal ideal polarizer a complementary one exists, so that the tandem of their operators uniquely determines their (common) unitary polar component.

On the estimation of the domain of attraction for discrete-time switched and hybrid nonlinear systems

NASA Astrophysics Data System (ADS)

Kit Luk, Chuen; Chesi, Graziano

2015-11-01

This paper addresses the estimation of the domain of attraction for discrete-time nonlinear systems where the vector field is subject to changes. First, the paper considers the case of switched systems, where the vector field is allowed to arbitrarily switch among the elements of a finite family. Second, the paper considers the case of hybrid systems, where the state space is partitioned into several regions described by polynomial inequalities, and the vector field is defined on each region independently from the other ones. In both cases, the problem consists of computing the largest sublevel set of a Lyapunov function included in the domain of attraction. An approach is proposed for solving this problem based on convex programming, which provides a guaranteed inner estimate of the sought sublevel set. The conservatism of the provided estimate can be decreased by increasing the size of the optimisation problem. Some numerical examples illustrate the proposed approach.

An artificial neural network model for periodic trajectory generation

NASA Astrophysics Data System (ADS)

Shankar, S.; Gander, R. E.; Wood, H. C.

A neural network model based on biological systems was developed for potential robotic application. The model consists of three interconnected layers of artificial neurons or units: an input layer subdivided into state and plan units, an output layer, and a hidden layer between the two outer layers which serves to implement nonlinear mappings between the input and output activation vectors. Weighted connections are created between the three layers, and learning is effected by modifying these weights. Feedback connections between the output and the input state serve to make the network operate as a finite state machine. The activation vector of the plan units of the input layer emulates the supraspinal commands in biological central pattern generators in that different plan activation vectors correspond to different sequences or trajectories being recalled, even with different frequencies. Three trajectories were chosen for implementation, and learning was accomplished in 10,000 trials. The fault tolerant behavior, adaptiveness, and phase maintenance of the implemented network are discussed.

Better Together: Association With 'Candidatus Liberibacter Asiaticus' Increases the Reproductive Fitness of Its Insect Vector, Diaphorina citri (Hemiptera: Liviidae).

PubMed

Pelz-Stelinski, K S; Killiny, N

2016-05-01

The duration of the evolutionary association between a pathogen and vector can be inferred based on the strength of their mutualistic interactions. A well-adapted pathogen is likely to confer some benefit or, at a minimum, exhibit low pathogenicity toward its host vector. Coevolution of the two toward a mutually beneficial association appears to have occurred between the citrus greening disease pathogen, Candidatus Liberibacter asiaticus (Las), and its insect vector, the Asian citrus psyllid, Diaphorina citri (Kuwayama). To better understand the dynamics facilitating transmission, we evaluated the effects of Las infection on the fitness of its vector. Diaphorina citri harboring Las were more fecund than their uninfected counterparts; however, their nymphal development rate and adult survival were comparatively reduced. The finite rate of population increase and net reproductive rate were both greater among Las-infected D. citri as compared with uninfected counterparts, indicating that overall population fitness of infected psyllids was improved given the greater number of offspring produced. Previous reports of transovarial transmission, in conjunction with increased fecundity and population growth rates of Las-positive D. citri found in the current investigation, suggest a long evolutionary relationship between pathogen and vector. The survival of Las-infected adult D. citri was lower compared with uninfected D. citri , which suggests that there may be a fitness trade-off in response to Las infection. A beneficial effect of a plant pathogen on vector fitness may indicate that the pathogen developed a relationship with the insect before secondarily moving to plants.

Better Together: Association With ‘Candidatus Liberibacter Asiaticus’ Increases the Reproductive Fitness of Its Insect Vector, Diaphorina citri (Hemiptera: Liviidae)

PubMed Central

Pelz-Stelinski, K. S.; Killiny, N.

2016-01-01

The duration of the evolutionary association between a pathogen and vector can be inferred based on the strength of their mutualistic interactions. A well-adapted pathogen is likely to confer some benefit or, at a minimum, exhibit low pathogenicity toward its host vector. Coevolution of the two toward a mutually beneficial association appears to have occurred between the citrus greening disease pathogen, Candidatus Liberibacter asiaticus (Las), and its insect vector, the Asian citrus psyllid, Diaphorina citri (Kuwayama). To better understand the dynamics facilitating transmission, we evaluated the effects of Las infection on the fitness of its vector. Diaphorina citri harboring Las were more fecund than their uninfected counterparts; however, their nymphal development rate and adult survival were comparatively reduced. The finite rate of population increase and net reproductive rate were both greater among Las-infected D. citri as compared with uninfected counterparts, indicating that overall population fitness of infected psyllids was improved given the greater number of offspring produced. Previous reports of transovarial transmission, in conjunction with increased fecundity and population growth rates of Las-positive D. citri found in the current investigation, suggest a long evolutionary relationship between pathogen and vector. The survival of Las-infected adult D. citri was lower compared with uninfected D. citri, which suggests that there may be a fitness trade-off in response to Las infection. A beneficial effect of a plant pathogen on vector fitness may indicate that the pathogen developed a relationship with the insect before secondarily moving to plants. PMID:27418697

Effective gravitational couplings for cosmological perturbations in generalized Proca theories

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

2016-08-01

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

Turbulence and mixing from optimal perturbations to a stratified shear layer

NASA Astrophysics Data System (ADS)

Kaminski, Alexis; Caulfield, C. P.; Taylor, John

2014-11-01

The stability and mixing of stratified shear layers is a canonical problem in fluid dynamics with relevance to flows in the ocean and atmosphere. The Miles-Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the gradient Richardson number, Rig is less than 1/4 somewhere in the flow. However, substantial transient growth of non-normal modes may be possible at finite times even when Rig > 1 / 4 everywhere in the flow. We have calculated the ``optimal perturbations'' associated with maximum perturbation energy gain for a stably-stratified shear layer. These optimal perturbations are then used to initialize direct numerical simulations. For small but finite perturbation amplitudes, the optimal perturbations grow at the predicted linear rate initially, but then experience sufficient transient growth to become nonlinear and susceptible to secondary instabilities, which then break down into turbulence. Remarkably, this occurs even in flows for which Rig > 1 / 4 everywhere. We will describe the nonlinear evolution of the optimal perturbations and characterize the resulting turbulence and mixing.

Magnetic-field-induced mixed-level Kondo effect in two-level systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Arturo; Ngo, Anh T.; Ulloa, Sergio E.

2016-10-17

We consider a two-orbital impurity system with intra-and interlevel Coulomb repulsion that is coupled to a single conduction channel. This situation can generically occur in multilevel quantum dots or in systems of coupled quantum dots. For finite energy spacing between spin-degenerate orbitals, an in-plane magnetic field drives the system from a local-singlet ground state to a "mixed-level" Kondo regime, where the Zeeman-split levels are degenerate for opposite-spin states. We use the numerical renormalization group approach to fully characterize this mixed-level Kondo state and discuss its properties in terms of the applied Zeeman field, temperature, and system parameters. Under suitable conditions,more » the total spectral function is shown to develop a Fermi-level resonance, so that the linear conductance of the system peaks at a finite Zeeman field while it decreases as a function of temperature. These features, as well as the local moment and entropy contribution of the impurity system, are commensurate with Kondo physics, which can be studied in suitably tuned quantum dot systems.« less

Development and Application of Benchmark Examples for Mixed-Mode I/II Quasi-Static Delamination Propagation Predictions

NASA Technical Reports Server (NTRS)

Krueger, Ronald

2012-01-01

The development of benchmark examples for quasi-static delamination propagation prediction is presented. The example is based on a finite element model of the Mixed-Mode Bending (MMB) specimen for 50% mode II. The benchmarking is demonstrated for Abaqus/Standard, however, the example is independent of the analysis software used and allows the assessment of the automated delamination propagation prediction capability in commercial finite element codes based on the virtual crack closure technique (VCCT). First, a quasi-static benchmark example was created for the specimen. Second, starting from an initially straight front, the delamination was allowed to propagate under quasi-static loading. Third, the load-displacement as well as delamination length versus applied load/displacement relationships from a propagation analysis and the benchmark results were compared, and good agreement could be achieved by selecting the appropriate input parameters. The benchmarking procedure proved valuable by highlighting the issues associated with choosing the input parameters of the particular implementation. Overall, the results are encouraging, but further assessment for mixed-mode delamination fatigue onset and growth is required.

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

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

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Combined-probability space and certainty or uncertainty relations for a finite-level quantum system

NASA Astrophysics Data System (ADS)

Sehrawat, Arun

2017-08-01

The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys certain quantum constraints, which are triangle inequalities in our case. Such a restricted set of combined vectors, called the combined-probability space, is presented here for a d -level quantum system (qudit). The combined space is a compact convex subset of a Euclidean space, and all its extreme points come from a family of parametric curves. Considering a suitable concave function on the combined space to estimate the uncertainty, we deliver an uncertainty relation by finding its global minimum on the curves for a qudit. If one chooses an appropriate concave (or convex) function, then there is no need to search for the absolute minimum (maximum) over the whole space; it will be on the parametric curves. So these curves are quite useful for establishing an uncertainty (or a certainty) relation for a general pair of settings. We also demonstrate that many known tight certainty or uncertainty relations for a qubit can be obtained with the triangle inequalities.

Estimation of Rank Correlation for Clustered Data

PubMed Central

Rosner, Bernard; Glynn, Robert

2017-01-01

It is well known that the sample correlation coefficient (Rxy) is the maximum likelihood estimator (MLE) of the Pearson correlation (ρxy) for i.i.d. bivariate normal data. However, this is not true for ophthalmologic data where X (e.g., visual acuity) and Y (e.g., visual field) are available for each eye and there is positive intraclass correlation for both X and Y in fellow eyes. In this paper, we provide a regression-based approach for obtaining the MLE of ρxy for clustered data, which can be implemented using standard mixed effects model software. This method is also extended to allow for estimation of partial correlation by controlling both X and Y for a vector U of other covariates. In addition, these methods can be extended to allow for estimation of rank correlation for clustered data by (a) converting ranks of both X and Y to the probit scale, (b) estimating the Pearson correlation between probit scores for X and Y, and (c) using the relationship between Pearson and rank correlation for bivariate normally distributed data. The validity of the methods in finite-sized samples is supported by simulation studies. Finally, two examples from ophthalmology and analgesic abuse are used to illustrate the methods. PMID:28399615

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).