A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE PAGES

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.; ...

2016-09-18

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

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

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

Plasmon confinement in fractal quantum systems

NASA Astrophysics Data System (ADS)

Westerhout, Tom; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

2018-05-01

Recent progress in the fabrication of materials has made it possible to create arbitrary nonperiodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the quantum plasmonic properties of electron gases in complex geometries. In this work we study systems with a fractal dimension. We calculate the full dielectric functions of two prototypical fractals with different ramification numbers, namely the Sierpinski carpet and gasket. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum level.

Iterative design of one- and two-dimensional FIR digital filters. [Finite duration Impulse Response

NASA Technical Reports Server (NTRS)

Suk, M.; Choi, K.; Algazi, V. R.

1976-01-01

The paper describes a new iterative technique for designing FIR (finite duration impulse response) digital filters using a frequency weighted least squares approximation. The technique is as easy to implement (via FFT) and as effective in two dimensions as in one dimension, and there are virtually no limitations on the class of filter frequency spectra approximated. An adaptive adjustment of the frequency weight to achieve other types of design approximation such as Chebyshev type design is discussed.

Homological dimensions and Van den Bergh isomorphisms for nuclear Fréchet algebras

NASA Astrophysics Data System (ADS)

Pirkovskii, Alexei Yu

2012-08-01

We prove the equation \\operatorname{w{.}dg} A=\\operatorname{w{.}db} A for every nuclear Fréchet-Arens-Michael algebra A of finite weak bidimension, where \\operatorname{w{.}dg} A is the weak global dimension and \\operatorname{w{.}db} A the weak bidimension of A. Assuming that A has a projective bimodule resolution of finite type, we establish the estimate \\operatorname{db}A\\le\\operatorname{dg}A+1, where \\operatorname{dg} A is the global dimension and \\operatorname{db} A the bidimension of A. We also prove that \\operatorname{dg}A=\\operatorname{db}A=\\operatorname{w{.}dg}A=\\operatorname{w{.}db} A=n for all nuclear Fréchet-Arens-Michael algebras satisfying the Van den Bergh conditions \\operatorname{VdB}(n). As an application, we calculate the homological dimensions of smooth and complex-analytic quantum tori.

Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1993-01-01

This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

[Research Progress and Prospect of Applications of Finite Element Method in Lumbar Spine Biomechanics].

PubMed

Zhang, Zhenjun; Li, Yang; Liao, Zhenhua; Liu, Weiqiang

2016-12-01

Based on the application of finite element analysis in spine biomechanics,the research progress of finite element method applied in lumbar spine mechanics is reviewed and the prospect is forecasted.The related works,including lumbar ontology modeling,clinical application research,and occupational injury and protection,are summarized.The main research areas of finite element method are as follows:new accurate modeling process,the optimized simulation method,diversified clinical effect evaluation,and the clinical application of artificial lumbar disc.According to the recent research progress,the application prospects of finite element method,such as automation and individuation of modeling process,evaluation and analysis of new operation methods and simulation of mechanical damage and dynamic response,are discussed.The purpose of this paper is to provide the theoretical reference and practical guidance for the clinical lumbar problems by reviewing the application of finite element method in the field of the lumbar spine biomechanics.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Factors Influencing Progressive Failure Analysis Predictions for Laminated Composite Structure

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2008-01-01

Progressive failure material modeling methods used for structural analysis including failure initiation and material degradation are presented. Different failure initiation criteria and material degradation models are described that define progressive failure formulations. These progressive failure formulations are implemented in a user-defined material model for use with a nonlinear finite element analysis tool. The failure initiation criteria include the maximum stress criteria, maximum strain criteria, the Tsai-Wu failure polynomial, and the Hashin criteria. The material degradation model is based on the ply-discounting approach where the local material constitutive coefficients are degraded. Applications and extensions of the progressive failure analysis material model address two-dimensional plate and shell finite elements and three-dimensional solid finite elements. Implementation details are described in the present paper. Parametric studies for laminated composite structures are discussed to illustrate the features of the progressive failure modeling methods that have been implemented and to demonstrate their influence on progressive failure analysis predictions.

An evaluation of a coupled microstructural approach for the analysis of functionally graded composites via the finite-element method

NASA Technical Reports Server (NTRS)

Pindera, Marek-Jerzy; Dunn, Patrick

1995-01-01

A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.

Unexpected finite size effects in interfacial systems: Why bigger is not always better—Increase in uncertainty of surface tension with bulk phase width

NASA Astrophysics Data System (ADS)

Longford, Francis G. J.; Essex, Jonathan W.; Skylaris, Chris-Kriton; Frey, Jeremy G.

2018-06-01

We present an unexpected finite size effect affecting interfacial molecular simulations that is proportional to the width-to-surface-area ratio of the bulk phase Ll/A. This finite size effect has a significant impact on the variance of surface tension values calculated using the virial summation method. A theoretical derivation of the origin of the effect is proposed, giving a new insight into the importance of optimising system dimensions in interfacial simulations. We demonstrate the consequences of this finite size effect via a new way to estimate the surface energetic and entropic properties of simulated air-liquid interfaces. Our method is based on macroscopic thermodynamic theory and involves comparing the internal energies of systems with varying dimensions. We present the testing of these methods using simulations of the TIP4P/2005 water forcefield and a Lennard-Jones fluid model of argon. Finally, we provide suggestions of additional situations, in which this finite size effect is expected to be significant, as well as possible ways to avoid its impact.

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

NASA Astrophysics Data System (ADS)

Anderson, R.; Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Quezada de Luna, M.; Rieben, R.; Tomov, V.

2017-04-01

In this work we present a FCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported.

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

Stauffer, D.

After improving the Monte Carlo statistics, Derrida`s exponent {theta} for the never damaged sites in Ising models at finite temperatures is shown to be compatible with {theta}(T = 0) = 0.22 in two dimensions. In three and more dimensions the number of these sites decays differently from zero temperature

Effect of grid transparency and finite collector size on determining ion temperature and density by the retarding potential analyzer

NASA Technical Reports Server (NTRS)

Troy, B. E., Jr.; Maier, E. J.

1975-01-01

The effects of the grid transparency and finite collector size on the values of thermal ion density and temperature determined by the standard RPA (retarding potential analyzer) analysis method are investigated. The current-voltage curves calculated for varying RPA parameters and a given ion mass, temperature, and density are analyzed by the standard RPA method. It is found that only small errors in temperature and density are introduced for an RPA with typical dimensions, and that even when the density error is substantial for nontypical dimensions, the temperature error remains minimum.

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.

Scalable direct Vlasov solver with discontinuous Galerkin method on unstructured mesh.

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

Xu, J.; Ostroumov, P. N.; Mustapha, B.

2010-12-01

This paper presents the development of parallel direct Vlasov solvers with discontinuous Galerkin (DG) method for beam and plasma simulations in four dimensions. Both physical and velocity spaces are in two dimesions (2P2V) with unstructured mesh. Contrary to the standard particle-in-cell (PIC) approach for kinetic space plasma simulations, i.e., solving Vlasov-Maxwell equations, direct method has been used in this paper. There are several benefits to solving a Vlasov equation directly, such as avoiding noise associated with a finite number of particles and the capability to capture fine structure in the plasma. The most challanging part of a direct Vlasov solvermore » comes from higher dimensions, as the computational cost increases as N{sup 2d}, where d is the dimension of the physical space. Recently, due to the fast development of supercomputers, the possibility has become more realistic. Many efforts have been made to solve Vlasov equations in low dimensions before; now more interest has focused on higher dimensions. Different numerical methods have been tried so far, such as the finite difference method, Fourier Spectral method, finite volume method, and spectral element method. This paper is based on our previous efforts to use the DG method. The DG method has been proven to be very successful in solving Maxwell equations, and this paper is our first effort in applying the DG method to Vlasov equations. DG has shown several advantages, such as local mass matrix, strong stability, and easy parallelization. These are particularly suitable for Vlasov equations. Domain decomposition in high dimensions has been used for parallelization; these include a highly scalable parallel two-dimensional Poisson solver. Benchmark results have been shown and simulation results will be reported.« less

Exterior dimension of fat fractals

NASA Technical Reports Server (NTRS)

Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.

1985-01-01

Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.

Microscopic processes controlling the Herschel-Bulkley exponent

NASA Astrophysics Data System (ADS)

Lin, Jie; Wyart, Matthieu

2018-01-01

The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent n =1 /β . A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to β =2 in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to β =1 with logarithmic correction. This result supports that HL is not a suitable explanation for the value of β , which is instead significantly affected by finite-dimensional effects. From considerations on elastoplastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that β =1 +1 /(d -df) , where df is the fractal dimension of avalanches and d the spatial dimension. Measurements of df then supports that β ≈2.1 and β ≈1.7 in two and three dimensions, respectively. We discuss theoretical arguments leading to approximations of β in finite dimensions.

Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles.

PubMed

Rajesh, R; Krishnamurthy, Supriya

2002-10-01

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation, and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady state, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite-size system, however, continues to show a signature of the original transition, and we characterize the finite-size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.

Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

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

Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis

This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.

A progress report on estuary modeling by the finite-element method

USGS Publications Warehouse

Gray, William G.

1978-01-01

Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)

User-Defined Material Model for Progressive Failure Analysis

NASA Technical Reports Server (NTRS)

Knight, Norman F. Jr.; Reeder, James R. (Technical Monitor)

2006-01-01

An overview of different types of composite material system architectures and a brief review of progressive failure material modeling methods used for structural analysis including failure initiation and material degradation are presented. Different failure initiation criteria and material degradation models are described that define progressive failure formulations. These progressive failure formulations are implemented in a user-defined material model (or UMAT) for use with the ABAQUS/Standard1 nonlinear finite element analysis tool. The failure initiation criteria include the maximum stress criteria, maximum strain criteria, the Tsai-Wu failure polynomial, and the Hashin criteria. The material degradation model is based on the ply-discounting approach where the local material constitutive coefficients are degraded. Applications and extensions of the progressive failure analysis material model address two-dimensional plate and shell finite elements and three-dimensional solid finite elements. Implementation details and use of the UMAT subroutine are described in the present paper. Parametric studies for composite structures are discussed to illustrate the features of the progressive failure modeling methods that have been implemented.

Quantum gravity as an information network self-organization of a 4D universe

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-10-01

I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension 4. The spectral dimension is lower than the Hausdorff dimension: it coincides with the Hausdorff dimension 4 at a first quantum phase transition corresponding to an IR fixed point, while at a second quantum phase transition describing small scales space-time dissolves into disordered information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. At finite temperatures the universe graph emerges without a big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no space-time inside and with "Schwarzschild-like" horizons with a lower spectral dimension.

Continuum Vlasov Simulation in Four Phase-space Dimensions

NASA Astrophysics Data System (ADS)

Cohen, B. I.; Banks, J. W.; Berger, R. L.; Hittinger, J. A.; Brunner, S.

2010-11-01

In the VALHALLA project, we are developing scalable algorithms for the continuum solution of the Vlasov-Maxwell equations in two spatial and two velocity dimensions. We use fourth-order temporal and spatial discretizations of the conservative form of the equations and a finite-volume representation to enable adaptive mesh refinement and nonlinear oscillation control [1]. The code has been implemented with and without adaptive mesh refinement, and with electromagnetic and electrostatic field solvers. A goal is to study the efficacy of continuum Vlasov simulations in four phase-space dimensions for laser-plasma interactions. We have verified the code in examples such as the two-stream instability, the weak beam-plasma instability, Landau damping, electron plasma waves with electron trapping and nonlinear frequency shifts [2]^ extended from 1D to 2D propagation, and light wave propagation.^ We will report progress on code development, computational methods, and physics applications. This work was performed under the auspices of the U.S. DOE by LLNL under contract no. DE-AC52-07NA27344. This work was funded by the Lab. Dir. Res. and Dev. Prog. at LLNL under project tracking code 08-ERD-031. [1] J.W. Banks and J.A.F. Hittinger, to appear in IEEE Trans. Plas. Sci. (Sept., 2010). [2] G.J. Morales and T.M. O'Neil, Phys. Rev. Lett. 28,417 (1972); R. L. Dewar, Phys. Fluids 15,712 (1972).

Dynamical transition for a particle in a squared Gaussian potential

NASA Astrophysics Data System (ADS)

Touya, C.; Dean, D. S.

2007-02-01

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by ψ = phi2/2 where phi is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

NASA Astrophysics Data System (ADS)

Malakar, Kanaya; Jemseena, V.; Kundu, Anupam; Vijay Kumar, K.; Sabhapandit, Sanjib; Majumdar, Satya N.; Redner, S.; Dhar, Abhishek

2018-04-01

We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady-state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady-state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain with an absorbing boundary condition at the origin. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verification of our analytical results.

Escape and finite-size scaling in diffusion-controlled annihilation

DOE PAGES

Ben-Naim, Eli; Krapivsky, Paul L.

2016-12-16

In this paper, we study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial dimensions d>2 where a finite number of particles typically survive the annihilation process. Using scaling techniques we investigate the average number of surviving particles, M, as a function of the initial number of particles, N. In three dimensions, for instance, we find the scaling law M ~ N 1/3 in the asymptotic regime N»1. We show that two time scales govern the reaction kinetics: the diffusionmore » time scale, T ~ N 2/3, and the escape time scale, τ ~ N 4/3. The vast majority of annihilation events occur on the diffusion time scale, while no annihilation events occur beyond the escape time scale.« less

Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions

DTIC Science & Technology

1989-10-01

paper, we study fast parallel preconditioners for systems of equations arising from the p-version finite element method. The p-version finite element...computations and the solution of a relatively small global auxiliary problem. We study two different methods. In the first (Section 3), the global...20], will be studied in the next section. Problem (3.12) is obviously much more easily solved than the original problem ,nd the procedure is highly

Conductance of finite systems and scaling in localization theory

NASA Astrophysics Data System (ADS)

Suslov, I. M.

2012-11-01

The conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)). Usually it is defined by the Landauer-type formulas, which remain open the following questions: (a) exclusion of the contact resistance in the many-channel case; (b) correspondence of the Landauer conductance with internal properties of the system; (c) relation with the diffusion coefficient D(ω, q) of an infinite system. The answers to these questions are obtained below in the framework of two approaches: (1) self-consistent theory of localization by Vollhardt and Wölfle, and (2) quantum mechanical analysis based on the shell model. Both approaches lead to the same definition for the conductance of a finite system, closely related to the Thouless definition. In the framework of the self-consistent theory, the relations of finite-size scaling are derived and the Gell-Mann-Low functions β( g) for space dimensions d = 1, 2, 3 are calculated. In contrast to the previous attempt by Vollhardt and Wölfle (1982), the metallic and localized phase are considered from the same standpoint, and the conductance of a finite system has no singularity at the critical point. In the 2D case, the expansion of β( g) in 1/ g coincides with results of the σ-model approach on the two-loop level and depends on the renormalization scheme in higher loops; the use of dimensional regularization for transition to dimension d = 2 + ɛ looks incompatible with the physical essence of the problem. The results are compared with numerical and physical experiments. A situation in higher dimensions and the conditions for observation of the localization law σ(ω) ∝ - iω for conductivity are discussed.

The constraint method: A new finite element technique. [applied to static and dynamic loads on plates

NASA Technical Reports Server (NTRS)

Tsai, C.; Szabo, B. A.

1973-01-01

An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.

User's guide for analysis of finite elastoplastic deformation: The FIPDEF and FIPAX programs for the CDC 6600

NASA Technical Reports Server (NTRS)

Osias, J. R.

1974-01-01

Computer programs are presented which provide incremental finite-element analysis capability for problems of quasi-static, finite, elastoplastic deformation in two spatial dimensions (plane strain, plane stress, axisymmetric). Monotonic or cyclic loading of isotropic hardening materials is considered. The only restriction on the form of the stress-strain curve is that the rate of work hardening exceed some small positive value. The user's guide assumes familiarity with both finite-element analysis and FORTRAN IV programming for the CDC 6600. Sufficient information is provided to support problem solving ultization of the programs.

Bose-Einstein condensation in chains with power-law hoppings: Exact mapping on the critical behavior in d-dimensional regular lattices.

PubMed

Dias, W S; Bertrand, D; Lyra, M L

2017-06-01

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d>4.

Bose-Einstein condensation in chains with power-law hoppings: Exact mapping on the critical behavior in d -dimensional regular lattices

NASA Astrophysics Data System (ADS)

Dias, W. S.; Bertrand, D.; Lyra, M. L.

2017-06-01

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d >4 .

Incompressible Navier-Stokes Solvers in Primative Variables and their Applications to Steady and Unsteady Flow Simulations

NASA Technical Reports Server (NTRS)

Kiris, Cetin C.; Kwak, Dochan; Rogers, Stuart E.

2002-01-01

This paper reviews recent progress made in incompressible Navier-Stokes simulation procedures and their application to problems of engineering interest. Discussions are focused on the methods designed for complex geometry applications in three dimensions, and thus are limited to primitive variable formulation. A summary of efforts in flow solver development is given followed by numerical studies of a few example problems of current interest. Both steady and unsteady solution algorithms and their salient features are discussed. Solvers discussed here are based on a structured-grid approach using either a finite -difference or a finite-volume frame work. As a grand-challenge application of these solvers, an unsteady turbopump flow simulation procedure has been developed which utilizes high performance computing platforms. In the paper, the progress toward the complete simulation capability of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of two parallel computing algorithms that have been implemented in the INS3D code. The relative motion of the grid systems for the rotorstator interaction was obtained using overact grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on SCSI Origin 3000 systems at NASA Ames Research Center. The same procedure has been extended to the development of NASA-DeBakey Ventricular Assist Device (VAD) that is based on an axial blood pump. Computational, and clinical analysis of this device are presented.

Sign phase transition in the problem of interfering directed paths

NASA Astrophysics Data System (ADS)

Baldwin, C. L.; Laumann, C. R.; Spivak, B.

2018-01-01

We investigate the statistical properties of interfering directed paths in disordered media. At long distance, the average sign of the sum over paths may tend to zero (sign disordered) or remain finite (sign ordered) depending on dimensionality and the concentration of negative scattering sites x . We show that in two dimensions the sign-ordered phase is unstable even for arbitrarily small x by identifying rare destabilizing events. In three dimensions, we present strong evidence that there is a sign phase transition at a finite xc>0 . These results have consequences for several different physical systems. In two-dimensional insulators at low temperature, the variable-range-hopping magnetoresistance is always negative, while in three dimensions, it changes sign at the point of the sign phase transition. We also show that in the sign-disordered regime a small magnetic field may enhance superconductivity in a random system of D -wave superconducting grains embedded in a metallic matrix. Finally, the existence of the sign phase transition in three dimensions implies new features in the spin-glass phase diagram at high temperature.

Analysis of the mechanical stresses on a squirrel cage induction motor by the finite element method

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

Jun, C.H.; Nicolas, A.

1999-05-01

The mechanical deformations and stresses have been analyzed by the Finite Element Method (FEM) in 3 dimensions on the rotor bars of a small squirrel cage induction motor. The authors considered the magnetic forces and the centrifugal forces as sources which provoked the deformations and stresses on the rotor bars. The mechanical calculations have been performed after doing the electromagnetic Finite Element modeling on the motor in steady states with various slip conditions.

Analysis of the transient behavior of rubbing components

NASA Technical Reports Server (NTRS)

Quezdou, M. B.; Mullen, R. L.

1986-01-01

Finite element equations are developed for studying deformations and temperatures resulting from frictional heating in sliding system. The formulation is done for linear steady state motion in two dimensions. The equations include the effect of the velocity on the moving components. This gives spurious oscillations in their solutions by Galerkin finite element methods. A method called streamline upwind scheme is used to try to deal with this deficiency. The finite element program is then used to investigate the friction of heating in gas path seal.

Entanglement sharing via qudit channels: Nonmaximally entangled states may be necessary for one-shot optimal singlet fraction and negativity

NASA Astrophysics Data System (ADS)

Pal, Rajarshi; Bandyopadhyay, Somshubhro

2018-03-01

We consider the problem of establishing entangled states of optimal singlet fraction and negativity between two remote parties for every use of a noisy quantum channel and trace-preserving local operations and classical communication (LOCC) under the assumption that the parties do not share prior correlations. We show that for a family of quantum channels in every finite dimension d ≥3 , one-shot optimal singlet fraction and entanglement negativity are attained only with appropriate nonmaximally entangled states. A consequence of our results is that the ordering of entangled states in all finite dimensions may not be preserved under trace-preserving LOCC.

Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element

NASA Technical Reports Server (NTRS)

Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.

2010-01-01

Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.

On special Lie algebras having a faithful module with Krull dimension

NASA Astrophysics Data System (ADS)

Pikhtilkova, O. A.; Pikhtilkov, S. A.

2017-02-01

For special Lie algebras we prove an analogue of Markov's theorem on {PI}-algebras having a faithful module with Krull dimension: the solubility of the prime radical. We give an example of a semiprime Lie algebra that has a faithful module with Krull dimension but cannot be represented as a subdirect product of finitely many prime Lie algebras. We prove a criterion for a semiprime Lie algebra to be representable as such a subdirect product.

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.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Random-field-induced disordering mechanism in a disordered ferromagnet: Between the Imry-Ma and the standard disordering mechanism

NASA Astrophysics Data System (ADS)

Andresen, Juan Carlos; Katzgraber, Helmut G.; Schechter, Moshe

2017-12-01

Random fields disorder Ising ferromagnets by aligning single spins in the direction of the random field in three space dimensions, or by flipping large ferromagnetic domains at dimensions two and below. While the former requires random fields of typical magnitude similar to the interaction strength, the latter Imry-Ma mechanism only requires infinitesimal random fields. Recently, it has been shown that for dilute anisotropic dipolar systems a third mechanism exists, where the ferromagnetic phase is disordered by finite-size glassy domains at a random field of finite magnitude that is considerably smaller than the typical interaction strength. Using large-scale Monte Carlo simulations and zero-temperature numerical approaches, we show that this mechanism applies to disordered ferromagnets with competing short-range ferromagnetic and antiferromagnetic interactions, suggesting its generality in ferromagnetic systems with competing interactions and an underlying spin-glass phase. A finite-size-scaling analysis of the magnetization distribution suggests that the transition might be first order.

Effective dimension reduction for sparse functional data

PubMed Central

YAO, F.; LEI, E.; WU, Y.

2015-01-01

Summary We propose a method of effective dimension reduction for functional data, emphasizing the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects. The proposed method borrows strength across the entire sample and provides a way to characterize the effective dimension reduction space, via functional cumulative slicing. Our theoretical study reveals a bias-variance trade-off associated with the regularizing truncation and decaying structures of the predictor process and the effective dimension reduction space. A simulation study and an application illustrate the superior finite-sample performance of the method. PMID:26566293

Random walks on combs

NASA Astrophysics Data System (ADS)

Durhuus, Bergfinnur; Jonsson, Thordur; Wheater, John F.

2006-02-01

We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds, we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.

On the Hausdorff dimension faithfulness connected with Q_{\\infty} -expansion

NASA Astrophysics Data System (ADS)

Liu, Jia; Zhang, Zhenliang

2017-06-01

In this paper, we show that, the family of all possible unions of finitely many consecutive cylinders of the same rank of a Q∞ -expansion is faithful for the Hausdorff dimension calculations. Applying this result, we give a necessary and sufficient condition for the family of all cylinders of the Q∞ -expansion to be faithful for Hausdorff dimension calculation on the unit interval. This answers an open problem mentioned in Albeverio et al (2016 Math. Nachr. at press (https//:doi.org/10.1002/mana.201500471)).

SPIREs: A Finite-Difference Frequency-Domain electromagnetic solver for inhomogeneous magnetized plasma cylinders

NASA Astrophysics Data System (ADS)

Melazzi, D.; Curreli, D.; Manente, M.; Carlsson, J.; Pavarin, D.

2012-06-01

We present SPIREs (plaSma Padova Inhomogeneous Radial Electromagnetic solver), a Finite-Difference Frequency-Domain (FDFD) electromagnetic solver in one dimension for the rapid calculation of the electromagnetic fields and the deposited power of a large variety of cylindrical plasma problems. The two Maxwell wave equations have been discretized using a staggered Yee mesh along the radial direction of the cylinder, and Fourier transformed along the other two dimensions and in time. By means of this kind of discretization, we have found that mode-coupling of fast and slow branches can be fully resolved without singularity issues that flawed other well-established methods in the past. Fields are forced by an antenna placed at a given distance from the plasma. The plasma can be inhomogeneous, finite-temperature, collisional, magnetized and multi-species. Finite-temperature Maxwellian effects, comprising Landau and cyclotron damping, have been included by means of the plasma Z dispersion function. Finite Larmor radius effects have been neglected. Radial variations of the plasma parameters are taken into account, thus extending the range of applications to a large variety of inhomogeneous plasma systems. The method proved to be fast and reliable, with accuracy depending on the spatial grid size. Two physical examples are reported: fields in a forced vacuum waveguide with the antenna inside, and forced plasma oscillations in the helicon radiofrequency range.

Natural frequencies of thin rectangular plates clamped on contour using the Finite Element Method

NASA Astrophysics Data System (ADS)

(Barboni Haţiegan, L.; Haţiegan, C.; Gillich, G. R.; Hamat, C. O.; Vasile, O.; Stroia, M. D.

2018-01-01

This paper presents the determining of natural frequencies of plates without and with damages using the finite element method of SolidWorks program. The first thirty natural frequencies obtained for thin rectangular rectangular plates clamped on contour without and with central damages a for different dimensions. The relative variation of natural frequency was determined and the obtained results by the finite element method (FEM) respectively relative variation of natural frequency, were graphically represented according to their vibration natural modes. Finally, the obtained results were compared.

SUTRA (Saturated-Unsaturated Transport). A Finite-Element Simulation Model for Saturated-Unsaturated, Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically-Reactive Single-Species Solute Transport.

DTIC Science & Technology

1984-12-30

as three dimensional, when the assumption is made that all SUTRA parameters and coefficients have a constant value in the third space direction. A...finite element. The type of element employed by SUTRA for two-dimensional simulation is a quadrilateral which has a finite thickness in the third ... space dimension. This type of a quad- rilateral element and a typical two-dimensional mesh is shown in Figure 3.1. - All twelve edges of the two

Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Démery, Vincent; Rosso, Alberto

2018-06-01

The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force . At small disorder, we unveil an intermediary linear regime for characterized by the renormalized mobility . Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

A corrected model for static and dynamic electromechanical instability of narrow nanotweezers: Incorporation of size effect, surface layer and finite dimensions

NASA Astrophysics Data System (ADS)

Koochi, Ali; Hosseini-Toudeshky, Hossein; Abadyan, Mohamadreza

2018-03-01

Herein, a corrected theoretical model is proposed for modeling the static and dynamic behavior of electrostatically actuated narrow-width nanotweezers considering the correction due to finite dimensions, size dependency and surface energy. The Gurtin-Murdoch surface elasticity in conjunction with the modified couple stress theory is employed to consider the coupling effect of surface stresses and size phenomenon. In addition, the model accounts for the external force corrections by incorporating the impact of narrow width on the distribution of Casimir attraction, van der Waals (vdW) force and the fringing field effect. The proposed model is beneficial for the precise modeling of the narrow nanotweezers in nano-scale.

Radiative corrections to masses and couplings in universal extra dimensions

NASA Astrophysics Data System (ADS)

Freitas, Ayres; Kong, Kyoungchul; Wiegand, Daniel

2018-03-01

Models with an orbifolded universal extra dimension receive important loop-induced corrections to the masses and couplings of Kaluza-Klein (KK) particles. The dominant contributions stem from so-called boundary terms which violate KK number. Previously, only the parts of these boundary terms proportional to ln(Λ R) have been computed, where R is the radius of the extra dimension and Λ is cut-off scale. However, for typical values of Λ R ˜ 10 · · · 50, the logarithms are not particularly large and non-logarithmic contributions may be numerically important. In this paper, these remaining finite terms are computed and their phenomenological impact is discussed. It is shown that the finite terms have a significant impact on the KK mass spectrum. Furthermore, one finds new KK-number violating interactions that do not depend on ln(Λ R) but nevertheless are non-zero. These lead to new production and decay channels for level-2 KK particles at colliders.

Determination of Fracture Parameters for Multiple Cracks of Laminated Composite Finite Plate

NASA Astrophysics Data System (ADS)

Srivastava, Amit Kumar; Arora, P. K.; Srivastava, Sharad Chandra; Kumar, Harish; Lohumi, M. K.

2018-04-01

A predictive method for estimation of stress state at zone of crack tip and assessment of remaining component lifetime depend on the stress intensity factor (SIF). This paper discusses the numerical approach for prediction of first ply failure load (FL), progressive failure load, SIF and critical SIF for multiple cracks configurations of laminated composite finite plate using finite element method (FEM). The Hashin and Chang failure criterion are incorporated in ABAQUS using subroutine approach user defined field variables (USDFLD) for prediction of progressive fracture response of laminated composite finite plate, which is not directly available in the software. A tensile experiment on laminated composite finite plate with stress concentration is performed to validate the numerically predicted subroutine results, shows excellent agreement. The typical results are presented to examine effect of changing the crack tip distance (S), crack offset distance (H), and stacking fiber angle (θ) on FL, and SIF .

Accuracy of finite-difference modeling of seismic waves : Simulation versus laboratory measurements

NASA Astrophysics Data System (ADS)

Arntsen, B.

2017-12-01

The finite-difference technique for numerical modeling of seismic waves is still important and for some areas extensively used.For exploration purposes is finite-difference simulation at the core of both traditional imaging techniques such as reverse-time migration and more elaborate Full-Waveform Inversion techniques.The accuracy and fidelity of finite-difference simulation of seismic waves are hard to quantify and meaningfully error analysis is really onlyeasily available for simplistic media. A possible alternative to theoretical error analysis is provided by comparing finite-difference simulated data with laboratory data created using a scale model. The advantage of this approach is the accurate knowledge of the model, within measurement precision, and the location of sources and receivers.We use a model made of PVC immersed in water and containing horizontal and tilted interfaces together with several spherical objects to generateultrasonic pressure reflection measurements. The physical dimensions of the model is of the order of a meter, which after scaling represents a model with dimensions of the order of 10 kilometer and frequencies in the range of one to thirty hertz.We find that for plane horizontal interfaces the laboratory data can be reproduced by the finite-difference scheme with relatively small error, but for steeply tilted interfaces the error increases. For spherical interfaces the discrepancy between laboratory data and simulated data is sometimes much more severe, to the extent that it is not possible to simulate reflections from parts of highly curved bodies. The results are important in view of the fact that finite-difference modeling is often at the core of imaging and inversion algorithms tackling complicatedgeological areas with highly curved interfaces.

Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media

NASA Astrophysics Data System (ADS)

Russian, Anna; Dentz, Marco; Gouze, Philippe

2017-08-01

Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency Rn, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q ≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.

Finite Density Condensation and Scattering Data: A Study in ϕ4 Lattice Field Theory

NASA Astrophysics Data System (ADS)

Gattringer, Christof; Giuliani, Mario; Orasch, Oliver

2018-06-01

We study the quantum field theory of a charged ϕ4 field in lattice regularization at finite density and low temperature in 2 and 4 dimensions with the goal of analyzing the connection of condensation phenomena to scattering data in a nonperturbative way. The sign problem of the theory at nonzero chemical potential μ is overcome by using a worldline representation for the Monte Carlo simulation. At low temperature we study the particle number as a function of μ and observe the steps for 1-, 2-, and 3-particle condensation. We determine the corresponding critical values μncrit , n =1 , 2, 3 and analyze their dependence on the spatial extent L of the lattice. Linear combinations of the μncrit give the interaction energies in the 2- and 3-particle sectors and their dependence on L is related to scattering data by Lüscher's formula and its generalizations to three particles. For two dimensions we determine the scattering phase shift and for four dimensions the scattering length. We cross-check our results with a determination of the mass and the 2- and 3-particle energies from conventional 2-, 4-, and 6-point correlators at zero chemical potential. The letter demonstrates that the physics of condensation at finite density and low temperature is closely related to scattering data of a quantum field theory.

Enabling Quantitative Optical Imaging for In-die-capable Critical Dimension Targets

PubMed Central

Barnes, B.M.; Henn, M.-A.; Sohn, M. Y.; Zhou, H.; Silver, R. M.

2017-01-01

Dimensional scaling trends will eventually bring semiconductor critical dimensions (CDs) down to only a few atoms in width. New optical techniques are required to address the measurement and variability for these CDs using sufficiently small in-die metrology targets. Recently, Qin et al. [Light Sci Appl, 5, e16038 (2016)] demonstrated quantitative model-based measurements of finite sets of lines with features as small as 16 nm using 450 nm wavelength light. This paper uses simulation studies, augmented with experiments at 193 nm wavelength, to adapt and optimize the finite sets of features that work as in-die-capable metrology targets with minimal increases in parametric uncertainty. A finite element based solver for time-harmonic Maxwell's equations yields two- and three-dimensional simulations of the electromagnetic scattering for optimizing the design of such targets as functions of reduced line lengths, fewer number of lines, fewer focal positions, smaller critical dimensions, and shorter illumination wavelength. Metrology targets that exceeded performance requirements are as short as 3 μm for 193 nm light, feature as few as eight lines, and are extensible to sub-10 nm CDs. Target areas measured at 193 nm can be fifteen times smaller in area than current state-of-the-art scatterometry targets described in the literature. This new methodology is demonstrated to be a promising alternative for optical model-based in-die CD metrology. PMID:28757674

Decay of superconducting correlations for gauged electrons in dimensions D ≤ 4

NASA Astrophysics Data System (ADS)

Tada, Yasuhiro; Koma, Tohru

2018-03-01

We study lattice superconductors coupled to gauge fields, such as an attractive Hubbard model in electromagnetic fields, with a standard gauge fixing. We prove upper bounds for a two-point Cooper pair correlation at finite temperatures in spatial dimensions D ≤ 4. The upper bounds decay exponentially in three dimensions and by power law in four dimensions. These imply the absence of the superconducting long-range order for the Cooper pair amplitude as a consequence of fluctuations of the gauge fields. Since our results hold for the gauge fixing Hamiltonian, they cannot be obtained as a corollary of Elitzur's theorem.

From nonfinite to finite 1D arrays of origami tiles.

PubMed

Wu, Tsai Chin; Rahman, Masudur; Norton, Michael L

2014-06-17

CONSPECTUS: DNA based nanotechnology provides a basis for high-resolution fabrication of objects almost without physical size limitations. However, the pathway to large-scale production of large objects is currently unclear. Operationally, one method forward is to use high information content, large building blocks, which can be generated with high yield and reproducibility. Although flat DNA origami naturally invites comparison to pixels in zero, one, and two dimensions and voxels in three dimensions and has provided an excellent mechanism for generating blocks of significant size and complexity and a multitude of shapes, the field is young enough that a single "brick" has not become the standard platform used by the majority of researchers in the field. In this Account, we highlight factors we considered that led to our adoption of a cross-shaped, non-space-filling origami species, designed by Dr. Liu of the Seeman laboratory, as the building block ideal for use in the fabrication of finite one-dimensional arrays. Three approaches that can be employed for uniquely coding origami-origami linkages are presented. Such coding not only provides the energetics for tethering the species but also uniquely designates the relative orientation of the origami building blocks. The strength of the coding approach implemented in our laboratory is demonstrated using examples of oligomers ranging from finite multimers composed of four, six, and eight origami structures to semi-infinite polymers (100mers). Two approaches to finite array design and the series of assembly steps that each requires are discussed. The process of AFM observation for array characterization is presented as a critical case study. For these soft species, the array images do not simply present the solution phase geometry projected onto a two-dimensional surface. There are additional perturbations associated with fluidic forces associated with sample preparation. At this time, reconstruction of the "true" or average solution structures for blocks is more readily achieved using computer models than using direct imaging methods. The development of scalable 1D-origami arrays composed of uniquely addressable components is a logical, if not necessary, step in the evolution of higher order fully addressable structures. Our research into the fabrication of arrays has led us to generate a listing of several important areas of future endeavor. Of high importance is the re-enforcement of the mechanical properties of the building blocks and the organization of multiple arrays on a surface of technological importance. While addressing this short list of barriers to progress will prove challenging, coherent development along each of these lines of inquiry will accelerate the appearance of commercial scale molecular manufacturing.

Revisiting 2D Lattice Based Spin Flip-Flop Ising Model: Magnetic Properties of a Thin Film and Its Temperature Dependence

ERIC Educational Resources Information Center

Singh, Satya Pal

2014-01-01

This paper presents a brief review of Ising's work done in 1925 for one dimensional spin chain with periodic boundary condition. Ising observed that no phase transition occurred at finite temperature in one dimension. He erroneously generalized his views in higher dimensions but that was not true. In 1941 Kramer and Wannier obtained…

Deposition and growth of domains in one dimension

NASA Astrophysics Data System (ADS)

Rodgers, G. J.; Tavassoli, Z.

1998-09-01

A model of deposition and growth in one dimension is studied in which finite sized domains are deposited by the random sequential adsorption process. The domains then grow with a time dependent growth rate. When the initial deposited domains are monomers and dimers the coverage is found exactly for a number of different growth rates. A continuum version of this model is also considered.

HEMP 3D: A finite difference program for calculating elastic-plastic flow, appendix B

NASA Astrophysics Data System (ADS)

Wilkins, Mark L.

1993-05-01

The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations listed below are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time.

High speed inviscid compressible flow by the finite element method

NASA Technical Reports Server (NTRS)

Zienkiewicz, O. C.; Loehner, R.; Morgan, K.

1984-01-01

The finite element method and an explicit time stepping algorithm which is based on Taylor-Galerkin schemes with an appropriate artificial viscosity is combined with an automatic mesh refinement process which is designed to produce accurate steady state solutions to problems of inviscid compressible flow in two dimensions. The results of two test problems are included which demonstrate the excellent performance characteristics of the proposed procedures.

Errors due to the truncation of the computational domain in static three-dimensional electrical impedance tomography.

PubMed

Vauhkonen, P J; Vauhkonen, M; Kaipio, J P

2000-02-01

In electrical impedance tomography (EIT), an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. The currents spread out in three dimensions and therefore off-plane structures have a significant effect on the reconstructed images. A question arises: how far from the current carrying electrodes should the discretized model of the object be extended? If the model is truncated too near the electrodes, errors are produced in the reconstructed images. On the other hand if the model is extended very far from the electrodes the computational time may become too long in practice. In this paper the model truncation problem is studied with the extended finite element method. Forward solutions obtained using so-called infinite elements, long finite elements and separable long finite elements are compared to the correct solution. The effects of the truncation of the computational domain on the reconstructed images are also discussed and results from the three-dimensional (3D) sensitivity analysis are given. We show that if the finite element method with ordinary elements is used in static 3D EIT, the dimension of the problem can become fairly large if the errors associated with the domain truncation are to be avoided.

A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)

NASA Astrophysics Data System (ADS)

Brell, Courtney G.

2016-01-01

We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realized with local interactions in {{{R}}}3, we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.

Three-dimension finite-element analyses of multiple electrodes bipolar RF global endometrial ablation

NASA Astrophysics Data System (ADS)

Hu, Tao; Panhao, Tang; Xiao, Jiahua

2015-03-01

Radio-frequency ablation (RFA) is a minimally invasive surgical procedure to thermally ablate the targeted diseased tissue. There have been many finite-element method (FEM) studies of cardiac and hepatic RFA, but hardly find any FEM study on endometrial ablation for abnormal uterine bleeding. In this paper, a FEM model was generated to analyze the temperature distribution of bipolar RF global endometrial ablation with three pairs of bipolar electrodes placed at the perimeter of the uterine cavity. COMSOL was utilized to calculate the RF electric fields and temperature fields by numerically solving the bioheat equation in the triangle uterine cavity range. The 55°C isothermal surfaces show the shape of the ablation dimensions (depth and width), which reasonably matched the experimental results.

Efficiency of encounter-controlled reaction between diffusing reactants in a finite lattice: Non-nearest-neighbor effects

NASA Astrophysics Data System (ADS)

Bentz, Jonathan L.; Kozak, John J.; Nicolis, Gregoire

2005-08-01

The influence of non-nearest-neighbor displacements on the efficiency of diffusion-reaction processes involving one and two mobile diffusing reactants is studied. An exact analytic result is given for dimension d=1 from which, for large lattices, one can recover the asymptotic estimate reported 30 years ago by Lakatos-Lindenberg and Shuler. For dimensions d=2,3 we present numerically exact values for the mean time to reaction, as gauged by the mean walklength before reactive encounter, obtained via the theory of finite Markov processes and supported by Monte Carlo simulations. Qualitatively different results are found between processes occurring on d=1 versus d>1 lattices, and between results obtained assuming nearest-neighbor (only) versus non-nearest-neighbor displacements.

Black hole evolution by spectral methods

NASA Astrophysics Data System (ADS)

Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, Gregory B.

2000-10-01

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast with finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.

Ghost-free, finite, fourth-order D = 3 gravity.

PubMed

Deser, S

2009-09-04

Canonical analysis of a recently proposed linear + quadratic curvature gravity model in D = 3 establishes its pure, irreducibly fourth derivative, quadratic curvature limit as both ghost-free and power-counting UV finite, thereby maximally violating standard folklore. This limit is representative of a generic class whose kinetic terms are conformally invariant in any dimension, but it is unique in simultaneously avoiding the transverse-traceless graviton ghosts plaguing D > 3 quadratic actions as well as double pole propagators in its other variables. While the two-term model is also unitary, its additional mode's second-derivative nature forfeits finiteness.

Un-collided-flux preconditioning for the first order transport equation

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

Rigley, M.; Koebbe, J.; Drumm, C.

2013-07-01

Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

Finite-time stabilization of chaotic gyros based on a homogeneous supertwisting-like algorithm

NASA Astrophysics Data System (ADS)

Khamsuwan, Pitcha; Sangpet, Teerawat; Kuntanapreeda, Suwat

2018-01-01

This paper presents a finite-time stabilization scheme for nonlinear chaotic gyros. The scheme utilizes a supertwisting-like continuous control algorithm for the systems of dimension more than one with a Lipschitz disturbance. The algorithm yields finite-time convergence similar to that produces by discontinuous sliding mode control algorithms. To design the controller, the nonlinearities in the gyro are treated as a disturbance in the system. Thanks to the dissipativeness of chaotic systems, the nonlinearities also possess the Lipschitz property. Numerical results are provided to illustrate the effectiveness of the scheme.

Simulation of wave propagation in three-dimensional random media

NASA Astrophysics Data System (ADS)

Coles, Wm. A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1995-04-01

Quantitative error analyses for the simulation of wave propagation in three-dimensional random media, when narrow angular scattering is assumed, are presented for plane-wave and spherical-wave geometry. This includes the errors that result from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive indices of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared with the spatial spectra of

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

Khodam-Mohammadi, A.; Monshizadeh, M.

We give a review of the existence of Taub-NUT/bolt solutions in Einstein Gauss-Bonnet gravity with the parameter {alpha} in six dimensions. Although the spacetime with base space S{sup 2}xS{sup 2} has a curvature singularity at r=N, which does not admit NUT solutions, we may proceed with the same computations as in the CP{sup 2} case. The investigation of thermodynamics of NUT/bolt solutions in six dimensions is carried out. We compute the finite action, mass, entropy, and temperature of the black hole. Then the validity of the first law of thermodynamics is demonstrated. It is shown that in NUT solutions allmore » thermodynamic quantities for both base spaces are related to each other by substituting {alpha}{sup CP{sup k}}=[(k+1)/k]{alpha}{sup S{sup 2}}{sup xS{sup 2}}{sup x...S{sub k}{sup 2}}. So, no further information is given by investigating NUT solutions in the S{sup 2}xS{sup 2} case. This relation is not true for bolt solutions. A generalization of the thermodynamics of black holes to arbitrary even dimensions is made using a new method based on the Gibbs-Duhem relation and Gibbs free energy for NUT solutions. According to this method, the finite action in Einstein Gauss-Bonnet is obtained by considering the generalized finite action in Einstein gravity with an additional term as a function of {alpha}. Stability analysis is done by investigating the heat capacity and entropy in the allowed range of {alpha}, {lambda}, and N. For NUT solutions in d dimensions, there exists a stable phase at a narrow range of {alpha}. In six-dimensional bolt solutions, the metric is completely stable for B=S{sup 2}xS{sup 2} and is completely unstable for the B=CP{sup 2} case.« less

Maximum likelihood estimation of finite mixture model for economic data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-06-01

Finite mixture model is a mixture model with finite-dimension. This models are provides a natural representation of heterogeneity in a finite number of latent classes. In addition, finite mixture models also known as latent class models or unsupervised learning models. Recently, maximum likelihood estimation fitted finite mixture models has greatly drawn statistician's attention. The main reason is because maximum likelihood estimation is a powerful statistical method which provides consistent findings as the sample sizes increases to infinity. Thus, the application of maximum likelihood estimation is used to fit finite mixture model in the present paper in order to explore the relationship between nonlinear economic data. In this paper, a two-component normal mixture model is fitted by maximum likelihood estimation in order to investigate the relationship among stock market price and rubber price for sampled countries. Results described that there is a negative effect among rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia.

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

Representations of the Extended Poincare Superalgebras in Four Dimensions

NASA Astrophysics Data System (ADS)

Griffis, John D.

Eugene Wigner used the Poincare group to induce representations from the fundamental internal space-time symmetries of (special) relativistic quantum particles. Wigner's students spent considerable amount of time translating passages of this paper into more detailed and accessible papers and books. In 1975, R. Haag et al. investigated the possible extensions of the symmetries of relativistic quantum particles. They showed that the only consistent (super)symmetric extensions to the standard model of physics are obtained by using super charges to generate the odd part of a Lie superalgebra whose even part is generated by the Poincare group; this theory has become known as supersymmetry. In this paper, R. Haag et al. used a notation called supermultiplets to give the dimension of a representation and its multiplicity; this notation is described mathematically in chapter 5 of this thesis. By 1980 S. Ferrara et al. began classifying the representations of these algebras for dimensions greater than four, and in 1986 Strathdee published considerable work listing some representations for the Poincare superalgebra in any finite dimension. This work has been continued to date. We found the work of S. Ferrara et al. to be essential to our understanding extended supersymmetries. However, this paper was written using imprecise language meant for physicists, so it was far from trivial to understand the mathematical interpretation of this work. In this thesis, we provide a "translation" of the previous results (along with some other literature on the Extended Poincare Superalgebras) into a rigorous mathematical setting, which makes the subject more accessible to a larger audience. Having a mathematical model allows us to give explicit results and detailed proofs. Further, this model allows us to see beyond just the physical interpretation and it allows investigation by a purely mathematically adept audience. Our work was motivated by a paper written in 2012 by M. Chaichian et al, which classified all of the unitary, irreducible representations of the extended Poincare superalgebra in three dimensions. We consider only the four dimensional case, which is of interest to physicists working on quantum supergravity models without cosmological constant, and we provide explicit branching rules for the invariant subgroups corresponding to the most physically relevant symmetries of the irreducible representations of the Extended Poincare Superalgebra in four dimensions. However, it is possible to further generalize this work into any finite dimension. Such work would classify all possible finitely extended supersymmetric models.

A Novel Multiscale Physics Based Progressive Failure Methodology for Laminated Composite Structures

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.; Bednarcyk, Brett A.; Collier, Craig S.; Yarrington, Phillip W.

2008-01-01

A variable fidelity, multiscale, physics based finite element procedure for predicting progressive damage and failure of laminated continuous fiber reinforced composites is introduced. At every integration point in a finite element model, progressive damage is accounted for at the lamina-level using thermodynamically based Schapery Theory. Separate failure criteria are applied at either the global-scale or the microscale in two different FEM models. A micromechanics model, the Generalized Method of Cells, is used to evaluate failure criteria at the micro-level. The stress-strain behavior and observed failure mechanisms are compared with experimental results for both models.

Comparison of Damage Path Predictions for Composite Laminates by Explicit and Standard Finite Element Analysis Tools

NASA Technical Reports Server (NTRS)

Bogert, Philip B.; Satyanarayana, Arunkumar; Chunchu, Prasad B.

2006-01-01

Splitting, ultimate failure load and the damage path in center notched composite specimens subjected to in-plane tension loading are predicted using progressive failure analysis methodology. A 2-D Hashin-Rotem failure criterion is used in determining intra-laminar fiber and matrix failures. This progressive failure methodology has been implemented in the Abaqus/Explicit and Abaqus/Standard finite element codes through user written subroutines "VUMAT" and "USDFLD" respectively. A 2-D finite element model is used for predicting the intra-laminar damages. Analysis results obtained from the Abaqus/Explicit and Abaqus/Standard code show good agreement with experimental results. The importance of modeling delamination in progressive failure analysis methodology is recognized for future studies. The use of an explicit integration dynamics code for simple specimen geometry and static loading establishes a foundation for future analyses where complex loading and nonlinear dynamic interactions of damage and structure will necessitate it.

Accumulation of planets into the proto-planetary cloud as a process of occurring an amount of characteristic scales into the nonlinear self organized dynamical systems

NASA Astrophysics Data System (ADS)

Professor Khachay, Yurie

2015-04-01

Two characteristic times are significant for evolution the interior of the homogeneous proto-planetary cloud: the time of bodies free fall towards the clouds mass center and the time of sound distribution through the cloud. With the beginning of proto-planetary disk fragmentation and accumulation of the proto-planets from the bodies and particles there are formed matter content heterogeneities of the finite dimension, heterogeneities of temperature, density and values of kinetic coefficients. The system became more and more complicated with interior interconnections. By the growing of the bodies the difference between the values of the characteristic times and dimensions become larger. The dynamical evolution of the system we could observe with use the numerical modeling of the Earth and Moon formation into the 3-D model [1,2]. The fact, that the linear dimensions of the objects during the accumulation process change from the centimeter and meter dimensions to some thousands of kilometers significantly prevent the mathematical description of these processes. The corresponding values of the no dimensional similarity criterions, which are included into the systems of differential equations, which describe the proto-planetary growing, the conditions for entropy and mass on the growing surface, the equations of the impulse balance, energy and mass into the interior parts of the planet change on an orders of values. Therefore we used very detailed space and time grids for solution the problem using the method of finite differences. The additional complications occur according to necessity to take into account the nonlinear dependence of matter viscosity from the temperature, pressure and chemical matter content. At last we took into account the principal random distribution of heterogeneities, stipulated by bodies and particles falling. Only progression towards that direction and constructing corresponding systems of observation and interpretation allow to hope receiving more and more realistic models of self organizing structures and to understand the laws of their reconstruction during the complicated process of planetary accumulation. The work is fulfilled by partly support of RFBR (grant N13-05-00138). References. 1. Y. Khachay , V. Anfilogov , and A. Antipin (2014) Numerical Results of 3-D Modeling of Moon Accumulation // Geophysical Research Abstracts, Vol. 16, EGU2014-1011 2. Y.Khachay, A.Antipin and V.Anfilogov (2014)Numerical modeling of temperature distribution on the stage of Earth's accumulation in a frame of 3-D model and peculiarities of its initial minerageny. Ural geophysical bulletin 1: 81-85.

On inducing finite dimensional physical field representations for massless particles in even dimensions

NASA Technical Reports Server (NTRS)

Bhansali, Vineer

1993-01-01

Assuming trivial action of Euclidean translations, the method of induced representations is used to derive a correspondence between massless field representations transforming under the full generalized even dimensional Lorentz group, and highest weight states of the relevant little group. This gives a connection between 'helicity' and 'chirality' in all dimensions. Restrictions on 'gauge independent' representations for physical particles that this induction imposes are also stated.

Topological order, entanglement, and quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Mazáč, Dalimil; Hamma, Alioscia

2012-09-01

We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the confinement-deconfinement transitions in the corresponding Z2 gauge theories. This implies that the thermal stability of topological entropy corresponds to the stability of quantum (classical) memory. The implications for the understanding of ergodicity breaking in topological phases are discussed.

Critical behavior and dimension crossover of pion superfluidity

NASA Astrophysics Data System (ADS)

Wang, Ziyue; Zhuang, Pengfei

2016-09-01

We investigate the critical behavior of pion superfluidity in the framework of the functional renormalization group (FRG). By solving the flow equations in the SU(2) linear sigma model at finite temperature and isospin density, and making comparison with the fixed point analysis of a general O (N ) system with continuous dimension, we find that the pion superfluidity is a second order phase transition subject to an O (2 ) universality class with a dimension crossover from dc=4 to dc=3 . This phenomenon provides a concrete example of dimension reduction in thermal field theory. The large-N expansion gives a temperature independent critical exponent β and agrees with the FRG result only at zero temperature.

Pelvic modelling and the comparison between plate position for double pelvic osteotomy using artificial cancellous bone and finite element analysis.

PubMed

McCartney, William; MacDonald, Bryan; Ober, Ciprian Andrei; Lostado-Lorza, Rubén; Gómez, Fátima Somovilla

2018-03-20

Finite element analysis was used to compare fixation methods for double pelvic osteotomy (DPO). Using 3D scanning a stereolithography (stl) image was produced of a canine pelvis and this was subsequently refined in computer aided design (CAD). Using the CAD files, the images were imported in MSC Marc software to produce a working finite element (FE) model with 3 dimensional tetrahedral elements with linear shaped functions. The dimensions of a precontoured pelvic osteotomy plate with eight screws and a twisted seven screw straight plate were used to build the 2 fixations implants for the FE models. An equivalent load of 300 N was applied progressively on all FE models in order to facilitate its convergence. The load was applied in a distributed manner on the femur-hip joint contact area in order to simulate the actual behavior of the joint. The aim of the present study was to analyze the difference in stiffness and behavior under loading between a lateral vs ventral plate fixation, with unlocked screws and different gap scenarios, for stabilization of a pelvic osteotomy using finite element analysis. From both configurations the maximum displacement of the ventral plate with 7 screws without gap had a value of 1.988 mm, while in the DPO plate had a maximum displacement of 2.191 mm. The load applied for each of the different configurations studied when a gap of 1° was considered and also when a condition of no gap was considered. The ventral plate was stiffer than the lateral plate when a gap was not present. When the gap was closed in the ventral plate, the stiffness increased until a point that remained constant. Ventral plate fixation can be as or more stiff as lateral plate fixation and provides flexible fixation. This behavior should reduce screw loosening. Using ventral plate fixation is recommended to reduce screw loosening or failure.

Exploring the Relationship between the Three Dimensions of Self-Authorship

ERIC Educational Resources Information Center

Pizzolato, Jane Elizabeth; Olson, Avery B.

2016-01-01

Through a year-long study of welfare-to-work students in the community college CalWORKs program, we investigated what self-authorship development looks like by examining developmental progress, and whether there are patterns in development along the three dimensions of self-authorship. Findings demonstrate progress toward self-authorship, but…

Single-Track Melt-Pool Measurements and Microstructures in Inconel 625

NASA Astrophysics Data System (ADS)

Ghosh, Supriyo; Ma, Li; Levine, Lyle E.; Ricker, Richard E.; Stoudt, Mark R.; Heigel, Jarred C.; Guyer, Jonathan E.

2018-06-01

We use single-track laser melting experiments and simulations on Inconel 625 to estimate the dimensions and microstructure of the resulting melt pool. Our work is based on a design-of-experiments approach which uses multiple laser power and scan speed combinations. Single-track experiments generated melt pools of certain dimensions that showed reasonable agreement with our finite-element calculations. Phase-field simulations were used to predict the size and segregation of the cellular microstructure that formed along the melt-pool boundaries for the solidification conditions that changed as a function of melt-pool dimensions.

Single-Track Melt-Pool Measurements and Microstructures in Inconel 625

NASA Astrophysics Data System (ADS)

Ghosh, Supriyo; Ma, Li; Levine, Lyle E.; Ricker, Richard E.; Stoudt, Mark R.; Heigel, Jarred C.; Guyer, Jonathan E.

2018-02-01

We use single-track laser melting experiments and simulations on Inconel 625 to estimate the dimensions and microstructure of the resulting melt pool. Our work is based on a design-of-experiments approach which uses multiple laser power and scan speed combinations. Single-track experiments generated melt pools of certain dimensions that showed reasonable agreement with our finite-element calculations. Phase-field simulations were used to predict the size and segregation of the cellular microstructure that formed along the melt-pool boundaries for the solidification conditions that changed as a function of melt-pool dimensions.

Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics

NASA Astrophysics Data System (ADS)

Mera, Bruno; Vlachou, Chrysoula; Paunković, Nikola; Vieira, Vítor R.; Viyuela, Oscar

2018-03-01

We study finite-temperature dynamical quantum phase transitions (DQPTs) by means of the fidelity and the interferometric Loschmidt echo (LE) induced metrics. We analyze the associated dynamical susceptibilities (Riemannian metrics), and derive analytic expressions for the case of two-band Hamiltonians. At zero temperature, the two quantities are identical, nevertheless, at finite temperatures they behave very differently. Using the fidelity LE, the zero-temperature DQPTs are gradually washed away with temperature, while the interferometric counterpart exhibits finite-temperature phase transitions. We analyze the physical differences between the two finite-temperature LE generalizations, and argue that, while the interferometric one is more sensitive and can therefore provide more information when applied to genuine quantum (microscopic) systems, when analyzing many-body macroscopic systems, the fidelity-based counterpart is a more suitable quantity to study. Finally, we apply the previous results to two representative models of topological insulators in one and two dimensions.

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

Finite-size Scaling of the Density of States in Photonic Band Gap Crystals

NASA Astrophysics Data System (ADS)

Hasan, Shakeeb Bin; Mosk, Allard P.; Vos, Willem L.; Lagendijk, Ad

2018-06-01

The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size L of a crystal, how fast does the DOS approach the infinite-crystal limit? We present a theory for finite crystals that includes Bloch-mode broadening due to the presence of crystal boundaries. Our results demonstrate that the DOS for frequencies inside a band gap has a 1 /L scale dependence for crystals in one, two and three dimensions.

Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system

NASA Technical Reports Server (NTRS)

Giles, G. L.; Rogers, J. L., Jr.

1982-01-01

The methodology used to implement structural sensitivity calculations into a major, general-purpose finite-element analysis system (SPAR) is described. This implementation includes a generalized method for specifying element cross-sectional dimensions as design variables that can be used in analytically calculating derivatives of output quantities from static stress, vibration, and buckling analyses for both membrane and bending elements. Limited sample results for static displacements and stresses are presented to indicate the advantages of analytically calculating response derivatives compared to finite difference methods. Continuing developments to implement these procedures into an enhanced version of SPAR are also discussed.

Evaluation of Progressive Failure Analysis and Modeling of Impact Damage in Composite Pressure Vessels

NASA Technical Reports Server (NTRS)

Sanchez, Christopher M.

2011-01-01

NASA White Sands Test Facility (WSTF) is leading an evaluation effort in advanced destructive and nondestructive testing of composite pressure vessels and structures. WSTF is using progressive finite element analysis methods for test design and for confirmation of composite pressure vessel performance. Using composite finite element analysis models and failure theories tested in the World-Wide Failure Exercise, WSTF is able to estimate the static strength of composite pressure vessels. Additionally, test and evaluation on composites that have been impact damaged is in progress so that models can be developed to estimate damage tolerance and the degradation in static strength.

Toric-boson model: Toward a topological quantum memory at finite temperature

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Castelnovo, Claudio; Chamon, Claudio

2009-06-01

We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the intervention from the external world, that is, without error correction. We study the toric code in two dimensions with an additional bosonic field that couples to the defects, in the presence of a generic environment at finite temperature: the toric-boson model. Although the coupling constants for the bare model are not finite in the thermodynamic limit, the model has a finite spectrum. We show that in the topological phase, there is a finite temperature below which open strings are confined and therefore the lifetime of the memory can be made arbitrarily (polynomially) long in system size. The interaction with the bosonic field yields a long-range attractive force between the end points of open strings but leaves closed strings and topological order intact.

Theory of a Nearly Two-Dimensional Dipolar Bose Gas

DTIC Science & Technology

2016-05-11

temperatures, and when roton excitations are present. Further, BECs in nearly 2D geometries take the form of quasi -condensates, or BECs with finite spatial...extent. Quasi -condensates behave like BECs on shorter length scales, but not on longer length scales. The project incorporates the presence of a quasi ... Quasi -Condensate 23 J. Superfluidity 25 III. Results 26 A. Three Dimensions with Contact Interactions 26 B. Two Dimensions with Contact Interactions

Asymptotic Charges at Null Infinity in Any Dimension

NASA Astrophysics Data System (ADS)

Campoleoni, Andrea; Francia, Dario; Heissenberg, Carlo

2018-03-01

We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time dimension, both even and odd, greater than or equal to three. After discussing non-linear Yang-Mills theory and revisiting linearised gravity, our investigation extends to cover the infrared behaviour of bosonic massless quanta of any spin.

Convergence of finite difference transient response computations for thin shells.

NASA Technical Reports Server (NTRS)

Sobel, L. H.; Geers, T. L.

1973-01-01

Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.

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

Analysis of transient, linear wave propagation in shells by the finite difference method

NASA Technical Reports Server (NTRS)

Geers, T. L.; Sobel, L. H.

1971-01-01

The applicability of the finite difference method to propagation problems in shells, and the response of a cylindrical shell with cutouts to both longitudinal and radial transient excitations are investigated. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. The short wave length limitations of thin shell theory create significant convergence difficulties may often be overcome through proper selection of finite difference mesh dimensions and temporal or spatial smoothing of the excitation. Cutouts produce moderate changes in early and intermediate time response of a cylindrical shell to axisymmetric pulse loads applied at one end. The cutouts may facilitate the undesirable late-time transfer of load-injected extensional energy into nonaxisymmetric flexural response.

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.

Analysis of three-dimensional-cavity-backed aperture antennas using a Combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction technique

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.; Cockrell, C. R.; Beck, F. B.

1995-01-01

A combined finite element method (FEM) and method of moments (MoM) technique is presented to analyze the radiation characteristics of a cavity-fed aperture in three dimensions. Generalized feed modeling has been done using the modal expansion of fields in the feed structure. Numerical results for some feeding structures such as a rectangular waveguide, circular waveguide, and coaxial line are presented. The method also uses the geometrical theory of diffraction (GTD) to predict the effect of a finite ground plane on radiation characteristics. Input admittance calculations for open radiating structures such as a rectangular waveguide, a circular waveguide, and a coaxial line are shown. Numerical data for a coaxial-fed cavity with finite ground plane are verified with experimental data.

Health-related quality of life impact in a randomised phase III study of the combination of dabrafenib and trametinib versus dabrafenib monotherapy in patients with BRAF V600 metastatic melanoma.

PubMed

Schadendorf, Dirk; Amonkar, Mayur M; Stroyakovskiy, Daniil; Levchenko, Evgeny; Gogas, Helen; de Braud, Filippo; Grob, Jean-Jacques; Bondarenko, Igor; Garbe, Claus; Lebbe, Celeste; Larkin, James; Chiarion-Sileni, Vanna; Millward, Michael; Arance, Ana; Mandalà, Mario; Flaherty, Keith T; Nathan, Paul; Ribas, Antoni; Robert, Caroline; Casey, Michelle; DeMarini, Douglas J; Irani, Jhangir G; Aktan, Gursel; Long, Georgina V

2015-05-01

To present the impact of treatments on health-related quality of life (HRQoL) from the double-blind, randomised phase III COMBI-d study that investigated the combination of dabrafenib and trametinib versus dabrafenib monotherapy in patients with BRAF V600E/K-mutant metastatic melanoma. COMBI-d showed significantly prolonged progression-free survival for the combination. HRQoL was evaluated using the European Organisation for Research and Treatment of Cancer Quality of Life Questionnaire-C30, a generic cancer questionnaire (completed at baseline, during study treatment, at progression and post progression) assessing various dimensions (global health/QoL, functional status, and symptom impact). A mixed-model, repeated-measures analyses of covariance evaluated differences between arms. Questionnaire completion rates were >95% at baseline, >85% to week 40 and >70% at disease progression. Baseline scores across both arms were comparable for all dimensions. Global health dimension scores were significantly better at weeks 8, 16 and 24 for patients receiving the combination during treatment and at progression. The majority of functional dimension scores (physical, social, role, emotional and cognitive functioning) trended in favour of the combination. Pain scores were significantly improved and clinically meaningful (6-13 point difference) for patients receiving the combination for all follow-up assessments versus those receiving dabrafenib monotherapy. For other symptom dimensions (nausea and vomiting, diarrhoea, dyspnoea, and constipation), scores trended in favour of dabrafenib monotherapy. This analysis demonstrates that the combination of dabrafenib and trametinib provides better preservation of HRQoL and pain improvements versus dabrafenib monotherapy while also delaying progression. (Clinicaltrials.gov registration number: NCT01584648). Copyright © 2015 Elsevier Ltd. All rights reserved.

User-defined Material Model for Thermo-mechanical Progressive Failure Analysis

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2008-01-01

Previously a user-defined material model for orthotropic bimodulus materials was developed for linear and nonlinear stress analysis of composite structures using either shell or solid finite elements within a nonlinear finite element analysis tool. Extensions of this user-defined material model to thermo-mechanical progressive failure analysis are described, and the required input data are documented. The extensions include providing for temperature-dependent material properties, archival of the elastic strains, and a thermal strain calculation for materials exhibiting a stress-free temperature.

Simulating Progressive Damage of Notched Composite Laminates with Various Lamination Schemes

NASA Astrophysics Data System (ADS)

Mandal, B.; Chakrabarti, A.

2017-05-01

A three dimensional finite element based progressive damage model has been developed for the failure analysis of notched composite laminates. The material constitutive relations and the progressive damage algorithms are implemented into finite element code ABAQUS using user-defined subroutine UMAT. The existing failure criteria for the composite laminates are modified by including the failure criteria for fiber/matrix shear damage and delamination effects. The proposed numerical model is quite efficient and simple compared to other progressive damage models available in the literature. The efficiency of the present constitutive model and the computational scheme is verified by comparing the simulated results with the results available in the literature. A parametric study has been carried out to investigate the effect of change in lamination scheme on the failure behaviour of notched composite laminates.

On the dimension of complex responses in nonlinear structural vibrations

NASA Astrophysics Data System (ADS)

Wiebe, R.; Spottswood, S. M.

2016-07-01

The ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace, mechanical, and civil engineering. Extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models. Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy. In this context, the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response. Thus, an important step is characterizing the dimensionality of complex nonlinear responses of structures. In this work, the dimensionality of the nonlinear response of a post-buckled beam is investigated. Significant detail is dedicated to carefully introducing the experiment, the verification of a finite element model, and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case. It is shown that with minor modifications, the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap-through, non-snap-through, random, and deterministic loads. The state-space dimension of the nonlinear system in question increased from 2-to-10 as the system response moved from simple, low-level harmonic to chaotic snap-through. Beyond the problem studied herein, the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems, and eventually as a tool for adaptive dimension-reduction in numerical modeling. The results are especially relevant in the aerospace industry for the design of thin structures such as beams, panels, and shells, which are all capable of spatio-temporally complex dynamic responses that are difficult and computationally expensive to model.

Predicting Failure Progression and Failure Loads in Composite Open-Hole Tension Coupons

NASA Technical Reports Server (NTRS)

Arunkumar, Satyanarayana; Przekop, Adam

2010-01-01

Failure types and failure loads in carbon-epoxy [45n/90n/-45n/0n]ms laminate coupons with central circular holes subjected to tensile load are simulated using progressive failure analysis (PFA) methodology. The progressive failure methodology is implemented using VUMAT subroutine within the ABAQUS(TradeMark)/Explicit nonlinear finite element code. The degradation model adopted in the present PFA methodology uses an instantaneous complete stress reduction (COSTR) approach to simulate damage at a material point when failure occurs. In-plane modeling parameters such as element size and shape are held constant in the finite element models, irrespective of laminate thickness and hole size, to predict failure loads and failure progression. Comparison to published test data indicates that this methodology accurately simulates brittle, pull-out and delamination failure types. The sensitivity of the failure progression and the failure load to analytical loading rates and solvers precision is demonstrated.

Kinetics of diffusion-controlled annihilation with sparse initial conditions

DOE PAGES

Ben-Naim, Eli; Krapivsky, Paul

2016-12-16

Here, we study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, both disappear. We also focus on sparse initial conditions where particles occupy a subspace of dimension δ that is embedded in a larger space of dimension d. Furthermore, we find that the co-dimension Δ = d - δ governs the behavior. All particles disappear when the co-dimension is sufficiently small, Δ ≤ 2; otherwise, a finite fraction of particles indefinitely survive. We establish the asymptotic behavior of the probability S(t) that a test particle survives until time t. When the subspace is a line, δ = 1, we find inverse logarithmic decay,more » $$S\\sim {(\\mathrm{ln}t)}^{-1}$$, in three dimensions, and a modified power-law decay, $$S\\sim (\\mathrm{ln}t){t}^{-1/2}$$, in two dimensions. In general, the survival probability decays algebraically when Δ < 2, and there is an inverse logarithmic decay at the critical co-dimension Δ = 2.« less

Universality and tails of long-range interactions in one dimension

NASA Astrophysics Data System (ADS)

Valiente, Manuel; Öhberg, Patrik

2017-07-01

Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional s -wave scattering, we show how generic asymptotic interaction tails can be accounted for in the long-distance limit of scattering wave functions. This is made possible by introducing a generalization of the collisional phase shifts to include space dependence. We show that this distance dependence is universal, in that it does not depend on short-distance details of the interaction. The energy dependence is also universal, and is fully determined by the asymptotic tails of the two-body potential. As an important application of our findings, we describe how to eliminate finite-size effects with long-range potentials in the calculation of scattering phase shifts from exact diagonalization. We show that even with moderately small system sizes it is possible to accurately extract phase shifts that would otherwise be plagued with finite-size errors. We also consider multichannel scattering, focusing on the estimation of open channel asymptotic interaction strengths via finite-size analysis.

The experimental-theoretical model of the jet HF induction discharge of atmospheric pressure

NASA Astrophysics Data System (ADS)

Gainullin, R.; Kirpichnikov, A.

2017-11-01

The paper considers theexperimental-theoretical model devised to determine the regularities of the quasi-stationary electromagnetic field structure of the HFI discharge burning in the inductor of finite dimensions at atmospheric pressure.

The effect of grid transparency and finite collector size on determining ion temperature and density by the retarding potential analyzer

NASA Technical Reports Server (NTRS)

Troy, B. E., Jr.; Maier, E. J.

1973-01-01

The analysis of ion data from retarding potential analyzers (RPA's) is generally done under the planar approximation, which assumes that the grid transparency is constant with angle of incidence and that all ions reaching the plane of the collectors are collected. These approximations are not valid for situations in which the ion thermal velocity is comparable to the vehicle velocity, causing ions to enter the RPA with high average transverse velocity. To investigate these effects, the current-voltage curves for H+ at 4000 K were calculated, taking into account the finite collector size and the variation of grid transparency with angle. These curves are then analyzed under the planar approximation. The results show that only small errors in temperature and density are introduced for an RPA with typical dimensions; and that even when the density error is substantial for non-typical dimensions, the temperature error remains minimal.

Generalized Knudsen Number for Unsteady Fluid Flow.

PubMed

Kara, V; Yakhot, V; Ekinci, K L

2017-02-17

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Generalized Knudsen Number for Unsteady Fluid Flow

NASA Astrophysics Data System (ADS)

Kara, V.; Yakhot, V.; Ekinci, K. L.

2017-02-01

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Symmetry breaking and the geometry of reduced density matrices

NASA Astrophysics Data System (ADS)

Zauner, V.; Draxler, D.; Vanderstraeten, L.; Haegeman, J.; Verstraete, F.

2016-11-01

The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of these convex bodies exhibit non-analyticities, which signal the emergence of symmetry breaking and of an associated order parameter and also show different characteristics for different types of phase transitions. We illustrate this with three paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model, the classical q-state Potts model in two-dimensions at finite temperature and the ideal Bose gas in three-dimensions at finite temperature. This state based viewpoint on phase transitions provides a unique novel tool for studying exotic many body phenomena in quantum and classical systems.

Pairing induced superconductivity in holography

NASA Astrophysics Data System (ADS)

Bagrov, Andrey; Meszena, Balazs; Schalm, Koenraad

2014-09-01

We study pairing induced superconductivity in large N strongly coupled systems at finite density using holography. In the weakly coupled dual gravitational theory the mechanism is conventional BCS theory. An IR hard wall cut-off is included to ensure that we can controllably address the dynamics of a single confined Fermi surface. We address in detail the interplay between the scalar order parameter field and fermion pairing. Adding an explicitly dynamical scalar operator with the same quantum numbers as the fermion-pair, the theory experiences a BCS/BEC crossover controlled by the relative scaling dimensions. We find the novel result that this BCS/BEC crossover exposes resonances in the canonical expectation value of the scalar operator. This occurs not only when the scaling dimension is degenerate with the Cooper pair, but also with that of higher derivative paired operators. We speculate that a proper definition of the order parameter which takes mixing with these operators into account stays finite nevertheless.

Improved finite-difference computation of the van der Waals force: One-dimensional case

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

Pinto, Fabrizio

2009-10-15

We present an improved demonstration of the calculation of Casimir forces in one-dimensional systems based on the recently proposed numerical imaginary frequency Green's function computation approach. The dispersion force on two thick lossy dielectric slabs separated by an empty gap and placed within a perfectly conducting cavity is obtained from the Green's function of the modified Helmholtz equation by means of an ordinary finite-difference method. In order to demonstrate the possibility to develop algorithms to explore complex geometries in two and three dimensions to higher order in the mesh spacing, we generalize existing classical electromagnetism algebraic methods to generate themore » difference equations for dielectric boundaries not coinciding with any grid points. Diagnostic tests are presented to monitor the accuracy of our implementation of the method and follow-up applications in higher dimensions are introduced.« less

Structural Health Monitoring for a Z-Type Special Vehicle

PubMed Central

Yuan, Chaolin; Ren, Liang; Li, Hongnan

2017-01-01

Nowadays there exist various kinds of special vehicles designed for some purposes, which are different from regular vehicles in overall dimension and design. In that case, accidents such as overturning will lead to large economical loss and casualties. There are still no technical specifications to follow to ensure the safe operation and driving of these special vehicles. Owing to the poor efficiency of regular maintenance, it is more feasible and effective to apply real-time monitoring during the operation and driving process. In this paper, the fiber Bragg grating (FBG) sensors are used to monitor the safety of a z-type special vehicle. Based on the structural features and force distribution, a reasonable structural health monitoring (SHM) scheme is presented. Comparing the monitoring results with the finite element simulation results guarantees the accuracy and reliability of the monitoring results. Large amounts of data are collected during the operation and driving progress to evaluate the structural safety condition and provide reference for SHM systems developed for other special vehicles. PMID:28587161

A Numerical Solution of the Second-Order-Nonlinear Acoustic Wave Equation in One and in Three Dimensions.

DTIC Science & Technology

1981-01-08

95 Limits of Applicability of Weak-Finite- Amplitude Theory ... ............ 100 Near- Field Calibration of Parametric Sources...concerning the amount of energy that may be trans- mitted to the far field by various types of signals. CPOIi eslu er 06]i C) 3O d SIM aC NOI.LjZI’IS...ducers at finite amplitudes, conclusions are presented concerning the amount of energy that may be transmitted to the far field by various types of

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.

Moving finite elements in 2-D

NASA Technical Reports Server (NTRS)

Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.

1983-01-01

The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system

NASA Technical Reports Server (NTRS)

Giles, G. L.; Rogers, J. L., Jr.

1982-01-01

The implementation includes a generalized method for specifying element cross-sectional dimensions as design variables that can be used in analytically calculating derivatives of output quantities from static stress, vibration, and buckling analyses for both membrane and bending elements. Limited sample results for static displacements and stresses are presented to indicate the advantages of analytically calclating response derivatives compared to finite difference methods. Continuing developments to implement these procedures into an enhanced version of the system are also discussed.

Linear dimension reduction and Bayes classification

NASA Technical Reports Server (NTRS)

Decell, H. P., Jr.; Odell, P. L.; Coberly, W. A.

1978-01-01

An explicit expression for a compression matrix T of smallest possible left dimension K consistent with preserving the n variate normal Bayes assignment of X to a given one of a finite number of populations and the K variate Bayes assignment of TX to that population was developed. The Bayes population assignment of X and TX were shown to be equivalent for a compression matrix T explicitly calculated as a function of the means and covariances of the given populations.

A Learning Progression for Geometrical Measurement in One, Two, and Three Dimensions. Research Report. ETS RR-17-55

ERIC Educational Resources Information Center

Kim, Eun Mi; Haberstroh, Jeff; Peters, Stephanie; Howell, Heather; Olah, Leslie Nabors

2017-01-01

As part of the CBAL® learning and assessment initiative in mathematics, we developed a hypothesized learning progression (LP) for geometrical measurement in 1, 2, and 3 dimensions based on a synthesis of empirical literature in this field and through expert review. The geometrical measurement LP is intended to represent a developmental progression…

Compact objects in pure Lovelock theory

NASA Astrophysics Data System (ADS)

Dadhich, Naresh; Hansraj, Sudan; Chilambwe, Brian

For static fluid interiors of compact objects in pure Lovelock gravity (involving only one Nth order term in the equation), we establish similarity in solutions for the critical odd and even d = 2N + 1, 2N + 2 dimensions. It turns out that in critical odd d = 2N + 1 dimensions, there cannot exist any bound distribution with a finite radius, while in critical even d = 2N + 2 dimensions, all solutions have similar behavior. For exhibition of similarity, we would compare star solutions for N = 1, 2 in d = 4 Einstein and d = 6 in Gauss-Bonnet theory, respectively. We also obtain the pure Lovelock analogue of the Finch-Skea model.

Characterization of the Coupling Between Adjacent Finite Ground Coplanar (FGC) Waveguides

NASA Technical Reports Server (NTRS)

Ponchak, George E.; Katehi, Linda P. B.; Tentzeris, Emmanouil M.

1997-01-01

Coupling between adjacent Finite Ground Coplanar (FGC) waveguides as a function of the line geometry is presented for the first time. A two Dimension-Finite Difference Time Domain (2D-FDTD) analysis and measurements are used to show that the coupling decreases as the line to line separation and the grOUnd plane width increases. Furthermore, it is shown that for a given spacing between the center lines of two FGC lines, the coupling is lower if the ground plane width is smaller Lastly, electric field plots generated from the 2D-FDTD technique are presented which demonstrate a strong slotline mode is established in the coupled FGC line.

Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs

NASA Astrophysics Data System (ADS)

Zhao, Yan; Belov, Pavel A.; Hao, Yang

2006-06-01

In this paper, a spatially dispersive finite-difference time-domain (FDTD) method to model wire media is developed and validated. Sub-wavelength imaging properties of the finite wire medium slabs are examined. It is demonstrated that the slab with its thickness equal to an integer number of half-wavelengths is capable of transporting images with sub-wavelength resolution from one interface of the slab to another. It is also shown that the operation of such transmission devices is not sensitive to their transverse dimensions, which can be made even comparable to the wavelength. In this case, the edge diffractions are negligible and do not disturb the image formation.

Scattering from finite bodies of translation - Plates, curved surfaces, and noncircular cylinders

NASA Astrophysics Data System (ADS)

Medgyesi-Mitschang, L. N.; Putnam, J. M.

1983-11-01

Electromagnetic scattering from finite, conducting bodies of translation (BOT) is examined using a formulation based on the electric field integral equation (EFIE) and solved by the method of moments (MM). The present approach provides a systematic, unified treatment for a wide class of finite, thin scatterers at all angles of illumination and polarization. Both concave and convex surfaces are considered. An entire-domain Galerkin expansion along one dimension of the body and a piecewise continuous one along the other are used to represent the unknown current variations. The scattering cross sections, obtained with this formulation, are compared with published results using more specialized methods and further confirmed by experimental measurements.

Baryonic popcorn

NASA Astrophysics Data System (ADS)

Kaplunovsky, Vadim; Melnikov, Dmitry; Sonnenschein, Jacob

2012-11-01

In the large N c limit cold dense nuclear matter must be in a lattice phase. This applies also to holographic models of hadron physics. In a class of such models, like the generalized Sakai-Sugimoto model, baryons take the form of instantons of the effective flavor gauge theory that resides on probe flavor branes. In this paper we study the phase structure of baryonic crystals by analyzing discrete periodic configurations of such instantons. We find that instanton configurations exhibit a series of "popcorn" transitions upon increasing the density. Through these transitions normal (3D) lattices expand into the transverse dimension, eventually becoming a higher dimensional (4D) multi-layer lattice at large densities. We consider 3D lattices of zero size instantons as well as 1D periodic chains of finite size instantons, which serve as toy models of the full holographic systems. In particular, for the finite-size case we determine solutions of the corresponding ADHM equations for both a straight chain and for a 2D zigzag configuration where instantons pop up into the holographic dimension. At low density the system takes the form of an "abelian anti- ferromagnetic" straight periodic chain. Above a critical density there is a second order phase transition into a zigzag structure. An even higher density yields a rich phase space characterized by the formation of multi-layer zigzag structures. The finite size of the lattices in the transverse dimension is a signal of an emerging Fermi sea of quarks. We thus propose that the popcorn transitions indicate the onset of the "quarkyonic" phase of the cold dense nuclear matter.

Geometric MCMC for infinite-dimensional inverse problems

NASA Astrophysics Data System (ADS)

Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.

2017-04-01

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

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.

Quantum field theory on toroidal topology: Algebraic structure and applications

NASA Astrophysics Data System (ADS)

Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.

2014-05-01

The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particle physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matter physics. The theory on a torus ΓDd=(S1)d×RD-d is developed from a Lie-group representation and c*c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real- and imaginary-time versions, is addressed by focusing on its topological structure, the torus Γ41. The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac fields on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on the hadronic phase structure are investigated, taking into account density and temperature. As a final application, effects of extra spatial dimensions are addressed, by developing a quantum electrodynamics in a five-dimensional space-time, where the fifth-dimension is compactified on a torus. The formalism, initially developed for particle physics, provides results compatible with other trials of probing the existence of extra-dimensions.

The cyclic and fractal seismic series preceding an mb 4.8 earthquake on 1980 February 14 near the Virgin Islands

USGS Publications Warehouse

Varnes, D.J.; Bufe, C.G.

1996-01-01

Seismic activity in the 10 months preceding the 1980 February 14, mb 4.8 earthquake in the Virgin Islands, reported on by Frankel in 1982, consisted of four principal cycles. Each cycle began with a relatively large event or series of closely spaced events, and the duration of the cycles progressively shortened by a factor of about 3/4. Had this regular shortening of the cycles been recognized prior to the earthquake, the time of the next episode of setsmicity (the main shock) might have been closely estimated 41 days in advance. That this event could be much larger than the previous events is indicated from time-to-failure analysis of the accelerating rise in released seismic energy, using a non-linear time- and slip-predictable foreshock model. Examination of the timing of all events in the sequence shows an even higher degree of order. Rates of seismicity, measured by consecutive interevent times, when plotted on an iteration diagram of a rate versus the succeeding rate, form a triangular circulating trajectory. The trajectory becomes an ascending helix if extended in a third dimension, time. This construction reveals additional and precise relations among the time intervals between times of relatively high or relatively low rates of seismic activity, including period halving and doubling. The set of 666 time intervals between all possible pairs of the 37 recorded events appears to be a fractal; the set of time points that define the intervals has a finite, non-integer correlation dimension of 0.70. In contrast, the average correlation dimension of 50 random sequences of 37 events is significantly higher, dose to 1.0. In a similar analysis, the set of distances between pairs of epicentres has a fractal correlation dimension of 1.52. Well-defined cycles, numerous precise ratios among time intervals, and a non-random temporal fractal dimension suggest that the seismic series is not a random process, but rather the product of a deterministic dynamic system.

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).

Operator mixing in the ɛ -expansion: Scheme and evanescent-operator independence

NASA Astrophysics Data System (ADS)

Di Pietro, Lorenzo; Stamou, Emmanuel

2018-03-01

We consider theories with fermionic degrees of freedom that have a fixed point of Wilson-Fisher type in noninteger dimension d =4 -2 ɛ . Due to the presence of evanescent operators, i.e., operators that vanish in integer dimensions, these theories contain families of infinitely many operators that can mix with each other under renormalization. We clarify the dependence of the corresponding anomalous-dimension matrix on the choice of renormalization scheme beyond leading order in ɛ -expansion. In standard choices of scheme, we find that eigenvalues at the fixed point cannot be extracted from a finite-dimensional block. We illustrate in examples a truncation approach to compute the eigenvalues. These are observable scaling dimensions, and, indeed, we find that the dependence on the choice of scheme cancels. As an application, we obtain the IR scaling dimension of four-fermion operators in QED in d =4 -2 ɛ at order O (ɛ2).

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.

Subleading soft theorem for multiple soft gravitons

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2017-12-01

We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.

The p- and h-p Versions of the Finite Element Method: An Overview

DTIC Science & Technology

1989-05-01

and h-p versions was studied in detail for 1 dimension in [48] and for 2 dimensions in [491. Let us mention some one dimensional results. We consider...Supercomputing in the Automotive Industry, Oct. 25-28 1988, Seville Spain, Report of Noetic Tech., St. Louis, NO 63117. 70. H. Vogelius, An analysis of the p...collaboration with govern- ment agencies such as the National Bureau of Standards. " To be an international center of study and research for foreign

Fast-dynamo action in unsteady flows and maps in three dimensions

NASA Technical Reports Server (NTRS)

Bayly, B. J.; Childress, S.

1987-01-01

Unsteady fast-dynamo action is obtained in a family of stretch-fold-shear maps applied to a spatially periodic magnetic field in three dimensions. Exponential growth of a mean field in the limit of vanishing diffusivity is demonstrated by a numerical method which alternates instantaneous deformations with molecular diffusion over a finite time interval. Analysis indicates that the dynamo is a coherent feature of the large scales, essentially independent of the cascade of structure to small scales.

Reflections on conformal spectra

DOE PAGES

Kim, Hyungrok; Kravchuk, Petr; Ooguri, Hirosi

2016-04-29

Here, we use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions Δ 0 of external operators. We use these symmetries to motivate universal upper bounds on the spectrum and the operator product expansion coefficients, which we then derive by independent techniques. Some of the bounds for four-point functions are valid for finite Δ 0 as well as for large Δ 0.more » We discuss a similar symmetry in a large spacetime dimension limit. Finally, we comment on the analogue of the Cardy formula and sparse light spectrum condition for the four-point function.« less

The ABC of stereotypes about groups: Agency/socioeconomic success, conservative-progressive beliefs, and communion.

PubMed

Koch, Alex; Imhoff, Roland; Dotsch, Ron; Unkelbach, Christian; Alves, Hans

2016-05-01

Previous research argued that stereotypes differ primarily on the 2 dimensions of warmth/communion and competence/agency. We identify an empirical gap in support for this notion. The theoretical model constrains stereotypes a priori to these 2 dimensions; without this constraint, participants might spontaneously employ other relevant dimensions. We fill this gap by complementing the existing theory-driven approaches with a data-driven approach that allows an estimation of the spontaneously employed dimensions of stereotyping. Seven studies (total N = 4,451) show that people organize social groups primarily based on their agency/socioeconomic success (A), and as a second dimension, based on their conservative-progressive beliefs (B). Communion (C) is not found as a dimension by its own, but rather as an emergent quality in the two-dimensional space of A and B, resulting in a 2D ABC model of stereotype content about social groups. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Investigation of the Statistics of Pure Tone Sound Power Injection from Low Frequency, Finite Sized Sources in a Reverberant Room

NASA Technical Reports Server (NTRS)

Smith, Wayne Farrior

1973-01-01

The effect of finite source size on the power statistics in a reverberant room for pure tone excitation was investigated. Theoretical results indicate that the standard deviation of low frequency, pure tone finite sources is always less than that predicted by point source theory and considerably less when the source dimension approaches one-half an acoustic wavelength or greater. A supporting experimental study was conducted utilizing an eight inch loudspeaker and a 30 inch loudspeaker at eleven source positions. The resulting standard deviation of sound power output of the smaller speaker is in excellent agreement with both the derived finite source theory and existing point source theory, if the theoretical data is adjusted to account for experimental incomplete spatial averaging. However, the standard deviation of sound power output of the larger speaker is measurably lower than point source theory indicates, but is in good agreement with the finite source theory.

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

Recent Progress in the p and h-p Version of the Finite Element Method.

DTIC Science & Technology

1987-07-01

code PROBE which was developed recently by NOETIC Technologies, St. Louis £54]. PROBE solves two dimensional problems of linear elasticity, stationary...of the finite element method was studied in detail from various point of view. We will mention here some essential illustrative results. In one...28) Bathe, K. J., Brezzi, F., Studies of finite element procedures - the INF-SUP condition, equivalent forms and applications in Reliability of

Surface cracks in a plate of finite width under tension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

The problem of a finite plate containing collinear surface cracks is considered and solved by using the line spring model with plane elasticity and Reissner's plate theory. The main focus is on the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors in an effort to provide extensive numerical results which may be useful in applications. Some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks, and two corner cracks for wide range of relative dimensions. Particularly in corner cracks, the agreement with the finite element solution is surprisingly very good. The results are obtained for semi-elliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Surface cracks in a plate of finite width under extension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Gaussian impurity moving through a Bose-Einstein superfluid

NASA Astrophysics Data System (ADS)

Pinsker, Florian

2017-09-01

In this paper a finite Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial dimensions. The Bogoliubov equation solutions for the condensate perturbed by a finite impurity are calculated in the co-moving frame. From these solutions the total energy of the perturbed system is determined as a function of the width and the amplitude of the moving Gaussian impurity and its velocity. In addition we derive the drag force the finite sized impurity approximately experiences as it moves through the superfluid, which proves the existence of a superfluid phase for finite extensions of the impurities below the speed of sound. Finally we find that the force increases with velocity until an inflection point from which it decreases again in 2 and 3d.

Scaling relationships of channel networks at large scales: Examples from two large-magnitude watersheds in Brittany, France

NASA Astrophysics Data System (ADS)

Crave, A.; Davy, P.

1997-01-01

We present a statistical analysis on two watersheds in French Brittany whose drainage areas are about 10,000 and 2000 km2. The channel system was analysed from the digitised blue lines of the 1:100,000 map and from a 250-m DEM. Link lengths follow an exponential distribution, consistent with the Markovian model of channel branching proposed by Smart (1968). The departure from the exponential distribution for small lengths, that has been extensively discussed before, results from a statistical effect due to the finite number of channels and junctions. The Strahler topology applied on channels defines a self-similar organisation whose similarity dimension is about 1.7, that is clearly smaller than the value of 2 expected for a random organisation. The similarity dimension is consistent with an independent measurement of the Horton ratios of stream numbers and lengths. The variables defined by an upstream integral (drainage area, mainstream length, upstream length) follow power-law distributions limited at large scales by a finite size effect, due to the finite area of the watersheds. A special emphasis is given to the exponent of the drainage area, aA, that has been previously discussed in the context of different aggregation models relevant to channel network growth. We show that aA is consistent with 4/3, a value that was obtained and analytically demonstrated from directed random walk aggregating models, inspired by the model of Scheidegger (1967). The drainage density and mainstream length present no simple scaling with area, except at large areas where they tend to trivial values: constant density and square root of drainage area, respectively. These asymptotic limits necessarily imply that the space dimension of channel networks is 2, equal to the embedding space. The limits are reached for drainage areas larger than 100 km2. For smaller areas, the asymptotic limit represents either a lower bound (drainage density) or an upper bound (mainstream length) of the distributions. Because the fluctuations of the drainage density slowly converge to a finite limit, the system could be adequately described as a fat fractal, where the average drainage density is the sum of a constant plus a fluctuation decreasing as a power law with integrating area. A fat fractal hypothesis could explain why the similarity dimension is not equal to the fractal capacity dimension, as it is for thin fractals. The physical consequences are not yet really understood, but we draw an analogy with a directed aggregating system where the growth process involves both stochastic and deterministic growth. These models are known to be fat fractals, and the deterministic growth, which constitutes a fundamental ingredient of these models, could be attributed in river systems to the role of terrestrial gravity.

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

Parallel, adaptive finite element methods for conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.

1994-01-01

We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.

Simulation of wave propagation in three-dimensional random media

NASA Technical Reports Server (NTRS)

Coles, William A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1993-01-01

Quantitative error analysis for simulation of wave propagation in three dimensional random media assuming narrow angular scattering are presented for the plane wave and spherical wave geometry. This includes the errors resulting from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive index of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared to the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent.

Preliminary structural sizing of a Mach 3.0 high-speed civil transport model

NASA Technical Reports Server (NTRS)

Blackburn, Charles L.

1992-01-01

An analysis has been performed pertaining to the structural resizing of a candidate Mach 3.0 High Speed Civil Transport (HSCT) conceptual design using a computer program called EZDESIT. EZDESIT is a computer program which integrates the PATRAN finite element modeling program to the COMET finite element analysis program for the purpose of calculating element sizes or cross sectional dimensions. The purpose of the present report is to document the procedure used in accomplishing the preliminary structural sizing and to present the corresponding results.

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of nonrelativistic fermions in one dimension

NASA Astrophysics Data System (ADS)

Loheac, Andrew C.; Drut, Joaquín E.

2017-05-01

We analyze the pressure and density equations of state of unpolarized nonrelativistic fermions at finite temperature in one spatial dimension with contact interactions. For attractively interacting regimes, we perform a third-order lattice perturbation theory calculation, assess its convergence properties by comparing with hybrid Monte Carlo results (there is no sign problem in this regime), and demonstrate agreement with real Langevin calculations. For repulsive interactions, we present lattice perturbation theory results as well as complex Langevin calculations, with a modified action to prevent uncontrolled excursions in the complex plane. Although perturbation theory is a common tool, our implementation of it is unconventional; we use a Hubbard-Stratonovich transformation to decouple the system and automate the application of Wick's theorem, thus generating the diagrammatic expansion, including symmetry factors, at any desired order. We also present an efficient technique to tackle nested Matsubara frequency sums without relying on contour integration, which is independent of dimension and applies to both relativistic and nonrelativistic systems, as well as all energy-independent interactions. We find exceptional agreement between perturbative and nonperturbative results at weak couplings, and furnish predictions based on complex Langevin at strong couplings. We additionally present perturbative calculations of up to the fifth-order virial coefficient for repulsive and attractive couplings. Both the lattice perturbation theory and complex Langevin formalisms can easily be extended to a variety of situations including polarized systems, bosons, and higher dimension.

New Computer Simulations of Macular Neural Functioning

NASA Technical Reports Server (NTRS)

Ross, Muriel D.; Doshay, D.; Linton, S.; Parnas, B.; Montgomery, K.; Chimento, T.

1994-01-01

We use high performance graphics workstations and supercomputers to study the functional significance of the three-dimensional (3-D) organization of gravity sensors. These sensors have a prototypic architecture foreshadowing more complex systems. Scaled-down simulations run on a Silicon Graphics workstation and scaled-up, 3-D versions run on a Cray Y-MP supercomputer. A semi-automated method of reconstruction of neural tissue from serial sections studied in a transmission electron microscope has been developed to eliminate tedious conventional photography. The reconstructions use a mesh as a step in generating a neural surface for visualization. Two meshes are required to model calyx surfaces. The meshes are connected and the resulting prisms represent the cytoplasm and the bounding membranes. A finite volume analysis method is employed to simulate voltage changes along the calyx in response to synapse activation on the calyx or on calyceal processes. The finite volume method insures that charge is conserved at the calyx-process junction. These and other models indicate that efferent processes act as voltage followers, and that the morphology of some afferent processes affects their functioning. In a final application, morphological information is symbolically represented in three dimensions in a computer. The possible functioning of the connectivities is tested using mathematical interpretations of physiological parameters taken from the literature. Symbolic, 3-D simulations are in progress to probe the functional significance of the connectivities. This research is expected to advance computer-based studies of macular functioning and of synaptic plasticity.

Fermion determinants in static, inhomogeneous magnetic fields

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

Fry, M.P.

1995-01-15

The renormalized fermionic determinant of QED in 3+1 dimensions, det[sub ren], in a static, unidirectional, inhomogeneous magnetic field with finite flux can be calculated from the massive Euclidean Schwinger model's determinant det[sub Sch] in the same field by integrating det[sub Sch] over the fermion's mass. Since det[sub ren] for general fields is central to QED, it is desirable to have nonperturbative information on this determinant, even for the restricted magnetic fields considered here. To this end we continue our study of the physically relevant determinant det[sub Sch]. It is shown that the contribution of the massless Schwinger model to det[submore » Sch] is canceled by a contribution from the massive sector of QED in 1+1 dimensions and that zero modes are suppressed in det[sub Sch]. We then calculate det[sub Sch] analytically in the presence of a finite flux, cylindrical magnetic field. Its behavior for large flux and small fermion mass suggests that the zero-energy bound states of the two-dimensional Pauli Hamiltonian are the controlling factor in the growth of ln det[sub Sch]. Evidence is presented that det[sub Sch] does not converge to the determinant of the massless Schwinger model in the small mass limit for finite, nonzero flux magnetic fields.« less

Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1998-01-01

We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

Vacuum energy in Einstein-Gauss-Bonnet anti-de Sitter gravity

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

Kofinas, Georgios; Olea, Rodrigo

2006-10-15

A finite action principle for Einstein-Gauss-Bonnet anti-de Sitter gravity is achieved by supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions. For even dimensions, this term is given by the boundary contribution in the Euler theorem with a coupling constant fixed, demanding the spacetime to have constant (negative) curvature in the asymptotic region. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. A well-posed variational principle leads to an appropriate definition of energy and other conserved quantities using the Noether theorem, andmore » to a correct description of black hole thermodynamics. In particular, this procedure assigns a nonzero energy to anti-de Sitter spacetime in all odd dimensions.« less

Quantifying and Qualifying USGS ShakeMap Uncertainty

USGS Publications Warehouse

Wald, David J.; Lin, Kuo-Wan; Quitoriano, Vincent

2008-01-01

We describe algorithms for quantifying and qualifying uncertainties associated with USGS ShakeMap ground motions. The uncertainty values computed consist of latitude/longitude grid-based multiplicative factors that scale the standard deviation associated with the ground motion prediction equation (GMPE) used within the ShakeMap algorithm for estimating ground motions. The resulting grid-based 'uncertainty map' is essential for evaluation of losses derived using ShakeMaps as the hazard input. For ShakeMap, ground motion uncertainty at any point is dominated by two main factors: (i) the influence of any proximal ground motion observations, and (ii) the uncertainty of estimating ground motions from the GMPE, most notably, elevated uncertainty due to initial, unconstrained source rupture geometry. The uncertainty is highest for larger magnitude earthquakes when source finiteness is not yet constrained and, hence, the distance to rupture is also uncertain. In addition to a spatially-dependant, quantitative assessment, many users may prefer a simple, qualitative grading for the entire ShakeMap. We developed a grading scale that allows one to quickly gauge the appropriate level of confidence when using rapidly produced ShakeMaps as part of the post-earthquake decision-making process or for qualitative assessments of archived or historical earthquake ShakeMaps. We describe an uncertainty letter grading ('A' through 'F', for high to poor quality, respectively) based on the uncertainty map. A middle-range ('C') grade corresponds to a ShakeMap for a moderate-magnitude earthquake suitably represented with a point-source location. Lower grades 'D' and 'F' are assigned for larger events (M>6) where finite-source dimensions are not yet constrained. The addition of ground motion observations (or observed macroseismic intensities) reduces uncertainties over data-constrained portions of the map. Higher grades ('A' and 'B') correspond to ShakeMaps with constrained fault dimensions and numerous stations, depending on the density of station/data coverage. Due to these dependencies, the letter grade can change with subsequent ShakeMap revisions if more data are added or when finite-faulting dimensions are added. We emphasize that the greatest uncertainties are associated with unconstrained source dimensions for large earthquakes where the distance term in the GMPE is most uncertain; this uncertainty thus scales with magnitude (and consequently rupture dimension). Since this distance uncertainty produces potentially large uncertainties in ShakeMap ground-motion estimates, this factor dominates over compensating constraints for all but the most dense station distributions.

Small covers of graph-associahedra and realization of cycles

NASA Astrophysics Data System (ADS)

Gaifullin, A. A.

2016-11-01

An oriented connected closed manifold M^n is called a URC-manifold if for any oriented connected closed manifold N^n of the same dimension there exists a nonzero-degree mapping of a finite-fold covering \\widehat{M}^n of M^n onto N^n. This condition is equivalent to the following: for any n-dimensional integral homology class of any topological space X, a multiple of it can be realized as the image of the fundamental class of a finite-fold covering \\widehat{M}^n of M^n under a continuous mapping f\\colon \\widehat{M}^n\\to X. In 2007 the author gave a constructive proof of Thom's classical result that a multiple of any integral homology class can be realized as an image of the fundamental class of an oriented smooth manifold. This construction yields the existence of URC-manifolds of all dimensions. For an important class of manifolds, the so-called small covers of graph-associahedra corresponding to connected graphs, we prove that either they or their two-fold orientation coverings are URC-manifolds. In particular, we obtain that the two-fold covering of the small cover of the usual Stasheff associahedron is a URC-manifold. In dimensions 4 and higher, this manifold is simpler than all the previously known URC-manifolds. Bibliography: 39 titles.

Exact Green's functions for a Brownian particle reversibly binding to a fixed target in a finite, two-dimensional, circular domain

NASA Astrophysics Data System (ADS)

Kalay, Ziya

2012-06-01

Despite the apparent need to study reversible reactions between molecules confined to a two-dimensional space such as the cell membrane, exact Green’s functions for this case have not been reported. Here we present exact analytical Green’s functions for a Brownian particle reversibly reacting with a fixed reaction center in a finite two-dimensional circular region with reflecting or absorbing boundaries, considering either a spherically symmetric initial distribution or a particle that is initially bound. We show that Green’s function can be used to predict the effect of measurement uncertainties on the outcome of single-particle/molecule-tracking experiments in which molecular interactions are investigated. Hence, we bridge the gap between previously known solutions in one dimension (Agmon 1984 J. Chem. Phys. 81 2811) and three dimensions (Kim and Shin 1999 Phys. Rev. Lett. 82 1578), and provide an example of how the knowledge of Green’s function can be used to predict experimentally accessible quantities.

A piece of cake: the ground-state energies in γ i -deformed = 4 SYM theory at leading wrapping order

NASA Astrophysics Data System (ADS)

Fokken, Jan; Sieg, Christoph; Wilhelm, Matthias

2014-09-01

In the non-supersymmetric γi-deformed = 4 SYM theory, the scaling dimensions of the operators tr[ Z L ] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L ≥ 3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Lüscher corrections, TBA and Y-system equations. At L = 2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing β-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken — even in the 't Hooft limit. [Figure not available: see fulltext.

Spin Hartree-Fock approach to studying quantum Heisenberg antiferromagnets in low dimensions

NASA Astrophysics Data System (ADS)

Werth, A.; Kopietz, P.; Tsyplyatyev, O.

2018-05-01

We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order 1 /T expansions.

Complete band gaps in a polyvinyl chloride (PVC) phononic plate with cross-like holes: numerical design and experimental verification.

PubMed

Miniaci, Marco; Marzani, Alessandro; Testoni, Nicola; De Marchi, Luca

2015-02-01

In this work the existence of band gaps in a phononic polyvinyl chloride (PVC) plate with a square lattice of cross-like holes is numerically and experimentally investigated. First, a parametric analysis is carried out to find plate thickness and cross-like holes dimensions capable to nucleate complete band gaps. In this analysis the band structures of the unitary cell in the first Brillouin zone are computed by exploiting the Bloch-Floquet theorem. Next, time transient finite element analyses are performed to highlight the shielding effect of a finite dimension phononic region, formed by unitary cells arranged into four concentric square rings, on the propagation of guided waves. Finally, ultrasonic experimental tests in pitch-catch configuration across the phononic region, machined on a PVC plate, are executed and analyzed. Very good agreement between numerical and experimental results are found confirming the existence of the predicted band gaps. Copyright © 2014 Elsevier B.V. All rights reserved.

Finite difference time domain implementation of surface impedance boundary conditions

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.

1991-01-01

Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In the finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Here, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration. Extensions to three dimensions should be straightforward.

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

Trellis coding with multidimensional QAM signal sets

NASA Technical Reports Server (NTRS)

Pietrobon, Steven S.; Costello, Daniel J.

1993-01-01

Trellis coding using multidimensional QAM signal sets is investigated. Finite-size 2D signal sets are presented that have minimum average energy, are 90-deg rotationally symmetric, and have from 16 to 1024 points. The best trellis codes using the finite 16-QAM signal set with two, four, six, and eight dimensions are found by computer search (the multidimensional signal set is constructed from the 2D signal set). The best moderate complexity trellis codes for infinite lattices with two, four, six, and eight dimensions are also found. The minimum free squared Euclidean distance and number of nearest neighbors for these codes were used as the selection criteria. Many of the multidimensional codes are fully rotationally invariant and give asymptotic coding gains up to 6.0 dB. From the infinite lattice codes, the best codes for transmitting J, J + 1/4, J + 1/3, J + 1/2, J + 2/3, and J + 3/4 bit/sym (J an integer) are presented.

The Effects of Finite Sampling on State Assessment Sample Requirements. NAEP Validity Studies. Working Paper Series.

ERIC Educational Resources Information Center

Chromy, James R.

This study addressed statistical techniques that might ameliorate some of the sampling problems currently facing states with small populations participating in State National Assessment of Educational Progress (NAEP) assessments. The study explored how the application of finite population correction factors to the between-school component of…

Complex-time singularity and locality estimates for quantum lattice systems

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

Bouch, Gabriel

2015-12-15

We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas related to the Eden growth process and lattice trees. Finally, we demonstrate with a specific family of lattice trees in the plane why this approach breaks down in dimensions greater than one and prove that there exist interactions for which the complex-time dynamics blows-up in finite imaginary time. .

Fractal universe and quantum gravity.

PubMed

Calcagni, Gianluca

2010-06-25

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.

Entropy Inequality Violations from Ultraspinning Black Holes.

PubMed

Hennigar, Robie A; Mann, Robert B; Kubizňák, David

2015-07-17

We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.

Magic informationally complete POVMs with permutations

NASA Astrophysics Data System (ADS)

Planat, Michel; Gedik, Zafer

2017-09-01

Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation (Planat, Rukhsan-Ul-Haq 2017 Adv. Math. Phys. 2017, 5287862 (doi:10.1155/2017/5287862)). We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such informationally complete POVMs, investigated in dimensions 2-12, exhibit simple finite geometries in their projector products and, for dimensions 4 and 8 and 9, relate to two-qubit, three-qubit and two-qutrit contextuality.

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.

Finite element methodology for integrated flow-thermal-structural analysis

NASA Technical Reports Server (NTRS)

Thornton, Earl A.; Ramakrishnan, R.; Vemaganti, G. R.

1988-01-01

Papers entitled, An Adaptive Finite Element Procedure for Compressible Flows and Strong Viscous-Inviscid Interactions, and An Adaptive Remeshing Method for Finite Element Thermal Analysis, were presented at the June 27 to 29, 1988, meeting of the AIAA Thermophysics, Plasma Dynamics and Lasers Conference, San Antonio, Texas. The papers describe research work supported under NASA/Langley Research Grant NsG-1321, and are submitted in fulfillment of the progress report requirement on the grant for the period ending February 29, 1988.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

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

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

The Effect of Scale Dependent Discretization on the Progressive Failure of Composite Materials Using Multiscale Analyses

NASA Technical Reports Server (NTRS)

Ricks, Trenton M.; Lacy, Thomas E., Jr.; Pineda, Evan J.; Bednarcyk, Brett A.; Arnold, Steven M.

2013-01-01

A multiscale modeling methodology, which incorporates a statistical distribution of fiber strengths into coupled micromechanics/ finite element analyses, is applied to unidirectional polymer matrix composites (PMCs) to analyze the effect of mesh discretization both at the micro- and macroscales on the predicted ultimate tensile (UTS) strength and failure behavior. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a PMC tensile specimen that initiates at the repeating unit cell (RUC) level. Three different finite element mesh densities were employed and each coupled with an appropriate RUC. Multiple simulations were performed in order to assess the effect of a statistical distribution of fiber strengths on the bulk composite failure and predicted strength. The coupled effects of both the micro- and macroscale discretizations were found to have a noticeable effect on the predicted UTS and computational efficiency of the simulations.

Size-dependent chemical transformation, structural phase-change, and optical properties of nanowires

PubMed Central

Piccione, Brian; Agarwal, Rahul; Jung, Yeonwoong; Agarwal, Ritesh

2013-01-01

Nanowires offer a unique approach for the bottom up assembly of electronic and photonic devices with the potential of integrating photonics with existing technologies. The anisotropic geometry and mesoscopic length scales of nanowires also make them very interesting systems to study a variety of size-dependent phenomenon where finite size effects become important. We will discuss the intriguing size-dependent properties of nanowire systems with diameters in the 5 – 300 nm range, where finite size and interfacial phenomena become more important than quantum mechanical effects. The ability to synthesize and manipulate nanostructures by chemical methods allows tremendous versatility in creating new systems with well controlled geometries, dimensions and functionality, which can then be used for understanding novel processes in finite-sized systems and devices. PMID:23997656

Effect of Ply Orientation and Crack Location on SIFs in Finite Multilayers with Aligned Cracks

NASA Astrophysics Data System (ADS)

Chen, Linfeng; Pindera, Marek-Jerzy

2008-02-01

An exact elasticity solution is presented for arbitrarily laminated finite multilayers in a state of generalized plane deformation under horizontally pinned end constraints that are weakened by aligned cracks. Based on half-range Fourier series and the local/global stiffness matrix approach, the mixed boundary-value problem is reduced to Cauchy-type singular integral equations in the unknown displacement discontinuities. Solution to these equations is obtained using the approach developed by Erdogan and co-workers. Numerical results quantify the thus-far undocumented geometric and material effects on Mode I, II and III stress intensity factors in composite multilayers with interacting cracks under uniform vertical displacement. These effects include finite dimensions, crack location, material anisotropy due to a unidirectional fiber-reinforced layer/s orientation, and orientational grading.

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

ISPAN (Interactive Stiffened Panel Analysis): A tool for quick concept evaluation and design trade studies

NASA Technical Reports Server (NTRS)

Hairr, John W.; Dorris, William J.; Ingram, J. Edward; Shah, Bharat M.

1993-01-01

Interactive Stiffened Panel Analysis (ISPAN) modules, written in FORTRAN, were developed to provide an easy to use tool for creating finite element models of composite material stiffened panels. The modules allow the user to interactively construct, solve and post-process finite element models of four general types of structural panel configurations using only the panel dimensions and properties as input data. Linear, buckling and post-buckling solution capability is provided. This interactive input allows rapid model generation and solution by non finite element users. The results of a parametric study of a blade stiffened panel are presented to demonstrate the usefulness of the ISPAN modules. Also, a non-linear analysis of a test panel was conducted and the results compared to measured data and previous correlation analysis.

The nature of the laning transition in two dimensions

NASA Astrophysics Data System (ADS)

Glanz, T.; Löwen, H.

2012-11-01

If a binary colloidal mixture is oppositely driven by an external field, a transition towards a laned state occurs at sufficiently large drives, where particles driven alike form elongated structures (‘lanes’) characterized by a large correlation length ξ along the drive. Here we perform extensive Brownian dynamics computer simulations on a two-dimensional equimolar binary Yukawa system driven by a constant force that acts oppositely on the two species. We systematically address finite-size effects on lane formation by exploring large systems up to 262 144 particles under various boundary conditions. It is found that the correlation length ξ along the field depends exponentially on the driving force (or Peclet number). Conversely, in a finite system, ξ reaches a fraction of the system size at a driving force which is logarithmic in the system size, implying massive finite-size corrections. For a fixed finite drive, ξ does not diverge in the thermodynamic limit. Therefore, though laning has a signature as a sharp transition in a finite system, it is a smooth crossover in the thermodynamic limit.

Chiral anomaly and anomalous finite-size conductivity in graphene

NASA Astrophysics Data System (ADS)

Shen, Shun-Qing; Li, Chang-An; Niu, Qian

2017-09-01

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two spin degenerate pairs of massless two-dimensional Dirac fermions with different chirality. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of a zigzag nanoribbon and some anomalous transport properties. Here it is proposed that the Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges of Dirac fermions at different valleys can be realized in a confined ribbon of finite width, even in the absence of a magnetic field. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and is inversely proportional to the square of the lateral dimension W, which is different from the finite-size correction inversely proportional to W from the boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and it is measurable experimentally. This finding provides an alternative platform to explore the purely quantum mechanical effect in graphene.

Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation.

PubMed

Sikora, Jamie; Varvitsiotis, Antonios; Wei, Zhaohui

2016-08-05

Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation. In this Letter, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a given two-party quantum correlation. We show that our bound is tight on many well-known correlations and discuss how it can rule out correlations of having a finite-dimensional quantum representation. We show that our bound is multiplicative under product correlations and also that it can witness the nonconvexity of certain restricted-dimensional quantum correlations.

Rogue-wave bullets in a composite (2+1)D nonlinear medium.

PubMed

Chen, Shihua; Soto-Crespo, Jose M; Baronio, Fabio; Grelu, Philippe; Mihalache, Dumitru

2016-07-11

We show that nonlinear wave packets localized in two dimensions with characteristic rogue wave profiles can propagate in a third dimension with significant stability. This unique behavior makes these waves analogous to light bullets, with the additional feature that they propagate on a finite background. Bulletlike rogue-wave singlet and triplet are derived analytically from a composite (2+1)D nonlinear wave equation. The latter can be interpreted as the combination of two integrable (1+1)D models expressed in different dimensions, namely, the Hirota equation and the complex modified Korteweg-de Vries equation. Numerical simulations confirm that the generation of rogue-wave bullets can be observed in the presence of spontaneous modulation instability activated by quantum noise.

A duality web in condensed matter systems

NASA Astrophysics Data System (ADS)

Ma, Chen-Te

2018-03-01

We study various dualities in condensed matter systems. The dualities in three dimensions can be derived from a conjecture of a duality between a Dirac fermion theory and an interacting scalar field theory at a Wilson-Fisher fixed point and zero temperature in three dimensions. We show that the dualities are not affected by non-trivial holonomy, use a mean-field method to study the dualities, and discuss the dualities at a finite temperature. Finally, we combine a bulk theory, which is an Abelian p-form theory with a theta term in 2 p + 2 dimensions, and a boundary theory, which is a 2 p + 1 dimensional theory, to discuss constraints and difficulties of a 2 p + 1 dimensional duality web.

Spatial Dimension as a Variable in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Doren, Douglas James

Several approximation methods potentially useful in electronic structure calculations are developed. These methods all treat the spatial dimension, D, as a variable. In an Introduction, the motivations for these methods are described, with special attention to the semiclassical 1/D expansion. Several terms in this expansion have been calculated for two-electron atoms. The results have qualitative appeal but poor convergence properties when D = 3. Chapter 1 shows that this convergence problem is due to singularities in the energy at D = 1 and a method of removing their effects is demonstrated. Chapter 2 treats several model problems, showing how to identify special dimensions at which the energy becomes singular or the Hamiltonian simplifies. Expansions are developed about these special finite values of D which are quite accurate at low order, regardless of the physical parameters of the Hamiltonian. In Chapter 3, expansions about singular points in the energy at finite values of D are used to resum the 1/D series in cases where its leading orders are not sufficient. This leads to a hybrid expansion which typically improves on both the 1/D and the finite D series. These methods are applied in Chapter 4 to two -electron atoms. The ground state energy of few-electron systems is dominated by the presence of a pole when D = 1. The residue of this pole is determined by the eigenvalue of a simple limiting Schrodinger equation. The limit and first order correction are determined for both unapproximated nonrelativistic two-electron atoms and the Hartree-Fock approximation to them. The hybrid expansion using only the first few terms in the 1/D series determines the energy at arbitrary D, providing estimates accurate to four or five figures when D = 3. Degeneracies between D = 3 states and those in nonphysical dimensions are developed in Chapter 5 which provide additional applications for this series. Chapter 6 illustrates these methods in an application to the H(' -) ion, an especially stringent test case. Proposals for future work in this field are described in the final chapter.

On the explicit construction of Parisi landscapes in finite dimensional Euclidean spaces

NASA Astrophysics Data System (ADS)

Fyodorov, Y. V.; Bouchaud, J.-P.

2007-12-01

An N-dimensional Gaussian landscape with multiscale translation-invariant logarithmic correlations has been constructed, and the statistical mechanics of a single particle in this environment has been investigated. In the limit of a high dimensional N → ∞, the free energy of the system in the thermodynamic limit coincides with the most general version of Derrida’s generalized random energy model. The low-temperature behavior depends essentially on the spectrum of length scales involved in the construction of the landscape. The construction is argued to be valid in any finite spatial dimensions N ≥1.

Characteristics of fluid flow in the combustion synthesis of TiC from the elements

NASA Technical Reports Server (NTRS)

Valone, S. M.; Behrens, R. G.

1987-01-01

The results of a numerical investigation of finite reservoir effects on capillary spreading at small reservoir dimensions are presently related to wave propagation phenomena in the combustion synthesis of TiC from its two elemental constituents. It is noted that gravitational forces can affect bubble coalescence by nonbuoyant means under the suitable conditions, although these conditions are expected to be rare in combustion synthesis. Finite-curved reservoirs can drive capillary flow due to surface tension and wall contact forces; these cause the wall and the metal to be completely reconfigured during combustion synthesis.

Resistive and Hall weighting functions in three dimensions

NASA Astrophysics Data System (ADS)

Koon, D. W.; Knickerbocker, C. J.

1998-10-01

The authors extend their study of the effect of macroscopic impurities on resistive and Hall measurements to include objects of finite thickness. The effect of such impurities is calculated for a series of rectangular parallelepipeds with two current and two voltage contacts on the corners of one square face. The weighting functions display singularities near these contacts, but these are shown to vanish in the two-dimensional limit, in agreement with previous results. Finally, it is shown that while Hall measurements principally sample the plane of the electrodes, resistivity measurements sample more of the interior of an object of finite thickness.

Quantum statistical mechanics of nonrelativistic membranes: crumpling transition at finite temperature

NASA Astrophysics Data System (ADS)

Borelli, M. E. S.; Kleinert, H.; Schakel, Adriaan M. J.

2000-03-01

The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to stiffen the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.

Computational simulation of progressive fracture in fiber composites

NASA Technical Reports Server (NTRS)

Chamis, C. C.

1986-01-01

Computational methods for simulating and predicting progressive fracture in fiber composite structures are presented. These methods are integrated into a computer code of modular form. The modules include composite mechanics, finite element analysis, and fracture criteria. The code is used to computationally simulate progressive fracture in composite laminates with and without defects. The simulation tracks the fracture progression in terms of modes initiating fracture, damage growth, and imminent global (catastrophic) laminate fracture.

Incipient singularities in the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Siggia, E. D.; Pumir, A.

1985-01-01

Infinite pointwise stretching in a finite time for general initial conditions is found in a simulation of the Biot-Savart equation for a slender vortex tube in three dimensions. Viscosity is ineffective in limiting the divergence in the vorticity as long as it remains concentrated in tubes. Stability has not been shown.

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Three-dimensional fluid-structure interaction case study on cubical fluid cavity with flexible bottom

NASA Astrophysics Data System (ADS)

Ghelardi, Stefano; Rizzo, Cesare; Villa, Diego

2017-12-01

In this paper, we report our study on a numerical fluid-structure interaction problem originally presented by Mok et al. (2001) in two dimensions and later studied in three dimensions by Valdés Vazquez (2007), Lombardi (2012), and Trimarchi (2012). We focus on a 3D test case in which we evaluated the sensitivity of several input parameters on the fluid and structural results. In particular, this analysis provides a starting point from which we can look deeper into specific aspects of these simulations and analyze more realistic cases, e.g., in sails design. In this study, using the commercial software ADINA™, we addressed a well-known unsteadiness problem comprising a square box representing the fluid domain with a flexible bottom modeled with structural shell elements. We compared data from previously published work whose authors used the same numerical approach, i.e., a partitioned approach coupling a finite volume solver (for the fluid domain) and a finite element solver (for the solid domain). Specifically, we established several benchmarks and made comparisons with respect to fluid and solid meshes, structural element types, and structural damping, as well as solution algorithms. Moreover, we compared our method with a monolithic finite element solution method. Our comparisons of new and old results provide an outline of best practices for such simulations.

Finite-size scaling of eigenstate thermalization

NASA Astrophysics Data System (ADS)

Beugeling, W.; Moessner, R.; Haque, Masudul

2014-04-01

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic nonintegrable systems these fluctuations scale with a universal power law D-1/2 with the dimension D of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models and several observables for each model. Each family includes integrable members and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

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.

CT artifact recognition for the nuclear technologist.

PubMed

Popilock, Robert; Sandrasagaren, Kumar; Harris, Lowell; Kaser, Keith A

2008-06-01

The goal of this article is to make the PET/CT and SPECT/CT operator aware of common artifacts found in CT. In diagnostic imaging, the ability to render an accurate diagnosis requires the technologist to take steps to optimize image quality and recognize when image quality has been compromised-that is, when there is an image artifact. One way these artifacts occur is through the inability of the CT linear attenuation image to precisely represent the linear attenuation map of a 2-dimensional section through the body. The reasons for this inability are multifold. First, CT is subject to the laws of x-ray quantum physics resulting in noise in all CT images. Moreover, all current CT x-ray systems generate a spectrum of energies. Also, CT scanners use detectors of finite dimension, as are the x-ray focal spots; reconstruct images from a finite number of samples distributed over a finite number of views; and acquire the data for each reconstruction over a finite period.

Computation of three-dimensional nozzle-exhaust flow fields with the GIM code

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Anderson, P. G.

1978-01-01

A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology.

Finite plate thickness effects on the Rayleigh-Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Polavarapu, Rinosh; Banerjee, Arindam

2017-11-01

The majority of theoretical studies have tackled the Rayleigh-Taylor instability (RTI) problem in solids using an infinitely thick plate. Recent theoretical studies by Piriz et al. (PRE 95, 053108, 2017) have explored finite thickness effects. We seek to validate this recent theoretical estimate experimentally using our rotating wheel RTI experiment in an accelerated elastic-plastic material. The test section consists of a container filled with air and mayonnaise (a non-Newtonian emulsion) with an initial perturbation between two materials. The plate thickness effects are studied by varying the depth of the soft-solid. A set of experiments is run by employing different initial conditions with different container dimensions. Additionally, the effect of acceleration rate (driving pressure rise time) on the instability threshold with reference to the finite thickness will also be inspected. Furthermore, the experimental results are compared to the analytical strength models related to finite thickness effects on RTI. Authors acknowledge financial support from DOE-SSAA Grant # DE-NA0003195 and LANL subcontract #370333.

Computing an upper bound on contact stress with surrogate duality

NASA Astrophysics Data System (ADS)

Xuan, Zhaocheng; Papadopoulos, Panayiotis

2016-07-01

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.

Structural behavior of composites with progressive fracture

NASA Technical Reports Server (NTRS)

Minnetyan, L.; Murthy, P. L. N.; Chamis, C. C.

1989-01-01

The objective of the study is to unify several computational tools developed for the prediction of progressive damage and fracture with efforts for the prediction of the overall response of damaged composite structures. In particular, a computational finite element model for the damaged structure is developed using a computer program as a byproduct of the analysis of progressive damage and fracture. Thus, a single computational investigation can predict progressive fracture and the resulting variation in structural properties of angleplied composites.

The singularity structure of scale-invariant rank-2 Coulomb branches

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Long, Cody; Martone, Mario

2018-05-01

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 N=2 superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the U(1) R symmetry. A set of novel topological and geometric results are developed which promise to be useful for the study and classification of Coulomb branch geometries at all ranks.

Soft A 4→Z 3 symmetry breaking and cobimaximal neutrino mixing

DOE PAGES

Ma, Ernest

2016-03-28

In this study, I propose a model of radiative charged-lepton and neutrino masses with A 4 symmetry. The soft breaking of A 4 to Z 3 lepton triality is accomplished by dimension-three terms. The breaking of Z 3 by dimension-two terms allows cobimaximal neutrino mixing (θ 13 ≠ 0, θ 23 = π/4, δ cp=π/2) to be realized with only very small finite calculable deviations from the residual Z 3 lepton triality. This construction solves a long-standing technical problem inherent in renormalizable A 4 models since their inception.

Energy and contact of the one-dimensional Fermi polaron at zero and finite temperature.

PubMed

Doggen, E V H; Kinnunen, J J

2013-07-12

We use the T-matrix approach for studying highly polarized homogeneous Fermi gases in one dimension with repulsive or attractive contact interactions. Using this approach, we compute ground state energies and values for the contact parameter that show excellent agreement with exact and other numerical methods at zero temperature, even in the strongly interacting regime. Furthermore, we derive an exact expression for the value of the contact parameter in one dimension at zero temperature. The model is then extended and used for studying the temperature dependence of ground state energies and the contact parameter.

Summation by parts, projections, and stability

NASA Technical Reports Server (NTRS)

Olsson, Pelle

1993-01-01

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Small violations of Bell inequalities for multipartite pure random states

NASA Astrophysics Data System (ADS)

Drumond, Raphael C.; Duarte, Cristhiano; Oliveira, Roberto I.

2018-05-01

For any finite number of parts, measurements, and outcomes in a Bell scenario, we estimate the probability of random N-qudit pure states to substantially violate any Bell inequality with uniformly bounded coefficients. We prove that under some conditions on the local dimension, the probability to find any significant amount of violation goes to zero exponentially fast as the number of parts goes to infinity. In addition, we also prove that if the number of parts is at least 3, this probability also goes to zero as the local Hilbert space dimension goes to infinity.

Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

NASA Astrophysics Data System (ADS)

Monard, François; Rim, Donsub

2018-07-01

We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality ultrasound modulated electrical impedance tomography for instance. We improve on the algorithms previously derived in Bal et al (2013 Inverse Problems Imaging 7 353–75) Monard and Bal (2013 Commun. PDE 38 1183–207) for both isotropic and anisotropic cases, and we address the well-known issue of vanishing determinants in particular. The algorithm is implemented and we provide numerical results that illustrate the improvements.

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

NASA Astrophysics Data System (ADS)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

Spontaneous magnetic order in complex materials: Role of longitudinal spin-orbit interactions

NASA Astrophysics Data System (ADS)

Chakraborty, Subrata; Vijay, Amrendra

2017-06-01

We show that the longitudinal spin-orbit interactions (SOI) critically determine the fate of spontaneous magnetic order (SMO) in complex materials. To study the magnetic response of interacting electrons constituting the material, we implement an extension of the Hubbard model that faithfully accounts for the SOI. Next, we use the double-time Green functions of quantum statistical mechanics to obtain the spontaneous magnetization, Msp , and thence ascertain the possibility of SMO. For materials with quenched SOI, in an arbitrary dimension, Msp vanishes at finite temperatures, implying the presence of the disordered (paramagnetic) phase. This is consistent with and goes beyond the Bogolyubov's inequality based analysis in one and two dimensions. In the presence of longitudinal SOI, Msp , for materials in an arbitrary dimension, remains non-zero at finite temperatures, which indicates the existence of the ordered (ferromagnetic) phase. As a plausible experimental evidence of the present SOI-based phenomenology, we discuss, inter alia, a recent experimental study on Y4Mn1-xGa12-yGey, an intermetallic compound, which exhibits a magnetic phase transition (paramagnetic to ferromagnetic) upon tuning the fraction of Ge atoms and thence the vacancies of the magnetic centers in this system. The availability of Ge atoms to form a direct chemical bond with octahedral Mn in this material appears to quench the SOI and, as a consequence, favours the formation of the disordered (paramagnetic) phase.

Optimum design of bolted composite lap joints under mechanical and thermal loading

NASA Astrophysics Data System (ADS)

Kradinov, Vladimir Yurievich

A new approach is developed for the analysis and design of mechanically fastened composite lap joints under mechanical and thermal loading. Based on the combined complex potential and variational formulation, the solution method satisfies the equilibrium equations exactly while the boundary conditions are satisfied by minimizing the total potential. This approach is capable of modeling finite laminate planform dimensions, uniform and variable laminate thickness, laminate lay-up, interaction among bolts, bolt torque, bolt flexibility, bolt size, bolt-hole clearance and interference, insert dimensions and insert material properties. Comparing to the finite element analysis, the robustness of the method does not decrease when modeling the interaction of many bolts; also, the method is more suitable for parametric study and design optimization. The Genetic Algorithm (GA), a powerful optimization technique for multiple extrema functions in multiple dimensions search spaces, is applied in conjunction with the complex potential and variational formulation to achieve optimum designs of bolted composite lap joints. The objective of the optimization is to acquire such a design that ensures the highest strength of the joint. The fitness function for the GA optimization is based on the average stress failure criterion predicting net-section, shear-out, and bearing failure modes in bolted lap joints. The criterion accounts for the stress distribution in the thickness direction at the bolt location by applying an approach utilizing a beam on an elastic foundation formulation.

A theoretical analysis and finite element simulation of fixator-bone system stiffness on healing progression.

PubMed

Li, Jianfeng; Zhao, Xia; Hu, Xiaojie; Tao, Chunjing; Ji, Run

2018-03-01

The unilateral external fixator has become a quick and easy application for fracture stabilization of the extremities; the main value for evaluation of mechanical stability of the external fixator is stiffness. The stiffness property of the external fixator affects the local biomechanical environment of fractured bone. In this study, a theoretical model with changing Young's modulus of the callus is established by using the Castigliano's theory, investigating compression stiffness, torsional stiffness and bending stiffness of the fixator-bone system during the healing process. The effects of pin deviation angle on three stiffness methods are also investigated. In addition, finite element simulation is discussed regarding the stress distribution between the fixator and bone. The results reveal the three stiffness evaluation methods are similar for the fixator-bone system. Finite element simulation shows that with increased healing time, the transmission of the load between the fixator and bone are different. In addition, the finite element analyses verify the conclusions obtained from the theoretical model. This work helps orthopedic doctors to monitor the progression of fracture healing and determine the appropriate time for removal of a fixation device and provide important theoretical methodology.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Finite Progressive Planning for the Assembly Process in Footwear

NASA Astrophysics Data System (ADS)

Reyes, John; Aldás, Darwin; Salazar, Edisson; Armendáriz, Evelyn; Álvarez, Kevin; Núñez, José; García, Mario

2017-06-01

The scheduling of the operations of a manufacturing system is recognized for its efficiency in establishing a characteristic rate of production based on the forecasting of the ending date of an order. However, progressive planning focused on the footwear industries has not been studied in detail, since it is limited by the use of machines and supply according to the demand of the production line, whose development is based on just in time. The study proposes a finite progressive planning model in the area of footwear assembly that begins with analysis of the demand and identification of manufacturing constraints in order to establish an optimal ordering sequence. The results show manufacturing requirements through production orders that automatically determine production shifts per order, through experimentation of scenarios, the 25% increase in productivity indicators and a 31% improvement in efficiency are established. This improvement represents higher benefits for the industrial sector when establishing planning in the workplace.

An alternative view of continuous forest inventories

Treesearch

Francis A. Roesch

2008-01-01

A generalized three-dimensional concept of continuous forest inventories applicable to all common forest sample designs is presented and discussed. The concept recognizes the forest through time as a three-dimensional population, two dimensions in land area and the third in time. The sample is selected from a finite three-dimensional partitioning of the population. The...

Statistical mechanics of a single particle in a multiscale random potential: Parisi landscapes in finite-dimensional Euclidean spaces

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.; Bouchaud, Jean-Philippe

2008-08-01

We construct an N-dimensional Gaussian landscape with multiscale, translation invariant, logarithmic correlations and investigate the statistical mechanics of a single particle in this environment. In the limit of high dimension N → ∞ the free energy of the system and overlap function are calculated exactly using the replica trick and Parisi's hierarchical ansatz. In the thermodynamic limit, we recover the most general version of the Derrida's generalized random energy model (GREM). The low-temperature behaviour depends essentially on the spectrum of length scales involved in the construction of the landscape. If the latter consists of K discrete values, the system is characterized by a K-step replica symmetry breaking solution. We argue that our construction is in fact valid in any finite spatial dimensions N >= 1. We discuss the implications of our results for the singularity spectrum describing multifractality of the associated Boltzmann-Gibbs measure. Finally we discuss several generalizations and open problems, such as the dynamics in such a landscape and the construction of a generalized multifractal random walk.

Nonlinear finite-element analysis of nanoindentation of viral capsids

NASA Astrophysics Data System (ADS)

Gibbons, Melissa M.; Klug, William S.

2007-03-01

Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage ϕ29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of ≈280-360MPa for CCMV and ≈4.5GPa for ϕ29 .

Fabrication and characterization of THUNDER actuators—pre-stress-induced nonlinearity in the actuation response

NASA Astrophysics Data System (ADS)

Kim, Younghoon; Cai, Ling; Usher, Timothy; Jiang, Qing

2009-09-01

This paper documents an experimental and theoretical investigation into characterizing the mechanical configurations and performances of THUNDER actuators, a type of piezoelectric actuator known for their large actuation displacements, through fabrication, measurements and finite element analysis. Five groups of such actuators with different dimensions were fabricated using identical fabrication parameters. The as-fabricated arched configurations, resulting from the thermo-mechanical mismatch among the constituent layers, and their actuation performances were characterized using an experimental set-up based on a laser displacement sensor and through numerical simulations with ANSYS, a widely used commercial software program for finite element analysis. This investigation shows that the presence of large residual stresses within the piezoelectric ceramic layer, built up during the fabrication process, leads to significant nonlinear electromechanical coupling in the actuator response to the driving electric voltage, and it is this nonlinear coupling that is responsible for the large actuation displacements. Furthermore, the severity of the residual stresses, and thus the nonlinearity, increases with increasing substrate/piezoelectric thickness ratio and, to a lesser extent, with decreasing in-plane dimensions of the piezoelectric layer.

Transverse Tensile Properties of 3 Dimension-4 Directional Braided Cf/SiC Composite Based on Double-Scale Model

NASA Astrophysics Data System (ADS)

Niu, Xuming; Sun, Zhigang; Song, Yingdong

2017-11-01

In this thesis, a double-scale model for 3 Dimension-4 directional(3D-4d) braided C/SiC composites(CMCs) has been proposed to investigate mechanical properties of it. The double-scale model involves micro-scale which takes fiber/matrix/porosity in fibers tows into consideration and the unit cell scale which considers the 3D-4d braiding structure. Basing on the Micro-optical photographs of composite, we can build a parameterized finite element model that reflects structure of 3D-4d braided composites. The mechanical properties of fiber tows in transverse direction are studied by combining the crack band theory for matrix cracking and cohesive zone model for interface debonding. Transverse tensile process of 3D-4d CMCs can be simulated by introducing mechanical properties of fiber tows into finite element of 3D-4d braided CMCs. Quasi-static tensile tests of 3D-4d braided CMCs have been performed with PWS-100 test system. The predicted tensile stress-strain curve by the double scale model finds good agreement with the experimental results.

Double-trace flows and the swampland

NASA Astrophysics Data System (ADS)

Giombi, Simone; Perlmutter, Eric

2018-03-01

We explore the idea that large N, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite k, deformed by \\int O^2, where O is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in 1 /N. This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large N CFT3 with an Einstein gravity dual.

Modeling the Formation of Transverse Weld during Billet-on-Billet Extrusion

PubMed Central

Mahmoodkhani, Yahya; Wells, Mary; Parson, Nick; Jowett, Chris; Poole, Warren

2014-01-01

A comprehensive mathematical model of the hot extrusion process for aluminum alloys has been developed and validated. The plasticity module was developed using a commercial finite element package, DEFORM-2D, a transient Lagrangian model which couples the thermal and deformation phenomena. Validation of the model against industrial data indicated that it gave excellent predictions of the pressure during extrusion. The finite element predictions of the velocity fields were post-processed to calculate the thickness of the surface cladding as one billet is fed in after another through the die (i.e., the transverse weld). The mathematical model was then used to assess the effect a change in feeder dimensions would have on the shape, thickness and extent of the transverse weld during extrusion. Experimental measurements for different combinations of billet materials show that the model is able to accurately predict the transverse weld shape as well as the clad surface layer to thicknesses of 50 μm. The transverse weld is significantly affected by the feeder geometry shape, but the effects of ram speed, billet material and temperature on the transverse weld dimensions are negligible. PMID:28788629

Quantum gravity in three dimensions, Witten spinors and the quantisation of length

NASA Astrophysics Data System (ADS)

Wieland, Wolfgang

2018-05-01

In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is introduced that couples the gravitational field in the interior to a two-dimensional conformal field theory for an SU (2) boundary spinor, whose norm determines the conformal factor between the fiducial boundary metric and the physical metric in the bulk. The equations of motion for this boundary spinor are derived from the boundary action and turn out to be the two-dimensional analogue of the Witten equations appearing in Witten's proof of the positive mass theorem. The paper concludes with some comments on the resulting quantum theory. It is shown, in particular, that the length of a one-dimensional cross section of the boundary turns into a number operator on the Fock space of the theory. The spectrum of this operator is discrete and matches the results from loop quantum gravity in the spin network representation.

Simulation and evaluation of rupturable coated capsules by finite element method.

PubMed

Yang, Yan; Fang, Jie; Shen, Lian; Shan, Weiguang

2017-03-15

The objective of this study was to simulate and evaluate the burst behavior of rupturable coated capsules by finite element method (FEM). Film and coated capsules were prepared by dip-coating method and their dimensions were determined by stereomicroscope. Mechanical properties of the film were measured by tensile test and used as material properties of FEM models. Swelling pressure was determined by restrained expansion method and applied to the internal surface of FEM models. Water uptake of coated capsules was determined to study the formation of internal pressure. Burst test and in vitro dissolution was used to verify the FEM models, which were used to study and predict the coating burst behavior. Simulated results of coating burst behavior were well agreed with the experiment results. Swelling pressure, material properties and dimensions of coating had influence on the maximum stress. Burst pressure and critical L-HPC content were calculated for burst prediction and formulation optimization. FEM simulation was a feasible way to simulate and evaluate the burst behavior of coated capsules. Copyright © 2017 Elsevier B.V. All rights reserved.

Incommensurate crystallography without additional dimensions.

PubMed

Kocian, Philippe

2013-07-01

It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve compatible with the parameterization of the considered space. In particular, attention is drawn to the fact that one and only one finite and free module of the Lie algebra of the group of translations can generate both modulated and non-modulated lattices, the modulated character being given only by the parameterization of the space in which the lattice is generated. Moreover, it is shown that the diffraction pattern of a structure is directly linked to the action of that free and finite module. In the Fourier transform of a whole structure, the Fourier transform of the electron density of one unit cell (i.e. the structure factor) appears concretely, whether the structure is modulated or not. Thus, there exists a neat separation: the geometrical aspect on the one hand and the action of the group on the other, without requiring additional dimensions.

An efficient Matlab script to calculate heterogeneous anisotropically elastic wave propagation in three dimensions

USGS Publications Warehouse

Boyd, O.S.

2006-01-01

We have created a second-order finite-difference solution to the anisotropic elastic wave equation in three dimensions and implemented the solution as an efficient Matlab script. This program allows the user to generate synthetic seismograms for three-dimensional anisotropic earth structure. The code was written for teleseismic wave propagation in the 1-0.1 Hz frequency range but is of general utility and can be used at all scales of space and time. This program was created to help distinguish among various types of lithospheric structure given the uneven distribution of sources and receivers commonly utilized in passive source seismology. Several successful implementations have resulted in a better appreciation for subduction zone structure, the fate of a transform fault with depth, lithospheric delamination, and the effects of wavefield focusing and defocusing on attenuation. Companion scripts are provided which help the user prepare input to the finite-difference solution. Boundary conditions including specification of the initial wavefield, absorption and two types of reflection are available. ?? 2005 Elsevier Ltd. All rights reserved.

Can phoretic particles swim in two dimensions?

NASA Astrophysics Data System (ADS)

Sondak, David; Hawley, Cory; Heng, Siyu; Vinsonhaler, Rebecca; Lauga, Eric; Thiffeault, Jean-Luc

2016-12-01

Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows, and ultimately the swimming velocity may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Péclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.

Optical Manifestations of the Electron-Electron Interaction

NASA Astrophysics Data System (ADS)

Portengen, Taco

1995-01-01

In this thesis, two optical manifestations of the electron-electron interaction are studied: the Fermi -edge singularity in doped quantum wells and quantum wires, and second-harmonic generation in mixed-valent compounds. First, we construct a theory of the Fermi-edge singularity that can systematically account for the finite mass of a hole created in the valence subband of a quantum well or quantum wire. The dynamical response for finite hole mass depends crucially on the dimensionality of the Fermi sea. Whereas in three dimensions the infrared divergence is suppressed, in two dimensions a one-over-square-root singularity survives, while in one dimension the spectrum is even more singular with recoil than without recoil. This explains the large optical singularities observed in quantum wires. Correlations change the prefactor, but not the exponent of the threshold behaviour in two and in three dimensions, while in one dimension, they affect neither the prefactor nor the exponent. Second, we apply our theory to the Frohlich polaron, a manifestation of the electron-phonon rather than the electron-electron interaction. The new method of calculating the Green's function removes unphysical features of the conventional cumulant expansion that had remained unnoticed in the literature up to now. Third, in an effort to investigate the impact of coherence on optical properties, we calculate the linear and nonlinear optical characteristics of mixed-valent compounds. Second -harmonic generation can only occur for solutions of the theoretical Falicov-Kimball model that have a built-in coherence between the itinerant d-electrons and localized f-holes. By contrast, second-harmonic generation cannot occur for solutions with f-site occupation as a good quantum number. The interaction between optically created quasiparticles leads to a threshold singularity in the absorption spectrum, and greatly enhances the second-harmonic conversion efficiency at half the gap frequency. As an experimental test of coherence we propose the measurement of the second-harmonic susceptibility of SmB_6..

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

A three-dimensional thermal finite element analysis of AISI 304 stainless steel and copper dissimilar weldment

NASA Astrophysics Data System (ADS)

Singh, Gurdeep; Saxena, Ravindra K.; Pandey, Sunil

2018-04-01

The aim of this study to developed a 3-D thermal finite element model for dissimilar material welding of AISI-304 stainless steel and copper. Welding of similar material is widely studied using experimental and numerical methods but the problem becomes trivial for the welding of dissimilar materials especially in ferrous and nonferrous materials. Finite element analysis of dissimilar material welding is a cost-effective method for the understanding and analysis of the process. The finite element analysis has been performed to predict the heat affected zone and temperature distribution in AISI-304 stainless steel and copper dissimilar weldment using MSC Marc 2017®. Due to the difference in physical properties of these materials the behavior of heat affected zone and temperature distribution are perceived to be different. To verify the accuracy of the thermal finite element model, the welding process was simulated with butt-welded joints having same dimensions and parameters from Attarha and Far [1]. It is found from the study that the heat affected zone is larger in copper weld pads than in AISI 304 stainless steel due to large difference in thermal conductivity of these two weld pads.

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Optimizing Nanoscale Quantitative Optical Imaging of Subfield Scattering Targets

PubMed Central

Henn, Mark-Alexander; Barnes, Bryan M.; Zhou, Hui; Sohn, Martin; Silver, Richard M.

2016-01-01

The full 3-D scattered field above finite sets of features has been shown to contain a continuum of spatial frequency information, and with novel optical microscopy techniques and electromagnetic modeling, deep-subwavelength geometrical parameters can be determined. Similarly, by using simulations, scattering geometries and experimental conditions can be established to tailor scattered fields that yield lower parametric uncertainties while decreasing the number of measurements and the area of such finite sets of features. Such optimized conditions are reported through quantitative optical imaging in 193 nm scatterfield microscopy using feature sets up to four times smaller in area than state-of-the-art critical dimension targets. PMID:27805660

A Kernel-Free Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 4

NASA Technical Reports Server (NTRS)

Park, Young-Keun; Fahrenthold, Eric P.

2004-01-01

An improved hybrid particle-finite element method has been developed for the simulation of hypervelocity impact problems. Unlike alternative methods, the revised formulation computes the density without reference to any kernel or interpolation functions, for either the density or the rate of dilatation. This simplifies the state space model and leads to a significant reduction in computational cost. The improved method introduces internal energy variables as generalized coordinates in a new formulation of the thermomechanical Lagrange equations. Example problems show good agreement with exact solutions in one dimension and good agreement with experimental data in a three dimensional simulation.

On the sighting of unicorns: A variational approach to computing invariant sets in dynamical systems

NASA Astrophysics Data System (ADS)

Junge, Oliver; Kevrekidis, Ioannis G.

2017-06-01

We propose to compute approximations to invariant sets in dynamical systems by minimizing an appropriate distance between a suitably selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments, that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topology, dimension, and stability, such as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function, which yields more evenly distributed approximating finite point sets, and illustrate the procedure through corresponding numerical experiments.

On the sighting of unicorns: A variational approach to computing invariant sets in dynamical systems.

PubMed

Junge, Oliver; Kevrekidis, Ioannis G

2017-06-01

We propose to compute approximations to invariant sets in dynamical systems by minimizing an appropriate distance between a suitably selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments, that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topology, dimension, and stability, such as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function, which yields more evenly distributed approximating finite point sets, and illustrate the procedure through corresponding numerical experiments.

A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

NASA Technical Reports Server (NTRS)

Steger, J. L.; Dougherty, F. C.; Benek, J. A.

1983-01-01

A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

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

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1975-10-01

The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P$sub 1$) in up to three- dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First- order perturbation analysis capability is available at the macroscopic cross section level. (auth)

A two-dimensional, finite-difference model of the oxidation of a uranium carbide fuel pellet

NASA Astrophysics Data System (ADS)

Shepherd, James; Fairweather, Michael; Hanson, Bruce C.; Heggs, Peter J.

2015-12-01

The oxidation of spent uranium carbide fuel, a candidate fuel for Generation IV nuclear reactors, is an important process in its potential reprocessing cycle. However, the oxidation of uranium carbide in air is highly exothermic. A model has therefore been developed to predict the temperature rise, as well as other useful information such as reaction completion times, under different reaction conditions in order to help in deriving safe oxidation conditions. Finite difference-methods are used to model the heat and mass transfer processes occurring during the reaction in two dimensions and are coupled to kinetics found in the literature.

Active invisibility cloaks in one dimension

NASA Astrophysics Data System (ADS)

Mostafazadeh, Ali

2015-06-01

We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential, v (x ) , unidirectionally reflectionless or invisible at a wave number, k0, of our choice. We give explicit analytic expressions for three classes of cloaking potentials which achieve this goal while preserving some or all of the other scattering properties of v (x ) . The cloaking potentials we construct are the sum of up to three constituent unidirectionally invisible potentials. We discuss their utility in making v (x ) bidirectionally invisible at k0 and demonstrate the application of our method to obtain antireflection and invisibility cloaks for a Bragg reflector.

Hyperscaling breakdown and Ising spin glasses: The Binder cumulant

NASA Astrophysics Data System (ADS)

Lundow, P. H.; Campbell, I. A.

2018-02-01

Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region.

FAST TRACK COMMUNICATION: Ground-state fidelity and entanglement entropy for the quantum three-state Potts model in one spatial dimension

NASA Astrophysics Data System (ADS)

Dai, Yan-Wei; Hu, Bing-Quan; Zhao, Jian-Hui; Zhou, Huan-Qiang

2010-09-01

The ground-state fidelity per lattice site is computed for the quantum three-state Potts model in a transverse magnetic field on an infinite-size lattice in one spatial dimension in terms of the infinite matrix product state algorithm. It is found that, on the one hand, a pinch point is identified on the fidelity surface around the critical point, and on the other hand, the ground-state fidelity per lattice site exhibits bifurcations at pseudo critical points for different values of the truncation dimension, which in turn approach the critical point as the truncation dimension becomes large. This implies that the ground-state fidelity per lattice site enables us to capture spontaneous symmetry breaking when the control parameter crosses the critical value. In addition, a finite-entanglement scaling of the von Neumann entropy is performed with respect to the truncation dimension, resulting in a precise determination of the central charge at the critical point. Finally, we compute the transverse magnetization, from which the critical exponent β is extracted from the numerical data.

Generation of a composite grid for turbine flows and consideration of a numerical scheme

NASA Technical Reports Server (NTRS)

Choo, Y.; Yoon, S.; Reno, C.

1986-01-01

A composite grid was generated for flows in turbines. It consisted of the C-grid (or O-grid) in the immediate vicinity of the blade and the H-grid in the middle of the blade passage between the C-grids and in the upstream region. This new composite grid provides better smoothness, resolution, and orthogonality than any single grid for a typical turbine blade with a large camber and rounded leading and trailing edges. The C-H (or O-H) composite grid has an unusual grid point that is connected to more than four neighboring nodes in two dimensions (more than six neighboring nodes in three dimensions). A finite-volume lower-upper (LU) implicit scheme to be used on this grid poses no problem and requires no special treatment because each interior cell of this composite grid has only four neighboring cells in two dimensions (six cells in three dimensions). The LU implicit scheme was demonstrated to be efficient and robust for external flows in a broad flow regime and can be easily applied to internal flows and extended from two to three dimensions.

Gradient optimization of finite projected entangled pair states

NASA Astrophysics Data System (ADS)

Liu, Wen-Yuan; Dong, Shao-Jun; Han, Yong-Jian; Guo, Guang-Can; He, Lixin

2017-05-01

Projected entangled pair states (PEPS) methods have been proven to be powerful tools to solve strongly correlated quantum many-body problems in two dimensions. However, due to the high computational scaling with the virtual bond dimension D , in a practical application, PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, frustrated systems. Optimization of the ground state using the imaginary time evolution method with a simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that by combining the imaginary time evolution method with a simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking advantage of massive parallel computing, we can study quantum systems with larger bond dimensions up to D =10 without resorting to any symmetry. Benchmark tests of the method on the J1-J2 model give impressive accuracy compared with exact results.

PRELIMINARY PROGRESS IN THE DEVELOPMENT OF DUCTILE-PHASE TOUGHENED TUNGSTEN FOR PLASMA-FACING MATERIALS: DUAL-PHASE FINITE ELEMENT DAMAGE MODELS

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

Henager, Charles H.; Nguyen, Ba Nghiep; Kurtz, Richard J.

The objective of this study is to develop a finite element continuum damage model suitable for modeling deformation, cracking, and crack bridging for W-Cu, W-Ni-Fe, and other ductile phase toughened W-composites, or more generally, any multi-phase composite structure where two or more phases undergo cooperative deformation in a composite system.

Applying Item Response Theory methods to design a learning progression-based science assessment

NASA Astrophysics Data System (ADS)

Chen, Jing

Learning progressions are used to describe how students' understanding of a topic progresses over time and to classify the progress of students into steps or levels. This study applies Item Response Theory (IRT) based methods to investigate how to design learning progression-based science assessments. The research questions of this study are: (1) how to use items in different formats to classify students into levels on the learning progression, (2) how to design a test to give good information about students' progress through the learning progression of a particular construct and (3) what characteristics of test items support their use for assessing students' levels. Data used for this study were collected from 1500 elementary and secondary school students during 2009--2010. The written assessment was developed in several formats such as the Constructed Response (CR) items, Ordered Multiple Choice (OMC) and Multiple True or False (MTF) items. The followings are the main findings from this study. The OMC, MTF and CR items might measure different components of the construct. A single construct explained most of the variance in students' performances. However, additional dimensions in terms of item format can explain certain amount of the variance in student performance. So additional dimensions need to be considered when we want to capture the differences in students' performances on different types of items targeting the understanding of the same underlying progression. Items in each item format need to be improved in certain ways to classify students more accurately into the learning progression levels. This study establishes some general steps that can be followed to design other learning progression-based tests as well. For example, first, the boundaries between levels on the IRT scale can be defined by using the means of the item thresholds across a set of good items. Second, items in multiple formats can be selected to achieve the information criterion at all the defined boundaries. This ensures the accuracy of the classification. Third, when item threshold parameters vary a bit, the scoring rubrics and the items need to be reviewed to make the threshold parameters similar across items. This is because one important design criterion of the learning progression-based items is that ideally, a student should be at the same level across items, which means that the item threshold parameters (d1, d 2 and d3) should be similar across items. To design a learning progression-based science assessment, we need to understand whether the assessment measures a single construct or several constructs and how items are associated with the constructs being measured. Results from dimension analyses indicate that items of different carbon transforming processes measure different aspects of the carbon cycle construct. However, items of different practices assess the same construct. In general, there are high correlations among different processes or practices. It is not clear whether the strong correlations are due to the inherent links among these process/practice dimensions or due to the fact that the student sample does not show much variation in these process/practice dimensions. Future data are needed to examine the dimensionalities in terms of process/practice in detail. Finally, based on item characteristics analysis, recommendations are made to write more discriminative CR items and better OMC, MTF options. Item writers can follow these recommendations to write better learning progression-based items.

Disease Severity and Progression in Progressive Supranuclear Palsy and Multiple System Atrophy: Validation of the NNIPPS – PARKINSON PLUS SCALE

PubMed Central

Payan, Christine A. M.; Viallet, François; Landwehrmeyer, Bernhard G.; Bonnet, Anne-Marie; Borg, Michel; Durif, Franck; Lacomblez, Lucette; Bloch, Frédéric; Verny, Marc; Fermanian, Jacques; Agid, Yves; Ludolph, Albert C.

2011-01-01

Background The Natural History and Neuroprotection in Parkinson Plus Syndromes (NNIPPS) study was a large phase III randomized placebo-controlled trial of riluzole in Progressive Supranuclear Palsy (PSP, n = 362) and Multiple System Atrophy (MSA, n = 398). To assess disease severity and progression, we constructed and validated a new clinical rating scale as an ancillary study. Methods and Findings Patients were assessed at entry and 6-montly for up to 3 years. Evaluation of the scale's psychometric properties included reliability (n = 116), validity (n = 760), and responsiveness (n = 642). Among the 85 items of the initial scale, factor analysis revealed 83 items contributing to 15 clinically relevant dimensions, including Activity of daily Living/Mobility, Axial bradykinesia, Limb bradykinesia, Rigidity, Oculomotor, Cerebellar, Bulbar/Pseudo-bulbar, Mental, Orthostatic, Urinary, Limb dystonia, Axial dystonia, Pyramidal, Myoclonus and Tremor. All but the Pyramidal dimension demonstrated good internal consistency (Cronbach α≥0.70). Inter-rater reliability was high for the total score (Intra-class coefficient = 0.94) and 9 dimensions (Intra-class coefficient = 0.80–0.93), and moderate (Intra-class coefficient = 0.54–0.77) for 6. Correlations of the total score with other clinical measures of severity were good (rho≥0.70). The total score was significantly and linearly related to survival (p<0.0001). Responsiveness expressed as the Standardized Response Mean was high for the total score slope of change (SRM = 1.10), though higher in PSP (SRM = 1.25) than in MSA (SRM = 1.0), indicating a more rapid progression of PSP. The slope of change was constant with increasing disease severity demonstrating good linearity of the scale throughout disease stages. Although MSA and PSP differed quantitatively on the total score at entry and on rate of progression, the relative contribution of clinical dimensions to overall severity and progression was similar. Conclusions The NNIPPS-PPS has suitable validity, is reliable and sensitive, and therefore is appropriate for use in clinical studies with PSP or MSA. Trial Registration ClinicalTrials.gov NCT00211224 PMID:21829612

Spatial Thinking as the Dimension of Progress in an Astronomy Learning Progression

ERIC Educational Resources Information Center

Plummer, Julia D.

2014-01-01

The big idea of "celestial motion", observational astronomy phenomena explained by the relative position and motion of objects in the solar system and beyond, is central to astronomy in primary and secondary education. In this paper, I argue that students' progress in developing productive, scientific explanations for this class of…

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Eigensolution of finite element problems in a completely connected parallel architecture

NASA Technical Reports Server (NTRS)

Akl, F.; Morel, M.

1989-01-01

A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm is successfully implemented on a tightly coupled MIMD parallel processor. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts, and the dimension of the subspace on the performance of the algorithm is investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18, and 3.61 are achieved on two, four, six, and eight processors, respectively.

Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Dániel; Zaletel, Michael P.; Moore, Joel E.

2013-10-01

We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

Affine cellularity of finite type KLR algebras, and homomorphisms between Specht modules for KLR algebras in affine type A

NASA Astrophysics Data System (ADS)

Loubert, Joseph William

This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras Ralpha of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in Ralpha are generated by idempotents. This in particular implies the (known) result that the global dimension of Ralpha is finite. In the second part we use the presentation of the Specht modules given by Kleshchev-Mathas-Ram to derive results about Specht modules. In particular, we determine all homomorphisms from an arbitrary Specht module to a fixed Specht module corresponding to any hook partition. Along the way, we give a complete description of the action of the standard KLR generators on the hook Specht module. This work generalizes a result of James. This dissertation includes previously published coauthored material.

Hydrodynamic interaction of two particles in confined linear shear flow at finite Reynolds number

NASA Astrophysics Data System (ADS)

Yan, Yiguang; Morris, Jeffrey F.; Koplik, Joel

2007-11-01

We discuss the hydrodynamic interactions of two solid bodies placed in linear shear flow between parallel plane walls in a periodic geometry at finite Reynolds number. The computations are based on the lattice Boltzmann method for particulate flow, validated here by comparison to previous results for a single particle. Most of our results pertain to cylinders in two dimensions but some examples are given for spheres in three dimensions. Either one mobile and one fixed particle or else two mobile particles are studied. The motion of a mobile particle is qualitatively similar in both cases at early times, exhibiting either trajectory reversal or bypass, depending upon the initial vector separation of the pair. At longer times, if a mobile particle does not approach a periodic image of the second, its trajectory tends to a stable limit point on the symmetry axis. The effect of interactions with periodic images is to produce nonconstant asymptotic long-time trajectories. For one free particle interacting with a fixed second particle within the unit cell, the free particle may either move to a fixed point or take up a limit cycle. Pairs of mobile particles starting from symmetric initial conditions are shown to asymptotically reach either fixed points, or mirror image limit cycles within the unit cell, or to bypass one another (and periodic images) indefinitely on a streamwise periodic trajectory. The limit cycle possibility requires finite Reynolds number and arises as a consequence of streamwise periodicity when the system length is sufficiently short.

Scaling relations for watersheds

NASA Astrophysics Data System (ADS)

Fehr, E.; Kadau, D.; Araújo, N. A. M.; Andrade, J. S., Jr.; Herrmann, H. J.

2011-09-01

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical simulations. We find the fractal dimension of the watersheds to generally decrease with the Hurst exponent, which quantifies the degree of spatial correlations. Moreover, in two dimensions, our results match the range of fractal dimensions 1.10≤df≤1.15 observed for natural landscapes. We report that the watershed is strongly affected by local perturbations. For perturbed two and three dimensional systems, we observe a power-law scaling behavior for the distribution of areas (volumes) enclosed by the original and the displaced watershed and for the distribution of distances between outlets. Finite-size effects are analyzed and the resulting scaling exponents are shown to depend significantly on the Hurst exponent. The intrinsic relation between watershed and invasion percolation, as well as relations between exponents conjectured in previous studies with two dimensional systems, are now confirmed by our results in three dimensions.

On the complexity and approximability of some Euclidean optimal summing problems

NASA Astrophysics Data System (ADS)

Eremeev, A. V.; Kel'manov, A. V.; Pyatkin, A. V.

2016-10-01

The complexity status of several well-known discrete optimization problems with the direction of optimization switching from maximum to minimum is analyzed. The task is to find a subset of a finite set of Euclidean points (vectors). In these problems, the objective functions depend either only on the norm of the sum of the elements from the subset or on this norm and the cardinality of the subset. It is proved that, if the dimension of the space is a part of the input, then all these problems are strongly NP-hard. Additionally, it is shown that, if the space dimension is fixed, then all the problems are NP-hard even for dimension 2 (on a plane) and there are no approximation algorithms with a guaranteed accuracy bound for them unless P = NP. It is shown that, if the coordinates of the input points are integer, then all the problems can be solved in pseudopolynomial time in the case of a fixed space dimension.

Variational extension of the mean spherical approximation to arbitrary dimensions

NASA Astrophysics Data System (ADS)

Velázquez, Esov S.; Blum, Lesser; Frisch, Harry L.

1997-10-01

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limit T ΔS MSA / ΔE MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while for d=2 this limit is 1.

Fortuin-Kasteleyn and damage-spreading transitions in random-bond Ising lattices

NASA Astrophysics Data System (ADS)

Lundow, P. H.; Campbell, I. A.

2012-10-01

The Fortuin-Kasteleyn and heat-bath damage-spreading temperatures TFK(p) and TDS(p) are studied on random-bond Ising models of dimensions 2-5 and as functions of the ferromagnetic interaction probability p; the conjecture that TDS(p)˜TFK(p) is tested. It follows from a statement by Nishimori that in any such system, exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn TFK(p) transition line and the Nishimori line [pNL,FK,TNL,FK]. There are no finite-size corrections for this intersection point. In dimension 3, at the intersection concentration [pNL,FK], the damage spreading TDS(p) is found to be equal to TFK(p) to within 0.1%. For the other dimensions, however, TDS(p) is observed to be systematically a few percent lower than TFK(p).

Nonlinear Waves.

DTIC Science & Technology

1988-02-01

in Multi- dimensions II, P.M. Santini and A.S. Fokas, preprint INS#67, 1986. The Recursion Operator of the Kadomtsev - Petviashvili Equation and the...solitons, multidimensional inverse problems, Painleve equations , direct linearizations of certain nonlinear wave equations , DBAR problems, Riemann...the Navy is (a) the recent discovery that many of the equations describing ship hydrodynamics in channels of finite depth obey nonlinear equations

Spinning Q-balls in the complex signum-Gordon model

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

Arodz, H.; Karkowski, J.; Swierczynski, Z.

2009-09-15

Rotational excitations of compact Q-balls in the complex signum-Gordon model in 2+1 dimensions are investigated. We find that almost all such spinning Q-balls have the form of a ring of strictly finite width. In the limit of large angular momentum M{sub z}, their energy is proportional to |M{sub z}|{sup 1/5}.

Optical response of bowtie antennas

NASA Astrophysics Data System (ADS)

Guo, Ying-Nan; Pan, Shi; Li, Xu-Feng; Wang, Shuo; Wang, Qiao

2010-10-01

Optical properties of bowtie antennas are investigated using a numerical method of finite-difference time-domain (FDTD). The optical response in the antenna feed gap is simulated as functions of its geometry parameters (flare angle, arm length, apex width, thickness, gap dimension, as well as the index of substrate), which provide a clear guideline to exploit such antenna structures in practice.

Effective equilibrium picture in the x y model with exponentially correlated noise

NASA Astrophysics Data System (ADS)

Paoluzzi, Matteo; Marconi, Umberto Marini Bettolo; Maggi, Claudio

2018-02-01

We study the effect of exponentially correlated noise on the x y model in the limit of small correlation time, discussing the order-disorder transition in the mean field and the topological transition in two dimensions. We map the steady states of the nonequilibrium dynamics into an effective equilibrium theory. In the mean field, the critical temperature increases with the noise correlation time τ , indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite-size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations.

Bound states in string nets

NASA Astrophysics Data System (ADS)

Schulz, Marc Daniel; Dusuel, Sébastien; Vidal, Julien

2016-11-01

We discuss the emergence of bound states in the low-energy spectrum of the string-net Hamiltonian in the presence of a string tension. In the ladder geometry, we show that a single bound state arises either for a finite tension or in the zero-tension limit depending on the theory considered. In the latter case, we perturbatively compute the binding energy as a function of the total quantum dimension. We also address this issue in the honeycomb lattice where the number of bound states in the topological phase depends on the total quantum dimension. Finally, the internal structure of these bound states is analyzed in the zero-tension limit.

Singular flow dynamics in three space dimensions driven by advection

NASA Astrophysics Data System (ADS)

Karimov, A. R.; Schamel, H.

2002-03-01

The initial value problem of an ideal, compressible fluid is investigated in three space dimensions (3D). Starting from a situation where the inertia terms dominate over the force terms in Euler's equation we explore by means of the Lagrangian flow description the basic flow properties. Special attention is drawn to the appearance of singularities in the flow pattern at finite time. Classes of initial velocity profiles giving rise to collapses of density and vorticity are found. This paper, hence, furnishes evidence of focused singularities for coherent structures obeying the 3D Euler equation and applies to potential as well as vortex flows.

Effective equilibrium picture in the xy model with exponentially correlated noise.

PubMed

Paoluzzi, Matteo; Marconi, Umberto Marini Bettolo; Maggi, Claudio

2018-02-01

We study the effect of exponentially correlated noise on the xy model in the limit of small correlation time, discussing the order-disorder transition in the mean field and the topological transition in two dimensions. We map the steady states of the nonequilibrium dynamics into an effective equilibrium theory. In the mean field, the critical temperature increases with the noise correlation time τ, indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite-size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations.

Nucleation and growth in one dimension

NASA Astrophysics Data System (ADS)

Ben-Naim, E.; Krapivsky, P. L.

1996-10-01

We study statistical properties of the Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model in one dimension. We obtain exact results for the gap density as well as the island distribution. When all nucleation events occur simultaneously, we show that the island distribution has discontinuous derivatives on the rays xn(t)=nt, n=1,2,3... . We introduce an accelerated growth mechanism with growth rate increasing linearly with the island size. We solve for the interisland gap density and show that the system reaches complete coverage in a finite time and that the near-critical behavior of the system is robust; i.e., it is insensitive to details such as the nucleation mechanism.

Mott transition between a spin-liquid insulator and a metal in three dimensions.

PubMed

Podolsky, Daniel; Paramekanti, Arun; Kim, Yong Baek; Senthil, T

2009-05-08

We study a bandwidth controlled Mott metal-insulator transition (MIT) from a Fermi-liquid metal to a quantum spin-liquid insulator in three dimensions. Using a slave rotor approach including gauge fluctuations, we obtain a continuous MIT and discuss finite temperature crossovers in its vicinity. We show that the specific heat C approximately Tlnln(1/T) at the MIT and that the metallic state near the MIT should exhibit a "conductivity minimum" as a function of temperature. We suggest Na4Ir3O8 as a candidate to test our predictions and compute its electron spectral function at the MIT.

Analytical Proof That There is no Effect of Confinement or Curvature on the Maxwell-Boltzmann Collision Frequency

NASA Astrophysics Data System (ADS)

Carnio, Brett N.; Elliott, Janet A. W.

2014-08-01

The number of Maxwell-Boltzmann particles that hit a flat wall in infinite space per unit area per unit time is a well-known result. As new applications are arising in micro and nanotechnologies there are a number of situations in which a rarefied gas interacts with either a flat or curved surface in a small confined geometry. Thus, it is necessary to prove that the Maxwell-Boltzmann collision frequency result holds even if a container's dimensions are on the order of nanometers and also that this result is valid for both a finite container with flat walls (a rectangular container) and a finite container with a curved wall (a cylindrical container). An analytical proof confirms that the Maxwell-Boltzmann collision frequencies for either a finite rectangular container or a finite cylindrical container are both equal to the well-known result obtained for a flat wall in infinite space. A major aspect of this paper is the introduction of a mathematical technique to solve the arising infinite sum of integrals whose integrands depend on the Maxwell-Boltzmann velocity distribution.

Efficient finite element simulation of slot spirals, slot radomes and microwave structures

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.

1995-01-01

This progress report contains the following two documents: (1) 'Efficient Finite Element Simulation of Slot Antennas using Prismatic Elements' - A hybrid finite element-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic elements are used to reduce the redundant sampling rates and ease the mesh generation process. Numerical results for an antenna slot and frequency selective surfaces are presented to demonstrate the validity and capability of the technique; and (2) 'Application and Design Guidelines of the PML Absorber for Finite Element Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain finite element simulations has several advantages. In this paper we present the application of PML for microwave circuit simulations along with design guidelines to obtain a desired level of absorption. Different feeding techniques are also investigated for improved accuracy.

A stochastic-field description of finite-size spiking neural networks

PubMed Central

Longtin, André

2017-01-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

2002-01-01

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions

NASA Astrophysics Data System (ADS)

Hoffman, M. D.; Loheac, A. C.; Porter, W. J.; Drut, J. E.

2017-03-01

Motivated by advances in the manipulation and detection of ultracold atoms with multiple internal degrees of freedom, we present a finite-temperature lattice Monte Carlo calculation of the density and pressure equations of state, as well as Tan's contact, of attractively interacting SU(4)- and SU(6)-symmetric fermion systems in one spatial dimension. We also furnish a nonperturbative proof of a universal relation whereby quantities computable in the SU(2) case completely determine the virial coefficients of the SU(Nf) case. These one-dimensional systems are appealing because they can be experimentally realized in highly constrained traps and because of the dominant role played by correlations. The latter are typically nonperturbative and are crucial for understanding ground states and quantum phase transitions. While quantum fluctuations are typically overpowered by thermal ones in one and two dimensions at any finite temperature, we find that quantum effects do leave their imprint in thermodynamic quantities. Our calculations show that the additional degrees of freedom, relative to the SU(2) case, provide a dramatic enhancement of the density and pressure (in units of their noninteracting counterparts) in a wide region around vanishing β μ , where β is the inverse temperature and μ the chemical potential. As shown recently in experiments, the thermodynamics we explore here can be measured in a controlled and precise fashion in highly constrained traps and optical lattices. Our results are a prediction for such experiments in one dimension with atoms of high nuclear spin.

Scientific progress without increasing verisimilitude: In response to Niiniluoto.

PubMed

Rowbottom, Darrell P

2015-06-01

First, I argue that scientific progress is possible in the absence of increasing verisimilitude in science's theories. Second, I argue that increasing theoretical verisimilitude is not the central, or primary, dimension of scientific progress. Third, I defend my previous argument that unjustified changes in scientific belief may be progressive. Fourth, I illustrate how false beliefs can promote scientific progress in ways that cannot be explicated by appeal to verisimilitude. Copyright © 2015 Elsevier Ltd. All rights reserved.

Physics in One Dimension

ERIC Educational Resources Information Center

Bertel, Erminald

2013-01-01

Due to progress in nanotechnology high-quality quantum wires can nowadays be fabricated. The behavior of particles in one dimension differs significantly from that in three-dimensional (3D) systems, yet the physics of such low-dimensional systems is generally not very well represented in standard undergraduate or graduate curricula. For instance,…

Continental Drift: A Discussion Strategy for Secondary School

ERIC Educational Resources Information Center

Paixao, Isabel; Calado, Silvia; Ferreira, Silvia; Salves, Vanda; Smorais, Ana M.

2004-01-01

The paper describes a discussion strategy for secondary school students. The strategy focus the various dimensions of Science, especially the internal sociological and philosophical dimensions. Students are expected to learn more about Science, namely the role of controversy for scientific progress. The article contains key questions for the…

Evaluation of a Progressive Failure Analysis Methodology for Laminated Composite Structures

NASA Technical Reports Server (NTRS)

Sleight, David W.; Knight, Norman F., Jr.; Wang, John T.

1997-01-01

A progressive failure analysis methodology has been developed for predicting the nonlinear response and failure of laminated composite structures. The progressive failure analysis uses C plate and shell elements based on classical lamination theory to calculate the in-plane stresses. Several failure criteria, including the maximum strain criterion, Hashin's criterion, and Christensen's criterion, are used to predict the failure mechanisms. The progressive failure analysis model is implemented into a general purpose finite element code and can predict the damage and response of laminated composite structures from initial loading to final failure.

Stability and phase transition of skyrmion crystals generated by Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

El Hog, Sahbi; Bailly-Reyre, Aurélien; Diep, H. T.

2018-06-01

We generate a crystal of skyrmions in two dimensions using a Heisenberg Hamiltonian including the ferromagnetic interaction J, the Dzyaloshinskii-Moriya interaction D, and an applied magnetic field H. The ground state (GS) is determined by minimizing the interaction energy. We show that the GS is a skyrmion crystal in a region of (D, H) . The stability of this skyrmion crystalline phase at finite temperatures is shown by a study of the time-dependence of the order parameter using Monte Carlo simulations. We observe that the relaxation is very slow and follows a stretched exponential law. The skyrmion crystal phase is shown to undergo a transition to the paramagnetic state at a finite temperature.

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

NASA Astrophysics Data System (ADS)

Regnier, D.; Verrière, M.; Dubray, N.; Schunck, N.

2016-03-01

We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.

Accuracy of a class of concurrent algorithms for transient finite element analysis

NASA Technical Reports Server (NTRS)

Ortiz, Michael; Sotelino, Elisa D.; Nour-Omid, Bahram

1988-01-01

The accuracy of a new class of concurrent procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.

Bin packing problem solution through a deterministic weighted finite automaton

NASA Astrophysics Data System (ADS)

Zavala-Díaz, J. C.; Pérez-Ortega, J.; Martínez-Rebollar, A.; Almanza-Ortega, N. N.; Hidalgo-Reyes, M.

2016-06-01

In this article the solution of Bin Packing problem of one dimension through a weighted finite automaton is presented. Construction of the automaton and its application to solve three different instances, one synthetic data and two benchmarks are presented: N1C1W1_A.BPP belonging to data set Set_1; and BPP13.BPP belonging to hard28. The optimal solution of synthetic data is obtained. In the first benchmark the solution obtained is one more container than the ideal number of containers and in the second benchmark the solution is two more containers than the ideal solution (approximately 2.5%). The runtime in all three cases was less than one second.

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.

Gapless Spin-Liquid Ground State in the S =1 /2 Kagome Antiferromagnet

NASA Astrophysics Data System (ADS)

Liao, H. J.; Xie, Z. Y.; Chen, J.; Liu, Z. Y.; Xie, H. D.; Huang, R. Z.; Normand, B.; Xiang, T.

2017-03-01

The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S =1 /2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result.

Development of a Finite-Difference Time Domain (FDTD) Model for Propagation of Transient Sounds in Very Shallow Water.

PubMed

Sprague, Mark W; Luczkovich, Joseph J

2016-01-01

This finite-difference time domain (FDTD) model for sound propagation in very shallow water uses pressure and velocity grids with both 3-dimensional Cartesian and 2-dimensional cylindrical implementations. Parameters, including water and sediment properties, can vary in each dimension. Steady-state and transient signals from discrete and distributed sources, such as the surface of a vibrating pile, can be used. The cylindrical implementation uses less computation but requires axial symmetry. The Cartesian implementation allows asymmetry. FDTD calculations compare well with those of a split-step parabolic equation. Applications include modeling the propagation of individual fish sounds, fish aggregation sounds, and distributed sources.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

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

Assessment of the performance of rigid pavement back-calculation through finite element modeling

NASA Astrophysics Data System (ADS)

Shoukry, Samir N.; William, Gergis W.; Martinelli, David R.

1999-02-01

This study focuses on examining the behavior of rigid pavement layers during the Falling Weight Deflectometer (FWD) test. Factors affecting the design of a concrete slab, such as whether the joints are doweled or undoweled and the spacing between the transverse joints, were considered in this study. Explicit finite element analysis was employed to investigate pavement layers' responses to the action of the impulse of the FWD test. Models of various dimensions were developed to satisfy the factors under consideration. The accuracy of the finite element models developed in this investigation was verified by comparing the finite element- generated deflection basin with that experimentally measured during an actual test. The results showed that the measured deflection basin can be reproduced through finite element modeling of the pavement structure. The resulting deflection basins from the use FE modeling was processed in order to backcalculate pavement layer moduli. This approach provides a method for the evaluation of the performance of existing backcalculation programs which are based on static elastic layer analysis. Based upon the previous studies conducted for the selection of software, three different backcalculation programs were chosen for the evaluation: MODULUS5.0, EVERCALC4.0, and MODCOMP3. The results indicate that ignoring the dynamic nature of the load may lead to crude results, especially during backcalculation procedures.

Optical frequency selective surface design using a GPU accelerated finite element boundary integral method

NASA Astrophysics Data System (ADS)

Ashbach, Jason A.

Periodic metallodielectric frequency selective surface (FSS) designs have historically seen widespread use in the microwave and radio frequency spectra. By scaling the dimensions of an FSS unit cell for use in a nano-fabrication process, these concepts have recently been adapted for use in optical applications as well. While early optical designs have been limited to wellunderstood geometries or optimized pixelated screens, nano-fabrication, lithographic and interconnect technology has progressed to a point where it is possible to fabricate metallic screens of arbitrary geometries featuring curvilinear or even three-dimensional characteristics that are only tens of nanometers wide. In order to design an FSS featuring such characteristics, it is important to have a robust numerical solver that features triangular elements in purely two-dimensional geometries and prismatic or tetrahedral elements in three-dimensional geometries. In this dissertation, a periodic finite element method code has been developed which features prismatic elements whose top and bottom boundaries are truncated by numerical integration of the boundary integral as opposed to an approximate representation found in a perfectly matched layer. However, since no exact solution exists for the calculation of triangular elements in a boundary integral, this process can be time consuming. To address this, these calculations were optimized for parallelization such that they may be done on a graphics processor, which provides a large increase in computational speed. Additionally, a simple geometrical representation using a Bezier surface is presented which provides generality with few variables. With a fast numerical solver coupled with a lowvariable geometric representation, a heuristic optimization algorithm has been used to develop several optical designs such as an absorber, a circular polarization filter, a transparent conductive surface and an enhanced, optical modulator.

Two-point correlation function for Dirichlet L-functions

NASA Astrophysics Data System (ADS)

Bogomolny, E.; Keating, J. P.

2013-03-01

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.

Universalities of thermodynamic signatures in topological phases

PubMed Central

Kempkes, S. N.; Quelle, A.; Smith, C. Morais

2016-01-01

Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase transition the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter. PMID:27929041

Universalities of thermodynamic signatures in topological phases.

PubMed

Kempkes, S N; Quelle, A; Smith, C Morais

2016-12-08

Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase transition the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter.

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems

NASA Astrophysics Data System (ADS)

Dashti-Naserabadi, H.; Najafi, M. N.

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension Du=4 . After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d -dimensional cross sections and the d -dimensional BTW model for d =2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops df, which is found to be 1.50 ±0.02 ≈3/2 =dfGFF .

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems.

PubMed

Dashti-Naserabadi, H; Najafi, M N

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension D_{u}=4. After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d-dimensional cross sections and the d-dimensional BTW model for d=2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops d_{f}, which is found to be 1.50±0.02≈3/2=d_{f}^{GFF}.

Effects of transverse temperature field nonuniformity on stress in silicon sheet growth

NASA Technical Reports Server (NTRS)

Mataga, P. A.; Hutchinson, J. W.; Chalmers, B.; Bell, R. O.; Kalejs, J. P.

1987-01-01

Stress and strain rate distributions are calculated using finite element analysis for steady-state growth of thin silicon sheet temperature nonuniformities imposed in the transverse (sheet width) dimension. Significant reductions in residual stress are predicted to occur for the case where the sheet edge is cooled relative to its center provided plastic deformation with high creep rates is present.

A superconducting nanowire can be modeled by using SPICE

NASA Astrophysics Data System (ADS)

Berggren, Karl K.; Zhao, Qing-Yuan; Abebe, Nathnael; Chen, Minjie; Ravindran, Prasana; McCaughan, Adam; Bardin, Joseph C.

2018-05-01

Modeling of superconducting nanowire single-photon detectors typically requires custom simulations or finite-element analysis in one or two dimensions. Here, we demonstrate two simplified one-dimensional SPICE models of a superconducting nanowire that can quickly and efficiently describe the electrical characteristics of a superconducting nanowire. These models may be of particular use in understanding alternative architectures for nanowire detectors and readouts.

Detecting Lower Bounds to Quantum Channel Capacities.

PubMed

Macchiavello, Chiara; Sacchi, Massimiliano F

2016-04-08

We propose a method to detect lower bounds to quantum capacities of a noisy quantum communication channel by means of a few measurements. The method is easily implementable and does not require any knowledge about the channel. We test its efficiency by studying its performance for most well-known single-qubit noisy channels and for the generalized Pauli channel in an arbitrary finite dimension.

A low-background piston-cylinder-type hybrid high pressure cell for muon-spin rotation/relaxation experiments

NASA Astrophysics Data System (ADS)

Shermadini, Z.; Khasanov, R.; Elender, M.; Simutis, G.; Guguchia, Z.; Kamenev, K. V.; Amato, A.

2017-10-01

A low background double-wall piston-cylinder-type pressure cell is developed at the Paul Scherrer Institute. The cell is made from BERYLCO-25 (beryllium copper) and MP35N nonmagnetic alloys with the design and dimensions which are specifically adapted to muon-spin rotation/relaxation (μSR) measurements. The mechanical design and performance of the pressure cell are evaluated using finite-element analysis (FEA). By including the measured stress-strain characteristics of the materials into the finite-element model, the cell dimensions are optimized with the aim to reach the highest possible pressure while maintaining the sample space large (6 mm in diameter and 12 mm high). The presented unconventional design of the double-wall piston-cylinder pressure cell with a harder outer MP35N sleeve and a softer inner CuBe cylinder enables pressures of up to 2.6 GPa to be reached at ambient temperature, corresponding to 2.2 GPa at low temperatures without any irreversible damage to the pressure cell. The nature of the muon stopping distribution, mainly in the sample and in the CuBe cylinder, results in a low-background μSR signal.

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Modelling cell motility and chemotaxis with evolving surface finite elements

PubMed Central

Elliott, Charles M.; Stinner, Björn; Venkataraman, Chandrasekhar

2012-01-01

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction–diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/∼maskae/CV_Warwick/Chemotaxis.html. PMID:22675164

The Hawk-Dove game in phenotypically homogeneous and heterogeneous populations of finite dimension

NASA Astrophysics Data System (ADS)

Laruelle, Annick; da Silva Rocha, André Barreira; Escobedo, Ramón

2018-02-01

The Hawk-Dove game played between individuals in populations of finite dimension is analyzed by means of a stochastic model. We take into account both cases when all individuals in the population are either phenotypically homogeneous or heterogeneous. A strategy in the model is a gene representing the probability of playing the Hawk strategy. Individual interactions at the microscopic level are described by a genetic algorithm where evolution results from the interplay among selection, mutation, drift and cross-over of genes. We show that the behavioral patterns observed at the macroscopic level can be reproduced as the emergent result of individual interactions governed by the rules of the Hawk-Dove game at the microscopic level. We study how the results of the genetic algorithm compare with those obtained in evolutionary game theory, finding that, although genes continuously change both their presence and frequency in the population over time, the population average behavior always achieves stationarity and, when this happens, the final average strategy played in the population oscillates around the evolutionarily stable strategy in the homogeneous population case or the neutrally stable set in the heterogeneous population case.

NiMnGa/Si Shape Memory Bimorph Nanoactuation

NASA Astrophysics Data System (ADS)

Lambrecht, Franziska; Lay, Christian; Aseguinolaza, Iván R.; Chernenko, Volodymyr; Kohl, Manfred

2016-12-01

The size dependences of thermal bimorph and shape memory effect of nanoscale shape memory alloy (SMA)/Si bimorph actuators are investigated in situ in a scanning electron microscope and by finite element simulations. By combining silicon nanomachining and magnetron sputtering, freestanding NiMnGa/Si bimorph cantilever structures with film/substrate thickness of 200/250 nm and decreasing lateral dimensions are fabricated. Electrical resistance and mechanical beam bending tests upon direct Joule heating demonstrate martensitic phase transformation and reversible thermal bimorph effect, respectively. Corresponding characteristics are strongly affected by the large temperature gradient in the order of 50 K/µm forming along the nano bimorph cantilever upon electro-thermal actuation, which, in addition, depends on the size-dependent heat conductivity in the Si nano layer. Furthermore, the martensitic transformation temperatures show a size-dependent decrease by about 40 K for decreasing lateral dimensions down to 200 nm. The effects of heating temperature and stress distribution on the nanoactuation performance are analyzed by finite element simulations revealing thickness ratio of SMA/Si of 90/250 nm to achieve an optimum SME. Differential thermal expansion and thermo-elastic effects are discriminated by comparative measurements and simulations on Ni/Si bimorph reference actuators.

Finite element analysis on preferable I-bar clasp shape.

PubMed

Sato, Y; Tsuga, K; Abe, Y; Asahara, S; Akagawa, Y

2001-05-01

An I-bar clasp is one of the most popular direct retainers for distal-extension removable partial dentures. However, no adequate information is available on preferable shape as determined by biomechanics. This study aimed (1) to investigate, by finite element analysis (FEA), the dimensions and stress of I-bar clasps having the same stiffness, and (2) to estimate a mechanically preferable clasp design. Three-dimensional FEA models of I-bar clasps were created with vertical and horizontal straight sections connected by a curved section characterized by six parameters: thickness of the clasp tip, width of the clasp tip, radius of the curvature, horizontal distance between the base and the vertical axis, vertical dimension between the tip and the horizontal axis, and taper (change of width per unit length along the axis). Stress was calculated with a concentrated load of 5 N applied 2 mm from the tip of the clasp in the buccal direction. A thinner and wider clasp having an taper of 0.020-0.023 and radius of curvature of 2.75-3.00 showed less stress. The results suggest that such a shape might be the preferable I-bar clasp shape as biomechanical viewpoint.

Thermodynamic glass transition in a spin glass without time-reversal symmetry

PubMed Central

Baños, Raquel Alvarez; Cruz, Andres; Fernandez, Luis Antonio; Gil-Narvion, Jose Miguel; Gordillo-Guerrero, Antonio; Guidetti, Marco; Iñiguez, David; Maiorano, Andrea; Marinari, Enzo; Martin-Mayor, Victor; Monforte-Garcia, Jorge; Muñoz Sudupe, Antonio; Navarro, Denis; Parisi, Giorgio; Perez-Gaviro, Sergio; Ruiz-Lorenzo, Juan Jesus; Schifano, Sebastiano Fabio; Seoane, Beatriz; Tarancon, Alfonso; Tellez, Pedro; Tripiccione, Raffaele; Yllanes, David

2012-01-01

Spin glasses are a longstanding model for the sluggish dynamics that appear at the glass transition. However, spin glasses differ from structural glasses in a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behavior of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d < 6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method. PMID:22493229

Engineering photonic nanojet by a graded-index micro-cuboid

NASA Astrophysics Data System (ADS)

Liu, Cheng-Yang; Yen, Tzu-Ping; Minin, Oleg V.; Minin, Igor V.

2018-04-01

In the present paper the basic characteristics (length, peak intensity, and full-width half-maximum) of nanojets formed in the vicinity of dielectric core-shell cuboids with different types of index grading are investigated by finite-difference time domain method. The latitudinal and longitudinal sizes of a nanojet and its peak intensity depending on the optical contrast variation of cuboids core-shells are numerically investigated. It has been shown that it is possible to control and elongate the nanojet abnormally. It also was shown that graded cuboid with dimensions of 4 × 4 × 4 wavelength may has FWHM of a jet less than uniform cuboid with dimensions of 1 × 1 × 1 wavelength. At wavelength of 600 nm graded index cuboid with dimensions of 4 × 4 × 4 wavelength and index grading = 2 allow to form photonic jet with FWHM about 232 nm or 0.39 wavelength.

Numerical investigation of a tunable band-pass plasmonic filter with a hollow-core ring resonator

NASA Astrophysics Data System (ADS)

Setayesh, Amir; Mirnaziry, S. Reza; Sadegh Abrishamian, Mohammad

2011-03-01

In this study, a compact nanoscale plasmonic filter which consists of two metal-insulator-metal (MIM) waveguides coupled to each other by a rectangular ring resonator is presented and investigated numerically. The propagating modes of surface plasmon polaritons (SPPs) are studied in this structure. By replacing a portion of the ring core with air, while the outer dimensions of the structure are kept constant, we illustrate the possibility of the redshift of resonant wavelengths in order to tune the resonance modes. This feature is useful for integrated circuits in which we have limitations on the outer dimensions of the filter structure and it is not possible to enlarge the dimension of the ring resonator to reach longer resonant wavelengths. The corresponding results are illustrated by the 2D finite-difference time-domain (FDTD) method. The proposed structure has potential applications in plasmonic integrated circuits and can be simply fabricated.

Mean first passage time of active Brownian particle in one dimension

NASA Astrophysics Data System (ADS)

Scacchi, A.; Sharma, A.

2018-02-01

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modelled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate r on the mean first passage time to a fixed target of a single free active Brownian particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate r* for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.

Memory effects in active particles with exponentially correlated propulsion

NASA Astrophysics Data System (ADS)

Sandford, Cato; Grosberg, Alexander Y.

2018-01-01

The Ornstein-Uhlenbeck particle (OUP) model imagines a microscopic swimmer propelled by an active force which is correlated with itself on a finite time scale. Here we investigate the influence of external potentials on an ideal suspension of OUPs, in both one and two spatial dimensions, with particular attention paid to the pressure exerted on "confining walls." We employ a mathematical connection between the local density of OUPs and the statistics of their propulsion force to demonstrate the existence of an equation of state in one dimension. In higher dimensions we show that active particles generate a nonconservative force field in the surrounding medium. A simplified far-from-equilibrium model is proposed to account for OUP behavior in the vicinity of potentials. Building on this, we interpret simulations of OUPs in more complicated situations involving asymmetrical and spatially curved potentials, and characterize the resulting inhomogeneous stresses in terms of competing active length scales.

Universal Non-Debye Scaling in the Density of States of Amorphous Solids.

PubMed

Charbonneau, Patrick; Corwin, Eric I; Parisi, Giorgio; Poncet, Alexis; Zamponi, Francesco

2016-07-22

At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher packing fractions remains, however, unclear. One might expect to find a simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field in nature, however, these solutions are only strictly valid in the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, away from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio evolves as dimension increases.

[Effects of Geometrical Dimensions and Material Properties on the Rotation Characteristics of Head].

PubMed

Chen, Yue; Cui, Shihai; Li, Haiyan; Ruan, Shijie

2016-08-01

The validated finite element head model(FEHM)of a 3-year-old child,a 6-year-old child and a 50 th percentile adult were used to investigate the effects of head dimension and material parameters of brain tissues on the head rotational responses based on experimental design.Results showed that the effects of head dimension and directions of rotation on the head rotational responses were not significant under the same rotational loading condition,and the same results appeared in the viscoelastic material parameters of brain tissues.However,the head rotational responses were most sensitive to the shear modulus(G)of brain tissues relative to decay constant(β)and bulk modulus(K).Therefore,the selection of material parameters of brain tissues is most important to the accuracy of simulation results,especially in the study of brain injury criterion under the rotational loading conditions.

Jones index, secret sharing and total quantum dimension

NASA Astrophysics Data System (ADS)

Fiedler, Leander; Naaijkens, Pieter; Osborne, Tobias J.

2017-02-01

We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible to a malicious party, and argue that the total quantum dimension quantifies how well we can perform this task. We then argue that this can be made mathematically rigorous using the index theory of subfactors, originally due to Jones and later extended by Kosaki and Longo. This theory provides us with a ‘relative entropy’ of two von Neumann algebras and a quantum channel, and we argue how these can be used to quantify how much classical information two parties can hide form an adversary. We also review the total quantum dimension in finite systems, in particular how it relates to topological entanglement entropy. It is known that the latter also has an interpretation in terms of secret sharing schemes, although this is shown by completely different methods from ours. Our work provides a different and independent take on this, which at the same time is completely mathematically rigorous. This complementary point of view might be beneficial, for example, when studying the stability of the total quantum dimension when the system is perturbed.

GENOA-PFA: Progressive Fracture in Composites Simulated Computationally

NASA Technical Reports Server (NTRS)

Murthy, Pappu L. N.

2000-01-01

GENOA-PFA is a commercial version of the Composite Durability Structural Analysis (CODSTRAN) computer program that simulates the progression of damage ultimately leading to fracture in polymer-matrix-composite (PMC) material structures under various loading and environmental conditions. GENOA-PFA offers several capabilities not available in other programs developed for this purpose, making it preferable for use in analyzing the durability and damage tolerance of complex PMC structures in which the fiber reinforcements occur in two- and three-dimensional weaves and braids. GENOA-PFA implements a progressive-fracture methodology based on the idea that a structure fails when flaws that may initially be small (even microscopic) grow and/or coalesce to a critical dimension where the structure no longer has an adequate safety margin to avoid catastrophic global fracture. Damage is considered to progress through five stages: (1) initiation, (2) growth, (3) accumulation (coalescence of propagating flaws), (4) stable propagation (up to the critical dimension), and (5) unstable or very rapid propagation (beyond the critical dimension) to catastrophic failure. The computational simulation of progressive failure involves formal procedures for identifying the five different stages of damage and for relating the amount of damage at each stage to the overall behavior of the deteriorating structure. In GENOA-PFA, mathematical modeling of the composite physical behavior involves an integration of simulations at multiple, hierarchical scales ranging from the macroscopic (lamina, laminate, and structure) to the microscopic (fiber, matrix, and fiber/matrix interface), as shown in the figure. The code includes algorithms to simulate the progression of damage from various source defects, including (1) through-the-thickness cracks and (2) voids with edge, pocket, internal, or mixed-mode delaminations.

Diagnostic Errors in Ambulatory Care: Dimensions and Preventive Strategies

ERIC Educational Resources Information Center

Singh, Hardeep; Weingart, Saul N.

2009-01-01

Despite an increasing focus on patient safety in ambulatory care, progress in understanding and reducing diagnostic errors in this setting lag behind many other safety concerns such as medication errors. To explore the extent and nature of diagnostic errors in ambulatory care, we identified five dimensions of ambulatory care from which errors may…

Guidelines for VCCT-Based Interlaminar Fatigue and Progressive Failure Finite Element Analysis

NASA Technical Reports Server (NTRS)

Deobald, Lyle R.; Mabson, Gerald E.; Engelstad, Steve; Prabhakar, M.; Gurvich, Mark; Seneviratne, Waruna; Perera, Shenal; O'Brien, T. Kevin; Murri, Gretchen; Ratcliffe, James;

Postbuckling and Growth of Delaminations in Composite Plates Subjected to Axial Compression

NASA Technical Reports Server (NTRS)

Reeder, James R.; Chunchu, Prasad B.; Song, Kyongchan; Ambur, Damodar R.

2002-01-01

The postbuckling response and growth of circular delaminations in flat and curved plates are investigated as part of a study to identify the criticality of delamination locations through the laminate thickness. The experimental results from tests on delaminated plates are compared with finite element analysis results generated using shell models. The analytical prediction of delamination growth is obtained by assessing the strain energy release rate results from the finite element model and comparing them to a mixed-mode fracture toughness failure criterion. The analytical results for onset of delamination growth compare well with experimental results generated using a 3-dimensional displacement visualization system. The record of delamination progression measured in this study has resulted in a fully 3-dimensional test case with which progressive failure models can be validated.

Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: A new method of interpolation and analysis of errors

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2004-01-01

This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497-511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, "cage-shell" interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size - A coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.

Progressive fracture of fiber composites

NASA Technical Reports Server (NTRS)

Irvin, T. B.; Ginty, C. A.

1983-01-01

Refined models and procedures are described for determining progressive composite fracture in graphite/epoxy angleplied laminates. Lewis Research Center capabilities are utilized including the Real Time Ultrasonic C Scan (RUSCAN) experimental facility and the Composite Durability Structural Analysis (CODSTRAN) computer code. The CODSTRAN computer code is used to predict the fracture progression based on composite mechanics, finite element stress analysis, and fracture criteria modules. The RUSCAN facility, CODSTRAN computer code, and scanning electron microscope are used to determine durability and identify failure mechanisms in graphite/epoxy composites.

Progress on the three-particle quantization condition

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

Briceno, Raul; Hansen, Mawell T.; Sharpe, Stephen R.

2016-10-01

We report progress on extending the relativistic model-independent quantization condition for three particles, derived previously by two of us, to a broader class of theories, as well as progress on checking the formalism. In particular, we discuss the extension to include the possibility of 2->3 and 3->2 transitions and the calculation of the finite-volume energy shift of an Efimov-like three-particle bound state. The latter agrees with the results obtained previously using non-relativistic quantum mechanics.

Progress in Modeling Nonlinear Dendritic Evolution in Two and Three Dimensions, and Its Mathematical Justification

NASA Technical Reports Server (NTRS)

Tanveer, S.; Foster, M. R.

2002-01-01

We report progress in three areas of investigation related to dendritic crystal growth. Those items include: 1. Selection of tip features dendritic crystal growth; 2) Investigation of nonlinear evolution for two-sided model; and 3) Rigorous mathematical justification.

Flexible metamaterial absorbers for stealth applications at terahertz frequencies.

PubMed

Iwaszczuk, Krzysztof; Strikwerda, Andrew C; Fan, Kebin; Zhang, Xin; Averitt, Richard D; Jepsen, Peter Uhd

2012-01-02

We have wrapped metallic cylinders with strongly absorbing metamaterials. These resonant structures, which are patterned on flexible substrates, smoothly coat the cylinder and give it an electromagnetic response designed to minimize its radar cross section. We compare the normal-incidence, small-beam reflection coefficient with the measurement of the far-field bistatic radar cross section of the sample, using a quasi-planar THz wave with a beam diameter significantly larger than the sample dimensions. In this geometry we demonstrate a near-400-fold reduction of the radar cross section at the design frequency of 0.87 THz. In addition we discuss the effect of finite sample dimensions and the spatial dependence of the reflection spectrum of the metamaterial.

Tracking fronts in solutions of the shallow-water equations

NASA Astrophysics Data System (ADS)

Bennett, Andrew F.; Cummins, Patrick F.

1988-02-01

A front-tracking algorithm of Chern et al. (1986) is tested on the shallow-water equations, using the Parrett and Cullen (1984) and Williams and Hori (1970) initial state, consisting of smooth finite amplitude waves depending on one space dimension alone. At high resolution the solution is almost indistinguishable from that obtained with the Glimm algorithm. The latter is known to converge to the true frontal solution, but is 20 times less efficient at the same resolution. The solutions obtained using the front-tracking algorithm at 8 times coarser resolution are quite acceptable, indicating a very substantial gain in efficiency, which encourages application in realistic ocean models possessing two or three space dimensions.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

NASA Astrophysics Data System (ADS)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Skeletal assessment with finite element analysis: relevance, pitfalls and interpretation.

PubMed

Campbell, Graeme Michael; Glüer, Claus-C

2017-07-01

Finite element models simulate the mechanical response of bone under load, enabling noninvasive assessment of strength. Models generated from quantitative computed tomography (QCT) incorporate the geometry and spatial distribution of bone mineral density (BMD) to simulate physiological and traumatic loads as well as orthopaedic implant behaviour. The present review discusses the current strengths and weakness of finite element models for application to skeletal biomechanics. In cadaver studies, finite element models provide better estimations of strength compared to BMD. Data from clinical studies are encouraging; however, the superiority of finite element models over BMD measures for fracture prediction has not been shown conclusively, and may be sex and site dependent. Therapeutic effects on bone strength are larger than for BMD; however, model validation has only been performed on untreated bone. High-resolution modalities and novel image processing methods may enhance the structural representation and predictive ability. Despite extensive use of finite element models to study orthopaedic implant stability, accurate simulation of the bone-implant interface and fracture progression remains a significant challenge. Skeletal finite element models provide noninvasive assessments of strength and implant stability. Improved structural representation and implant surface interaction may enable more accurate models of fragility in the future.

Finite element modelling of aluminum alloy 2024-T3 under transverse impact loading

NASA Astrophysics Data System (ADS)

Abdullah, Ahmad Sufian; Kuntjoro, Wahyu; Yamin, A. F. M.

2017-12-01

Fiber metal laminate named GLARE is a new aerospace material which has great potential to be widely used in future lightweight aircraft. It consists of aluminum alloy 2024-T3 and glass-fiber reinforced laminate. In order to produce reliable finite element model of impact response or crashworthiness of structure made of GLARE, one can initially model and validate the finite element model of the impact response of its constituents separately. The objective of this study was to develop a reliable finite element model of aluminum alloy 2024-T3 under low velocity transverse impact loading using commercial software ABAQUS. Johnson-Cook plasticity and damage models were used to predict the alloy's material properties and impact behavior. The results of the finite element analysis were compared to the experiment that has similar material and impact conditions. Results showed good correlations in terms of impact forces, deformation and failure progressions which concluded that the finite element model of 2024-T3 aluminum alloy under low velocity transverse impact condition using Johnson-Cook plastic and damage models was reliable.

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Yates, E. Carson, Jr.; Whitlow, Woodrow, Jr.

1987-01-01

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral equations and finite difference methods for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite difference solution of the transonic small perturbation equation, the integral equation program is given primary emphasis here because it is less well known.

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Yates, E. Carson, Jr.; Whitlow, Woodrow, Jr.

1987-01-01

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral-equations and finite-difference method for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite-difference solution of the transonic small-perturbation equation, the integral-equation program is given primary emphasis here because it is less well known.

A Large-scale Finite Element Model on Micromechanical Damage and Failure of Carbon Fiber/Epoxy Composites Including Thermal Residual Stress

NASA Astrophysics Data System (ADS)

Liu, P. F.; Li, X. K.

2018-06-01

The purpose of this paper is to study micromechanical progressive failure properties of carbon fiber/epoxy composites with thermal residual stress by finite element analysis (FEA). Composite microstructures with hexagonal fiber distribution are used for the representative volume element (RVE), where an initial fiber breakage is assumed. Fiber breakage with random fiber strength is predicted using Monte Carlo simulation, progressive matrix damage is predicted by proposing a continuum damage mechanics model and interface failure is simulated using Xu and Needleman's cohesive model. Temperature dependent thermal expansion coefficients for epoxy matrix are used. FEA by developing numerical codes using ANSYS finite element software is divided into two steps: 1. Thermal residual stresses due to mismatch between fiber and matrix are calculated; 2. Longitudinal tensile load is further exerted on the RVE to perform progressive failure analysis of carbon fiber/epoxy composites. Numerical convergence is solved by introducing the viscous damping effect properly. The extended Mori-Tanaka method that considers interface debonding is used to get homogenized mechanical responses of composites. Three main results by FEA are obtained: 1. the real-time matrix cracking, fiber breakage and interface debonding with increasing tensile strain is simulated. 2. the stress concentration coefficients on neighbouring fibers near the initial broken fiber and the axial fiber stress distribution along the broken fiber are predicted, compared with the results using the global and local load-sharing models based on the shear-lag theory. 3. the tensile strength of composite by FEA is compared with those by the shear-lag theory and experiments. Finally, the tensile stress-strain curve of composites by FEA is applied to the progressive failure analysis of composite pressure vessel.

A Large-scale Finite Element Model on Micromechanical Damage and Failure of Carbon Fiber/Epoxy Composites Including Thermal Residual Stress

NASA Astrophysics Data System (ADS)

Liu, P. F.; Li, X. K.

2017-09-01

The purpose of this paper is to study micromechanical progressive failure properties of carbon fiber/epoxy composites with thermal residual stress by finite element analysis (FEA). Composite microstructures with hexagonal fiber distribution are used for the representative volume element (RVE), where an initial fiber breakage is assumed. Fiber breakage with random fiber strength is predicted using Monte Carlo simulation, progressive matrix damage is predicted by proposing a continuum damage mechanics model and interface failure is simulated using Xu and Needleman's cohesive model. Temperature dependent thermal expansion coefficients for epoxy matrix are used. FEA by developing numerical codes using ANSYS finite element software is divided into two steps: 1. Thermal residual stresses due to mismatch between fiber and matrix are calculated; 2. Longitudinal tensile load is further exerted on the RVE to perform progressive failure analysis of carbon fiber/epoxy composites. Numerical convergence is solved by introducing the viscous damping effect properly. The extended Mori-Tanaka method that considers interface debonding is used to get homogenized mechanical responses of composites. Three main results by FEA are obtained: 1. the real-time matrix cracking, fiber breakage and interface debonding with increasing tensile strain is simulated. 2. the stress concentration coefficients on neighbouring fibers near the initial broken fiber and the axial fiber stress distribution along the broken fiber are predicted, compared with the results using the global and local load-sharing models based on the shear-lag theory. 3. the tensile strength of composite by FEA is compared with those by the shear-lag theory and experiments. Finally, the tensile stress-strain curve of composites by FEA is applied to the progressive failure analysis of composite pressure vessel.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems; Part 1, Model description and user's manual

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration.The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Impact of health research on advances in knowledge, research capacity-building and evidence-informed policies: a case study on maternal mortality and morbidity in Brazil.

PubMed

Angulo-Tuesta, Antonia; Santos, Leonor Maria Pacheco; Natalizi, Daniel Alves

2016-04-01

National health research systems aim to generate high-quality knowledge so as to maintain and promote the population's health. This study aimed to analyze the impact of maternal mortality/morbidity research funded by the Brazilian Ministry of Health and institutional partners, on the dimensions: advancing in knowledge, research capacity-building and informing decision-making, within the framework of the Canadian Academy of Health Sciences. Descriptive study based on secondary data, conducted at a public university. The advancing in knowledge dimension was estimated from the principal investigators' publication counts and h-index. Data on research capacity-building were obtained from the Ministry of Health's information system. The informing decision-making dimension was analyzed from citations in Stork Network (Rede Cegonha) documents. Between 2002 and 2010, R$ 21.6 million were invested in 128 maternal mortality/morbidity projects. Over this period, the principal investigators published 174 articles, resulting in an h-index of 35, thus showing progress in the advancing in knowledge dimension. Within the research capacity-building dimension, training of 71 students (undergraduate/postgraduate) was observed. Progress in the informing decision-making dimension was modest: 73.5% of the 117 citations in the Stork Network documents were institutional documents and norms. One of the projects funded, the 2006/7 National Demography and Health Survey, was cited in program documents. Impacts were shown in the advancing in knowledge and research capacity-building dimensions. The health research system needs to incorporate research for evidence-informed policies.

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

Volume dependence of N-body bound states

NASA Astrophysics Data System (ADS)

König, Sebastian; Lee, Dean

2018-04-01

We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.

FRW Solutions and Holography from Uplifted AdS/CFT

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

Dong, Xi; Horn, Bart; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC

2012-02-15

Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to non-accelerating FRW. We present simple FRW solutions sourced by magnetic flavor branes and analyze correlation functions and particle and brane dynamics. To obtain a holographic description, we exhibit a time-dependent warped metric on the solution and interpret the resulting redshifted region as a Lorentzian low energy effective field theory in one fewer dimension. At finite times, this theory has a finite cutoff, a propagating lower dimensional graviton and a finite covariant entropy bound, but at late times themore » lower dimensional Planck mass and entropy go off to infinity in a way that is dominated by contributions from the low energy effective theory. This opens up the possibility of a precise dual at late times. We reproduce the time-dependent growth of the number of degrees of freedom in the system via a count of available microscopic states in the corresponding magnetic brane construction.« less

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

NASA Technical Reports Server (NTRS)

Glaisner, F.; Tezduyar, T. E.

1987-01-01

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.

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

Coupling Between CPW and Slotline Modes in Finite Ground CPW with Unequal Ground Plane Widths

NASA Technical Reports Server (NTRS)

Ponchak, George E.; Papapolymerou, John; Williams, W. D. (Technical Monitor); Tentzeris, Emmanouil M.

2002-01-01

The coupling between the desired CPW mode and the unwanted, slotline, mode is presented for finite ground coplanar waveguides with unequal ground plane widths. Measurements, quasi-static conformal mapping, and Method of Moment analysis are performed to determine the dependence of the slotline mode excitation on the physical dimensions of the FGC line and on the frequency range of operation. Introduction: Finite ground coplanar waveguide (FGC) is often used in low cost Monolithic Microwave Integrated Circuits (MMICs) because of its many advantages over microstrip and conventional CoPlanar Waveguide (CPW). It is uniplanar, which facilitates easy connection of series and shunt elements without via holes, supports a low loss, quasi-TEM mode over a wide frequency band, and since the ground planes are electrically and physically narrow, typically less than lambda/5 wide where lambda is the guided wavelength, they reduce the circuit size and the influence of higher order modes. However, they still support the parasitic slotline mode that plagues all CPW transmission lines.

Application of Dynamic Analysis in Semi-Analytical Finite Element Method.

PubMed

Liu, Pengfei; Xing, Qinyan; Wang, Dawei; Oeser, Markus

2017-08-30

Analyses of dynamic responses are significantly important for the design, maintenance and rehabilitation of asphalt pavement. In order to evaluate the dynamic responses of asphalt pavement under moving loads, a specific computational program, SAFEM, was developed based on a semi-analytical finite element method. This method is three-dimensional and only requires a two-dimensional FE discretization by incorporating Fourier series in the third dimension. In this paper, the algorithm to apply the dynamic analysis to SAFEM was introduced in detail. Asphalt pavement models under moving loads were built in the SAFEM and commercial finite element software ABAQUS to verify the accuracy and efficiency of the SAFEM. The verification shows that the computational accuracy of SAFEM is high enough and its computational time is much shorter than ABAQUS. Moreover, experimental verification was carried out and the prediction derived from SAFEM is consistent with the measurement. Therefore, the SAFEM is feasible to reliably predict the dynamic response of asphalt pavement under moving loads, thus proving beneficial to road administration in assessing the pavement's state.

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.

Shear Capacity of C-Shaped and L-Shaped Angle Shear Connectors

PubMed Central

Tahmasbi, Farzad; Maleki, Shervin; Shariati, Mahdi; Ramli Sulong, N. H.; Tahir, M. M.

2016-01-01

This paper investigates the behaviour of C-shaped and L-shaped angle shear connectors embedded in solid concrete slabs. An effective finite element model is proposed to simulate the push out tests of these shear connectors that encompass nonlinear material behaviour, large displacement and damage plasticity. The finite element models are validated against test results. Parametric studies using this nonlinear model are performed to investigate the variations in concrete strength and connector dimensions. The finite element analyses also confirm the test results that increasing the length of shear connector increases their shear strength proportionately. It is observed that the maximum stress in L-shaped angle connectors takes place in the weld attachment to the beam, whereas in the C-shaped angle connectors, it is in the attached leg. The location of maximum concrete compressive damage is rendered in each case. Finally, a new equation for prediction of the shear capacity of C-shaped angle connectors is proposed. PMID:27478894

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.

FRW solutions and holography from uplifted AdS/CFT systems

NASA Astrophysics Data System (ADS)

Dong, Xi; Horn, Bart; Matsuura, Shunji; Silverstein, Eva; Torroba, Gonzalo

2012-05-01

Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to nonaccelerating Friedmann-Robertson-Walker. We present simple Friedmann-Robertson-Walker solutions sourced by magnetic flavor branes and analyze correlation functions and particle and brane dynamics. To obtain a holographic description, we exhibit a time-dependent warped metric on the solution and interpret the resulting redshifted region as a Lorentzian low energy effective field theory in one fewer dimension. At finite times, this theory has a finite cutoff, a propagating lower-dimensional graviton, and a finite covariant entropy bound, but at late times the lower-dimensional Planck mass and entropy go off to infinity in a way that is dominated by contributions from the low energy effective theory. This opens up the possibility of a precise dual at late times. We reproduce the time-dependent growth of the number of degrees of freedom in the system via a count of available microscopic states in the corresponding magnetic brane construction.

Shear Capacity of C-Shaped and L-Shaped Angle Shear Connectors.

PubMed

Tahmasbi, Farzad; Maleki, Shervin; Shariati, Mahdi; Ramli Sulong, N H; Tahir, M M

2016-01-01

This paper investigates the behaviour of C-shaped and L-shaped angle shear connectors embedded in solid concrete slabs. An effective finite element model is proposed to simulate the push out tests of these shear connectors that encompass nonlinear material behaviour, large displacement and damage plasticity. The finite element models are validated against test results. Parametric studies using this nonlinear model are performed to investigate the variations in concrete strength and connector dimensions. The finite element analyses also confirm the test results that increasing the length of shear connector increases their shear strength proportionately. It is observed that the maximum stress in L-shaped angle connectors takes place in the weld attachment to the beam, whereas in the C-shaped angle connectors, it is in the attached leg. The location of maximum concrete compressive damage is rendered in each case. Finally, a new equation for prediction of the shear capacity of C-shaped angle connectors is proposed.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

NASA Astrophysics Data System (ADS)

Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell

2017-06-01

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.

PubMed

Nguyen, Vu-Hieu; Naili, Salah

2012-08-01

This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.

Simulation studies of vestibular macular afferent-discharge patterns using a new, quasi-3-D finite volume method

NASA Technical Reports Server (NTRS)

Ross, M. D.; Linton, S. W.; Parnas, B. R.

2000-01-01

A quasi-three-dimensional finite-volume numerical simulator was developed to study passive voltage spread in vestibular macular afferents. The method, borrowed from computational fluid dynamics, discretizes events transpiring in small volumes over time. The afferent simulated had three calyces with processes. The number of processes and synapses, and direction and timing of synapse activation, were varied. Simultaneous synapse activation resulted in shortest latency, while directional activation (proximal to distal and distal to proximal) yielded most regular discharges. Color-coded visualizations showed that the simulator discretized events and demonstrated that discharge produced a distal spread of voltage from the spike initiator into the ending. The simulations indicate that directional input, morphology, and timing of synapse activation can affect discharge properties, as must also distal spread of voltage from the spike initiator. The finite volume method has generality and can be applied to more complex neurons to explore discrete synaptic effects in four dimensions.

A Framework for the Design and Integration of Collaborative Classroom Games

ERIC Educational Resources Information Center

Echeverria, Alejandro; Garcia-Campo, Cristian; Nussbaum, Miguel; Gil, Francisca; Villalta, Marco; Amestica, Matias; Echeverria, Sebastian

2011-01-01

The progress registered in the use of video games as educational tools has not yet been successfully transferred to the classroom. In an attempt to close this gap, a framework was developed that assists in the design and classroom integration of educational games. The framework addresses both the educational dimension and the ludic dimension. The…

Multiple Counseling in Open and Closed Time-Extended Groups.

ERIC Educational Resources Information Center

Chambers, W. M.

The open time-extended group, run by multiple counselors, adds a facilitating dimension to the counseling function--a dimension that exemplifies the concepts of self-growth and self-actualization by first providing the atmosphere for the client and then by allowing him to progress at his own rate and to a depth which he determines. An open group…

Some calculable contributions to entanglement entropy.

PubMed

Hertzberg, Mark P; Wilczek, Frank

2011-02-04

Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on correlation length, we extract finite, calculable contributions to the entanglement entropy for a scalar field between the interior and exterior of a spatial domain of arbitrary shape. The leading term is proportional to the area of the dividing boundary; we also extract finite subleading contributions for a field defined in the bulk interior of a waveguide in 3+1 dimensions, including terms proportional to the waveguide's cross-sectional geometry: its area, perimeter length, and integrated curvature. We also consider related quantities at criticality and suggest a class of systems for which these contributions might be measurable.

Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

NASA Astrophysics Data System (ADS)

Huang, Juntao; Shu, Chi-Wang

2018-05-01

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.

Primary decomposition of zero-dimensional ideals over finite fields

NASA Astrophysics Data System (ADS)

Gao, Shuhong; Wan, Daqing; Wang, Mingsheng

2009-03-01

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

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

DOE PAGES

Regnier, D.; Verriere, M.; Dubray, N.; ...

2015-11-30

In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle amore » realistic calculation of fission dynamics.« less

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

NASA Technical Reports Server (NTRS)

Corral, Roque; Jimenez, Javier

1992-01-01

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Multi-Dimensional High Order Essentially Non-Oscillatory Finite Difference Methods in Generalized Coordinates

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1998-01-01

This project is about the development of high order, non-oscillatory type schemes for computational fluid dynamics. Algorithm analysis, implementation, and applications are performed. Collaborations with NASA scientists have been carried out to ensure that the research is relevant to NASA objectives. The combination of ENO finite difference method with spectral method in two space dimension is considered, jointly with Cai [3]. The resulting scheme behaves nicely for the two dimensional test problems with or without shocks. Jointly with Cai and Gottlieb, we have also considered one-sided filters for spectral approximations to discontinuous functions [2]. We proved theoretically the existence of filters to recover spectral accuracy up to the discontinuity. We also constructed such filters for practical calculations.

Anisotropic contraction of hydrogel reinforced by aligned fibers

NASA Astrophysics Data System (ADS)

Olvera de La Cruz, Monica; Liu, Shuangping

Hydrogel reinforced by aligned fibers can have strong anisotropic contraction or swelling behavior triggered by external stimuli, which has been largely employed in realizing soft actuators for artificial muscles as well as many biological systems. In this work, we investigate how this anisotropic behavior is controlled by the dimension of the embedded fibers and their reinforcement to the surrounding hydrogel. We describe the anisotropic contraction of hydrogels with rigid fibers using the Flory-Rehner thermodynamic model under periodic boundary conditions. It is found that a hydrogel reinforced by aligned fibers exhibits larger anisotropy when it is pre-stretched before contraction. Using finite element method, we further observe that the anisotropic contraction is dampened by reducing the fiber-fiber distance due to the finite size of the fibers.

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1983-01-01

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

Meshing of a Spiral Bevel Gearset with 3D Finite Element Analysis

NASA Technical Reports Server (NTRS)

Bibel, George D.; Handschuh, Robert

1996-01-01

Recent advances in spiral bevel gear geometry and finite element technology make it practical to conduct a structural analysis and analytically roll the gearset through mesh. With the advent of user specific programming linked to 3D solid modelers and mesh generators, model generation has become greatly automated. Contact algorithms available in general purpose finite element codes eliminate the need for the use and alignment of gap elements. Once the gearset is placed in mesh, user subroutines attached to the FE code easily roll the gearset through mesh. The method is described in detail. Preliminary results for a gearset segment showing the progression of the contact lineload is given as the gears roll through mesh.

Experimental evidence of phase coherence of magnetohydrodynamic turbulence in the solar wind: GEOTAIL satellite data.

PubMed

Koga, D; Chian, A C-L; Hada, T; Rempel, E L

2008-02-13

Magnetohydrodynamic (MHD) turbulence is commonly observed in the solar wind. Nonlinear interactions among MHD waves are likely to produce finite correlation of the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in the quasi-linear theory) or have a finite coherence. Using a method based on the surrogate data technique, we analysed the GEOTAIL magnetic field data to evaluate the phase coherence in MHD turbulence in the Earth's foreshock region. The results demonstrate the existence of finite phase correlation, indicating that nonlinear wave-wave interactions are in progress.

Two-level Schwartz methods for nonconforming finite elements and discontinuous coefficients

NASA Technical Reports Server (NTRS)

Sarkis, Marcus

1993-01-01

Two-level domain decomposition methods are developed for a simple nonconforming approximation of second order elliptic problems. A bound is established for the condition number of these iterative methods, which grows only logarithmically with the number of degrees of freedom in each subregion. This bound holds for two and three dimensions and is independent of jumps in the value of the coefficients.

The fundamentals of adaptive grid movement

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.

1990-01-01

Basic grid point movement schemes are studied. The schemes are referred to as adaptive grids. Weight functions and equidistribution in one dimension are treated. The specification of coefficients in the linear weight, attraction to a given grid or a curve, and evolutionary forces are considered. Curve by curve and finite volume methods are described. The temporal coupling of partial differential equations solvers and grid generators was discussed.

Wave Current Interactions and Wave-blocking Predictions Using NHWAVE Model

DTIC Science & Technology

2013-03-01

Navier-Stokes equation. In this approach, as with previous modeling techniques, there is difficulty in simulating the free surface that inhibits accurate...hydrostatic, free - surface , rotational flows in multiple dimensions. It is useful in predicting transformations of surface waves and rapidly varied...Stelling, G., and M. Zijlema, 2003: An accurate and efficient finite-differencing algorithm for non-hydrostatic free surface flow with application to

Computational Overlap Coupling Between Micropolar Linear Elastic Continuum Finite Elements and Nonlinear Elastic Spherical Discrete Elements in One Dimension

DTIC Science & Technology

2013-01-01

Cracking in asphalt pavement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Figure 2. 2D...metallic binder, figure 1(b)), particulate energetic materials (explosive crystalline grains with polymeric binder, figure 1(c)), asphalt pavement (stone...explosive HMX grains and at grain-matrix interfaces (2). (d) Cracking in asphalt pavement . 2 (i) it is limited by current computing power (even

Variable cross-section windings for efficiency improvement of electric machines

NASA Astrophysics Data System (ADS)

Grachev, P. Yu; Bazarov, A. A.; Tabachinskiy, A. S.

2018-02-01

Implementation of energy-saving technologies in industry is impossible without efficiency improvement of electric machines. The article considers the ways of efficiency improvement and mass and dimensions reduction of electric machines with electronic control. Features of compact winding design for stators and armatures are described. Influence of compact winding on thermal and electrical process is given. Finite element method was used in computer simulation.

Trabecular Bone Mechanical Properties and Fractal Dimension

NASA Technical Reports Server (NTRS)

Hogan, Harry A.

1996-01-01

Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again and also scanned using dual-energy X-ray absorptiometry (DEXA). Cube specimens are then cut from the slabs and tested mechanically in compression. Correlations between mechanical properties and fractal dimension will then be examined to assess and quantify the predictive capability of the fractal calculations.

Economic Perspectives of Technological Progress: New Dimensions for Forecasting Technology

ERIC Educational Resources Information Center

Twiss, Brian

1976-01-01

Discusses the causal relationship between the allocation of financial resources and technological growth. Argues that economic constraints are becoming an important determinant of technological progress that must be incorporated into technology forecasting techniques. (Available from IPC (America) Inc., 205 East 42 Street, New York, NY 10017;…

Progressive Fracture of Composite Structures

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Minnetyan, Levon

2008-01-01

A new approach is described for evaluating fracture in composite structures. This approach is independent of classical fracture mechanics parameters like fracture toughness. It relies on computational simulation and is programmed in a stand-alone integrated computer code. It is multiscale, multifunctional because it includes composite mechanics for the composite behavior and finite element analysis for predicting the structural response. It contains seven modules; layered composite mechanics (micro, macro, laminate), finite element, updating scheme, local fracture, global fracture, stress based failure modes, and fracture progression. The computer code is called CODSTRAN (Composite Durability Structural ANalysis). It is used in the present paper to evaluate the global fracture of four composite shell problems and one composite built-up structure. Results show that the composite shells and the built-up composite structure global fracture are enhanced when internal pressure is combined with shear loads.

Annual Review of Progress in Applied Computational Electromagnetics (4th), Held in Monterey, California on March 22-24, 1988

DTIC Science & Technology

1988-03-24

1430-1445 BREAK 1445-1645 EM CODE USERS PANEL DISCUSSION. Chaired by Wkn Breakal of LLNL. User community sugqestlons on needed enhancemento for EM Codes...I -"FINITE DIFFERENCE & FINITE ELEMENT METHC"S" Moderator: David E . Stein The LTV Aerospace and Defense Company "A Firite Element Analysis of...conduction (resulting from charge movement) or displacement ( e ,0 E /Wt) terms. The sum of these current densities are referred to as the Maxwell current

DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

NASA Astrophysics Data System (ADS)

Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske

2008-12-01

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1- p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh-Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.

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.

Stamping of Thin-Walled Structural Components with Magnesium Alloy AZ31 Sheets

NASA Astrophysics Data System (ADS)

Chen, Fuh-Kuo; Chang, Chih-Kun

2005-08-01

In the present study, the stamping process for manufacturing cell phone cases with magnesium alloy AZ31 sheets was studied using both the experimental approach and the finite element analysis. In order to determine the proper forming temperature and set up a fracture criterion, tensile tests and forming limit tests were first conducted to obtain the mechanical behaviors of AZ31 sheets at various elevated temperatures. The mechanical properties of Z31 sheets obtained from the experiments were then adopted in the finite element analysis to investigate the effects of the process parameters on the formability of the stamping process of cell phone cases. The finite element simulation results revealed that both the fracture and wrinkle defects could not be eliminated at the same time by adjusting blank-holder force or blank size. A drawbead design was then performed using the finite element simulations to determine the size and the location of drawbead required to suppress the wrinkle defect. An optimum stamping process, including die geometry, forming temperature, and blank dimension, was then determined for manufacturing the cell phone cases. The finite element analysis was validated by the good agreement between the simulation results and the experimental data. It confirms that the cell phone cases can be produced with magnesium alloy AZ31 sheet by the stamping process at elevated temperatures.

Probabilistic Structural Analysis Theory Development

NASA Technical Reports Server (NTRS)

Burnside, O. H.

1985-01-01

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

Anomalous Oxidative Diffusion in Titanium Pyrotechnic Powders

DOE PAGES

Erikson, William W.; Coker, Eric N.

2016-11-10

It has long been observed that oxidation processes in metals tend to follow a parabolic rate law associated with the growth of a surface oxide layer. Here we observe that for certain titanium powders, the expected parabolic law (∝t 1/2) is recovered, yet for others, the exponent differs significantly. One explanation for this non-parabolic, anomalous diffusion arises from fractal geometry. Theoretical considerations indicate that the time response of diffusion-limited processes in an object closely follow a power-law in time (t n) with n=(E–D)/2, where E is the object's Euclidean dimension and D is its boundary's Hausdorff dimension. Non-integer, (fractal) valuesmore » of D will result in n≠1/2. Finite element simulations of several canonical fractal objects were performed to verify the application of this theory; the results matched the theory well. Two different types of titanium powder were tested in isothermal thermogravimetric tests under dilute oxygen. Time-dependent mass uptake data were fit with power-law forms and the associated exponents were used to determine an equivalent fractal dimension. One Ti powder type has an implied surface dimension of ca. 2.3 to 2.5, suggesting fractal geometry may be operative. Finally, the other has a dimension near 2.0, indicating it behaves like traditional material.« less

Role of thermal two-phonon scattering for impurity dynamics in a low-dimensional Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Lausch, Tobias; Widera, Artur; Fleischhauer, Michael

2018-03-01

We numerically study the relaxation dynamics of a single, heavy impurity atom interacting with a finite one- or two-dimensional, ultracold Bose gas. While there is a clear separation of time scales between processes resulting from single- and two-phonon scattering in three spatial dimensions, the thermalization in lower dimensions is dominated by two-phonon processes. This is due to infrared divergences in the corresponding scattering rates in the thermodynamic limit, which are a manifestation of the Mermin-Wagner-Hohenberg theorem. This makes it necessary to include second-order phonon scattering above a crossover temperature T2ph . T2ph scales inversely with the system size and is much smaller than currently experimentally accessible.

A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions

NASA Astrophysics Data System (ADS)

Gilchrist, S. A.; Braun, D. C.; Barnes, G.

2016-12-01

Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.

Parameter dimension of turbulence-induced phase errors and its effects on estimation in phase diversity

NASA Technical Reports Server (NTRS)

Thelen, Brian J.; Paxman, Richard G.

1994-01-01

The method of phase diversity has been used in the context of incoherent imaging to estimate jointly an object that is being imaged and phase aberrations induced by atmospheric turbulence. The method requires a parametric model for the phase-aberration function. Typically, the parameters are coefficients to a finite set of basis functions. Care must be taken in selecting a parameterization that properly balances accuracy in the representation of the phase-aberration function with stability in the estimates. It is well known that over parameterization can result in unstable estimates. Thus a certain amount of model mismatch is often desirable. We derive expressions that quantify the bias and variance in object and aberration estimates as a function of parameter dimension.

Indulging anxiety: human enhancement from a Protestant perspective.

PubMed

Hanson, Mark J

1999-08-01

At the heart of any ethics of human enhancement must be some normative assumptions about human nature. The purpose of this essay is to draw on themes from a Protestant theological anthropology to provide a basis for understanding and evaluating the tension between maintaining our humanity and enhancing it. Drawing primarily on the work of theologian Reinhold Niebuhr, I interpret enhancement as proceeding from the anxiety that characterizes human experience at the juncture of freedom and finiteness. Religious and moral dimensions of human sinfulness are considered in relation to cultural values that motivate human enhancement generally. I employ these dimensions in a series of benchmarks to suggest a background of theological, anthropological, and moral considerations against which enhancement is not to be condemmed but rather critically evaluated.

Analysis of one dimension migration law from rainfall runoff on urban roof

NASA Astrophysics Data System (ADS)

Weiwei, Chen

2017-08-01

Research was taken on the hydrology and water quality process in the natural rain condition and water samples were collected and analyzed. The pollutant were included SS, COD and TN. Based on the mass balance principle, one dimension migration model was built for the rainfall runoff pollution in surface. The difference equation was developed according to the finite difference method, by applying the Newton iteration method for solving it. The simulated pollutant concentration process was in consistent with the measured value on model, and Nash-Sutcliffe coefficient was higher than 0.80. The model had better practicability, which provided evidence for effectively utilizing urban rainfall resource, non-point source pollution of making management technologies and measures, sponge city construction, and so on.

On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions.

PubMed

Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora

2017-11-01

In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14 , 1477-1500 (doi:10.4310/CMS.2016.v14.n6.a1)), it has been established that, for every arbitrarily slow convergence speed and every natural number d ∈{4,5,…}, there exist d -dimensional stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper, we strengthen the above result by proving that this slow convergence phenomenon also arises in two ( d =2) and three ( d =3) space dimensions.

Locality-preserving logical operators in topological stabilizer codes

NASA Astrophysics Data System (ADS)

Webster, Paul; Bartlett, Stephen D.

2018-01-01

Locality-preserving logical operators in topological codes are naturally fault tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure for finding all locality-preserving logical operators admitted by a large and important class of topological stabilizer codes. In particular, we focus on those equivalent to a stack of a finite number of surface codes of any spatial dimension, where our procedure fully specifies the group of locality-preserving logical operators. We also present examples of how our procedure applies to codes with different boundary conditions, including color codes and toric codes, as well as more general codes such as Abelian quantum double models and codes with fermionic excitations in more than two dimensions.

[Progression on finite element modeling method in scoliosis].

PubMed

Fan, Ning; Zang, Lei; Hai, Yong; Du, Peng; Yuan, Shuo

2018-04-25

Scoliosis is a complex spinal three-dimensional malformation with complicated pathogenesis, often associated with complications as thoracic deformity and shoulder imbalance. Because the acquisition of specimen or animal models are difficult, the biomechanical study of scoliosis is limited. In recent years, along with the development of the computer technology, software and image, the technology of establishing a finite element model of human spine is maturing and it has been providing strong support for the research of pathogenesis of scoliosis, the design and application of brace, and the selection of surgical methods. The finite element model method is gradually becoming an important tool in the biomechanical study of scoliosis. Establishing a high quality finite element model is the basis of analysis and future study. However, the finite element modeling process can be complex and modeling methods are greatly varied. Choosing the appropriate modeling method according to research objectives has become researchers' primary task. In this paper, the author reviews the national and international literature in recent years and concludes the finite element modeling methods in scoliosis, including data acquisition, establishment of the geometric model, the material properties, parameters setting, the validity of the finite element model validation and so on. Copyright© 2018 by the China Journal of Orthopaedics and Traumatology Press.

Evolution Of The Concept Of Dimension

NASA Astrophysics Data System (ADS)

Journeau, Philippe F.

2007-04-01

Concepts of time elapsing `in' a space measuring the real emerge over the centuries. But Kant refutes absolute time and defines it, with space, as forms reacting to Newtonian mechanics. Einstein and Minkowski open a 20th century where time is a dimension, a substratum of reality `with' space rather than `in' it. Kaluza-Klein and String theories then develop a trend of additional spatial dimensions while de Broglie and Bohm open the possiblity that form, to begin with wave, be a reality together `with' a space-time particle. Other recent theories, such as spin networks, causal sets and twistor theory, even head to the idea of other "systems of dimensions." On the basis of such progresses and recent experiments the paper then considers a background independent fourfold time-form-action-space system of dimensions.

The Sierpinski Triangle Plane

NASA Astrophysics Data System (ADS)

Ettestad, David; Carbonara, Joaquin

The Sierpinski Triangle (ST) is a fractal which has Haussdorf dimension log23 ≈ 1.585 that has been studied extensively. In this paper, we introduce the Sierpinski Triangle Plane (STP), an infinite extension of the ST that spans the entire real plane but is not a vector subspace or a tiling of the plane with a finite set of STs. STP is shown to be a radial fractal with many interesting and surprising properties.

On representations of the filiform Lie superalgebra Lm,n

NASA Astrophysics Data System (ADS)

Wang, Qi; Chen, Hongjia; Liu, Wende

2015-11-01

In this paper, we study the representations for the filiform Lie superalgebras Lm,n, a particular class of nilpotent Lie superalgebras. We determine the minimal dimension of a faithful module over Lm,n using the theory of linear algebra. In addition, using the method of Feingold and Frenkel (1985), we construct some finite and infinite dimensional modules over Lm,n on the Grassmann algebra and the mixed Clifford-Weyl algebra.

On the frames of spaces of finite-dimensional Lie algebras of dimension at most 6

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

Gorbatsevich, V V

2014-05-31

In this paper, the frames of spaces of complex n-dimensional Lie algebras (that is, the intersections of all irreducible components of these spaces) are studied. A complete description of the frames and their projectivizations for n ≤ 6 is given. It is also proved that for n ≤ 6 the projectivizations of these spaces are simply connected. Bibliography: 7 titles.

Design optimization of space structures

NASA Technical Reports Server (NTRS)

Felippa, Carlos

1991-01-01

The topology-shape-size optimization of space structures is investigated through Kikuchi's homogenization method. The method starts from a 'design domain block,' which is a region of space into which the structure is to materialize. This domain is initially filled with a finite element mesh, typically regular. Force and displacement boundary conditions corresponding to applied loads and supports are applied at specific points in the domain. An optimal structure is to be 'carved out' of the design under two conditions: (1) a cost function is to be minimized, and (2) equality or inequality constraints are to be satisfied. The 'carving' process is accomplished by letting microstructure holes develop and grow in elements during the optimization process. These holes have a rectangular shape in two dimensions and a cubical shape in three dimensions, and may also rotate with respect to the reference axes. The properties of the perforated element are obtained through an homogenization procedure. Once a hole reaches the volume of the element, that element effectively disappears. The project has two phases. In the first phase the method was implemented as the combination of two computer programs: a finite element module, and an optimization driver. In the second part, focus is on the application of this technique to planetary structures. The finite element part of the method was programmed for the two-dimensional case using four-node quadrilateral elements to cover the design domain. An element homogenization technique different from that of Kikuchi and coworkers was implemented. The optimization driver is based on an augmented Lagrangian optimizer, with the volume constraint treated as a Courant penalty function. The optimizer has to be especially tuned to this type of optimization because the number of design variables can reach into the thousands. The driver is presently under development.

A decentralized linear quadratic control design method for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1990-01-01

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.

Effect of Root Filling on Stress Distribution in Premolars with Endodontic-Periodontal Lesion: A Finite Elemental Analysis Study.

PubMed

Belli, Sema; Eraslan, Oğuz; Eskitascioglu, Gürcan

2016-01-01

Endodontic-periodontal (EP) lesions require both endodontic and periodontal therapies. Impermeable sealing of the root canal system after cleaning and shaping is essential for a successful endodontic treatment. However, complete healing of the hard and soft tissue lesions takes time, and diseased bone, periodontal ligament, and tooth fibrous joints are reported to have an increased failure risk for a given load. Considering that EP lesions may affect the biomechanics of teeth, this finite elemental analysis study aimed to test the effect of root fillings on stress distribution in premolars with EP lesions. Three finite elemental analysis models representing 3 different types of EP lesions (primary endodontic disease [PED], PED with secondary periodontic involvement, and true combined) were created. The root canals were assumed as nonfilled or filled with gutta-percha, gutta-percha/apical mineral trioxide aggregate (MTA) plug, and MTA-based sealer. Materials used were assumed to be homogenous and isotropic. A 300-N load was applied from the buccal cusp of the crown with a 135° angle. The Cosmoworks structural-analysis program (SolidWorks Corp, Waltham, MA) was used for analysis. Results were presented considering von Mises criteria. Stresses at the root apex increased with an increase in lesion dimensions. Root filling did not affect stress distribution in the PED model. An MTA plug or MTA-based sealer created more stress areas within the root compared with the others in the models representing PED with periodontic involvement and true combined lesions. Stresses at the apical end of the root increase with increases in lesion dimensions. MTA-based sealers or an MTA plug creates more stresses when there is periodontic involvement or a true combined lesion. Copyright © 2016 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Numerical Modeling of Poroelastic-Fluid Systems Using High-Resolution Finite Volume Methods

NASA Astrophysics Data System (ADS)

Lemoine, Grady

Poroelasticity theory models the mechanics of porous, fluid-saturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also been applied to modeling living bone and other porous media. Poroelastic media often interact with fluids, such as in ocean bottom acoustics or propagation of waves from soft tissue into bone. This thesis describes the development and testing of high-resolution finite volume numerical methods, and simulation codes implementing these methods, for modeling systems of poroelastic media and fluids in two and three dimensions. These methods operate on both rectilinear grids and logically rectangular mapped grids. To allow the use of these methods, Biot's equations of poroelasticity are formulated as a first-order hyperbolic system with a source term; this source term is incorporated using operator splitting. Some modifications are required to the classical high-resolution finite volume method. Obtaining correct solutions at interfaces between poroelastic media and fluids requires a novel transverse propagation scheme and the removal of the classical second-order correction term at the interface, and in three dimensions a new wave limiting algorithm is also needed to correctly limit shear waves. The accuracy and convergence rates of the methods of this thesis are examined for a variety of analytical solutions, including simple plane waves, reflection and transmission of waves at an interface between different media, and scattering of acoustic waves by a poroelastic cylinder. Solutions are also computed for a variety of test problems from the computational poroelasticity literature, as well as some original test problems designed to mimic possible applications for the simulation code.

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.

Multi-dimensional Fokker-Planck equation analysis using the modified finite element method

NASA Astrophysics Data System (ADS)

Náprstek, J.; Král, R.

2016-09-01

The Fokker-Planck equation (FPE) is a frequently used tool for the solution of cross probability density function (PDF) of a dynamic system response excited by a vector of random processes. FEM represents a very effective solution possibility, particularly when transition processes are investigated or a more detailed solution is needed. Actual papers deal with single degree of freedom (SDOF) systems only. So the respective FPE includes two independent space variables only. Stepping over this limit into MDOF systems a number of specific problems related to a true multi-dimensionality must be overcome. Unlike earlier studies, multi-dimensional simplex elements in any arbitrary dimension should be deployed and rectangular (multi-brick) elements abandoned. Simple closed formulae of integration in multi-dimension domain have been derived. Another specific problem represents the generation of multi-dimensional finite element mesh. Assembling of system global matrices should be subjected to newly composed algorithms due to multi-dimensionality. The system matrices are quite full and no advantages following from their sparse character can be profited from, as is commonly used in conventional FEM applications in 2D/3D problems. After verification of partial algorithms, an illustrative example dealing with a 2DOF non-linear aeroelastic system in combination with random and deterministic excitations is discussed.

Hopping and the Stokes–Einstein relation breakdown in simple glass formers

PubMed Central

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-01-01

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition—like that of other statistical systems—is exact when the spatial dimension d→∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, d=2,3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes–Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses. PMID:25288722

Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

NASA Astrophysics Data System (ADS)

Moosavi, S. Amin; Montakhab, Afshin

2014-05-01

Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (nonconservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibits true criticality for a wide range of noise in various dimensions, given that conservation is respected on the average. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for a sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, the addition of noise does not affect the exponents at the upper critical dimension (D =4). In addition to an extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for the general phenomena of criticality in nonequilibrium systems.

Hopping and the Stokes-Einstein relation breakdown in simple glass formers.

PubMed

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-10-21

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.

Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations

NASA Astrophysics Data System (ADS)

Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.

The Hamiltonian formulation of general relativity is considered in finite space-time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac-ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac-ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1990-01-01

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

The quantum Ising chain with a generalized defect

NASA Astrophysics Data System (ADS)

Grimm, Uwe

1990-08-01

The finite-size scaling properties of the quantum Ising chain with different types of generalized defects are studied. This not only means an alteration of the coupling constant as previously examined, but also an additional arbitrary transformation in the algebra of observables at one site of the chain. One can distinguish between two classes of generalized defects: on the one hand those which do not affect the finite-size integrability of the Ising chain, and on the other hand those that destroy this property. In this context, finite-size integrability is always understood as a synonym for the possibility to write the hamiltonian of the finite chain as a bilinear expression in fermionic operators by means of a Jordan-Wigner transformation. Concerning the first type of defect, an exact solution for the scaling spectrum is obtained for the most universal defect that preserves the global Z2 symmetry of the chain. It is shown that in the continuum limit this yields the same result as for one properly chosen ordinary defect, that is changing the coupling constant only, and thus the finite-size scaling spectra can be described by irreps of a shifted u(1) Kac-Moody algebra. The other type of defect is examined by means of numerical finite-size calculations. In contrast to the first case, these calculations suggest a non-continuous dependence of the scaling dimensions on the defect parameters. A conjecture for the operator content involving only one primary field of a Virasoro algebra with central charge c= {1}/{2} is given.

Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2016-11-01

To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.

Remote sensing applied to numerical modelling. [water resources pollution

NASA Technical Reports Server (NTRS)

Sengupta, S.; Lee, S. S.; Veziroglu, T. N.; Bland, R.

1975-01-01

Progress and remaining difficulties in the construction of predictive mathematical models of large bodies of water as ecosystems are reviewed. Surface temperature is at present the only variable than can be measured accurately and reliably by remote sensing techniques, but satellite infrared data are of sufficient resolution for macro-scale modeling of oceans and large lakes, and airborne radiometers are useful in meso-scale analysis (of lakes, bays, and thermal plumes). Finite-element and finite-difference techniques applied to the solution of relevant coupled time-dependent nonlinear partial differential equations are compared, and the specific problem of the Biscayne Bay and environs ecosystem is tackled in a finite-differences treatment using the rigid-lid model and a rigid-line grid system.

Higgs decays to Z Z and Z γ in the standard model effective field theory: An NLO analysis

NASA Astrophysics Data System (ADS)

Dawson, S.; Giardino, P. P.

2018-05-01

We calculate the complete one-loop electroweak corrections to the inclusive H →Z Z and H →Z γ decays in the dimension-6 extension of the Standard Model Effective Field Theory (SMEFT). The corrections to H →Z Z are computed for on-shell Z bosons and are a precursor to the physical H →Z f f ¯ calculation. We present compact numerical formulas for our results and demonstrate that the logarithmic contributions that result from the renormalization group evolution of the SMEFT coefficients are larger than the finite next-to-leading-order contributions to the decay widths. As a byproduct of our calculation, we obtain the first complete result for the finite corrections to Gμ in the SMEFT.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Holographic RG flows on curved manifolds and quantum phase transitions

NASA Astrophysics Data System (ADS)

Ghosh, J. K.; Kiritsis, E.; Nitti, F.; Witkowski, L. T.

2018-05-01

Holographic RG flows dual to QFTs on maximally symmetric curved manifolds (dS d , AdS d , and S d ) are considered in the framework of Einstein-dilaton gravity in d + 1 dimensions. A general dilaton potential is used and the flows are driven by a scalar relevant operator. The general properties of such flows are analyzed and the UV and IR asymptotics computed. New RG flows can appear at finite curvature which do not have a zero curvature counterpart. The so-called `bouncing' flows, where the β-function has a branch cut at which it changes sign, are found to persist at finite curvature. Novel quantum first-order phase transitions are found, triggered by a variation in the d-dimensional curvature in theories allowing multiple ground states.

Finite-size scaling analysis on the phase transition of a ferromagnetic polymer chain model

NASA Astrophysics Data System (ADS)

Luo, Meng-Bo

2006-01-01

The finite-size scaling analysis method is applied to study the phase transition of a self-avoiding walking polymer chain with spatial nearest-neighbor ferromagnetic Ising interaction on the simple cubic lattice. Assuming the scaling M2(T,n)=n-2β/ν[Φ0+Φ1n1/ν(T-Tc)+O(n2/ν(T-Tc)2)] with the square magnetization M2 as the order parameter and the chain length n as the size, we estimate the second-order phase-transition temperature Tc=1.784J/kB and critical exponents 2β/ν≈0.668 and ν ≈1.0. The self-diffusion constant and the chain dimensions ⟨R2⟩ and ⟨S2⟩ do not obey such a scaling law.

Energy bounds in designer gravity

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

Amsel, Aaron J.; Marolf, Donald

We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound in d{>=}4 spacetime dimensions. The boundary conditions in these ''designer gravity'' theories are defined in terms of an arbitrary function W. We give a general argument that the Hamiltonian generators of asymptotic symmetries for such systems will be finite, and proceed to construct these generators using the covariant phase space method. The direct calculation confirms that the generators are finite and shows that they take the form of the pure gravity result plus additional contributions from the scalar fields. Bymore » comparing the generators to the spinor charge, we derive a lower bound on the gravitational energy when W has a global minimum and the Breitenlohner-Freedman bound is not saturated.« less

Rényi and Tsallis formulations of separability conditions in finite dimensions

NASA Astrophysics Data System (ADS)

Rastegin, Alexey E.

2017-12-01

Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of Rényi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach based on the convolution of discrete probability distributions. Measurements on a total system are constructed of local ones according to the convolution scheme. Separability conditions are derived on the base of uncertainty relations of the Maassen-Uffink type as well as majorization relations. On each of subsystems, we use a pair of sets of subnormalized vectors that form rank-one POVMs. We also obtain entropic separability conditions for local measurements with a special structure, such as mutually unbiased bases and symmetric informationally complete measurements. The relevance of the derived separability conditions is demonstrated with several examples.

A three-dimensional FEM-DEM technique for predicting the evolution of fracture in geomaterials and concrete

NASA Astrophysics Data System (ADS)

Zárate, Francisco; Cornejo, Alejandro; Oñate, Eugenio

2018-07-01

This paper extends to three dimensions (3D), the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method and the discrete element method (DEM) approach (Zárate and Oñate in Comput Part Mech 2(3):301-314, 2015). Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple four-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.

A reduced-order integral formulation to account for the finite size effect of isotropic square panels using the transfer matrix method.

PubMed

Bonfiglio, Paolo; Pompoli, Francesco; Lionti, Riccardo

2016-04-01

The transfer matrix method is a well-established prediction tool for the simulation of sound transmission loss and the sound absorption coefficient of flat multilayer systems. Much research has been dedicated to enhancing the accuracy of the method by introducing a finite size effect of the structure to be simulated. The aim of this paper is to present a reduced-order integral formulation to predict radiation efficiency and radiation impedance for a panel with equal lateral dimensions. The results are presented and discussed for different materials in terms of radiation efficiency, sound transmission loss, and the sound absorption coefficient. Finally, the application of the proposed methodology for rectangular multilayer systems is also investigated and validated against experimental data.

Impact of finite receiver-aperture size in a non-line-of-sight single-scatter propagation model.

PubMed

Elshimy, Mohamed A; Hranilovic, Steve

2011-12-01

In this paper, a single-scatter propagation model is developed that expands the classical model by considering a finite receiver-aperture size for non-line-of-sight communication. The expanded model overcomes some of the difficulties with the classical model, most notably, inaccuracies in scenarios with short range and low elevation angle where significant scattering takes place near the receiver. The developed model does not approximate the receiver aperture as a point, but uses its dimensions for both field-of-view and solid-angle computations. To verify the model, a Monte Carlo simulation of photon transport in a turbid medium is applied. Simulation results for temporal responses and path losses are presented at a wavelength of 260 nm that lies in the solar-blind ultraviolet region.

Navier-Stokes relaxation to sinh-Poisson states at finite Reynolds numbers

NASA Technical Reports Server (NTRS)

Montgomery, David; Shan, Xiaowen; Matthaeus, William H.

1993-01-01

A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier-Stokes fluid to a 'most probable', or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables.

Self-Trapping Self-Repelling Random Walks

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2017-10-01

Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the "true self-avoiding walk" model of Amit, Parisi, and Peliti in two dimensions. The walks in it are self-repelling up to a characteristic time T* (which depends on various parameters), but spontaneously (i.e., without changing any control parameter) become self-trapping after that. For free walks, T* is astronomically large, but on finite lattices the transition is easily observable. In the self-trapped regime, walks are subdiffusive and intermittent, spending longer and longer times in small areas until they escape and move rapidly to a new area. In spite of this, these walks are extremely efficient in covering finite lattices, as measured by average cover times.

Wave energy focusing to subsurface poroelastic formations to promote oil mobilization

NASA Astrophysics Data System (ADS)

Karve, Pranav M.; Kallivokas, Loukas F.

2015-07-01

We discuss an inverse source formulation aimed at focusing wave energy produced by ground surface sources to target subsurface poroelastic formations. The intent of the focusing is to facilitate or enhance the mobility of oil entrapped within the target formation. The underlying forward wave propagation problem is cast in two spatial dimensions for a heterogeneous poroelastic target embedded within a heterogeneous elastic semi-infinite host. The semi-infiniteness of the elastic host is simulated by augmenting the (finite) computational domain with a buffer of perfectly matched layers. The inverse source algorithm is based on a systematic framework of partial-differential-equation-constrained optimization. It is demonstrated, via numerical experiments, that the algorithm is capable of converging to the spatial and temporal characteristics of surface loads that maximize energy delivery to the target formation. Consequently, the methodology is well-suited for designing field implementations that could meet a desired oil mobility threshold. Even though the methodology, and the results presented herein are in two dimensions, extensions to three dimensions are straightforward.

Inverse Jacobi multiplier as a link between conservative systems and Poisson structures

NASA Astrophysics Data System (ADS)

García, Isaac A.; Hernández-Bermejo, Benito

2017-08-01

Some aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that system are analyzed. From the local point of view, due to the flow-box theorem we restrict ourselves to neighborhoods of singularities. In this sense, we characterize Poisson structures around the typical zero-Hopf singularity in dimension 3 under the assumption of having a local analytic first integral with non-vanishing first jet by connecting with the classical Poincaré center problem. From the global point of view, we connect the property of being strictly conservative (the invariant measure must be positive) with the existence of a Poisson structure depending on the phase space dimension. Finally, weak conservativeness in dimension two is introduced by the extension of inverse Jacobi multipliers as weak solutions of its defining partial differential equation and some of its applications are developed. Examples including Lotka-Volterra systems, quadratic isochronous centers, and non-smooth oscillators are provided.

[Numerical modeling of shape memory alloy vascular stent's self-expandable progress and "optimized grid" of stent].

PubMed

Xu, Qiang; Liu, Yulan; Wang, Biao; He, Jin

2008-10-01

Vascular stent is an important medical appliance for angiocardiopathy. Its key deformation process is the expandable progress of stent in the vessel. The important deformation behaviour corresponds to two mechanics targets: deformation and stress. This paper is devoted to the research and development of vascular stent with proprietary intellectual property rights. The design of NiTinol self-expandable stent is optimized by means of finite element software. ANSYS is used to build the finite element simulation model of vascular stent; the molding material is NiTinol shape memory alloy. To cope with the factors that affect the structure of stent, the shape of grid and so on, the self-expanding process of Nitinol stent is simulated through computer. By making a comparison between two kinds of stents with similar grid structure, we present a new concept of "Optimized Grid" of stent.

Multiscale Multifunctional Progressive Fracture of Composite Structures

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Minnetyan, L.

2012-01-01

A new approach is described for evaluating fracture in composite structures. This approach is independent of classical fracture mechanics parameters like fracture toughness. It relies on computational simulation and is programmed in a stand-alone integrated computer code. It is multiscale, multifunctional because it includes composite mechanics for the composite behavior and finite element analysis for predicting the structural response. It contains seven modules; layered composite mechanics (micro, macro, laminate), finite element, updating scheme, local fracture, global fracture, stress based failure modes, and fracture progression. The computer code is called CODSTRAN (Composite Durability Structural ANalysis). It is used in the present paper to evaluate the global fracture of four composite shell problems and one composite built-up structure. Results show that the composite shells. Global fracture is enhanced when internal pressure is combined with shear loads. The old reference denotes that nothing has been added to this comprehensive report since then.

Modeling Progressive Damage Using Local Displacement Discontinuities Within the FEAMAC Multiscale Modeling Framework

NASA Technical Reports Server (NTRS)

Ranatunga, Vipul; Bednarcyk, Brett A.; Arnold, Steven M.

2010-01-01

A method for performing progressive damage modeling in composite materials and structures based on continuum level interfacial displacement discontinuities is presented. The proposed method enables the exponential evolution of the interfacial compliance, resulting in unloading of the tractions at the interface after delamination or failure occurs. In this paper, the proposed continuum displacement discontinuity model has been used to simulate failure within both isotropic and orthotropic materials efficiently and to explore the possibility of predicting the crack path, therein. Simulation results obtained from Mode-I and Mode-II fracture compare the proposed approach with the cohesive element approach and Virtual Crack Closure Techniques (VCCT) available within the ABAQUS (ABAQUS, Inc.) finite element software. Furthermore, an eccentrically loaded 3-point bend test has been simulated with the displacement discontinuity model, and the resulting crack path prediction has been compared with a prediction based on the extended finite element model (XFEM) approach.

Regularized finite element modeling of progressive failure in soils within nonlocal softening plasticity

NASA Astrophysics Data System (ADS)

Huang, Maosong; Qu, Xie; Lü, Xilin

2017-11-01

By solving a nonlinear complementarity problem for the consistency condition, an improved implicit stress return iterative algorithm for a generalized over-nonlocal strain softening plasticity was proposed, and the consistent tangent matrix was obtained. The proposed algorithm was embodied into existing finite element codes, and it enables the nonlocal regularization of ill-posed boundary value problem caused by the pressure independent and dependent strain softening plasticity. The algorithm was verified by the numerical modeling of strain localization in a plane strain compression test. The results showed that a fast convergence can be achieved and the mesh-dependency caused by strain softening can be effectively eliminated. The influences of hardening modulus and material characteristic length on the simulation were obtained. The proposed algorithm was further used in the simulations of the bearing capacity of a strip footing; the results are mesh-independent, and the progressive failure process of the soil was well captured.

Investigation of Micro-Scale Architectural Effects on Damage of Composites

NASA Technical Reports Server (NTRS)

Stier, Bertram; Bednarcyk, Brett A.; Simon, Jaan W.; Reese, Stefanie

2015-01-01

This paper presents a three-dimensional, energy based, anisotropic, stiffness reduction, progressive damage model for composite materials and composite material constituents. The model has been implemented as a user-defined constitutive model within the Abaqus finite element software package and applied to simulate the nonlinear behavior of a damaging epoxy matrix within a unidirectional composite material. Three different composite microstructures were considered as finite element repeating unit cells, with appropriate periodicity conditions applied at the boundaries. Results representing predicted transverse tensile, longitudinal shear, and transverse shear stress-strain curves are presented, along with plots of the local fields indicating the damage progression within the microstructure. It is demonstrated that the damage model functions appropriately at the matrix scale, enabling localization of the damage to simulate failure of the composite material. The influence of the repeating unit cell geometry and the effect of the directionality of the applied loading are investigated and discussed.

Progression of growth in the external ear from birth to maturity: a 2-year follow-up study in India.

PubMed

Purkait, Ruma

2013-06-01

This study aimed to follow the growth dynamics of auricular dimensions from birth to the age of 18 years. The norms of dimensions at different ages, the peak growth period and the maturity age of the dimensions are essential information to Physicians for early clinical diagnosis or for deciding the optimal time for surgery to correct abnormalities. For this study, 2,147 children belonging to central Indian population were measured in at least three sequential sessions. Eight dimensions including the physiognomic length and width of the ear and its morphologic width; conchal length, width, and depth; and lobular length and width were measured using anthropometric technique. Three new dimensions (tragal length and height and maximum width of the antihelix) were introduced in the study. Three indices (auricular, conchal, and lobular) also were derived. Most dimensions exhibited very rapid growth during the first 3-6 months of infancy and thereafter proceeded at a slow pace until adulthood. The smaller dimensions (conchal depth, tragal height, and maximum width of the antihelix) increased continuously throughout the growth period. At birth, most of the dimensions were 52-76 % of their adult size, while tragal length and height were less than half their adult size. Unlike the other dimensions, the lobule length was smaller in males, probably due to the higher frequency of hypoplastic and bow-shaped lobules among them. The width dimensions matured earlier, at 5.6-11 years, whereas the maturity age of lengths varied from 12 to 16 years. The data generated in the current study will be useful to Physicians as a guideline in correcting auricular deformity and in constructing age progression charts of the external ear. Knowledge concerning the maturation age of the ear will help law enforcement authorities in deciding when to use it for establishing personal identification. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Topics in strong Langmuir turbulence

NASA Technical Reports Server (NTRS)

Nicholson, D. R.

1983-01-01

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Topics in strong Langmuir turbulence

NASA Technical Reports Server (NTRS)

Nicholson, D. R.

1982-01-01

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Theory of nonlinear, distortive phenomena in solids: Martensitic, crack, and multiscale structures-phenomenology and physics. Progress summary, 1991--1994

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

Sethna, J.P.; Krumhansl, J.A.

1994-08-01

We have identified tweed precursors to martensitic phase transformations as a spin glass phase due to composition variations, and used simulations and exact replica theory predictions to predict diffraction peaks and model phase diagrams, and provide real space data for comparison to transmission electron micrograph images. We have used symmetry principles to derive the crack growth laws for mixed-mode brittle fracture, explaining the results for two-dimensional fracture and deriving the growth laws in three dimensions. We have used recent advances in dynamical critical phenomena to study hysteresis in disordered systems, explaining the return-point-memory effect, predicting distributions for Barkhausen noise, andmore » elucidating the transition from athermal to burst behavior in martensites. From a nonlinear lattice-dynamical model of a first-order transition using simulations, finite-size scaling, and transfer matrix methods, it is shown that heterophase transformation precursors cannot occur in a pure homogeneous system, thus emphasizing the role of disorder in real materials. Full integration of nonlinear Landau-Ginzburg continuum theory with experimental neutron-scattering data and first-principles calculations has been carried out to compute semi-quantitative values of the energy and thickness of twin boundaries in InTl and FePd martensites.« less

DRBEM solution of the acid-mediated tumour invasion model with time-dependent carrying capacities

NASA Astrophysics Data System (ADS)

Meral, Gülnihal

2017-07-01

It is known that the pH level of the extracellular tumour environment directly effects the progression of the tumour. In this study, the mathematical model for the acid-mediated tumour cell invasion consisting of a system of nonlinear reaction diffusion equations describing the interaction between the density of the tumour cells, normal cells and the concentration of ? protons produced by the tumour cells is solved numerically using the combined application of dual reciprocity boundary element method (DRBEM) and finite difference method. The space derivatives in the model are discretised by DRBEM using the fundamental solution of Laplace equation considering the time derivative and the nonlinearities as the nonhomogenity. The resulting systems of ordinary differential equations after the application of DRBEM are then discretised using forward difference. Because of the highly nonlinear character of the model, there arises difficulties in solving the model especially for two-dimensions and the boundary-only nature of DRBEM discretisation gives the advantage of having solutions with a lower computational cost. The proposed method is tested with different kinds of carrying capacities which also depend on time. The results of the numerical simulations are compared among each case and seen to confirm the expected behaviour of the model.

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

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

Zheng, Xiang; Yang, Chao; State Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190

2015-03-15

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracymore » (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.« less

Analytical and experimental studies on detection of longitudinal, L and inverted T cracks in isotropic and bi-material beams based on changes in natural frequencies

NASA Astrophysics Data System (ADS)

Ravi, J. T.; Nidhan, S.; Muthu, N.; Maiti, S. K.

2018-02-01

An analytical method for determination of dimensions of longitudinal crack in monolithic beams, based on frequency measurements, has been extended to model L and inverted T cracks. Such cracks including longitudinal crack arise in beams made of layered isotropic or composite materials. A new formulation for modelling cracks in bi-material beams is presented. Longitudinal crack segment sizes, for L and inverted T cracks, varying from 2.7% to 13.6% of length of Euler-Bernoulli beams are considered. Both forward and inverse problems have been examined. In the forward problems, the analytical results are compared with finite element (FE) solutions. In the inverse problems, the accuracy of prediction of crack dimensions is verified using FE results as input for virtual testing. The analytical results show good agreement with the actual crack dimensions. Further, experimental studies have been done to verify the accuracy of the analytical method for prediction of dimensions of three types of crack in isotropic and bi-material beams. The results show that the proposed formulation is reliable and can be employed for crack detection in slender beam like structures in practice.

Black holes in six-dimensional conformal gravity

NASA Astrophysics Data System (ADS)

Lü, H.; Pang, Yi; Pope, C. N.

2013-05-01

We study conformally invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely, Weyl-squared, and furthermore all solutions of Einstein gravity are also solutions of the conformal theory. By contrast, in six dimensions there are three independent conformally invariant polynomial terms one could consider. There is a unique linear combination (up to overall scale) for which Einstein metrics are also solutions, and this specific theory forms the focus of our attention in this paper. We reduce the equations of motion for the most general spherically symmetric black hole to a single fifth-order differential equation. We obtain the general solution in the form of an infinite series, characterized by five independent parameters, and we show how a finite three-parameter truncation reduces to the already known Schwarzschild-AdS metric and its conformal scaling. We derive general results for the thermodynamics and the first law for the full five-parameter solutions. We also investigate solutions in extended theories coupled to conformally invariant matter, and in addition we derive some general results for conserved charges in cubic-curvature theories in arbitrary dimensions.

Emergent dimensions and branes from large-N confinement

NASA Astrophysics Data System (ADS)

Cherman, Aleksey; Poppitz, Erich

2016-12-01

N =1 S U (N ) super-Yang-Mills theory on R3×S1 is believed to have a smooth dependence on the circle size L . Making L small leads to calculable nonperturbative color confinement, mass gap, and string tensions. For finite N , the small-L low-energy dynamics is described by a three-dimensional effective theory. The large-N limit, however, reveals surprises: the infrared dual description is in terms of a theory with an emergent fourth dimension, curiously reminiscent of T-duality in string theory. Here, however, the emergent dimension is a lattice, with momenta related to the S1-winding of the gauge field holonomy, which takes values in ZN. Furthermore, the low-energy description is given by a nontrivial gapless theory, with a space-like z =2 Lifshitz scale invariance and operators that pick up anomalous dimensions as L is increased. Supersymmetry-breaking deformations leave the long-distance theory scale-invariant, but change the Lifshitz scaling exponent to z =1 , and lead to an emergent Lorentz symmetry at small L . Adding a small number of fundamental fermion fields leads to matter localized on three-dimensional branes in the emergent four-dimensional theory.

Asymmetric fluid criticality. II. Finite-size scaling for simulations.

PubMed

Kim, Young C; Fisher, Michael E

2003-10-01

The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions L focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded "complete" thermodynamic (L--> infinity) scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling [Phys. Rev. E 67, 061506 (2003)] is extended to finite L, initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when L--> infinity, the second temperature derivative (d2musigma/dT2) of the chemical potential along the phase boundary musigmaT diverges when T-->Tc-. The finite-size behavior of various special critical loci in the temperature-density or (T,rho) plane, in particular, the k-inflection susceptibility loci and the Q-maximal loci--derived from QL(T,L) is identical with 2L/L where m is identical with rho-L--is carefully elucidated and shown to be of value in estimating Tc and rhoc. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent nu that confirms Ising-type character. The treatment is extended to the canonical representation where further complications appear.

Parallel eigenanalysis of finite element models in a completely connected architecture

NASA Technical Reports Server (NTRS)

Akl, F. A.; Morel, M. R.

1989-01-01

A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi) = (M)(phi)(omega), where (K) and (M) are of order N, and (omega) is order of q. The concurrent solution of the eigenproblem is based on the multifrontal/modified subspace method and is achieved in a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm was successfully implemented on a tightly coupled multiple-instruction multiple-data parallel processing machine, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macrotasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. A parallel finite element dynamic analysis program, p-feda, is documented and the performance of its subroutines in parallel environment is analyzed.

Reflection and diffraction corrections for nonlinear materials characterization by quasi-static pulse measurement

NASA Astrophysics Data System (ADS)

Nagy, Peter B.; Qu, Jianmin; Jacobs, Laurence J.

2014-02-01

A harmonic acoustic tone burst propagating through an elastic solid with quadratic nonlinearity produces not only a parallel burst of second harmonic but also an often neglected quasi-static pulse associated with the acoustic radiation-induced eigenstrain. Although initial analytical and experimental studies by Yost and Cantrell suggested that the pulse might have a right-angled triangular shape with the peak displacement at the leading edge being proportional to the length of the tone burst, more recent theoretical, analytical, numerical, and experimental studies proved that the pulse has a flat-top shape and the peak displacement is proportional to the propagation length. In this paper, analytical and numerical simulation results are presented to illustrate two types of finite-size effects. First, the finite axial dimension of the specimen cannot be simply accounted for by a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. Second, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second harmonic pulses generated by the same transducer. These finite-size effects can make the top of the quasi-static pulse sloped rather than flat and therefore must be taken into consideration in the interpretation of experimental data.

Reflection and diffraction corrections for nonlinear materials characterization by quasi-static pulse measurement

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

Nagy, Peter B.; Qu, Jianmin; Jacobs, Laurence J.

A harmonic acoustic tone burst propagating through an elastic solid with quadratic nonlinearity produces not only a parallel burst of second harmonic but also an often neglected quasi-static pulse associated with the acoustic radiation-induced eigenstrain. Although initial analytical and experimental studies by Yost and Cantrell suggested that the pulse might have a right-angled triangular shape with the peak displacement at the leading edge being proportional to the length of the tone burst, more recent theoretical, analytical, numerical, and experimental studies proved that the pulse has a flat-top shape and the peak displacement is proportional to the propagation length. In thismore » paper, analytical and numerical simulation results are presented to illustrate two types of finite-size effects. First, the finite axial dimension of the specimen cannot be simply accounted for by a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. Second, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second harmonic pulses generated by the same transducer. These finite-size effects can make the top of the quasi-static pulse sloped rather than flat and therefore must be taken into consideration in the interpretation of experimental data.« less

[Finite Element Modelling of the Eye for the Investigation of Accommodation].

PubMed

Martin, H; Stachs, O; Guthoff, R; Grabow, N

2016-12-01

Background: Accommodation research increasingly uses engineering methods. This article presents the use of the finite element method in accommodation research. Material and Methods: Geometry, material data and boundary conditions are prerequisites for the application of the finite element method. Published data on geometry and materials are reviewed. It is shown how boundary conditions are important and how they influence the results. Results: Two dimensional and three dimensional models of the anterior chamber of the eye are presented. With simple two dimensional models, it is shown that realistic results for the accommodation amplitude can always be achieved. More complex three dimensional models of the accommodation mechanism - including the ciliary muscle - require further investigations of the material data and of the morphology of the ciliary muscle, if they are to achieve realistic results for accommodation. Discussion and Conclusion: The efficiency and the limitations of the finite element method are especially clear for accommodation. Application of the method requires extensive preparation, including acquisition of geometric and material data and experimental validation. However, a validated model can be used as a basis for parametric studies, by systematically varying material data and geometric dimensions. This allows systematic investigation of how essential input parameters influence the results. Georg Thieme Verlag KG Stuttgart · New York.

Probabilistic structural analysis methods of hot engine structures

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Hopkins, D. A.

1989-01-01

Development of probabilistic structural analysis methods for hot engine structures is a major activity at Lewis Research Center. Recent activities have focused on extending the methods to include the combined uncertainties in several factors on structural response. This paper briefly describes recent progress on composite load spectra models, probabilistic finite element structural analysis, and probabilistic strength degradation modeling. Progress is described in terms of fundamental concepts, computer code development, and representative numerical results.

Numerical simulation on dimension decrease for annular casing of one centrifugal boiler circulation pump

NASA Astrophysics Data System (ADS)

Fan, Y. Z.; Zuo, Z. G.; Liu, S. H.; Wu, Y. L.; Sha, Y. J.

2012-11-01

Primary formulation derivation indicates that the dimension of one existing centrifugal boiler circulation pump casing is too large. As great manufacture cost can be saved by dimension decrease, a numerical simulation research is developed in this paper on dimension decrease for annular casing of this pump with a specific speed equaling to 189, which aims at finding an appropriately smaller dimension of the casing while hydraulic performance and strength performance will hardly be changed according to the requirements of the cooperative company. The research object is one existing centrifugal pump with a diffuser and a semi-spherical annular casing, working as the boiler circulation pump for (ultra) supercritical units in power plants. Dimension decrease, the modification method, is achieved by decreasing the existing casing's internal radius (marked as "Ri0") while keeping the wall thickness. The research analysis is based on primary formulation derivation, CFD (Computational Fluid Dynamics) simulation and FEM (Finite Element Method) simulation. Primary formulation derivation estimates that a design casing's internal radius should be less than 0.75 Ri0. CFD analysis indicates that smaller casing with 0.75 Ri0 has a worse hydraulic performance when working at large flow rates and a better hydraulic performance when working at small flow rates. In consideration of hydraulic performance and dimension decrease, an appropriate casing's internal radius is determined, which equals to 0.875 Ri0. FEM analysis then confirms that modified pump casing has nearly the same strength performance as the existing pump casing. It is concluded that dimension decrease can be an economical method as well as a practical method for large pumps in engineering fields.

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

PubMed

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.

A Longitudinal Study of Junior High School Students' Conceptions of the Structure of Materials

ERIC Educational Resources Information Center

Margel, Hannah; Eylon, Bat-Sheva; Scherz, Zahava

2008-01-01

This longitudinal study investigated the progression in junior high school (JHS) students' conceptions of the structure of matter while studying a new instructional approach dealing with "Materials." In particular, we studied the progression of students' learning along two dimensions: (a) the conceptual model; and (b) the context of application.…

Progressive Educational Practices and Environments in Sweden: Preparing Students to Live and Work in the Global Age

ERIC Educational Resources Information Center

Nordgren, R. D.

2006-01-01

A multi-site case study of three Swedish schools examined the dimensions of trust, responsibility, shared power (democracy), and global workforce competence as required by a decade-old national education reforms. A key finding was the existence of progressive educational practices including constructivist epistemology, evidenced by the schools'…

Electromagnetic deep-probing (100-1000 kms) of the Earth's interior from artificial satellites: Constraints on the regional emplacement of crustal resources

NASA Technical Reports Server (NTRS)

Hermance, J. F. (Principal Investigator)

1981-01-01

Efforts continue in the development of a computer program for looking at the coupling of finite dimensioned source fields with a laterally heterogeneous Earth. An algorithm for calculating a time-varying reference field using ground-based magnetic observatory data is also under development as part of the production of noise-free estimates of global electromagnetic response functions using Magsat data.

Calculating Required Substructure Damping to Meet Prescribed System Damping Levels

DTIC Science & Technology

2007-06-01

Rorres, Elementary Linear Algebra . New Jersey: John Wiley & Sons, 2005. 2. Klaus-Jurgen Bathe, Finite Element Procedures. New Jersey: Prentice Hall...will be covered in the explanation of orthogonal complement. The definitions are extracted from the book “ Linear Algebra and its Applications” by...TA = left nullspace of A; dimension m-r Applying the first part of the fundamental theorem of Linear Algebra we can now talk about the orthogonal

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

Finite size effects in the thermodynamics of a free neutral scalar field

NASA Astrophysics Data System (ADS)

Parvan, A. S.

2018-04-01

The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The symmetric square matrices of the bilinear forms on the vector space of fields in both configuration space and momentum space were found explicitly. The exact lattice results for the partition function were generalized to the three-dimensional spatial momentum space and the main thermodynamic quantities were derived both on the lattice and in the continuum limit. The thermodynamic properties and the finite volume corrections to the thermodynamic quantities of the free real scalar field were studied. We found that on the finite lattice the exact lattice results for the free massive neutral scalar field agree with the continuum limit only in the region of small values of temperature and volume. However, at these temperatures and volumes the continuum physical quantities for both massive and massless scalar field deviate essentially from their thermodynamic limit values and recover them only at high temperatures or/and large volumes in the thermodynamic limit.

Gauged supergravities from M-theory reductions

NASA Astrophysics Data System (ADS)

Katmadas, Stefanos; Tomasiello, Alessandro

2018-04-01

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Fermionic halos at finite temperature in AdS/CFT

NASA Astrophysics Data System (ADS)

Argüelles, Carlos R.; Grandi, Nicolás E.

2018-05-01

We explore the gravitational backreaction of a system consisting in a very large number of elementary fermions at finite temperature, in asymptotically AdS space. We work in the hydrodynamic approximation, and solve the Tolman-Oppenheimer-Volkoff equations with a perfect fluid whose equation of state takes into account both the relativistic effects of the fermionic constituents, as well as its finite temperature effects. We find a novel dense core-diluted halo structure for the density profiles in the AdS bulk, similarly as recently reported in flat space, for the case of astrophysical dark matter halos in galaxies. We further study the critical equilibrium configurations above which the core undergoes gravitational collapse towards a massive black hole, and calculate the corresponding critical central temperatures, for two qualitatively different central regimes of the fermions: the diluted-Fermi case, and the degenerate case. As a probe for the dual CFT, we construct the holographic two-point correlator of a scalar operator with large conformal dimension in the worldline limit, and briefly discuss on the boundary CFT effects at the critical points.

Application of Dynamic Analysis in Semi-Analytical Finite Element Method

PubMed Central

Oeser, Markus

2017-01-01

Analyses of dynamic responses are significantly important for the design, maintenance and rehabilitation of asphalt pavement. In order to evaluate the dynamic responses of asphalt pavement under moving loads, a specific computational program, SAFEM, was developed based on a semi-analytical finite element method. This method is three-dimensional and only requires a two-dimensional FE discretization by incorporating Fourier series in the third dimension. In this paper, the algorithm to apply the dynamic analysis to SAFEM was introduced in detail. Asphalt pavement models under moving loads were built in the SAFEM and commercial finite element software ABAQUS to verify the accuracy and efficiency of the SAFEM. The verification shows that the computational accuracy of SAFEM is high enough and its computational time is much shorter than ABAQUS. Moreover, experimental verification was carried out and the prediction derived from SAFEM is consistent with the measurement. Therefore, the SAFEM is feasible to reliably predict the dynamic response of asphalt pavement under moving loads, thus proving beneficial to road administration in assessing the pavement’s state. PMID:28867813

FEM simulation of single beard hair cutting with foil-blade-shaving system.

PubMed

Fang, Gang; Köppl, Alois

2015-06-01

The performance of dry-shavers depends on the interaction of the shaving components, hair and skin. Finite element models on the ABAQUS/Explicit platform are established to simulate the process of beard hair cutting. The skin is modelled as three-layer structure with a single cylindrical hair inserted into the skin. The material properties of skin are considered as Neo-Hookean hyper-elastic (epidermis) and Prony visco-elastic (dermis and hypodermis) with finite deformations. The hair is modelled as elastic-plastic material with shear damage. The cutting system is composed of a blade and a foil of shaver. The simulation results of cutting processes are analyzed, including the skin compression, hair bending, hair cutting and hair severance. Calculations of cutting loads, skin stress, and hair damage show the impact of clearance, skin bulge height, blade dimension and shape on cutting results. The details show the build-up of finite element models for hair cutting, and highlight the challenges arising during model construction and numerical simulation. Copyright © 2015 Elsevier Ltd. All rights reserved.

Calculation of reaction forces in the boiler supports using the method of equivalent stiffness of membrane wall.

PubMed

Sertić, Josip; Kozak, Dražan; Samardžić, Ivan

2014-01-01

The values of reaction forces in the boiler supports are the basis for the dimensioning of bearing steel structure of steam boiler. In this paper, the application of the method of equivalent stiffness of membrane wall is proposed for the calculation of reaction forces. The method of equalizing displacement, as the method of homogenization of membrane wall stiffness, was applied. On the example of "Milano" boiler, using the finite element method, the calculation of reactions in the supports for the real geometry discretized by the shell finite element was made. The second calculation was performed with the assumption of ideal stiffness of membrane walls and the third using the method of equivalent stiffness of membrane wall. In the third case, the membrane walls are approximated by the equivalent orthotropic plate. The approximation of membrane wall stiffness is achieved using the elasticity matrix of equivalent orthotropic plate at the level of finite element. The obtained results were compared, and the advantages of using the method of equivalent stiffness of membrane wall for the calculation of reactions in the boiler supports were emphasized.

Impeller deflection and modal finite element analysis.

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

Spencer, Nathan A.

2013-10-01

Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options suchmore » as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.« less

Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Singh, Rajiv R. P.

2015-10-01

We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies.

Simulating Initial and Progressive Failure of Open-Hole Composite Laminates under Tension

NASA Astrophysics Data System (ADS)

Guo, Zhangxin; Zhu, Hao; Li, Yongcun; Han, Xiaoping; Wang, Zhihua

2016-12-01

A finite element (FE) model is developed for the progressive failure analysis of fiber reinforced polymer laminates. The failure criterion for fiber and matrix failure is implemented in the FE code Abaqus using user-defined material subroutine UMAT. The gradual degradation of the material properties is controlled by the individual fracture energies of fiber and matrix. The failure and damage in composite laminates containing a central hole subjected to uniaxial tension are simulated. The numerical results show that the damage model can be used to accurately predicte the progressive failure behaviour both qualitatively and quantitatively.

Entanglement entropy of black holes and anti-de Sitter space/conformal-field-theory correspondence.

PubMed

Solodukhin, Sergey N

2006-11-17

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L(2)lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.

Persistence in a Random Bond Ising Model of Socio-Econo Dynamics

NASA Astrophysics Data System (ADS)

Jain, S.; Yamano, T.

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a finite temperature on hypercubic lattices in dimensions up to five. The model includes a "social" local field which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We find no evidence of "blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic fields. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in different scenarios.

Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

PubMed

Guérin, T; Dean, D S

2015-12-01

We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.

Random close packing of disks and spheres in confined geometries

NASA Astrophysics Data System (ADS)

Desmond, Kenneth W.; Weeks, Eric R.

2009-11-01

Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. In confined geometries, the structural properties of random-packed systems will change. To understand these changes, we study random close packing in finite-sized confined systems, in both two and three dimensions. Each packing consists of a 50-50 binary mixture with particle size ratio of 1.4. The presence of confining walls significantly lowers the overall maximum area fraction (or volume fraction in three dimensions). A simple model is presented, which quantifies the reduction in packing due to wall-induced structure. This wall-induced structure decays rapidly away from the wall, with characteristic length scales comparable to the small particle diameter.

Analytical Formulation for Sizing and Estimating the Dimensions and Weight of Wind Turbine Hub and Drivetrain Components

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

Guo, Y.; Parsons, T.; King, R.

This report summarizes the theory, verification, and validation of a new sizing tool for wind turbine drivetrain components, the Drivetrain Systems Engineering (DriveSE) tool. DriveSE calculates the dimensions and mass properties of the hub, main shaft, main bearing(s), gearbox, bedplate, transformer if up-tower, and yaw system. The level of fi¬ delity for each component varies depending on whether semiempirical parametric or physics-based models are used. The physics-based models have internal iteration schemes based on system constraints and design criteria. Every model is validated against available industry data or finite-element analysis. The verification and validation results show that the models reasonablymore » capture primary drivers for the sizing and design of major drivetrain components.« less

Representations of the Bondi—Metzner—Sachs group in three space—time dimensions

NASA Astrophysics Data System (ADS)

Melas, Evangelos

2017-01-01

The original Bondi-Metzner-Sachs group B is the common asymptotic symmetry group of all asymptotically at Lorentzian 4-dim space-times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). In 1973, with this motivation, P. J. McCarthy classified all relativistic B-invariant systems in terms of strongly continuous irreducible unitary representations (IRS) of B. Here, we construct the IRS of B(2, 1), the analogue of B, in 3 space-time dimensions. The IRS are induced from ‘little groups’ which are compact. The finite ‘little groups’ are cyclic groups of even order. The inducing construction is exhaustive notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.

An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three space dimensions IAT for reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2003-07-01

Solving systems of reaction-diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and CPU time. Herein, I present a new incomplete assembly procedure that is designed to reduce storage requirements. Incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction-diffusion systems. The effect of incomplete assembly on CPU time and storage and on the performance of the temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied.

Criticality and Connectivity in Macromolecular Charge Complexation

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

Qin, Jian; de Pablo, Juan J.

We examine the role of molecular connectivity and architecture on the complexation of ionic macromolecules (polyelectrolytes) of finite size. A unified framework is developed and applied to evaluate the electrostatic correlation free energy for point-like, rod-like, and coil-like molecules. That framework is generalized to molecules of variable fractal dimensions, including dendrimers. Analytical expressions for the free energy, correlation length, and osmotic pressure are derived, thereby enabling consideration of the effects of charge connectivity, fractal dimension, and backbone stiffness on the complexation behavior of a wide range of polyelectrolytes. Results are presented for regions in the immediate vicinity of the criticalmore » region and far from it. A transparent and explicit expression for the coexistence curve is derived in order to facilitate analysis of experimentally observed phase diagrams.« less

Multidimensional FEM-FCT schemes for arbitrary time stepping

NASA Astrophysics Data System (ADS)

Kuzmin, D.; Möller, M.; Turek, S.

2003-05-01

The flux-corrected-transport paradigm is generalized to finite-element schemes based on arbitrary time stepping. A conservative flux decomposition procedure is proposed for both convective and diffusive terms. Mathematical properties of positivity-preserving schemes are reviewed. A nonoscillatory low-order method is constructed by elimination of negative off-diagonal entries of the discrete transport operator. The linearization of source terms and extension to hyperbolic systems are discussed. Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided. The treatment of non-linearities and iterative solution of linear systems are addressed. The performance of the new algorithm is illustrated by numerical examples for the shock tube problem in one dimension and scalar transport equations in two dimensions.

Constraints on braneworld gravity models from a kinematic limit on the age of the black hole XTE J1118+480.

PubMed

Psaltis, Dimitrios

2007-05-04

In braneworld gravity models with a finite anti-de Sitter space (AdS) curvature in the extra dimension, the AdS/conformal field theory correspondence leads to a prediction for the lifetime of astrophysical black holes that is significantly smaller than the Hubble time, for asymptotic curvatures that are consistent with current experiments. Using the recent measurements of the position, three-dimensional spatial velocity, and mass of the black hole XTE J1118+480, I calculate a lower limit on its kinematic age of > or =11 Myr (95% confidence). This translates into an upper limit for the asymptotic AdS curvature in the extra dimensions of <0.08 mm, which significantly improves the limit obtained by table top experiments of sub mm gravity.

Analysis for the Progressive Failure Response of Textile Composite Fuselage Frames

NASA Technical Reports Server (NTRS)

Johnson, Eric R.; Boitnott, Richard L. (Technical Monitor)

2002-01-01

A part of aviation accident mitigation is a crashworthy airframe structure, and an important measure of merit for a crashworthy structure is the amount of kinetic energy that can be absorbed in the crush of the structure. Prediction of the energy absorbed from finite element analyses requires modeling the progressive failure sequence. Progressive failure modes may include material degradation, fracture and crack growth, and buckling and collapse. The design of crashworthy airframe components will benefit from progressive failure analyses that have been validated by tests. The subject of this research is the development of a progressive failure analysis for a textile composite, circumferential fuselage frame subjected to a quasi-static, crash-type load. The test data for the frame are reported, and these data are used to develop and to validate methods for the progressive failure response.

Personality traits and educational identity formation in late adolescents: longitudinal associations and academic progress.

PubMed

Klimstra, Theo A; Luyckx, Koen; Germeijs, Veerle; Meeus, Wim H J; Goossens, Luc

2012-03-01

Changes in personality traits in late adolescence and young adulthood are believed to co-occur with changes in identity, but little research is available that supports this hypothesis. The present study addressed this relatively understudied area of research by examining longitudinal associations of Big Five personality traits (i.e., Neuroticism, Extraversion, Openness, Agreeableness, and Conscientiousness) with dimensions of identity formation (i.e., identification with commitment and exploration in depth) in the domain of education. For this purpose, we used four annual waves of longitudinal data on 485 Belgian late adolescents (87.4% female; mean age at T1 = 18.6 years) covering a 3-year period. Multivariate growth models revealed that changes in Big Five personality traits were related to changes in identification with commitment and exploration in depth. Cross-lagged panel models uncovered that, except for Openness, all Big Five traits predicted educational identity dimensions. Educational identity dimensions only predicted Neuroticism. In addition, adolescents with higher levels on the personality trait of Conscientiousness faced fewer study delays. In sum, the present study adds to the growing literature that explores the antecedents, correlates, and consequences of personality trait development by uncovering the interplay of personality traits, educational identity dimensions, and academic progress in late adolescents.

Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

Failure Analysis of Discrete Damaged Tailored Extension-Shear-Coupled Stiffened Composite Panels

NASA Technical Reports Server (NTRS)

Baker, Donald J.

2005-01-01

The results of an analytical and experimental investigation of the failure of composite is tiffener panels with extension-shear coupling are presented. This tailored concept, when used in the cover skins of a tiltrotor aircraft wing has the potential for increasing the aeroelastic stability margins and improving the aircraft productivity. The extension-shear coupling is achieved by using unbalanced 45 plies in the skin. The failure analysis of two tailored panel configurations that have the center stringer and adjacent skin severed is presented. Finite element analysis of the damaged panels was conducted using STAGS (STructural Analysis of General Shells) general purpose finite element program that includes a progressive failure capability for laminated composite structures that is based on point-stress analysis, traditional failure criteria, and ply discounting for material degradation. The progressive failure predicted the path of the failure and maximum load capability. There is less than 12 percent difference between the predicted failure load and experimental failure load. There is a good match of the panel stiffness and strength between the progressive failure analysis and the experimental results. The results indicate that the tailored concept would be feasible to use in the wing skin of a tiltrotor aircraft.

MULTIGRID FOR THE MORTAR FINITE ELEMENT METHOD. (R825207)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Experimental and Numerical Study on the Tensile Behaviour of UACS/Al Fibre Metal Laminate

NASA Astrophysics Data System (ADS)

Xue, Jia; Wang, Wen-Xue; Zhang, Jia-Zhen; Wu, Su-Jun; Li, Hang

2015-10-01

A new fibre metal laminate fabricated with aluminium sheets and unidirectionally arrayed chopped strand (UACS) plies is proposed. The UACS ply is made by cutting parallel slits into a unidirectional carbon fibre prepreg. The UACS/Al laminate may be viewed as aluminium laminate reinforced by highly aligned, discontinuous carbon fibres. The tensile behaviour of UACS/Al laminate, including thermal residual stress and failure progression, is investigated through experiments and numerical simulation. Finite element analysis was used to simulate the onset and propagation of intra-laminar fractures occurring within slits of the UACS plies and delamination along the interfaces. The finite element models feature intra-laminar cohesive elements inserted into the slits and inter-laminar cohesive elements inserted at the interfaces. Good agreement are obtained between experimental results and finite element analysis, and certain limitations of the finite element models are observed and discussed. The combined experimental and numerical studies provide a detailed understanding of the tensile behaviour of UACS/Al laminates.

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.

Excitations in the Yang–Gaudin Bose gas

DOE PAGES

Robinson, Neil J.; Konik, Robert M.

2017-06-01

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

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

Robinson, Neil J.; Konik, Robert M.

Here, we study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang–Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at 2k F and a finite-momentum roton-like minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as 1/L for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the 2k F gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang–Gaudin Bose gas is also host to multi-spinon bound states, known asmore » $$\\Lambda$$ -strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length n $$\\Lambda$$-string dressed energies $$\\epsilon_n(\\lambda)$$ and the dressed energy $$\\epsilon(k)$$. We solve the Yang–Yang–Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length n $$\\Lambda$$ -string dressed energy is Lorentzian over a wide range of real string centers λ in the vicinity of $$\\lambda = 0$$ . We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.« less

Numerical study of anomalous dynamic scaling behaviour of (1+1)-dimensional Das Sarma-Tamborenea model

NASA Astrophysics Data System (ADS)

Xun, Zhi-Peng; Tang, Gang; Han, Kui; Hao, Da-Peng; Xia, Hui; Zhou, Wei; Yang, Xi-Quan; Wen, Rong-Ji; Chen, Yu-Ling

2010-07-01

In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the (1+1)-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the (1+1)-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L > 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma-Tamborenea model in 1+1 dimensions indeed exhibits intrinsic anomalous scaling behaviour.

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.

1996-01-01

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Simulating the interaction of the heliosphere with the local interstellar medium: MHD results from a finite volume approach, first bidimensional results

NASA Technical Reports Server (NTRS)

Chanteur, G.; Khanfir, R.

1995-01-01

We have designed a full compressible MHD code working on unstructured meshes in order to be able to compute accurately sharp structures embedded in large scale simulations. The code is based on a finite volume method making use of a kinetic flux splitting. A bidimensional version of the code has been used to simulate the interaction of a moving interstellar medium, magnetized or unmagnetized with a rotating and magnetized heliopspheric plasma source. Being aware that these computations are not realistic due to the restriction to two dimensions, we present it to demonstrate the ability of this new code to handle this problem. An axisymetric version, now under development, will be operational in a few months. Ultimately we plan to run a full 3d version.

Eisenstein series for infinite-dimensional U-duality groups

NASA Astrophysics Data System (ADS)

Fleig, Philipp; Kleinschmidt, Axel

2012-06-01

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.

Quantum key distribution for composite dimensional finite systems

NASA Astrophysics Data System (ADS)

Shalaby, Mohamed; Kamal, Yasser

2017-06-01

The application of quantum mechanics contributes to the field of cryptography with very important advantage as it offers a mechanism for detecting the eavesdropper. The pioneering work of quantum key distribution uses mutually unbiased bases (MUBs) to prepare and measure qubits (or qudits). Weak mutually unbiased bases (WMUBs) have weaker properties than MUBs properties, however, unlike MUBs, a complete set of WMUBs can be constructed for systems with composite dimensions. In this paper, we study the use of weak mutually unbiased bases (WMUBs) in quantum key distribution for composite dimensional finite systems. We prove that the security analysis of using a complete set of WMUBs to prepare and measure the quantum states in the generalized BB84 protocol, gives better results than using the maximum number of MUBs that can be constructed, when they are analyzed against the intercept and resend attack.

Critical behavior of the ideal-gas Bose-Einstein condensation in the Apollonian network.

PubMed

de Oliveira, I N; dos Santos, T B; de Moura, F A B F; Lyra, M L; Serva, M

2013-08-01

We show that the ideal Boson gas displays a finite-temperature Bose-Einstein condensation transition in the complex Apollonian network exhibiting scale-free, small-world, and hierarchical properties. The single-particle tight-binding Hamiltonian with properly rescaled hopping amplitudes has a fractal-like energy spectrum. The energy spectrum is analytically demonstrated to be generated by a nonlinear mapping transformation. A finite-size scaling analysis over several orders of magnitudes of network sizes is shown to provide precise estimates for the exponents characterizing the condensed fraction, correlation size, and specific heat. The critical exponents, as well as the power-law behavior of the density of states at the bottom of the band, are similar to those of the ideal Boson gas in lattices with spectral dimension d(s)=2ln(3)/ln(9/5)~/=3.74.

U.S. History Framework for the 2006 National Assessment of Educational Progress

ERIC Educational Resources Information Center

US Department of Education, 2006

2006-01-01

This document provides a guide for the development of the 2006 National Assessment of Education Progress (NAEP) U.S. History Assessment. NAEP measures the U.S. history knowledge and skills of students in grades 4, 8, and 12. According to the NAEP U.S. history framework, the assessment should be organized around three dimensions: historical themes,…

Algorithms for Zonal Methods and Development of Three Dimensional Mesh Generation Procedures.

DTIC Science & Technology

1984-02-01

a r-re complete set of equations is used, but their effect is imposed by means of a right hand side forcing function, not by means of a zonal boundary...modifications of flow-simulation algorithms The explicit finite-difference code of Magnus and are discussed. Computational tests in two dimensions...used to simplify the task of grid generation without an adverse achieve computational efficiency. More recently, effect on flow-field algorithms and

Design of Kinetic Energy Projectiles for Structural Integrity

DTIC Science & Technology

1981-09-01

wear, and good pressure sealing experience. Unfortunately, the constitutive relations for these materials are highly temperature and rate of loading...41’ M IA 0 41 Lii uci a.O 49= z 445 Before any grooves are dimensioned, the maximum shear stress at the interface must be determined from a finite...concentrations in these sensitive materials. Filet radii at the root of the tooth should be increased to the maximum size consistent with good fit between

A mixed formulation for interlaminar stresses in dropped-ply laminates

NASA Technical Reports Server (NTRS)

Harrison, Peter N.; Johnson, Eric R.

1993-01-01

A structural model is developed for the linear elastic response of structures consisting of multiple layers of varying thickness such as laminated composites containing internal ply drop-offs. The assumption of generalized plane deformation is used to reduce the solution domain to two dimensions while still allowing some out-of-plane deformation. The Hellinger-Reissner variational principle is applied to a layerwise assumed stress distribution with the resulting governing equations solved using finite differences.

Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

DOE PAGES

An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis

2016-03-14

The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. Wemore » show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.« less

Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

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

An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis

The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. Wemore » show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.« less

The study of mechanical behavior on the interface between calcar-defect femur and restorations by means of finite element analysis

NASA Astrophysics Data System (ADS)

Shi, X. H.; Jiang, W.; Chen, H. Z.; Zou, W.; Wang, W. D.; Guo, Z.; Luo, J. M.; Gu, Z. W.; Zhang, X. D.

2008-11-01

The mechanical behaviors of calcar-defected femur and restorations under physiological load are the key factors that will greatly influence the success of femur calcar defect repairing, especially the stress distribution on the bone-restoration interface. 3D finite elements analysis (FEA) was used to analyze the mechanical characters on the interfaces between femoral calcar defects and bone cement or HA restorations. Under the load of two times of a human weight (1436.03 N) and with the increase of the defect dimension from 6 mm to 12 mm, the maximal stresses on the surface of restorations are from 7.06 MPa to 11.89 MPa for bone cement and 2.97-9 MPa for HA separately. In this condition, HA restoration will probably be broken on the bone-restoration interface when the defect diameter is beyond 8 mm. Furthermore, under the load of 1.5 times of a human weight, HA restoration would not be safe unless the defect dimension is smaller than 10 mm, because the maximal stress (4.62 MPa) on the restoration is only a little lower than compressive strength of HA, otherwise the bone fixation device should be applied to ensure the safety. It is relatively safe for all restorations under all the tested defect sizes when the load is just the weight of a human body.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

A quantitative study on magnesium alloy stent biodegradation.

PubMed

Gao, Yuanming; Wang, Lizhen; Gu, Xuenan; Chu, Zhaowei; Guo, Meng; Fan, Yubo

2018-06-06

Insufficient scaffolding time in the process of rapid corrosion is the main problem of magnesium alloy stent (MAS). Finite element method had been used to investigate corrosion of MAS. However, related researches mostly described all elements suffered corrosion in view of one-dimensional corrosion. Multi-dimensional corrosions significantly influence mechanical integrity of MAS structures such as edges and corners. In this study, the effects of multi-dimensional corrosion were studied using experiment quantitatively, then a phenomenological corrosion model was developed to consider these effects. We implemented immersion test with magnesium alloy (AZ31B) cubes, which had different numbers of exposed surfaces to analyze differences of dimension. It was indicated that corrosion rates of cubes are almost proportional to their exposed-surface numbers, especially when pitting corrosions are not marked. The cubes also represented the hexahedron elements in simulation. In conclusion, corrosion rate of every element accelerates by increasing corrosion-surface numbers in multi-dimensional corrosion. The damage ratios among elements with the same size are proportional to the ratios of corrosion-surface numbers under uniform corrosion. The finite element simulation using proposed model provided more details of changes of morphology and mechanics in scaffolding time by removing 25.7% of elements of MAS. The proposed corrosion model reflected the effects of multi-dimension on corrosions. It would be used to predict degradation process of MAS quantitatively. Copyright © 2018 Elsevier Ltd. All rights reserved.

Three FORTRAN programs for finite-difference solutions to binary diffusion in one and two phases with composition-and time-dependent diffusion coefficients

USGS Publications Warehouse

Sanford, R.F.

1982-01-01

Geological examples of binary diffusion are numerous. They are potential indicators of the duration and rates of geological processes. Analytical solutions to the diffusion equations generally do not allow for variable diffusion coefficients, changing boundary conditions, and impingement of diffusion fields. The three programs presented here are based on Crank-Nicholson finite-difference approximations, which can take into account these complicating factors. Program 1 describes the diffusion of a component into an initially homogeneous phase that has a constant surface composition. Specifically it is written for Fe-Mg exchange in olivine at oxygen fugacities appropriate for the lunar crust, but other components, phases, or fugacities may be substituted by changing the values of the diffusion coefficient. Program 2 simulates the growth of exsolution lamellae. Program 3 describes the growth of reaction rims. These two programs are written for pseudobinary Ca-(Mg, Fe) exchange in pyroxenes. In all three programs, the diffusion coefficients and boundary conditions can be varied systematically with time. To enable users to employ widely different numerical values for diffusion coefficients and diffusion distance, the grid spacing in the space dimension and the increment by which the grid spacing in the time dimension is increased at each time step are input constants that can be varied each time the programs are run to yield a solution of the desired accuracy. ?? 1982.

A PARALLEL LEAST-SQUARES FINITE ELEMENT METHOD FOR INCOMPRESSIBLE FLOWS. (R825200)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Recent Advances in the Analysis of Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1997-01-01

A review of recent progress for the analysis of spiral bevel gears will be described. The foundation of this work relies on the description of the gear geometry of face-milled spiral bevel gears via the approach developed by Litvin. This methodology was extended by combining the basic gear design data with the manufactured surfaces using a differential geometry approach, and provides the data necessary for assembling three-dimensional finite element models. The finite element models have been utilized to conduct thermal and structural analysis of the gear system. Examples of the methods developed for thermal and structural/contact analysis are presented.

Probabilistic Fatigue Damage Prognosis Using a Surrogate Model Trained Via 3D Finite Element Analysis

NASA Technical Reports Server (NTRS)

Leser, Patrick E.; Hochhalter, Jacob D.; Newman, John A.; Leser, William P.; Warner, James E.; Wawrzynek, Paul A.; Yuan, Fuh-Gwo

2015-01-01

Utilizing inverse uncertainty quantification techniques, structural health monitoring can be integrated with damage progression models to form probabilistic predictions of a structure's remaining useful life. However, damage evolution in realistic structures is physically complex. Accurately representing this behavior requires high-fidelity models which are typically computationally prohibitive. In the present work, a high-fidelity finite element model is represented by a surrogate model, reducing computation times. The new approach is used with damage diagnosis data to form a probabilistic prediction of remaining useful life for a test specimen under mixed-mode conditions.

Analysis for the Progressive Failure Response of Textile Composite Fuselage Frames

NASA Technical Reports Server (NTRS)

Johnson, Eric R.; Boitnott, Richard L. (Technical Monitor)

2002-01-01

A part of aviation accident mitigation is a crash worthy airframe structure, and an important measure of merit for a crash worthy structure is the amount of kinetic energy that can be absorbed in the crush of the structure. Prediction of the energy absorbed from finite element analyses requires modeling the progressive failure sequence. Progressive failure modes may include material degradation, fracture and crack growth, and buckling and collapse. The design of crash worthy airframe components will benefit from progressive failure analyses that have been validated by tests. The subject of this research is the development of a progressive failure analysis for textile composite. circumferential fuselage frames subjected to a quasi-static, crash-type load. The test data for these frames are reported, and these data, along with stub column test data, are to be used to develop and to validate methods for the progressive failure response.