Embedded diagonally implicit Runge-Kutta algorithms on parallel computers
NASA Astrophysics Data System (ADS)
van der Houwen, P. J.; Sommeijer, B. P.; Couzy, W.
1992-01-01
This paper investigates diagonally implicit Runge-Kutta methods in which the implicit relations can be solved in parallel and are singly diagonal-implicit on each processor. The algorithms are based on diagonally implicit iteration of fully implicit Runge-Kutta methods of high order. The iteration scheme is chosen in such a way that the resulting algorithm is A(α ) -stable or L(α ) -stable with α equal or very close to π /2 . In this way, highly stable, singly diagonal-implicit Runge-Kutta methods of orders up to 10 can be constructed. Because of the iterative nature of the methods, embedded formulas of lower orders are automatically available, allowing a strategy for step and order variation.
Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order
Cong, Y. H.; Jiang, C. X.
2014-01-01
The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods. PMID:24977178
Diagonally implicit symplectic Runge-Kutta methods with high algebraic and dispersion order.
Cong, Y H; Jiang, C X
2014-01-01
The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods.
Singly implicit diagonally extended Runge-Kutta methods of fourth order
NASA Astrophysics Data System (ADS)
Skvortsov, L. M.
2014-05-01
Singly implicit diagonally extended Runge-Kutta methods make it possible to combine the merits of diagonally implicit methods (namely, the simplicity of implementation) and fully implicit ones (high stage order). Due to this combination, they can be very efficient at solving stiff and differential-algebraic problems. In this paper, fourth-order methods with an explicit first stage are examined. The methods have the third or fourth stage order. Consideration is given to an efficient implementation of these methods. The results of tests in which the proposed methods were compared with the fifth-order RADAU IIA method are presented.
Automatic integration of the reaction path using diagonally implicit Runge-Kutta methods.
Burger, Steven K; Yang, Weitao
2006-12-28
The diagonally implicit Runge-Kutta framework is shown to be a general form for constructing stable, efficient steepest descent reaction path integrators, of any order. With this framework tolerance driven, adaptive step-size methods can be constructed by embedding methods to obtain error estimates of each step without additional computational cost. There are many embedded and nonembedded, diagonally implicit Runge-Kutta methods available from the numerical analysis literature and these are reviewed for orders two, three, and four. New embedded methods are also developed which are tailored to the application of reaction path following. All integrators are summarized and compared for three systems: the Muller-Brown [Theor. Chem. Acta 53, 75 (1979)] potential and two gas phase chemical reactions. The results show that many of the methods are capable of integrating efficiently while reliably keeping the error bound within the desired tolerance. This allows the reaction path to be determined through automatic integration by only specifying the desired accuracy and transition state.
Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review
NASA Technical Reports Server (NTRS)
Kennedy, Christopher A.; Carpenter, Mark H.
2016-01-01
A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.
Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows
Zhong, Xiaolin
1996-10-01
This paper is concerned with time-stepping numerical methods for computing stiff semi-discrete systems of ordinary differential equations for transient hypersonic flows with thermo-chemical non-equilibrium. The stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite-rate thermo-chemical processes. Implicit methods are needed to treat the stiff terms while more efficient explicit methods can still be used for the nonstiff terms in the equations. This paper studies three different semi-implicit Runge-Kutta methods for additively split differential equations in the form of u{prime} = f(u) + g(u), where f is treated by explicit Runge-Kutta methods and g is simultaneously treated by three implicit Runge-Kutta methods: a diagonally implicit Runge-Kutta method and two linearized implicit Runge-Kutta methods. The coefficients of up to third-order accurate additive semi-implicit Runge-Kutta methods have been derived such that the methods are both high-order accurate and strongly A-stable for the implicit terms. The results of two numerical tests on the stability and accuracy properties of these methods are also presented in the paper. 26 refs., 10 figs., 2 tabs.
Stage-parallel fully implicit Runge-Kutta solvers for discontinuous Galerkin fluid simulations
NASA Astrophysics Data System (ADS)
Pazner, Will; Persson, Per-Olof
2017-04-01
In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge-Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems, which has seen success for fluid flow problems and discontinuous Galerkin discretizations. By transforming the resulting linear system of equations, one can obtain a method which is much less computationally expensive than the untransformed formulation, and which compares competitively with other time-integration schemes, such as diagonally implicit Runge-Kutta (DIRK) methods. We develop and test several ILU-based preconditioners effective for these large systems. We additionally employ a parallel-in-time strategy to compute the Runge-Kutta stages simultaneously. Numerical experiments are performed on the Navier-Stokes equations using Euler vortex and 2D and 3D NACA airfoil test cases in serial and in parallel settings. The fully implicit Radau IIA Runge-Kutta methods compare favorably with equal-order DIRK methods in terms of accuracy, number of GMRES iterations, number of matrix-vector multiplications, and wall-clock time, for a wide range of time steps.
Minimally implicit Runge-Kutta methods for Resistive Relativistic MHD
NASA Astrophysics Data System (ADS)
Aloy, Miguel-Á.; Cordero-Carrión, Isabel
2016-05-01
The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative extra loop in order to recover the primitive (physical) variables, the analytical inversion of the implicit operator is trivial and the several stages can actually be viewed as stages of explicit Runge-Kutta methods with an effective time-step. We test these methods with two different one-dimensional test beds in varied conductivity regimes, and show that our second-order schemes satisfy the theoretical expectations.
NASA Astrophysics Data System (ADS)
Conde, Sidafa; Gottlieb, Sigal; Grant, Zachary J.; Shadid, John N.
2017-07-01
High order strong stability preserving (SSP) time discretizations have proven beneficial for use with spatial discretizations with nonlinear stability properties for the solution of hyperbolic PDEs. Implicit SSP Runge-Kutta methods exist only up to sixth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: implicit SSP Runge-Kutta methods of any linear order exist. In the current work we aim to find implicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have varying designed orders of accuracy for nonlinear order. In this work we also extend the concept of varying orders of accuracy for linear and non linear components to the class of implicit-explicit (IMEX) Runge-Kutta methods methods, and present a method of this type.
On implicit Runge-Kutta methods for parallel computations
NASA Technical Reports Server (NTRS)
Keeling, Stephen L.
1987-01-01
Implicit Runge-Kutta methods which are well-suited for parallel computations are characterized. It is claimed that such methods are first of all, those for which the associated rational approximation to the exponential has distinct poles, and these are called multiply explicit (MIRK) methods. Also, because of the so-called order reduction phenomenon, there is reason to require that these poles be real. Then, it is proved that a necessary condition for a q-stage, real MIRK to be A sub 0-stable with maximal order q + 1 is that q = 1, 2, 3, or 5. Nevertheless, it is shown that for every positive integer q, there exists a q-stage, real MIRK which is I-stable with order q. Finally, some useful examples of algebraically stable MIRKs are given.
A Low-Dispersion and Low-Dissipation Implicit Runge-Kutta Scheme
Najafi-Yazdi, A.; Mongeau, L.
2012-01-01
A fourth-order, implicit, low-dispersion, and low-dissipation Runge-Kutta scheme is introduced. The scheme is optimized for minimal dissipation and dispersion errors. High order accuracy is achieved with fewer stages than standard explicit Runge-Kutta schemes. The scheme is designed to be As table for highly stiff problems. Possible applications include wall-bounded flows with solid boundaries in the computational domain, and sound generation by reacting flows. PMID:23243319
NASA Astrophysics Data System (ADS)
Langer, Stefan
2014-11-01
For unstructured finite volume methods an agglomeration multigrid with an implicit multistage Runge-Kutta method as a smoother is developed for solving the compressible Reynolds averaged Navier-Stokes (RANS) equations. The implicit Runge-Kutta method is interpreted as a preconditioned explicit Runge-Kutta method. The construction of the preconditioner is based on an approximate derivative. The linear systems are solved approximately with a symmetric Gauss-Seidel method. To significantly improve this solution method grid anisotropy is treated within the Gauss-Seidel iteration in such a way that the strong couplings in the linear system are resolved by tridiagonal systems constructed along these directions of strong coupling. The agglomeration strategy is adapted to this procedure by taking into account exactly these anisotropies in such a way that a directional coarsening is applied along these directions of strong coupling. Turbulence effects are included by a Spalart-Allmaras model, and the additional transport-type equation is approximately solved in a loosely coupled manner with the same method. For two-dimensional and three-dimensional numerical examples and a variety of differently generated meshes we show the wide range of applicability of the solution method. Finally, we exploit the GMRES method to determine approximate spectral information of the linearized RANS equations. This approximate spectral information is used to discuss and compare characteristics of multistage Runge-Kutta methods.
Parallel Implicit Runge-Kutta Methods Applied to Coupled Orbit/Attitude Propagation
NASA Astrophysics Data System (ADS)
Hatten, Noble; Russell, Ryan P.
2016-12-01
A variable-step Gauss-Legendre implicit Runge-Kutta (GLIRK) propagator is applied to coupled orbit/attitude propagation. Concepts previously shown to improve efficiency in 3DOF propagation are modified and extended to the 6DOF problem, including the use of variable-fidelity dynamics models. The impact of computing the stage dynamics of a single step in parallel is examined using up to 23 threads and 22 associated GLIRK stages; one thread is reserved for an extra dynamics function evaluation used in the estimation of the local truncation error. Efficiency is found to peak for typical examples when using approximately 8 to 12 stages for both serial and parallel implementations. Accuracy and efficiency compare favorably to explicit Runge-Kutta and linear-multistep solvers for representative scenarios. However, linear-multistep methods are found to be more efficient for some applications, particularly in a serial computing environment, or when parallelism can be applied across multiple trajectories.
NASA Astrophysics Data System (ADS)
Ismail, Amira; Gorgey, Annie
2015-10-01
Extrapolation involves taking a certain linear combination of the numerical solutions of a base method applied with different stepsizes to obtain greater accuracy. This linear combination is done so as to eliminate the leading error term. The technique of extrapolation in accelerating convergence has been successfully in numerical solution of ordinary differential equations. In this study, symmetric Runge-Kutta methods for solving linear and nonlinear stiff problem are considered. Symmetric methods admit asymptotic error expansion in even powers of the stepsize and are therefore of special interest because successive extrapolations can increase the order by two at time. Although extrapolation can give greater accuracy, due to the stepsize chosen, the numerical approximations are often destroy due to the accumulated round off errors. Therefore, it is important to control the rounding errors especially when applying extrapolation. One way to minimize round off errors is by applying compensated summation. In this paper, the numerical results are given for the symmetric Runge-Kutta methods Implicit Midpoint and Implicit Trapezoidal Rule applied with and without compensated summation. The result shows that symmetric methods with higher level extrapolation using compensated summation gives much smaller errors. On the other hand, symmetric methods without compensated summation when applied with extrapolation, the errors are affected badly by rounding errors.
Generalized disks of contractivity for explicit and implicit Runge-Kutta methods
NASA Technical Reports Server (NTRS)
Dahlquist, G.; Jeltsch, R.
1979-01-01
The A-contractivity of Runge-Kutta methods with respect to an inner product norm was investigated thoroughly by Butcher and Burrage (who used the term B-stability). Their theory is extended to contractivity in a region bounded by a circle through the origin. The largest possible circle is calculated for many known explicit Runge-Kutta methods. As a rule it is considerably smaller than the stability region, and in several cases it degenerates to a point. It is shown that an explicit Runge-Kutta method cannot be contractive in any circle of this class if it is more than fourth order accurate.
Implicit - symplectic partitioned (IMSP) Runge-Kutta schemes for predator-prey dynamics
NASA Astrophysics Data System (ADS)
Diele, F.; Marangi, C.; Ragni, S.
2012-09-01
In the study of the effects of habitat fragmentation on biodiversity the role of spatial processes reveals of great interest since both the variation of size of the domains as well as their heterogeneity largely affects the dynamics of species. In order to begin a preliminary study about the effects of habitat fragmentation on wolf - wild boar pair populating the Italian "Alta Murgia" Natura 2000 site, object of interest for FP7 project BIOSOS, (BIOdiversity multi-SOurce Monitoring System: from Space TO Species), spatially explicit models described by reaction-diffusion partial differential equations are considered. Numerical methods based on partitioned Runge-Kutta schemes which use an implicit scheme for the stiff diffusive term and a partitioned symplectic scheme for the reaction function are here proposed. We are motivated by the classical results about Lotka-Volterra model described by ordinary differential equations to which the spatially explicit model reduces for diffusion coefficients tending to zero: for their accurate solution symplectic schemes have to be used for an optimal long run preservation of the dynamics invariant. Moreover, for models based on logistic growth and Holling type II functional predator response we verify the better performance of our schemes when compared with classical implicit-explicit (IMEX) schemes on chaotic dynamics given in literature.
NASA Astrophysics Data System (ADS)
Cavaglieri, Daniele; Bewley, Thomas
2015-04-01
Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.
Spiteri, Raymond J; Dean, Ryan C
2008-05-01
Mathematical models of electric activity in cardiac tissue are becoming increasingly powerful tools in the study of cardiac arrhythmias. Considered here are mathematical models based on ordinary differential equations (ODEs) that describe the ionic currents at the myocardial cell level. Generating an efficient numerical solution of these ODEs is a challenging task, and, in fact, the physiological accuracy of tissue-scale models is often limited by the efficiency of the numerical solution process. In this paper, we examine the efficiency of the numerical solution of four cardiac electrophysiological models using implicit--explicit Runge-Kutta (IMEX-RK) splitting methods. We find that variable step-size implementations of IMEX-RK methods (ARK3 and ARK5) that take advantage of Jacobian structure clearly outperform the methods commonly used in practice.
NASA Astrophysics Data System (ADS)
Kazemi-Kamyab, V.; van Zuijlen, A. H.; Bijl, H.
2014-09-01
Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Since time-accurate computations of unsteady CHT can be computationally demanding, we consider the use of high order implicit time integration schemes which have the potential to be more efficient relative to the commonly used second order implicit schemes. We present a strongly-coupled solution algorithm where the high order L-stable explicit first-stage singly diagonally implicit Runge-Kutta (ESDIRK) schemes are used to advance the solution in time within each separate fluid and solid subdomains. Furthermore, the stability and rate of convergence of performing (Gauss-Seidel) subiterations at each stage of the ESDIRK schemes are analyzed. The results from solving a numerical example (an unsteady conjugate natural convection in an enclosure) show good agreement with the performed analytical stability analysis. In addition, the (computational) work-(temporal) precision character of several schemes in solving a strongly coupled CHT problem is compared over a range of accuracy requirements. From the efficiency investigation, it is observed that performing subiterations with the strongly-coupled ESDIRK algorithm is more efficient than lowering time-step size using a high order loosely-coupled IMEX algorithm. In addition, by using the ESDIRK schemes, gain in computational efficiency relative to Crank-Nicolson is observed for time-accurate solutions (a factor of 1.4 using the fourth order ESDIRK). The computational gain is higher for smaller tolerances.
Liu, Xiaodong; Xia, Yidong; Luo, Hong; ...
2016-10-05
A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less
Liu, Xiaodong; Xia, Yidong; Luo, Hong; Xuan, Lijun
2016-10-05
A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flows to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.
NASA Astrophysics Data System (ADS)
Kulikov, G. Yu.
2015-06-01
A technique for constructing nested implicit Runge-Kutta methods in the class of mono-implicit formulas of this type is studied. These formulas are highly efficient in practice, since the dimension of the original system of differential equations is preserved, which is not possible in the case of implicit multistage Runge-Kutta formulas of the general from. On the other hand, nested implicit Runge-Kutta methods inherit all major properties of general formulas of this form, such as A-stability, symmetry, and symplecticity in a certain sense. Moreover, they can have sufficiently high stage and classical orders and, without requiring high extra costs, can ensure dense output of integration results of the same accuracy as the order of the underlying method. Thus, nested methods are efficient when applied to the numerical integration of differential equations of various sorts, including stiff and nonstiff problems, Hamiltonian systems, and invertible equations. In this paper, previously proposed nested methods based on the Gauss quadrature formulas are generalized to Lobatto-type methods. Additionally, a unified technique for constructing all such methods is proposed. Its performance is demonstrated as applied to embedded examples of nested implicit formulas of various orders. All the methods constructed are supplied with tools for local error estimation and automatic variable-stepsize mesh generation based on an optimal stepsize selection. These numerical methods are verified by solving test problems with known solutions. Additionally, a comparative analysis of these methods with Matlab built-in solvers is presented.
NASA Astrophysics Data System (ADS)
Elkina, N. V.; Fedotov, A. M.; Herzing, C.; Ruhl, H.
2014-05-01
The Landau-Lifshitz equation provides an efficient way to account for the effects of radiation reaction without acquiring the nonphysical solutions typical for the Lorentz-Abraham-Dirac equation. We solve the Landau-Lifshitz equation in its covariant four-vector form in order to control both the energy and momentum of radiating particles. Our study reveals that implicit time-symmetric collocation methods of the Runge-Kutta-Nyström type are superior in accuracy and better at maintaining the mass-shell condition than their explicit counterparts. We carry out an extensive study of numerical accuracy by comparing the analytical and numerical solutions of the Landau-Lifshitz equation. Finally, we present the results of the simulation of particle scattering by a focused laser pulse. Due to radiation reaction, particles are less capable of penetrating into the focal region compared to the case where radiation reaction is neglected. Our results are important for designing forthcoming experiments with high intensity laser fields.
Elkina, N V; Fedotov, A M; Herzing, C; Ruhl, H
2014-05-01
The Landau-Lifshitz equation provides an efficient way to account for the effects of radiation reaction without acquiring the nonphysical solutions typical for the Lorentz-Abraham-Dirac equation. We solve the Landau-Lifshitz equation in its covariant four-vector form in order to control both the energy and momentum of radiating particles. Our study reveals that implicit time-symmetric collocation methods of the Runge-Kutta-Nyström type are superior in accuracy and better at maintaining the mass-shell condition than their explicit counterparts. We carry out an extensive study of numerical accuracy by comparing the analytical and numerical solutions of the Landau-Lifshitz equation. Finally, we present the results of the simulation of particle scattering by a focused laser pulse. Due to radiation reaction, particles are less capable of penetrating into the focal region compared to the case where radiation reaction is neglected. Our results are important for designing forthcoming experiments with high intensity laser fields.
Implicit High Order Strong Stability Preserving Runge-Kutta Time Discretizations
2009-02-05
Fahroo 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION / AVAILABILITY STATEMENT Distribution A... Wang (who presented his joint work with Ray Spiteri). Inma Higueras, Steven Ruuth and his student Colin Macdonald. This minisym- posia led to...Fraser University, Canada; Dong Wang , University of Illi- nois at Urbana-Champaign. (c) In Search of Implicit High-Order Strong Stability Preserving
NASA Technical Reports Server (NTRS)
Kanevsky, Alex
2004-01-01
My goal is to develop and implement efficient, accurate, and robust Implicit-Explicit Runge-Kutta (IMEX RK) methods [9] for overcoming geometry-induced stiffness with applications to computational electromagnetics (CEM), computational fluid dynamics (CFD) and computational aeroacoustics (CAA). IMEX algorithms solve the non-stiff portions of the domain using explicit methods, and isolate and solve the more expensive stiff portions using implicit methods. Current algorithms in CEM can only simulate purely harmonic (up to lOGHz plane wave) EM scattering by fighter aircraft, which are assumed to be pure metallic shells, and cannot handle the inclusion of coatings, penetration into and radiation out of the aircraft. Efficient MEX RK methods could potentially increase current CEM capabilities by 1-2 orders of magnitude, allowing scientists and engineers to attack more challenging and realistic problems.
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
NASA Technical Reports Server (NTRS)
Kennedy, Christopher A.; Carpenter, Mark H.
2001-01-01
Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, N = 2, additive Runge-Kutta ARK2 methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms are of equal order to those of the elemental methods. Derived ARK2 methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z(exp [I]) goes to infinity, and retain high stability efficiency in the absence of stiffness, z(exp [I]) goes to zero. Extrapolation-type stage-value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK2 error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods while offering error control and stage-value predictors.
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
NASA Technical Reports Server (NTRS)
Kennedy, Christopher A.; Carpenter, Mark H.
2002-01-01
Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one- dimensional convection-diffusion-reaction (CDR) equations. Accuracy, stability, conservation, and dense-output are first considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, (N = 2), additive Runge-Kutta (ARK(sub 2)) methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms of the partitioned method are of equal order to those of the elemental methods. Derived ARK(sub 2) methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z['] yields -infinity, and retain high stability efficiency in the absence of stiffness, z['] yield 0. Extrapolation-type stage- value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK(sub 2) error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK(sub 2) methods.
Extrapolated stabilized explicit Runge-Kutta methods
NASA Astrophysics Data System (ADS)
Martín-Vaquero, J.; Kleefeld, B.
2016-12-01
Extrapolated Stabilized Explicit Runge-Kutta methods (ESERK) are proposed to solve multi-dimensional nonlinear partial differential equations (PDEs). In such methods it is necessary to evaluate the function nt times per step, but the stability region is O (nt2). Hence, the computational cost is O (nt) times lower than for a traditional explicit algorithm. In that way stiff problems can be integrated by the use of simple explicit evaluations in which case implicit methods usually had to be used. Therefore, they are especially well-suited for the method of lines (MOL) discretizations of parabolic nonlinear multi-dimensional PDEs. In this work, first s-stages first-order methods with extended stability along the negative real axis are obtained. They have slightly shorter stability regions than other traditional first-order stabilized explicit Runge-Kutta algorithms (also called Runge-Kutta-Chebyshev codes). Later, they are used to derive nt-stages second- and fourth-order schemes using Richardson extrapolation. The stability regions of these fourth-order codes include the interval [ - 0.01nt2, 0 ] (nt being the number of total functions evaluations), which are shorter than stability regions of ROCK4 methods, for example. However, the new algorithms neither suffer from propagation of errors (as other Runge-Kutta-Chebyshev codes as ROCK4 or DUMKA) nor internal instabilities. Additionally, many other types of higher-order (and also lower-order) methods can be obtained easily in a similar way. These methods also allow adaptation of the length step with no extra cost. Hence, the stability domain is adapted precisely to the spectrum of the problem at the current time of integration in an optimal way, i.e., with minimal number of additional stages. We compare the new techniques with other well-known algorithms with good results in very stiff diffusion or reaction-diffusion multi-dimensional nonlinear equations.
Efficiency of Runge-Kutta methods in solving Kepler problem
NASA Astrophysics Data System (ADS)
Gorgey, Annie; Muhammad, Hafizul
2017-05-01
The aim of this research is to study the efficiency of symplectic and non-symplectic Runge-Kutta methods in solving Kepler problem. The numerical behavior of the Runge-Kutta (RK) methods that are symmetric such as the implicit midpoint rule (IMR), implicit trapezoidal rule (ITR), 2-stage and 2-stage Gauss (G2) method are compared with the non-symmetric Runge-Kutta methods such as the explicit and implicit Euler (EE and IE), explicit midpoint rule (EIMR), explicit trapezoidal rules (EITR), explicit 4-stage Runge-Kutta (RK4) method and 2-stage Radau IIA method (R2A). Kepler problem is one type of nonlinear Hamiltonian problem that describes the motion in a plane of a material point that is attracted towards the origin with a force inversely proportional to the distance squared. The exact solutions phase diagram produces a unit circle. The non-symplectic methods only reproduce a unit circle at certain time intervals while the symplectic methods do produce a unit circle at any time intervals. Some phase diagram show spiral in or spiral out patterns which means the solutions are running away from the unit circle. This also means that the absolute error will be increasing in long time integration. The numerical experiments for the Kepler problem are given for many time intervals and the results show that the most efficient method is G2 of order-4 and surprisingly RK4 seems to be efficient too although it is not a symplectic nor a symmetric method. The numerical results on Kepler problem concluded that, the higher the order of the method, the most efficient the method can be in solving Kepler problem despite whether they are explicit or implicit or symmetric and symplectic.
A Runge-Kutta Nystrom algorithm.
NASA Technical Reports Server (NTRS)
Bettis, D. G.
1973-01-01
A Runge-Kutta algorithm of order five is presented for the solution of the initial value problem where the system of ordinary differential equations is of second order and does not contain the first derivative. The algorithm includes the Fehlberg step control procedure.
Convergence acceleration of rational Runge-Kutta scheme for Euler and Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Morinishi, Koji; Nobuyuki, Satofuka
Modifications introduced to improve the performance of the rational-Runge-Kutta Euler/Navier-Stokes solver of Morishini and Satofuka (1987 and 1988) are discussed, summarizing the results of recent investigations. The derivation of the governing equations and the basic numerical procedure are outlined, and the use of the residual-averaging technique and multigrid methods to accelerate convergence is explained. Results are presented in graphs for (1) two-dimensional inviscid flow on a NACA 0012 airfoil at Mach 0.8 and angle of attack alpha = 1.25 deg, (2) two-dimensional viscous flow on an RAE 2822 airfoil at Mach 0.73 and alpha = 2.80 deg, and (3) three-dimensional inviscid flow on the ONERA M6 wing at Mach 0.84 and alpha = 3.06 deg. The steady-state convergence of the method is shown to be comparable to that of diagonalized implicit approximate-factorization schemes.
An unconditionally stable Runge-Kutta method for unsteady flows
NASA Technical Reports Server (NTRS)
Jorgenson, Philip C. E.; Chima, Rodrick V.
1989-01-01
A quasi-three-dimensional analysis was developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. The equations are integrated in time using a four-stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing was employed to accelerate the solution of the time accurate computations. The scheme is described and accuracy analyses are given. Results are shown for a supersonic through-flow fan designed for NASA Lewis. The rotor:stator blade ratio was taken as 1:1. Results are also shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Here the blade ratio is 2:3. Implicit residual smoothing was used to increase the time step limit of the unsmoothed scheme by a factor of six with negligible differences in the unsteady results. It is felt that the implicitly smoothed Runge-Kutta scheme is easily competitive with implicit schemes for unsteady flows while retaining the simplicity of an explicit scheme.
An unconditionally stable Runge-Kutta method for unsteady flows
NASA Technical Reports Server (NTRS)
Jorgenson, Philip C. E.; Chima, Rodrick V.
1988-01-01
A quasi-three dimensional analysis was developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. The equations are integrated in time using a four stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing was employed to accelerate the solution of the time accurate computations. The scheme is described and accuracy analyses are given. Results are shown for a supersonic through-flow fan designed for NASA Lewis. The rotor:stator blade ratio was taken as 1:1. Results are also shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Here the blade ratio is 2:3. Implicit residual smoothing was used to increase the time step limit of the unsmoothed scheme by a factor of six with negligible differences in the unsteady results. It is felt that the implicitly smoothed Runge-Kutta scheme is easily competitive with implicit schemes for unsteady flows while retaining the simplicity of an explicit scheme.
Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations
McKinney, W.R.
1989-01-01
Fully discrete approximations to 1-periodic solutions of the Generalized Korteweg de-Vries and the Cahn-Hilliard equations are analyzed. These approximations are generated by an Implicit Runge-Kutta method for the temporal discretization and a Galerkin Finite Element method for the spatial discretization. Furthermore, these approximations may be of arbitrarily high order. In particular, it is shown that the well-known order reduction phenomenon afflicting Implicit Runge Kutta methods does not occur. Numerical results supporting these optimal error estimates for the Korteweg-de Vries equation and indicating the existence of a slow motion manifold for the Cahn-Hilliard equation are also provided.
Stability of Runge-Kutta-Nystrom methods
NASA Astrophysics Data System (ADS)
Alonso-Mallo, I.; Cano, B.; Moreta, M. J.
2006-05-01
In this paper, a general and detailed study of linear stability of Runge-Kutta-Nystrom (RKN) methods is given. In the case that arbitrarily stiff problems are integrated, we establish a condition that RKN methods must satisfy so that a uniform bound for stability can be achieved. This condition is not satisfied by any method in the literature. Therefore, a stable method is constructed and some numerical comparisons are made.
Amplification and Suppression of Round-Off Error in Runge-Kutta Methods
ERIC Educational Resources Information Center
Prentice, J. S. C.
2011-01-01
A simple nonstiff linear initial-value problem is used to demonstrate the amplification of round-off error in the course of using a second-order Runge-Kutta method. This amplification is understood in terms of an appropriate expression for the global error. An implicit method is then used to show how the roundoff error may actually be suppressed.…
Exponential fitting BDF Runge Kutta algorithms
NASA Astrophysics Data System (ADS)
Vigo-Aguiar, J.; Martín-Vaquero, J.; Ramos, H.
2008-01-01
In other papers, the authors presented exponential fitting methods of BDF type. Now, these methods are used to derive some BDF-Runge-Kutta type formulas (of second-, third- and fourth-order), capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential with parameter A and ordinary polynomials. Theorems of the truncation error reveal the good behavior of the new methods for stiff problems. Plots of their absolute stability regions that include the whole of the negative real axis are provided. Different procedures to find the parameter of the method are proposed, using these techniques there will not be necessary to compute the exponential matrix at each step, even when nonlinear problems are integrated. Numerical examples underscore the efficiency of the proposed codes, especially when they are integrating stiff problems.
Scaled Runge-Kutta algorithms for handling dense output
NASA Technical Reports Server (NTRS)
Horn, M. K.
1981-01-01
Low order Runge-Kutta algorithms are developed which determine the solution of a system of ordinary differential equations at any point within a given integration step, as well as at the end of each step. The scaled Runge-Kutta methods are designed to be used with existing Runge-Kutta formulas, using the derivative evaluations of these defining algorithms as the core of the system. For a slight increase in computing time, the solution may be generated within the integration step, improving the efficiency of the Runge-Kutta algorithms, since the step length need no longer be severely reduced to coincide with the desired output point. Scaled Runge-Kutta algorithms are presented for orders 3 through 5, along with accuracy comparisons between the defining algorithms and their scaled versions for a test problem.
Composite group of explicit Runge-Kutta methods
NASA Astrophysics Data System (ADS)
Hamid, Fatin Nadiah Abd; Rabiei, Faranak; Ismail, Fudziah
2016-06-01
In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived. The proposed methods are two-step in nature and have less number of function evaluations compared to the existing Runge-Kutta method. The order conditions up to order four are obtained using rooted trees and composite rule introduced by J. C Butcher. The stability regions of RK3(2) and RK4(3) methods are presented and initial value problems of first order ordinary differential equations are carried out. Numerical results are compared with existing Runge-Kutta method.
A third order Runge-Kutta algorithm on a manifold
NASA Technical Reports Server (NTRS)
Crouch, P. E.; Grossman, R. G.; Yan, Y.
1992-01-01
A third order Runge-Kutta type algorithm is described with the property that it preserves certain geometric structures. In particular, if the algorithm is initialized on a Lie group, then the resulting iterates remain on the Lie group.
Galerkin/Runge-Kutta discretizations for semilinear parabolic equations
NASA Technical Reports Server (NTRS)
Keeling, Stephen L.
1987-01-01
A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high, optimal order convergence. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.
NASA Astrophysics Data System (ADS)
Emmrich, Etienne; Thalhammer, Mechthild
2010-04-01
Stiffly accurate implicit Runge-Kutta methods are studied for the time discretisation of nonlinear first-order evolution equations. The equation is supposed to be governed by a time-dependent hemicontinuous operator that is (up to a shift) monotone and coercive, and fulfills a certain growth condition. It is proven that the piecewise constant as well as the piecewise linear interpolant of the time-discrete solution converges towards the exact weak solution, provided the Runge-Kutta method is consistent and satisfies a stability criterion that implies algebraic stability; examples are the Radau IIA and Lobatto IIIC methods. The convergence analysis is also extended to problems involving a strongly continuous perturbation of the monotone main part.
Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Sanderse, B.
2013-01-01
Energy-conserving methods have recently gained popularity for the spatial discretization of the incompressible Navier-Stokes equations. In this paper implicit Runge-Kutta methods are investigated which keep this property when integrating in time. Firstly, a number of energy-conserving Runge-Kutta methods based on Gauss, Radau and Lobatto quadrature are constructed. These methods are suitable for convection-dominated problems (such as turbulent flows), because they do not introduce artificial diffusion and are stable for any time step. Secondly, to obtain robust time-integration methods that work also for stiff problems, the energy-conserving methods are extended to a new class of additive Runge-Kutta methods, which combine energy conservation with L-stability. In this class, the Radau IIA/B method has the best properties. Results for a number of test cases on two-stage methods indicate that for pure convection problems the additive Radau IIA/B method is competitive with the Gauss methods. However, for stiff problems, such as convection-dominated flows with thin boundary layers, both the higher order Gauss and Radau IIA/B method suffer from order reduction. Overall, the Gauss methods are the preferred method for energy-conserving time integration of the incompressible Navier-Stokes equations.
Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations
NASA Astrophysics Data System (ADS)
Hansen, Eskil
2007-08-01
Global error bounds are derived for full Galerkin/Runge-Kutta discretizations of nonlinear parabolic problems, including the evolution governed by the p-Laplacian with p[greater-or-equal, slanted]2. The analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants and an extended B-convergence theory. The global error is bounded in L2 by [Delta]xr/2+[Delta]tq, where r is the convergence order of the Galerkin method applied to the underlying stationary problem and q is the stiff order of the algebraically stable Runge-Kutta method.
A weighted Runge-Kutta discontinuous Galerkin method for wavefield modelling
NASA Astrophysics Data System (ADS)
He, Xijun; Yang, Dinghui; Wu, Hao
2015-03-01
In this paper, we propose a weighted Runge-Kutta (RK) discontinuous Galerkin (WRKDG) method for wavefield modelling. For this method, we first transform the seismic wave equations in 2-D heterogeneous anisotropic media into a first-order hyperbolic system, and then combine the discontinuous Galerkin method (DGM) with a weighted RK time discretization. The time discretization is based on an implicit diagonal RK method and an explicit technique, which changes the implicit RK method into an explicit one. In addition, we introduce a weighting factor in the process. Linear and quadratic polynomials for spatial basis functions are typically employed. We investigate the properties of the method in great detail, including the stability criteria and numerical dispersion relations for solving the 2-D acoustic equations. Our analysis indicates that the stability condition for the WRKDG method is more relaxed compared with the classic total variation diminishing (TVD) RK discontinuous Galerkin (RKDG) method, resulting in a 1.7 times superiority for P1 element and is about as efficient as TVD RKDG method for P2 element in computational efficiency. We also demonstrate that the WRKDG method can suppress numerical dispersion more efficiently than the staggered-grid (SG) method on the same grid. The WRKDG method is applied to simulate the wavefields in a large velocity contrast model, a 2-D homogeneous transversely isotropic (TI) model, a fluid-filled fracture model, and a 2-D SEG/EAGE salt dome model. Regular rectangular and irregular triangular elements are used. The numerical results show that the WRKDG method can effectively suppress numerical dispersion and provide accurate information on the wavefield on a coarse mesh. Therefore, the method evidently reduces the scale of the problem and increases computational efficiency. In addition, promising numerical tests show that the WRKDG method combines well with split perfectly matched layer boundary conditions.
Runge-Kutta Methods for Linear Ordinary Differential Equations
NASA Technical Reports Server (NTRS)
Zingg, David W.; Chisholm, Todd T.
1997-01-01
Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.
Trigonometrical fitting conditions for two derivative Runge Kutta methods
NASA Astrophysics Data System (ADS)
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2016-12-01
Trigonometrically fitted two derivative explicit Runge-Kutta methods are considered in this work. We give order conditions for trigonometrically fitted methods that use several evaluations of the f and the g functions. We present modified methods based on methods with several f evaluations and one g evaluation.
Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Swanson, Roy C., Jr.; Turkel, Eli; Rossow, C.-C.
2007-01-01
The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.
An unconditionally stable Runge-Kutta method for unsteady rotor-stator interaction
NASA Technical Reports Server (NTRS)
Chima, Rodrick V.; Jorgenson, Philip C. E.
1989-01-01
A quasi-three-dimensional analysis has been developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stress-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using an explicit four-stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing is used to increase the stability limit of the time-accurate computations. The scheme is described, and stability and accuracy analyses are given.
Explicit Runge-Kutta schemes for incompressible flow with improved energy-conservation properties
NASA Astrophysics Data System (ADS)
Capuano, F.; Coppola, G.; Rández, L.; de Luca, L.
2017-01-01
The application of pseudo-symplectic Runge-Kutta methods to the incompressible Navier-Stokes equations is discussed in this work. In contrast to fully energy-conserving, implicit methods, these are explicit schemes of order p that preserve kinetic energy to order q, with q > p. Use of explicit methods with improved energy-conservation properties is appealing for convection-dominated problems, especially in case of direct and large-eddy simulation of turbulent flows. A number of pseudo-symplectic methods are constructed for application to the incompressible Navier-Stokes equations and compared in terms of accuracy and efficiency by means of numerical simulations.
On spurious fixed points of Runge-Kutta methods
Vadillo, V.
1997-03-15
In this paper we investigate the onset of spurious fixed points when Runge-Kutta methods are applied to study the dynamics of differential equations. It is shown computationally that the spurious equilibria of Griffiths et al. are connected at infinity with fixed points inherited from the differential equation. We introduce and study the concept of B-regularity which is in connection to the concept of regularity introduced by Iserles. 32 refs., 9 figs.
Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
NASA Astrophysics Data System (ADS)
Mei, Lijie; Wu, Xinyuan
2017-06-01
Symplecticity is also an important property for exponential Runge-Kutta (ERK) methods in the sense of structure preservation once the underlying problem is a Hamiltonian system, though ERK methods provide a good performance of higher accuracy and better efficiency than classical Runge-Kutta (RK) methods in dealing with stiff problems: y‧ (t) = My + f (y). On account of this observation, the main theme of this paper is to derive and analyze the symplectic conditions for ERK methods. Using the fundamental analysis of geometric integrators, we first establish one class of sufficient conditions for symplectic ERK methods. It is shown that these conditions will reduce to the conventional ones when M → 0, and this means that these conditions of symplecticity are extensions of the conventional ones in the literature. Furthermore, we also present a new class of structure-preserving ERK methods possessing the remarkable property of symplecticity. Meanwhile, the revised stiff order conditions are proposed and investigated in detail. Since the symplectic ERK methods are implicit and iterative solutions are required in practice, we also investigate the convergence of the corresponding fixed-point iterative procedure. Finally, the numerical experiments, including a nonlinear Schrödinger equation, a sine-Gordon equation, a nonlinear Klein-Gordon equation, and the well-known Fermi-Pasta-Ulam problem, are implemented in comparison with the corresponding symplectic RK methods and the prominent numerical results definitely coincide with the theories and conclusions made in this paper.
Some Optimal Runge-Kutta Collocation Methods for Stiff Problems and DAEs
NASA Astrophysics Data System (ADS)
Gonzalez-Pinto, S.; Hernández-Abreu, D.; Montijano, J. I.
2008-09-01
A new family of implicit Runge-Kutta methods was introduced at ICCAM 2008 (Gent) by the present authors. This family of methods is intended to solve numerically stiff problems and DAEs. The s-stage method (for s⩾3) has the following features: it is a collocation method depending on a real free parameter β, has classical convergence order 2s-3 and is strongly A-stable for β ranging in some nonempty open interval Is = (-γs,0). In addition, for β∈Is, all the collocation nodes fall in the interval [0,1]. Moreover, these methods also involve a similar computational cost as that of the corresponding counterpart in the Runge-Kutta Radau IIA family (the method having the same classical order) when solving for their stage values. However, our methods have the additional advantage of possessing a higher stage order than the respective Radau IIA counterparts. This circumstance is important when integrating stiff problems in which case most of numerical methods are affected by an order reduction. In this talk we discuss how to optimize the free parameter depending on the special features of the kind of stiff problems and DAEs to be solved. This point is highly important in order to make competitive our methods when compared with those of the Radau IIA family.
Generation and application of the equations of condition for high order Runge-Kutta methods
NASA Technical Reports Server (NTRS)
Haley, D. C.
1972-01-01
This thesis develops the equations of condition necessary for determining the coefficients for Runge-Kutta methods used in the solution of ordinary differential equations. The equations of condition are developed for Runge-Kutta methods of order four through order nine. Once developed, these equations are used in a comparison of the local truncation errors for several sets of Runge-Kutta coefficients for methods of order three up through methods of order eight.
Optimized fourth-order Runge-Kutta method for solving oscillatory problems
NASA Astrophysics Data System (ADS)
Hussain, Kasim; Ismail, Fudziah; Senu, Norazak; Rabiei, Faranak
2016-06-01
In this article, we develop a Runge-Kutta method with invalidation of phase lag, phase lag's derivatives and amplification error to solve second-order initial value problem (IVP) with oscillating solutions. The new method depends on the explicit Runge-Kutta method of algebraic order four. Numerical tests from its implementation to well-known oscillatory problems illustrate the robustness and competence of the new method as compared to the well-known Runge-Kutta methods in the scientific literature.
An explicit Runge-Kutta method for 3D turbulent incompressible flows
NASA Technical Reports Server (NTRS)
Sung, Chao-Ho; Lin, Cheng-Wen; Hung, C. M.
1988-01-01
A computer code has been developed to solve for the steady-state solution of the 3D incompressible Reynolds-averaged Navier-Stokes equations. The approach is based on the cell-center, central-difference, finite-volume formulation and an explicit one-step, multistage Runge-Kutta time-stepping scheme. The Baldwin-Lomax turbulence model is used. Techniques to accelerate the rate of convergence to a steady-state solution include the preconditioned method, the local time stepping, and the implicit residual smoothing. Improvements in computational efficiency have been demonstrated in several areas. This numerical procedure has been used to simulate the turbulent horseshoe vortex flow around an airfoil/flat-plate juncture.
Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3
NASA Astrophysics Data System (ADS)
Skvortsov, L. M.
2012-10-01
Stiffly accurate Runge-Kutta collocation methods with explicit first stage are examined. The parameters of these methods are chosen so as to minimize the errors in the solutions to differential-algebraic equations of indices 2 and 3. This construction results in methods for solving such equations that are superior to the available Runge-Kutta methods.
Exponentially fitted explicit Runge-Kutta-Nystrom methods
NASA Astrophysics Data System (ADS)
Franco, J. M.
2004-05-01
Exponentially fitted Runge-Kutta-Nystrom (EFRKN) methods for the numerical integration of second-order IVPs with oscillatory solutions are derived. These methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(λt),exp(-λt)}, , or equivalently {sin(ωt),cos(ωt)} when λ=iω, . Explicit EFRKN methods with two and three stages and algebraic orders 3 and 4 are constructed. In addition, a 4(3) embedded pair of explicit EFRKN methods based on the FSAL technique is obtained, which permits to introduce an error and step length control with a small cost added. Some numerical experiments show the efficiency of our explicit EFRKN methods when they are compared with other exponential fitting type codes proposed in the scientific literature.
NASA Astrophysics Data System (ADS)
Schippmann, Bianca; Burchard, Hans
Modelling biogeochemical processes in the surface ocean is still a difficult task due to the challenge to identify the most convenient integration scheme for the reaction terms. The scheme is expected to deal with the model characteristics of positivity and conservativity as well as with the different time scales involved, which occur e.g., whenever photochemical reactions take place in the water column. This paper presents a numerical comparison of the Rosenbrock methods, ROS3 and ROS4, often used for solving chemical reactions, to the explicit fourth-order Runge-Kutta method and the unconditionally positive modified Patankar schemes. Following their successful application in air chemistry, we here test the hypothesis that the Rosenbrock methods are an optimal choice for marine biogeochemical modelling in terms of efficiency and accuracy. In this study the schemes are compared in terms of runtime and accuracy and are applied to two test cases of different complexity: a zero-dimensional nutrient-phytoplankton-detritus (NPD)-type model and a one-dimensional nutrient-phytoplankton-zooplankton-detritus (NPZD)-type model. Applying the Rosenbrock methods to the simple NPD model shows their advantage over the other applied methods. They give the most accurate results of all solvers, especially for large step sizes, in less computing time due to their semi-implicitness and adaptive step sizing. On the contrary, for the one-dimensional NPZD model problem this is only the case in comparison to the Runge-Kutta solver, while their performance is worse than that of the second-order modified Patankar scheme. They need longer runtimes than the latter ones in order to achieve similarly accurate results. However, the modified Patankar schemes are not conservative if the system reactions contain more than one source compound. Thus, for more complex marine biogeochemical problems, it is recommended to apply the Rosenbrock methods while for simpler models the use of the second
Symplectic Partitioned Runge-Kutta Methods with Minimum Phase Lag - Case of 5 Stages
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2010-09-30
In this work we consider explicit Symplectic Partitioned Runge-Kutta methods (SPRK) with five stages for problems with separable Hamiltonian. We construct a new method with constant coefficients third algebraic order and eighth phase-lag order.
Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations
NASA Technical Reports Server (NTRS)
Yu, S. T.; Tsai, Y.-L. P.; Hsieh, K. C.
1992-01-01
An investigation of the Runge-Kutta time-stepping, combined with compact difference schemes to solve the unsteady Euler equations, is presented. Initially, a generalized form of a N-step Runge-Kutta technique is derived. By comparing this generalized form with its Taylor's series counterpart, the criteria for the three-step and four-step schemes to be of third- and fourth-order accurate are obtained.
Flux-vector splitting and Runge-Kutta methods for the Euler equations
NASA Technical Reports Server (NTRS)
Turkel, E.; Vanleer, B.
1984-01-01
Runge-Kutta schemes have been used as a method of solving the Euler equations exterior to an airfoil. In the past this has been coupled with central differences and an artificial vesocity in space. In this study the Runge-Kutta time-stepping scheme is coupled with an upwinded space approximation based on flux-vector splitting. Several acceleration techniques are also considered including a local time step, residual smoothing and multigrid.
Runge-Kutta and rational block methods for solving initial value problems
NASA Astrophysics Data System (ADS)
Mungkasi, Sudi; Christian, Agung
2017-01-01
Three methods to solve initial value problems are considered. The methods are the first order Euler’s, second order Heun’s, and rational block methods. The Euler’s and Heun’s methods are of the Runge-Kutta type. Numerical results show that the rational block method is more robust than Runge-Kutta type methods in solving initial value problems.
Discovery and Optimization of Low-Storage Runge-Kutta Methods
2015-06-01
NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE-KUTTA METHODS by Matthew T. Fletcher June 2015... DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE-KUTTA METH- ODS 5. FUNDING NUMBERS 6. AUTHOR(S) Matthew T. Fletcher 7. PERFORMING ORGANIZATION NAME(S...239–18 i THIS PAGE INTENTIONALLY LEFT BLANK ii Approved for public release; distribution is unlimited DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Hu, F.Q.; Manthey, J.L.; Hussaini, M.Y.
1996-03-01
In this paper, we investigate accurate and efficient time advancing methods for computational acoustics, where nondissipative and nondispersive properties are of critical importance. Our analysis pertains to the application of Runge-Kutta methods to high-order finite difference discretization. In many CFD applications, multistage Runge-Kutta schemes have often been favored for their low storage requirements and relatively large stability limits. For computing acoustic waves, however, the stability consideration alone is not sufficient, since the Runge-Kutta schemes entail both dissipation and dispersion errors. The time step is now limited by the tolerable dissipation and dispersion errors in the computation. In the present paper, it is shown that if the traditional Runge-Kutta schemes are used for time advancing in acoustic problems, time steps greatly smaller than those allowed by the stability limit are necessary. Low-dissipation and low-dispersion Runge-Kutta (LDDRK) schemes are proposed, based on an optimization that minimizes the dissipation and dispersion errors for wave propagation. Optimizations fo both single-step and two-step alternating schemes are considered. The proposed LDDRK schemes are remarkably more efficient than the classical Runge-Kutta schemes for acoustic computations. Moreover, low storage implementations of the optimized schemes are discussed. Special issues of implementing numerical boundary conditions in the LDDRK schemes are also addressed. 16 refs., 11 figs., 4 tabs.
A generalization of the Runge-Kutta iteration
NASA Astrophysics Data System (ADS)
Haelterman, R.; Vierendeels, J.; van Heule, D.
2009-02-01
Iterative solvers in combination with multi-grid have been used extensively to solve large algebraic systems. One of the best known is the Runge-Kutta iteration. We show that a generally used formulation [A. Jameson, Numerical solution of the Euler equations for compressible inviscid fluids, in: F. Angrand, A. Dervieux, J.A. Désidéri, R. Glowinski (Eds.), Numerical Methods for the Euler Equations of Fluid Dynamics, SIAM, Philadelphia, 1985, pp. 199-245] does not allow to form all possible polynomial transmittance functions and we propose a new formulation to remedy this, without using an excessive number of coefficients. After having converted the optimal parameters found in previous studies (e.g. [B. Van Leer, C.H. Tai, K.G. Powell, Design of optimally smoothing multi-stage schemes for the Euler equations, AIAA Paper 89-1923, 1989]) we compare them with those that we obtain when we optimize for an integrated 2-grid V-cycle and show that this results in superior performance using a low number of stages. We also propose a variant of our new formulation that roughly follows the idea of the Martinelli-Jameson scheme [A. Jameson, Analysis and design of numerical schemes for gas dynamics 1, artificial diffusion, upwind biasing, limiter and their effect on multigrid convergence, Int. J. Comput. Fluid Dyn. 4 (1995) 171-218; J.V. Lassaline, Optimal multistage relaxation coefficients for multigrid flow solvers. http://www.ryerson.ca/~jvl/papers/cfd2005.pdf] used on the advection-diffusion equation which that can be extended to other types. Gains in the order of 30%-50% have been shown with respect to classical iterative schemes on the advection equation. Better results were also obtained on the advection-diffusion equation than with the Martinelli-Jameson coefficients, but with less than half the number of matrix-vector multiplications.
Gwinner, J; Thalhammer, M
The convergence of full discretisations by implicit Runge-Kutta and nonconforming Galerkin methods applied to nonlinear evolutionary inequalities is studied. The scope of applications includes differential inclusions governed by a nonlinear operator that is monotone and fulfills a certain growth condition. A basic assumption on the considered class of stiffly accurate Runge-Kutta time discretisations is a stability criterion which is in particular satisfied by the Radau IIA and Lobatto IIIC methods. In order to allow nonconforming hp-finite element approximations of unilateral constraints, set convergence of convex subsets in the sense of Glowinski-Mosco-Stummel is utilised. An appropriate formulation of the fully discrete variational inequality is deduced on the basis of a characteristic example of use, a Signorini-type initial-boundary value problem. Under hypotheses close to the existence theory of nonlinear first-order evolutionary equations and inequalities involving a monotone main part, a convergence result for the piecewise constant in time interpolant is established.
NASA Astrophysics Data System (ADS)
Toulorge, T.; Desmet, W.
2012-02-01
We study the performance of methods of lines combining discontinuous Galerkin spatial discretizations and explicit Runge-Kutta time integrators, with the aim of deriving optimal Runge-Kutta schemes for wave propagation applications. We review relevant Runge-Kutta methods from literature, and consider schemes of order q from 3 to 4, and number of stages up to q + 4, for optimization. From a user point of view, the problem of the computational efficiency involves the choice of the best combination of mesh and numerical method; two scenarios are defined. In the first one, the element size is totally free, and a 8-stage, fourth-order Runge-Kutta scheme is found to minimize a cost measure depending on both accuracy and stability. In the second one, the elements are assumed to be constrained to such a small size by geometrical features of the computational domain, that accuracy is disregarded. We then derive one 7-stage, third-order scheme and one 8-stage, fourth-order scheme that maximize the stability limit. The performance of the three new schemes is thoroughly analyzed, and the benefits are illustrated with two examples. For each of these Runge-Kutta methods, we provide the coefficients for a 2 N-storage implementation, along with the information needed by the user to employ them optimally.
NASA Astrophysics Data System (ADS)
van de Vyver, Hans
2006-04-01
This paper provides an investigation of the stability properties of a family of exponentially fitted Runge-Kutta-Nystrom (EFRKN) methods. P-stability is a very important property usually demanded for the numerical solution of stiff oscillatory second-order initial value problems. P-stable EFRKN methods with arbitrary high order are presented in this work. We have proved our results based on a symmetry argument.
Constrained Galerkin variational integrators and modified constrained symplectic Runge-Kutta methods
NASA Astrophysics Data System (ADS)
Wenger, Theresa; Ober-Blöbaum, Sina; Leyendecker, Sigrid
2017-07-01
The presented constrained Galerkin variational integrators base on the higher order variational integrators in [1], now applied to holonomically constrained systems and are an extension of the constrained Galerkin methods in [2]. Sufficient conditions are given to obtain a stiffly accurate integration scheme, its structure preserving properties are analysed and the convergence order as well as the computational efficiency are investigated numerically. The equivalence to constrained symplectic Runge-Kutta methods is shown, with focus on a modified constrained symplectic Runge-Kutta method, that was first introduced in [3], there for the unconstrained case.
The numerical solution of differential algebraic systems using Runge-Kutta methods of special type
Coyle, J.J.
1989-01-01
In this dissertation the author is concerned with the solution of differential-algebraic equations using Runge Dutta methods whose coefficient matrices are singular. Not all such Runge Kutta methods are well defined when applied to differential-algebraic equations; however, Runge Kutta methods of special type are shown here to be well defined when applied to either constant coefficient or uniform index 1 differential-algebraic equations. He also derives conditions on the coefficients of such a method sufficient for any desired order.
A diagonally inverted LU implicit multigrid scheme
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.; Caughey, David A.; Chima, Rodrick V.
1988-01-01
A new Diagonally Inverted LU Implicit scheme is developed within the framework of the multigrid method for the 3-D unsteady Euler equations. The matrix systems that are to be inverted in the LU scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the Diagonalized ADI method, the time accuracy of the LU scheme is not reduced since the diagonalization procedure does not destroy time conservation. Even more importantly, this diagonalization significantly reduces the computational effort required to solve the LU approximation and therefore transforms it into a more efficient method of numerically solving the 3-D Euler equations.
A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator
Billet, G.; Ryan, J.
2011-02-20
A Runge-Kutta discontinuous Galerkin method to solve the hyperbolic part of reactive Navier-Stokes equations written in conservation form is presented. Complex thermodynamics laws are taken into account. Particular care has been taken to solve the stiff gaseous interfaces correctly with no restrictive hypothesis. 1D and 2D test cases are presented.
NASA Technical Reports Server (NTRS)
Cockrell, C. R.
1989-01-01
Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.
A fourth order modified trigonometrically fitted symplectic Runge-Kutta-Nyström method
NASA Astrophysics Data System (ADS)
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.
2013-10-01
In this work we construct a modified trigonometrically fitted symplectic Runge Kutta Nyström method based on the forth order five stages method of Calvo and Sanz-Serna. We apply the new method on the numerical integration of the two-body problem.
A Family of Trigonometrically-fitted Partitioned Runge-Kutta Symplectic Methods
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2007-12-26
We are presenting a family of trigonometrically fitted partitioned Runge-Kutta symplectic methods of fourth order with six stages. The solution of the one dimensional time independent Schroedinger equation is considered by trigonometrically fitted symplectic integrators. The Schroedinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential.
High phase-lag order Runge Kutta pairs of orders 8(7)
NASA Astrophysics Data System (ADS)
Tsitouras, Ch.; Famelis, Ioannis Th.
2017-07-01
In this work we present a representative of a new wider family of high phase-lag order 16 Runge-Kutta pairs of orders 8(7) with smaller principal local truncation term than the methods suggested in the literature. Numerical experiments justify the characteristics of the new method.
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Suresh, A.; Huynh, H.T.
1997-09-01
This report presents a new class of high-order monotonically-preserving schemes for numerical solution of conservation laws using the Runge-Kutta time stepping method. The interface values in this method is obtained by limiting higher-order polynomials.
Modified Runge-Kutta methods for solving ODES. M.S. Thesis
NASA Technical Reports Server (NTRS)
Vanvu, T.
1981-01-01
A class of Runge-Kutta formulas is examined which permit the calculation of an accurate solution anywhere in the interval of integration. This is used in a code which seldom has to reject a step; rather it takes a reduced step if the estimated error is too large. The absolute stability implications of this are examined.
Construction and Analysis of Multi-Rate Partitioned Runge-Kutta Methods
2012-06-01
ANALYSIS OF MULTI-RATE PARTITIONED RUNGE-KUTTA METHODS by Patrick R. Mugg June 2012 Thesis Advisor: Francis Giraldo Second Reader: Hong...POSTGRADUATE SCHOOL June 2012 Author: Patrick R. Mugg Approved by: Professor Francis Giraldo Thesis Advisor Associate...vs. Exact Solution for RK2 using 2nd Order CFD with x∆ = 0.02
Using 4th order Runge-Kutta method for solving a twisted Skyrme string equation
NASA Astrophysics Data System (ADS)
Hadi, Miftachul; Anderson, Malcolm; Husein, Andri
2016-03-01
We study numerical solution, especially using 4th order Runge-Kutta method, for solving a twisted Skyrme string equation. We find numerically that the value of minimum energy per unit length of vortex solution for a twisted Skyrmion string is 20.37 × 1060 eV/m.
A Runge-Kutta discontinuous finite element method for high speed flows
NASA Technical Reports Server (NTRS)
Bey, Kim S.; Oden, J. T.
1991-01-01
A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.
Efficient low-storage Runge-Kutta schemes with optimized stability regions
NASA Astrophysics Data System (ADS)
Niegemann, Jens; Diehl, Richard; Busch, Kurt
2012-01-01
A variety of numerical calculations, especially when considering wave propagation, are based on the method-of-lines, where time-dependent partial differential equations (PDEs) are first discretized in space. For the remaining time-integration, low-storage Runge-Kutta schemes are particularly popular due to their efficiency and their reduced memory requirements. In this work, we present a numerical approach to generate new low-storage Runge-Kutta (LSRK) schemes with optimized stability regions for advection-dominated problems. Adapted to the spectral shape of a given physical problem, those methods are found to yield significant performance improvements over previously known LSRK schemes. As a concrete example, we present time-domain calculations of Maxwell's equations in fully three-dimensional systems, discretized by a discontinuous Galerkin approach.
Runge-Kutta neural network for identification of dynamical systems in high accuracy.
Wang, Y J; Lin, C T
1998-01-01
This paper proposes Runge-Kutta neural networks (RKNNs) for identification of unknown dynamical systems described by ordinary differential equations (i.e., ordinary differential equation or ODE systems) with high accuracy. These networks are constructed according to the Runge-Kutta approximation method. The main attraction of the RKNNs is that they precisely estimate the changing rates of system states (i.e., the right-hand side of the ODE x =f(x)) directly in their subnetworks based on the space-domain interpolation within one sampling interval such that they can do long-term prediction of system state trajectories. We show theoretically the superior generalization and long-term prediction capability of the RKNNs over the normal neural networks. Two types of learning algorithms are investigated for the RKNNs, gradient-and nonlinear recursive least-squares-based algorithms. Convergence analysis of the learning algorithms is done theoretically. Computer simulations demonstrate the proved properties of the RKNNs.
A fourth-order Runge-Kutta method based on BDF-type Chebyshev approximations
NASA Astrophysics Data System (ADS)
Ramos, Higinio; Vigo-Aguiar, Jesus
2007-07-01
In this paper we consider a new fourth-order method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the method may be formulated in an equivalent way as a Runge-Kutta method having stage order four. The method thus obtained have good properties relatives to stability including an unbounded stability domain and large [alpha]-value concerning A([alpha])-stability. A strategy for changing the step size, based on a pair of methods in a similar way to the embedding pair in the Runge-Kutta schemes, is presented. The numerical examples reveals that this method is very promising when it is used for solving stiff initial-value problems.
Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients
NASA Technical Reports Server (NTRS)
Keeling, Stephen L.
1987-01-01
A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.
A fourth order modified trigonometrically fitted symplectic Runge-Kutta-Nyström method
NASA Astrophysics Data System (ADS)
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.
2014-12-01
In this work we construct a modified trigonometrically fitted symplectic Runge Kutta Nyström method based on the fourth order five stages method of Calvo and Sanz-Serna (1994). We apply the new method on the numerical integration of the two-dimensional harmonic oscillator, the two-body problem, a perturbed two-body problem and two two-dimensional nonlinear oscillatory Hamiltonian systems.
Fourth-order 2N-storage Runge-Kutta schemes
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Kennedy, Christopher A.
1994-01-01
A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations. A particular scheme is identified that has desirable efficiency characteristics for hyperbolic and parabolic initial (boundary) value problems. This scheme is competitive with the classical fourth-order method (high-storage) and is considerably more efficient and accurate than existing third-order low-storage schemes.
Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations
2015-06-01
Neumann analysis of the schemes into account. This work highlights that, for unsteady problems, both dissipation and dispersion errors must be accounted...problems, both dissipation and dispersion errors must be accounted for when selecting optimal Runge-Kutta time integrators. I. Introduction The use of...results to a broader class of high-order temporal and spatial schemes. Specifically, von Neumann analysis is performed to categorize the dissipation and
H[alpha]-stability of modified Runge-Kutta methods for nonlinear neutral pantograph equations
NASA Astrophysics Data System (ADS)
Ma, S. F.; Yang, Z. W.; Liu, M. Z.
2007-11-01
In this paper, we investigate H[alpha]-stability of algebraically stable Runge-Kutta methods with a variable stepsize for nonlinear neutral pantograph equations. As a result, the Radau IA, Radau IIA, Lobatto IIIC method, the odd-stage Gauss-Legendre methods and the one-leg [theta]-method with are H[alpha]-stable for nonlinear neutral pantograph equations. Some experiments are given.
NASA Astrophysics Data System (ADS)
Gleim, Tobias; Schröder, Bettina; Kuhl, Detlef
2017-07-01
This paper deals with the numerical simulation of multi-field problems in the context of functionally graded materials. The corresponding manufacturing sequences are mostly characterized by strong interacting fields with different physical behaviors, which additionally have high dynamic responses. In order to solve these distinct processes with a high accuracy in the time, various RUNGE-KUTTA methods are investigated. Furthermore, a h-error estimator and an embedded error estimator are considered for a qualitative evaluation of the results.
Active and passive symmetrization of Runge-Kutta Lobatto IIIA methods
NASA Astrophysics Data System (ADS)
Gorgey, A.; Chan, R. P. K.
2012-09-01
Symmetrization of the Runge-Kutta Gauss methods have been shown to be robust in solving stiff linear and nonlinear initial value ordinary differential equations [4]. The most efficient way of applying symmmetrization was found to be passive symmetrization with passive extrapolation. In this paper we investigate symmetrization of the Lobatto IIIA methods. We show numerically that the same strategy of using passive symmetrization applied with passive extrapolation of the Lobbatto IIIA methods is also most efficient in solving the nonlinear problems tested.
High-order implicit time-marching methods for unsteady fluid flow simulation
NASA Astrophysics Data System (ADS)
Boom, Pieter David
Unsteady computational fluid dynamics (CFD) is increasingly becoming a critical tool in the development of emerging technologies and modern aircraft. In spite of rapid mathematical and technological advancement, these simulations remain computationally intensive and time consuming. More efficient temporal integration will promote a wider use of unsteady analysis and extend its range of applicability. This thesis presents an investigation of efficient high-order implicit time-marching methods for application in unsteady compressible CFD. A generalisation of time-marching methods based on summation-by-parts (SBP) operators is described which reduces the number of stages required to obtain a prescribed order of accuracy, thus improving their efficiency. The classical accuracy and stability theory is formally extended for these generalised SBP (GSBP) methods, including superconvergence and nonlinear stability. Dual-consistent SBP and GSBP time-marching methods are shown to form a subclass of implicit Runge-Kutta methods, which enables extensions of nonlinear accuracy and stability results. A novel family of fully-implicit GSBP Runge-Kutta schemes based on Gauss quadrature are derived which are both algebraically stable and L-stable with order 2s - 1, where s is the number of stages. In addition, a numerical tool is developed for the construction and optimisation of general linear time-marching methods. The tool is applied to the development of several low-stage-order L-stable diagonally-implicit methods, including a diagonally-implicit GSBP Runge-Kutta scheme. The most notable and efficient method developed is a six-stage fifth-order L-stable stiffly-accurate explicit-first-stage singly-diagonally-implicit Runge-Kutta (ESDIRK5) method with stage order two. The theoretical results developed in this thesis are supported by numerical simulations, and the predicted relative efficiency of the schemes is realised.
Z, Wang; Q, Wang; DJ, Klinke
2017-01-01
Biological processes such as contagious disease spread patterns and tumor growth dynamics are modelled using a set of coupled differential equations. Experimental data is usually used to calibrate models so they can be used to make future predictions. In this study, numerical methods were implemented to approximate solutions to mathematical models that were not solvable analytically, such as a SARS model. More complex models such as a tumor growth model involve high-dimensional parameter spaces; efficient numerical simulation techniques were used to search for optimal or close-to-optimal parameter values in the equations. Runge-Kutta methods are a group of explicit and implicit numerical methods that effectively solve the ordinary differential equations in these models. Effects of the order and the step size of Runge-Kutta methods were studied in order to maximize the search accuracy and efficiency in parameter spaces of the models. Numerical simulation results showed that an order of four gave the best balance between truncation errors and the simulation speed for SIR, SARS, and tumormodels studied in the project. The optimal step size for differential equation solvers was found to be model-dependent. PMID:28220053
Z, Wang; Q, Wang; Dj, Klinke
2016-09-01
Biological processes such as contagious disease spread patterns and tumor growth dynamics are modelled using a set of coupled differential equations. Experimental data is usually used to calibrate models so they can be used to make future predictions. In this study, numerical methods were implemented to approximate solutions to mathematical models that were not solvable analytically, such as a SARS model. More complex models such as a tumor growth model involve high-dimensional parameter spaces; efficient numerical simulation techniques were used to search for optimal or close-to-optimal parameter values in the equations. Runge-Kutta methods are a group of explicit and implicit numerical methods that effectively solve the ordinary differential equations in these models. Effects of the order and the step size of Runge-Kutta methods were studied in order to maximize the search accuracy and efficiency in parameter spaces of the models. Numerical simulation results showed that an order of four gave the best balance between truncation errors and the simulation speed for SIR, SARS, and tumormodels studied in the project. The optimal step size for differential equation solvers was found to be model-dependent.
Equations of condition for high order Runge-Kutta-Nystrom formulae
NASA Technical Reports Server (NTRS)
Bettis, D. G.
1974-01-01
Derivation of the equations of condition of order eight for a general system of second-order differential equations approximated by the basic Runge-Kutta-Nystrom algorithm. For this general case, the number of equations of condition is considerably larger than for the special case where the first derivative is not present. Specifically, it is shown that, for orders two through eight, the number of equations for each order is 1, 1, 1, 2, 3, 5, and 9 for the special case and is 1, 1, 2, 5, 13, 34, and 95 for the general case.
NASA Technical Reports Server (NTRS)
Jameson, A.; Schmidt, Wolfgang; Turkel, Eli
1981-01-01
A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.
a New Methodology for the Construction of Optimized RUNGE-KUTTA-NYSTRÖM Methods
NASA Astrophysics Data System (ADS)
Papadopoulos, D. F.; Simos, T. E.
In this paper, a new Runge-Kutta-Nyström method of fourth algebraic order is developed. The new method has zero phase-lag, zero amplification error and zero first integrals of the previous properties. Numerical results indicate that the new method is very efficient for solving numerically the Schrödinger equation. We note that for the first time in the literature we use the requirement of vanishing the first integrals of phase-lag and amplification error in the construction of efficient methods for the numerical solution of the Schrödinger equation.
Application of a Runge-Kutta scheme for high-speed inviscid internal flows
NASA Technical Reports Server (NTRS)
Moitra, A.; Turkel, E.; Kumar, A.
1986-01-01
A multi-stage Runge-Kutta method is analyzed for solving the two-dimensional Euler equations for external and internal flow problems. Subsonic, supersonic and, highly supersonic flows are studied. Various techniques for accelerating the convergence to a steady state are described and analyzed. Effects of the grid aspect ratio on the rate of convergence are evaluated. An enthalpy damping technique applicable to supersonic flows is described in detail. Numerical results for supersonic flows containing both oblique and normal shocks are presented confirming the efficiency of the method.
NASA Astrophysics Data System (ADS)
Wang, Dongling; Xiao, Aiguo; Li, Xueyang
2013-02-01
Based on W-transformation, some parametric symplectic partitioned Runge-Kutta (PRK) methods depending on a real parameter α are developed. For α=0, the corresponding methods become the usual PRK methods, including Radau IA-IA¯ and Lobatto IIIA-IIIB methods as examples. For any α≠0, the corresponding methods are symplectic and there exists a value α∗ such that energy is preserved in the numerical solution at each step. The existence of the parameter and the order of the numerical methods are discussed. Some numerical examples are presented to illustrate these results.
Runge-Kutta and Lax-Wendroff discontinuous Galerkin methods for linear conservation laws
NASA Astrophysics Data System (ADS)
Shu, Chi-Wang
2017-07-01
In this talk we give a short summary of our recent work [5], jointly with Z. Sun, on establishing the equivalency of the Runge-Kutta discontinuous Galerkin (RKDG) methods and a class of Lax-Wendroff discontinuous Galerkin (LWDG) methods for solving linear conservation laws, as well as on stability analysis and error estimates for the LWDG methods for solving one- and two-dimensional linear conservation laws, regardless of whether they are equivalent to the RKDG methods or not. Our stability analysis includes multidimensional problems with divergence-free coefficients, and our error estimates include those for both the solution u and its first order time derivative ut.
NASA Technical Reports Server (NTRS)
Fehlberg, E.
1972-01-01
The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the truncation error in x. The formulas require fewer evaluations per stop than other Runge-Kutta-Nystrom formulas if the latter are operated by using the standard procedure for stepsize control. An example is presented. With results being of the same accuracy, Runge-Kutta-Nystrom formulas discussed save 50 percent or more computer time compared with other Runge-Kutta-Nystrom formulas.
NASA Astrophysics Data System (ADS)
Huang, Yong; Shi, Guo-Dong; Zhu, Ke-Yong
2016-06-01
This paper adopts the Runge-Kutta ray tracing method to obtain the ray-trajectory numerical solution in a two-dimensional gradient index medium. The emitting, absorbing and scattering processes are simulated by the Monte Carlo method. The temperature field and ray trajectory in the medium are obtained by the three methods, the Runge-Kutta ray tracing method, the ray tracing method with the cell model and the discrete curved ray tracing method with the linear refractive index cell model. Comparing the results of the three methods, it is found that the results by the Monte Carlo Runge-Kutta ray tracing method are of the highest accuracy. To improve the computational speed, the variable step-size Runge-Kutta ray tracing method is proposed, and the maximum relative error between the temperature field in the nonscattering medium by this method and the benchmark solution is less than 0.5%. The results also suggest that the Runge-Kutta ray tracing method would make the radiative transfer solution in the three-dimensional graded index media much easier.
Runge-Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Zhao, Jian; Tang, Huazhong
2017-08-01
This paper develops PK-based non-central and central Runge-Kutta discontinuous Galerkin (DG) methods with WENO limiter for the one- and two-dimensional special relativistic magnetohydrodynamical (RMHD) equations, K = 1 , 2 , 3. The non-central DG methods are locally divergence-free, while the central DG are ;exactly; divergence-free but have to find two approximate solutions defined on mutually dual meshes. The adaptive WENO limiter first identifies the ;troubled; cells by using a modified TVB minmod function, and then uses the WENO technique and the cell average values of the DG solutions in the neighboring cells as well as the original cell averages of the ;troubled; cells to locally reconstruct a new polynomial of degree (2 K + 1) inside the ;troubled; cells instead of the DG solution. The WENO limiting procedure does not destroy the locally or ;exactly; divergence-free property of magnetic field and is only employed for finite ;troubled; cells so that the computational cost can be as little as possible. Several test problems in one and two dimensions are solved by using our non-central and central Runge-Kutta DG methods with WENO limiter. The numerical results demonstrate that our methods are stable, accurate, and robust in resolving complex wave structures.
Modelling phase transition kinetics of chenodeoxycholic acid with the Runge-Kutta method.
Petkune, Sanita; Actins, Andris
2010-09-21
The phase transition kinetics of two chenodeoxycholic acid polymorphic modifications-form I (stable at high temperature), form III (stable at low temperature) and the amorphous phase has been examined under various conditions of temperature and relative humidity. Form III conversion to form I was examined at high temperature conditions and was found to be non-spontaneous, requiring seed crystals for initiation. The formation kinetic model of form I was created incorporating the three-dimensional seed crystal growth, the phase transition rate proportion to the surface area of form I crystals, and the influence of the amorphous phase surface area changes with an empirical stage pointer q that contained the incomplete transition of the amorphous phase to form I with a residue omega(A)(infinity). The extent of transition and the phase transition rate constant depended on form I seed crystal amount in the raw mixture, and on the sample preparation. To describe phase transition kinetic curves, we employed the Runge-Kutta differential equation numeric solving method. By combining the Runge-Kutta method with the multi-point optimization method, the average quadratic deviation of the experimental results from one calculated series was under 2%. Copyright 2010 Elsevier B.V. All rights reserved.
Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.
1991-09-01
A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs.
NASA Technical Reports Server (NTRS)
Lear, W. M.
1974-01-01
The integration is discussed of the vector differential equation X = F(x, t) from time t sub i to t sub (i = 1) where only the values of x sub i are available for the the integration. No previous values of x or x prime are used. Using an orbit integration problem, comparisons are made between Taylor series integrators and various types and orders of Runge-Kutta integrators. A fourth order Runge-Kutta type integrator for orbital work is presented, and approximate (there may be no exact) fifth order Runge-Kutta integrators are discussed. Also discussed and compared is a self starting integrator ising delta f/delta x. A numerical method for controlling the accuracy of integration is given, and the special equations for accurately integrating accelerometer data are shown.
Tremblay, Jean Christophe; Carrington, Tucker Jr.
2004-12-15
If the Hamiltonian is time dependent it is common to solve the time-dependent Schroedinger equation by dividing the propagation interval into slices and using an (e.g., split operator, Chebyshev, Lanczos) approximate matrix exponential within each slice. We show that a preconditioned adaptive step size Runge-Kutta method can be much more efficient. For a chirped laser pulse designed to favor the dissociation of HF the preconditioned adaptive step size Runge-Kutta method is about an order of magnitude more efficient than the time sliced method.
Tremblay, Jean Christophe; Carrington, Tucker
2004-12-15
If the Hamiltonian is time dependent it is common to solve the time-dependent Schrödinger equation by dividing the propagation interval into slices and using an (e.g., split operator, Chebyshev, Lanczos) approximate matrix exponential within each slice. We show that a preconditioned adaptive step size Runge-Kutta method can be much more efficient. For a chirped laser pulse designed to favor the dissociation of HF the preconditioned adaptive step size Runge-Kutta method is about an order of magnitude more efficient than the time sliced method. (c) 2004 American Institute of Physics
NASA Technical Reports Server (NTRS)
Cannizzaro, Frank E.; Ash, Robert L.
1992-01-01
A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.
Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes
NASA Astrophysics Data System (ADS)
Calvo, M.; González-Pinto, S.; Montijano, J. I.
2008-09-01
Modern codes for the numerical solution of Initial Value Problems (IVPs) in ODEs are based in adaptive methods that, for a user supplied tolerance [delta], attempt to advance the integration selecting the size of each step so that some measure of the local error is [similar, equals][delta]. Although this policy does not ensure that the global errors are under the prescribed tolerance, after the early studies of Stetter [Considerations concerning a theory for ODE-solvers, in: R. Burlisch, R.D. Grigorieff, J. Schröder (Eds.), Numerical Treatment of Differential Equations, Proceedings of Oberwolfach, 1976, Lecture Notes in Mathematics, vol. 631, Springer, Berlin, 1978, pp. 188-200; Tolerance proportionality in ODE codes, in: R. März (Ed.), Proceedings of the Second Conference on Numerical Treatment of Ordinary Differential Equations, Humbold University, Berlin, 1980, pp. 109-123] and the extensions of Higham [Global error versus tolerance for explicit Runge-Kutta methods, IMA J. Numer. Anal. 11 (1991) 457-480; The tolerance proportionality of adaptive ODE solvers, J. Comput. Appl. Math. 45 (1993) 227-236; The reliability of standard local error control algorithms for initial value ordinary differential equations, in: Proceedings: The Quality of Numerical Software: Assessment and Enhancement, IFIP Series, Springer, Berlin, 1997], it has been proved that in many existing explicit Runge-Kutta codes the global errors behave asymptotically as some rational power of [delta]. This step-size policy, for a given IVP, determines at each grid point tn a new step-size hn+1=h(tn;[delta]) so that h(t;[delta]) is a continuous function of t. In this paper a study of the tolerance proportionality property under a discontinuous step-size policy that does not allow to change the size of the step if the step-size ratio between two consecutive steps is close to unity is carried out. This theory is applied to obtain global error estimations in a few problems that have been solved with
Xiao Xiaotao; Wang Shaojie
2008-12-15
Hamiltonian correction method is proposed to improve the variable time-step fourth-order Runge-Kutta methods in computing guiding-center orbits in a tokamak. It is found that the new method can significantly improve the computation efficiency of the conventional Runge-Kutta method in simulation of the long-time behavior of the guiding-center orbits.
A Generalized 4th-Order Runge-Kutta Method for the Gross-Pitaevskii Equation
NASA Astrophysics Data System (ADS)
Kandes, Martin
2015-04-01
We present the implementation of a method-of-lines approach for numerically approximating solutions of the time-dependent Gross-Pitaevksii equation in non-uniformly rotating reference frames. Implemented in parallel using a hybrid MPI + OpenMP framework, which will allow for scalable, high-resolution numerical simulations, we utilize an explicit, generalized 4th-order Runge-Kutta time-integration scheme with 2nd- and 4th-order central differences to approximate the spatial derivatives in the equation. The principal objective of this project is to model the effect(s) of inertial forces on quantized vortices within weakly-interacting dilute atomic gas Bose-Einstein condensates in the mean-field limit of the Gross-Pitaevskii equation. Here, we discuss our work-to-date and preliminary results.
Runge-Kutta model-based nonlinear observer for synchronization and control of chaotic systems.
Beyhan, Selami
2013-07-01
This paper proposes a novel nonlinear gradient-based observer for synchronization and observer-based control of chaotic systems. The model is based on a Runge-Kutta model of the chaotic system where the evolution of the states or parameters is derived based on the error-square minimization. The stability and convergence conditions of observer and control methods are analyzed using a Lyapunov stability approach. In numerical simulations, the proposed observer and well-known sliding-mode observer are compared for the synchronization of a Lü chaotic system and observer-based stabilization of a Chen chaotic system. The noisy case for synchronization and parameter uncertainty case for stabilization are also considered for both observer-based methods. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
Hong Jialin . E-mail: lichun@lsec.cc.ac.cn
2006-01-20
In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law.
An explicit Runge-Kutta method for unsteady rotor/stator interaction
NASA Technical Reports Server (NTRS)
Jorgenson, Philip C. E.; Chima, Rodrick V.
1988-01-01
A quasi-three-dimensional rotor/stator analysis has been developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using a four-stage Runge-Kutta scheme with a constant timestep. Results are shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Euler and Navier-Stokes results are compared on the scaled single- and multi-passage machine. The method is relatively fast and the quasi-three-dimensional formulation is applicable to a wide range of turbomachinery geometries.
An explicit Runge-Kutta method for turbulent reacting flow calculations
NASA Technical Reports Server (NTRS)
Boretti, A. A.
1989-01-01
The paper presents a numerical method for the solution of the conservation equations governing steady, reacting, turbulent viscous flow in two-dimensional geometries, in both Cartesian and axisymmetric coordinates. These equations are written in Favre-averaged form and closed with a first order model. A two-equation K-epsilon model, where low Reynolds number and compressibility effects are included, and a modified eddy-break up model are used to simulate fluid mechanics turbulence, chemistry and turbulence-combustion interaction. The solution is obtained by using a pseudo-unsteady method with improved perturbation propagation properties. The equations are discretized in space by using a finite volume formulation. An explicit multi-stage dissipative Runge-Kutta algorithm is then used to advance the flow equations in the pseudo-time. The method is applied to the computation of both diffusion and premixed turbulent reacting flows. The computed temperature distributions compare favorably with experimental data.
An explicit Runge-Kutta method for unsteady rotor/stator interaction
NASA Technical Reports Server (NTRS)
Jorgenson, Philip C. E.; Chima, Rodrick V.
1988-01-01
A quasi-three-dimensional rotor/stator analysis has been developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using a four-stage Runge-Kutta scheme with a constant timestep. Results are shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Euler and Navier-Stokes results are compared on the scaled single- and multi-passage machine. The method is relatively fast and the quasi-three-dimensional formulation is applicable to a wide range of turbomachinery geometries.
NASA Technical Reports Server (NTRS)
Subramanian, S. V.; Bozzola, R.
1987-01-01
Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in solution procedures.
NASA Technical Reports Server (NTRS)
Subramanian, S. V.; Bozzola, R.
1985-01-01
Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The present study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions, and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in the solution procedure.
On spurious steady-state solutions of explicit Runge-Kutta schemes
NASA Technical Reports Server (NTRS)
Sweby, P. K.; Yee, H. C.; Griffiths, D. F.
1990-01-01
The bifurcation diagram associated with the logistic equation v sup n+1 = av sup n (1-v sup n) is by now well known, as is its equivalence to solving the ordinary differential equation u prime = alpha u (1-u) by the explicit Euler difference scheme. It has also been noted by Iserles that other popular difference schemes may not only exhibit period doubling and chaotic phenomena but also possess spurious fixed points. Runge-Kutta schemes applied to both the equation u prime = alpha u (1-u) and the cubic equation u prime = alpha u (1-u)(b-u) were studied computationally and analytically and their behavior was contrasted with the explicit Euler scheme. Their spurious fixed points and periodic orbits were noted. In particular, it was observed that these may appear below the linearized stability limits of the scheme and, consequently, computation may lead to erroneous results.
A computer program for determining truncation error coefficients for Runge-Kutta methods
NASA Technical Reports Server (NTRS)
Horn, M. K.
1980-01-01
The basic structure of a program to generate the truncation error coefficients for Runge-Kutta (RK) methods is reformulated to reduce storage requirements significantly and to accommodate variable dimensioning. This FORTRAN program, SUBROUTINE RKEQ, determines truncation error coefficients for RK algorithms for orders 1 through 10 and extends the order of coefficients through 12 with the 11th- and 12th-order terms determined following the patterns used to establish the lower order coefficients. Both subroutines (the original and RKEQ) are also written to treat RK m-fold methods which utilize m known derivatives of f to increase the order of the algorithm. Setting m = 0 gives the classical RK algorithm.
Explicit Runge-Kutta methods for the integration of rate-type constitutive equations
NASA Astrophysics Data System (ADS)
Hiley, R. A.; Rouainia, M.
2008-04-01
Modern constitutive models have the potential to improve the quality of engineering calculations involving non-linear anisotropic materials. The adoption of complex models in practice, however, depends on the availability of reliable and accurate solution methods for the stress point integration problem. This paper presents a modular implementation of explicit Runge-Kutta methods with error control, that is suitable for use, without change, with any rate-type constitutive model. The paper also shows how the complications caused by the algebraic constraint of conventional plasticity are resolved through a simple subloading modification. With this modification any rate-independent model can be implemented without difficulty, using the integration module as an accurate and robust standard procedure. The effectiveness and efficiency of the method are demonstrated through a comparative evaluation of second and fifth-order formulas, applied to a complex constitutive model for natural clay, full details of which are given.
GPU acceleration of Runge Kutta-Fehlberg and its comparison with Dormand-Prince method
NASA Astrophysics Data System (ADS)
Seen, Wo Mei; Gobithaasan, R. U.; Miura, Kenjiro T.
2014-07-01
There is a significant reduction of processing time and speedup of performance in computer graphics with the emergence of Graphic Processing Units (GPUs). GPUs have been developed to surpass Central Processing Unit (CPU) in terms of performance and processing speed. This evolution has opened up a new area in computing and researches where highly parallel GPU has been used for non-graphical algorithms. Physical or phenomenal simulations and modelling can be accelerated through General Purpose Graphic Processing Units (GPGPU) and Compute Unified Device Architecture (CUDA) implementations. These phenomena can be represented with mathematical models in the form of Ordinary Differential Equations (ODEs) which encompasses the gist of change rate between independent and dependent variables. ODEs are numerically integrated over time in order to simulate these behaviours. The classical Runge-Kutta (RK) scheme is the common method used to numerically solve ODEs. The Runge Kutta Fehlberg (RKF) scheme has been specially developed to provide an estimate of the principal local truncation error at each step, known as embedding estimate technique. This paper delves into the implementation of RKF scheme for GPU devices and compares its result with Dorman Prince method. A pseudo code is developed to show the implementation in detail. Hence, practitioners will be able to understand the data allocation in GPU, formation of RKF kernels and the flow of data to/from GPU-CPU upon RKF kernel evaluation. The pseudo code is then written in C Language and two ODE models are executed to show the achievable speedup as compared to CPU implementation. The accuracy and efficiency of the proposed implementation method is discussed in the final section of this paper.
NASA Astrophysics Data System (ADS)
Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.
2014-01-01
Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge-Kutta-like time-steps to advance the parabolic terms by a time-step that is s2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge-Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems - a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful in
Simos, T E; Aguiar, J V
2001-05-01
A modified Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems is developed in this paper. This new modified method is based on the classical Runge-Kutta method of algebraic order four. The numerical results indicate that this new method is more efficient for the numerical solution of the Schrödinger equation and related problems than the well known classical Runge-Kutta method of algebraic order four.
The design and applications of Runge-Kutta methods for the simulation of planetary orbits
NASA Astrophysics Data System (ADS)
Rabbi, S. M. Fajlay
Since the merger of physics and mathematics at the beginning of 1800s, system of finding solution to n-body problem has been intriguing mathematicians. The resulting differential equations can be solved by a variety of approaches -- for example, the Runge-Kutta Methods (RKn). In this thesis, after a brief historical overview of planetary science, RK3 methods are derived as a three-parameter family of solution methods. A particular instance of this family, FR3, is generated and subsequently tested to show it is indeed a third-order method. The planetary system is modeled as a system of differential of equations using laws of classical mechanics, and the models of planetary motions are generated applying RK4 methods. Kepler's laws of planetary motion are proved empirically using observed data taken from NASA. A new way of expressing Kepler's third law is presented: the orbital velocity of a planet decreases as inverse square root of its orbital radius. Simulation of Sun-Earth-Moon as well as solar system is conducted and compared to that of Dahir's and found is a very similar result. Also, the result of the entire solar system simulation closely matches to that of NASA. Initial position-velocity vectors are generated from NASA-JPL's ephemeris data using post-processing codes obtained from the University of Colorado.
Exponential Runge-Kutta integrators for modelling Predator-Prey interactions
NASA Astrophysics Data System (ADS)
Diele, F.; Marangi, C.; Ragni, S.
2012-09-01
Spatially explicit models consisting of reaction-diffusion partial differential equations are considered in order to model prey-predator interactions, since it is known that the role of spatial processes reveals of great interest in the study of the effects of habitat fragmentation on biodiversity. As almost all of the realistic models in biology, these models are nonlinear and their solution is not known in closed form. Our aim is approximating the solution itself by means of exponential Runge-Kutta integrators. Moreover, we apply the shift-and-invert Krylov approach in order to evaluate the entire functions needed for implementing the exponential method. This numerical procedure reveals to be very eff cient in avoiding numerical instability during the simulation, since it allows us to adopt high order in the accuracy. This work has received funding from the European Union's Seventh Framework Programme FP7/2007-2013, SPA.2010.1.1-04: "Stimulating the development of GMES services in specif c are", under grant agreement 263435, project title: Biodiversity Multi-Source Monitoring System:from Space To Species (BIOSOS) coordinated by CNR-ISSIA, Bari-Italy (http://www.biosos.eu).
Low-Storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Kennedy, Chistopher A.; Carpenter, Mark H.; Lewis, R. Michael
1999-01-01
The derivation of storage explicit Runge-Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier-Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, 16 ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods have been assessed using the differential equation testing code DETEST, and with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methane-air and hydrogen-air flames. Derived 3(2) and 4(3) pairs are competitive with existing full-storage methods. Although a substantial efficiency penalty accompanies use of two- and three-register, fifth-order methods, the best contemporary full-storage methods can be pearl), matched while still saving two to three registers of memory.
Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation
NASA Astrophysics Data System (ADS)
Su, Bo; Tuo, Xianguo; Xu, Ling
2017-08-01
Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.
A two-stage time-integration technique with Runge-Kutta methods
NASA Astrophysics Data System (ADS)
Nguyen, Chuong T.; Chau, Khanh N.; Kuhl, Detlef
2017-07-01
In this paper we present an implementation of the two-stage time-integration technique for solving semi-discrete systems of elastodynamics problems. This numerical approach effectively suppress the spurious high-frequency oscillations without affecting the accuracy of low modes, especially for long-term integration. At the stage of basic computations zero-dissipative Runge-Kutta methods are applied which yield no error accumulation due to numerical dissipation in the obtained solutions. Then for the suppression of spurious high-frequency oscillations, the filtering stage including pre- or/and post-processing are proceeded by using time integration methods with large numerical dissipation. Therein, the minimum necessary amount of numerical dissipation for filtering the spurious oscillations are determined by using a calibration procedure in which the amplitudes of spurious oscillations occurring the solution profile are minimized by varying stepsizes. The two-stage time integration technique is implemented to one- and two-dimensional wave propagation problems by employing both IsoGeometric Analysis (IGA) and standard Finite Element Method (FEM) for spatial discretization. We observe that the presented time technique achieve high accuracy for long-term integration solutions compared to the other existing time integration methods.
Runge-Kutta time semidiscretizations of semilinear PDEs with non-smooth data.
Wulff, Claudia; Evans, Chris
2016-01-01
We study semilinear evolution equations [Formula: see text] posed on a Hilbert space [Formula: see text], where A is normal and generates a strongly continuous semigroup, B is a smooth nonlinearity from [Formula: see text] to itself, and [Formula: see text], [Formula: see text], [Formula: see text]. In particular the one-dimensional semilinear wave equation and nonlinear Schrödinger equation with periodic, Neumann and Dirichlet boundary conditions fit into this framework. We discretize the evolution equation with an A-stable Runge-Kutta method in time, retaining continuous space, and prove convergence of order [Formula: see text] for non-smooth initial data [Formula: see text], where [Formula: see text], for a method of classical order p, extending a result by Brenner and Thomée for linear systems. Our approach is to project the semiflow and numerical method to spectral Galerkin approximations, and to balance the projection error with the error of the time discretization of the projected system. Numerical experiments suggest that our estimates are sharp.
On the application of runge-kutta methods to transport calculations
Nelson, P.; Jeffery, J.
1988-11-01
Under a definition suitable to the transport equation, it is shown that the (two-stage explicit) Runge-Kutta (RK) methods having order of at least 2, and requiring essentially only one source evaluation per cell, consist of a one-parameter family, plus two additional methods. Two of these, the midpoint corrector and improved Euler methods, are selected for detailed computational comparison with the classical diamond-difference and step characteristic methods. Extensive monodirectional calculations reveal that the RK methods display absolute instability for cell path lengths exceeding 2 mfp, but that they are nearly competitive with the classical methods for small cell widths. It is shown how the two subject RK methods can be augmented by closure approximations, so as to permit their use in source iteration for multiple-direction calculations. The results of such calculations show that for small cell widths, the RK methods again are nearly competitive in accuracy, although the absolute stability requirement can impose a stringent upper bound on the acceptable cell widths; the RK methods interact well with source iteration, even though they do not conserve particles; and the particular closure approximations selected retain the second-order accuracy of the basic underlying methods.
Runge-Kutta central discontinuous Galerkin BGK method for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Ren, Tan; Hu, Jun; Xiong, Tao; Qiu, Jing-Mei
2014-10-01
In this paper, we propose a Runge-Kutta (RK) central discontinuous Galerkin (CDG) gas-kinetic BGK method for the Navier-Stokes equations. The proposed method is based on the CDG method defined on two sets of overlapping meshes to avoid discontinuous solutions at cell interfaces, as well as the gas-kinetic BGK model to evaluate fluxes for both convection and diffusion terms. Redundant representation of the numerical solution in the CDG method offers great convenience in the design of gas-kinetic BGK fluxes. Specifically, the evaluation of fluxes at cell interfaces of one set of computational mesh is right inside the cells of the staggered mesh, hence the corresponding particle distribution function for flux evaluation is much simpler than that in existing gas-kinetic BGK methods. As a central scheme, the proposed CDG-BGK has doubled the memory requirement as the corresponding DG scheme; on the other hand, for the convection part, the CFL time step constraint of the CDG method for numerical stability is relatively large compared with that for the DG method. Numerical boundary conditions have to be treated with special care. Numerical examples for 1D and 2D viscous flow simulations are presented to validate the accuracy and robustness of the proposed RK CDG-BGK method.
NASA Astrophysics Data System (ADS)
Miller, J. A.; Piscicelli, M.
2005-12-01
The momentum diffusion or Fokker-Planck operator describes, at least approximately, the evolution of a distribution of particles interacting with a collection of scattering centers. The interactions can range from Coulomb collisions with particles of the same or another species, to resonant interactions with linear plasma waves, to nonresonant collisions with randomly-moving large-scale (compared to the particle gyroradius) magnetic inhomogeneities. Consequently, this operator is a common feature in descriptions of particle transport and stochastic acceleration by electromagnetic turbulence in a wide variety of astrophysical and space plasma situations. An analytical solution of a kinetic equation involving this operator is intractable in practical instances, and hence numerical solutions must be employed. We demonstrate how to transform the kinetic equation into an equivalent system of Stratonovich Stochastic Differential Equations, and present a high-order adaptive Runge-Kutta algorithm for their solution. This technique can provide accurate solutions of a kinetic equation over long timescales, and is easily adapted to take into account nonstochastic processes. This work was supported by NASA grant NAG5-12794
NASA Astrophysics Data System (ADS)
Langer, Stefan
2013-03-01
For unstructured finite volume methods, we present a line implicit Runge-Kutta method applied as smoother in an agglomerated multigrid algorithm to significantly improve the reliability and convergence rate to approximate steady-state solutions of the Reynolds-averaged Navier-Stokes equations. To describe turbulence, we consider a one-equation Spalart-Allmaras turbulence model. The line implicit Runge-Kutta method extends a basic explicit Runge-Kutta method by a preconditioner given by an approximate derivative of the residual function. The approximate derivative is only constructed along predetermined lines which resolve anisotropies in the given grid. Therefore, the method is a canonical generalisation of point implicit methods. Numerical examples demonstrate the improvements of the line implicit Runge-Kutta when compared with explicit Runge-Kutta methods accelerated with local time stepping.
NASA Astrophysics Data System (ADS)
Amalina Nisa Ariffin, Noor; Rosli, Norhayati; Syahidatul Ayuni Mazlan, Mazma; Samsudin, Adam
2017-09-01
Recently, modelling the biological systems by using stochastic differential equations (SDEs) are becoming an interest among researchers. In SDEs the random fluctuations are taking into account, which resulting to the complexity of finding the exact solution of SDEs and contribute to the increasing number of research focusing in finding the best numerical approach to solve the systems of SDEs. This paper will examine the performance of 4-stage stochastic Runge-Kutta (SRK4) and specific stochastic Runge-Kutta (SRKS) methods with order 1.5 in approximating the solution of stochastic model in biological system. A comparative study of SRK4 and SRKS method will be presented in this paper. The non-linear biological model will be used to examine the performance of both methods and the result of numerical experiment will be discussed.
Papadopoulos, D F; Anastassi, Z A; Simos, T E
2010-08-01
A new Runge-Kutta-Nyström method, with phase-lag and amplification error of order infinity, for the numerical solution of the Schrödinger equation is developed in this paper. The new method is based on the Runge-Kutta-Nyström method with fourth algebraic order, developed by Dormand, El-Mikkawy and Prince. Numerical illustrations indicate that the new method is much more efficient than other methods derived for the same purpose.
Projected implicit Runge-Kutta methods for differential-algebraic boundary value problems
Ascher, U. ); Petzoid, L. )
1990-09-01
Differential-algebraic boundary value problems arise in the modelling of singular optimal control problems and in parameter estimation for singular systems. A new class of numerical methods for these problems is introduced, and shown to overcome difficulties with previously defined numerical methods. 4 refs., 1 tab.
Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations
NASA Technical Reports Server (NTRS)
Yu, Sheng-Tao
1992-01-01
Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples
Zhang, Zhongxi; Chen, Liang; Bao, Xiaoyi
2010-04-12
A fourth-order Runge-Kutta in the interaction picture (RK4IP) method is presented for solving the coupled nonlinear Schr odinger equation (CNLSE) that governs the light propagation in optical fibers with randomly varying birefringence. The computational error of RK4IP is caused by the fourth-order Runge-Kutta algorithm, better than the split-step approximation limited by the step size. As a result, the step size of RK4IP can have the same order of magnitude as the dispersion length and/or the nonlinear length of the fiber, provided the birefringence effect is small. For communication fibers with random birefringence, the step size of RK4IP can be orders of magnitude larger than the correlation length and the beating length of the fibers, depending on the interaction between linear and nonlinear effects. Our approach can be applied to the fibers having the general form of local birefringence and treat the Kerr nonlinearity without approximation. Our RK4IP results agree well with those obtained from Manakov-PMD approximation, provided the polarization state can be mixed enough on the Poincar e sphere.
Cui, Hengfei; Wang, Desheng; Wan, Min; Zhang, Jun-Mei; Zhao, Xiaodan; Tan, Ru San; Huang, Weimin; Xiong, Wei; Duan, Yuping; Zhou, Jiayin; Luo, Tong; Kassab, Ghassan S; Zhong, Liang
2016-06-01
The CT angiography (CTA) is a clinically indicated test for the assessment of coronary luminal stenosis that requires centerline extractions. There is currently no centerline extraction algorithm that is automatic, real-time and very accurate. Therefore, we sought to (i) develop a hybrid approach by incorporating fast marching and Runge-Kutta based methods for the extraction of coronary artery centerlines from CTA; (ii) evaluate the accuracy of the present method compared to Van's method by using ground truth centerline as a reference; (iii) evaluate the coronary lumen area of our centerline method in comparison with the intravascular ultrasound (IVUS) as the standard of reference. The proposed method was found to be more computationally efficient, and performed better than the Van's method in terms of overlap measures (i.e., OV: [Formula: see text] vs. [Formula: see text]; OF: [Formula: see text] vs. [Formula: see text]; and OT: [Formula: see text] vs. [Formula: see text], all [Formula: see text]). In comparison with IVUS derived coronary lumen area, the proposed approach was more accurate than the Van's method. This hybrid approach by incorporating fast marching and Runge-Kutta based methods could offer fast and accurate extraction of centerline as well as the lumen area. This method may garner wider clinical potential as a real-time coronary stenosis assessment tool.
NASA Technical Reports Server (NTRS)
Fehlberg, E.
1974-01-01
Runge-Kutta-Nystrom formulas of the seventh, sixth, and fifth order were derived for the general second order (vector) differential equation written as the second derivative of x = f(t, x, the first derivative of x). The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the local truncation error in x, and they require no more evaluations per step than the earlier Runge-Kutta formulas for the first derivative of x = f(t, x). The developed formulas are expected to be time saving in comparison to the Runge-Kutta formulas for first-order differential equations, since it is not necessary to convert the second-order differential equations into twice as many first-order differential equations. The examples shown saved from 25 percent to 60 percent more computer time than the earlier formulas for first-order differential equations, and are comparable in accuracy.
NASA Astrophysics Data System (ADS)
Ahmad, Nur Amirah; Senu, Norazak
2017-08-01
A new embedded Two Derivative Runge-Kutta method (TDRK) based on First Same As Last (FSAL) technique for the numerical solution of first order Initial Value Problems (IVPs) is derived. We present an embedded 4(3) pair explicit fourth order TDRK method with a `small' principal local truncation error coefficient. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of our method in comparison with other existing embedded Runge-Kutta methods (RK) of the same order.
Two-Dimensional Inlet Simulation Using a Diagonal Implicit Algorithm
NASA Technical Reports Server (NTRS)
Chaussee, D.S.; Pulliam, T. H.
1981-01-01
A modification of an implicit approximate-factorization finite-difference algorithm applied to the two-dimensional Euler and Navier-Stokes equations in general curvilinear coordinates is presented for supersonic freestream flow about and through inlets. The modification transforms the coupled system of equations Into an uncoupled diagonal form which requires less computation work. For steady-state applications the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. Solutions are given for inviscid and laminar flow about a two-dimensional wedge inlet configuration. Comparisons are made between computed results and exact theory.
NASA Technical Reports Server (NTRS)
Shih, C. C.
1973-01-01
A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given, and comparisons with experimental data were made.
Xu, Zhiliang; Chen, Xu-Yan; Liu, Yingjie
2014-12-01
We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [9, 8, 7, 6] for solving conservation Laws with increased CFL numbers. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. Numerical computations for solving one-dimensional and two-dimensional scalar and systems of nonlinear hyperbolic conservation laws are performed with approximate solutions represented by piecewise quadratic and cubic polynomials, respectively. The hierarchical reconstruction [17, 33] is applied as a limiter to eliminate spurious oscillations in discontinuous solutions. From both numerical experiments and the analytic estimate of the CFL number of the newly formulated method, we find that: 1) this new formulation improves the CFL number over the original RKDG formulation by at least three times or more and thus reduces the overall computational cost; and 2) the new formulation essentially does not compromise the resolution of the numerical solutions of shock wave problems compared with ones computed by the RKDG method.
NASA Astrophysics Data System (ADS)
Steinhoff, Tim
2017-07-01
The coefficient matrix of a Runge-Kutta method of order p has to contain a block of size m ≥ p so that the respective method also has a stage order of p. If m = p and additionally a single point spectrum of the block is demanded all block coefficients and the respective relative step sizes are completely defined through that aside from a common factor, see e. g. [1]. This results in fixed stability properties for the stability functions of the block stages. To avoid such an imposition and to provide more freedom in the choice of coefficients we consider in this work a block of size m = p + 1 and derive conditions on a single point spectrum by means of a perturbed collocation ansatz. Our results also cover methods with an explicit first stage and imply classical results related to non-perturbed collocation. Additionally, we present some results that may prove beneficial in the actual construction of methods with a stage order of p and a block size of m = p + 1.
Xu, Zhiliang; Chen, Xu-Yan; Liu, Yingjie
2014-01-01
We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [9, 8, 7, 6] for solving conservation Laws with increased CFL numbers. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. Numerical computations for solving one-dimensional and two-dimensional scalar and systems of nonlinear hyperbolic conservation laws are performed with approximate solutions represented by piecewise quadratic and cubic polynomials, respectively. The hierarchical reconstruction [17, 33] is applied as a limiter to eliminate spurious oscillations in discontinuous solutions. From both numerical experiments and the analytic estimate of the CFL number of the newly formulated method, we find that: 1) this new formulation improves the CFL number over the original RKDG formulation by at least three times or more and thus reduces the overall computational cost; and 2) the new formulation essentially does not compromise the resolution of the numerical solutions of shock wave problems compared with ones computed by the RKDG method. PMID:25414520
NASA Astrophysics Data System (ADS)
Ma, Xiao; Yang, Dinghui
2017-06-01
The finite-difference method, which is an important numerical tool for solving seismic wave equations, is widely applied in simulation, wave-equation-based migration and inversion. As the seismic wave phase plays a critical role in forward simulation and inversion, it should be preserved during wavefield simulation. In this paper, we propose a type of phase-preserving stereomodelling method, which is simultaneously symplectic and low numerical dispersive. First, we propose three new time-marching schemes for solving wave equations that are optimal symplectic partitioned Runge-Kutta schemes with minimized phase errors. Relevant simulations on a harmonic oscillator show that even after 200 000 temporal iterations, our schemes can still avoid the phase drifting issue that appears in other symplectic schemes. We use these symplectic schemes as time integrators, and a numerically low dispersive operator called the stereomodelling discrete operator as a spatial discretization approach to solve seismic wave equations. Theoretical analysis on the stability conditions shows that the new methods are more stable than previous methods. We also investigate the numerical dispersion relations of the methods proposed in this study. To further investigate phase accuracy, we compare the numerical solutions generated by the proposed methods with analytic solutions. Several numerical experiments indicate that our proposed methods are efficient for various models and perform well with perfectly matched layer boundary conditions.
NASA Astrophysics Data System (ADS)
Ma, Xiao; Yang, Dinghui
2017-03-01
The finite-difference method, which is an important numerical tool for solving seismic wave equations, is widely applied in wavefield simulation, wave-equation-based migration and inversion. As the seismic wave phase plays a critical role in forward simulation and inversion, it should be preserved during wavefield simulation. In this paper, we propose a type of phase-preserving stereomodelling method, which is simultaneously symplectic and low numerical dispersive. First, we propose three new time-marching schemes for solving wave equations that are optimal symplectic partitioned Runge-Kutta schemes with minimized phase errors. Relevant simulations on a harmonic oscillator show that even after 200,000 temporal iterations, our schemes can still avoid the phase drifting issue that appears in other symplectic schemes. We use these symplectic schemes as time integrators, and a numerically low dispersive operator called the stereomodelling discrete operator as a spatial discretization approach to solve seismic wave equations. Theoretical analysis on the stability conditions shows that the new methods are more stable than previous methods. We also investigate the numerical dispersion relations of the methods proposed in this study. To further investigate phase accuracy, we compare the numerical solutions generated by the proposed methods with analytic solutions. Several numerical experiments indicate that our proposed methods are efficient for various models and perform well with perfectly matched layer boundary conditions.
NASA Astrophysics Data System (ADS)
Liu, Baiyili; Tang, Shaoqiang
2017-07-01
In this paper, we investigate the Runge-Kutta algorithm for the Nosé-Hoover heat bath of a harmonic chain. The Runge-Kutta algorithm is found to be unstable in long-time calculations, with the system temperature growing exponentially. The growth rate increases if time step size is chosen larger. By analyzing the Fourier spectra in both space (wave number) and time (frequency), we discover that the growth is caused by spurious energy accumulation, particularly at the largest wave number. Such accumulation may be explained by von Neumann analysis for an infinite chain, with the nonlinear heat bath being ignored. Furthermore, we propose to add a filter to remove excessive energy, which effectively stabilizes the algorithm.
NASA Astrophysics Data System (ADS)
Alonso-Mallo, I.; Cano, B.; Moreta, M. J.
2005-04-01
In this paper, we study the order reduction which turns up when explicit Runge-Kutta-Nystrom methods are used to discretize linear second order hyperbolic equations by means of the method of lines. The order observed in practice, including its fractional part, is obtained. It is also proved that the order reduction can be completely avoided taking the boundary values of the intermediate stages of the time semidiscretization. The numerical experiments confirm that the optimal order can be reached.
NASA Astrophysics Data System (ADS)
Zhang, Chao-Yuan; Ma, Xiao; Yang, Lei; Song, Guo-Jie
2014-03-01
We propose a symplectic partitioned Runge-Kutta (SPRK) method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic wave equation. Known as the eighth-order NSPRK method, this technique uses an eighth-order accurate nearly analytic discrete (NAD) operator to discretize high-order spatial differential operators and employs a second-order SPRK method to discretize temporal derivatives. The stability criteria and numerical dispersion relations of the eighth-order NSPRK method are given by a semi-analytical method and are tested by numerical experiments. We also show the differences of the numerical dispersions between the eighth-order NSPRK method and conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction (LWC) method and the eighth-order staggered-grid (SG) method. The result shows that the ability of the eighth-order NSPRK method to suppress the numerical dispersion is obviously superior to that of the conventional numerical methods. In the same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 times faster than the fourth-order SPRK, and the memory requirement is only approximately 47.17% of the fourth-order NSPRK method and 49.41 % of the fourth-order SPRK method, which indicates the highest computational efficiency. Modeling examples for the two-layer models such as the heterogeneous and Marmousi models show that the wavefields generated by the eighth-order NSPRK method are very clear with no visible numerical dispersion. These numerical experiments illustrate that the eighth-order NSPRK method can effectively suppress numerical dispersion when coarse grids are adopted. Therefore, this method can greatly decrease computer memory requirement and accelerate the forward modeling productivity. In general, the eighth-order NSPRK method has tremendous potential
NASA Astrophysics Data System (ADS)
Tsitouras, Ch.; Papageorgiou, G.; Kalvouridis, T.
1992-12-01
Runge-Kutta-Nystrom (RKN) codes for the solution of the initial value problem for the general second-order differential system were developed recently, although the methodology on which they are based was known many years ago. The efficiency of several general Runge-Kutta-Nystrom (GRKN) methods is examined by posing some criteria of cost and accuracy. These methods supplied with the corresponding interpolants are applied to some problems of celestial dynamics. The results obtained show that these codes have good responses in the approximation of the solution of these problems.
NASA Astrophysics Data System (ADS)
Mabssout, M.; Pastor, M.; Herreros, M. I.; Quecedo, M.
2006-11-01
This paper presents an alternative formulation of Solid Dynamics problems based on (i) a mathematical model consisting of a system of hyperbolic PDEs where the source term is originated by the viscoplastic strain rate and (ii) a splitting scheme where the two-step Taylor-Galerkin is used for the advective part of the PDE operator while the sources are integrated using a fourth-order Runge-Kutta. Use of the splitting scheme results in a higher accuracy than that of the original two-step Taylor-Galerkin. The scheme performs well when used with linear triangle or tetrahedra for (i) bending-dominated situations (ii) localized failure under dynamic conditions and keeps the advantages of the two-step Taylor-Galerkin concerning numerical dispersion and damping of short wavelengths. Copyright
NASA Astrophysics Data System (ADS)
Franco, J. M.; Gómez, I.
2013-04-01
The construction of high-order exponentially fitted Runge-Kutta-Nyström (EFRKN) methods of explicit type for the numerical solution of oscillatory differential systems is analyzed. Based on two basic symmetric and symplectic EFRKN methods of reference we present two procedures for constructing high-order explicit methods. The first procedure is based on composition methods and it allows the construction of high-order explicit EFRKN methods which are symmetric and symplectic. The second procedure is based on combining different EFRKN methods in order to construct embedded pairs of explicit parallel EFRKN methods which can be implemented in variable-step codes without additional cost. The numerical experiments carried out show the qualitative behavior and the efficiency of the new EFRKN methods when they are compared with some standard methods proposed in the scientific literature for solving second-order nonstiff differential systems. Catalogue identifier: AEOO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOO_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 2527 No. of bytes in distributed program, including test data, etc.: 107433 Distribution format: tar.gz Programming language: Fortran 77. Computer: Standard PC. Operating system: Windows. It might work with others. Successfully tested by CPC on Linux. RAM: For the test problems used less than 1 MB. Classification: 4.3, 4.12, 16.3, 17.17. Nature of problem: Some models in astronomy and astrophysics, quantum mechanics and nuclear physics lead to second-order oscillatory differential systems. The solution of these oscillatory models requires accurate and efficient numerical methods. The codes SVI-IIEXPOreferee.for and SVI-IIvarreferee.for were developed for this purpose. Solution method: We propose high-order exponentially fitted Runge-Kutta
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun
1993-01-01
The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.
A diagonal implicit scheme for computing flows with finite-rate chemistry
NASA Technical Reports Server (NTRS)
Eberhardt, Scott; Imlay, Scott
1990-01-01
A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.
NASA Astrophysics Data System (ADS)
Im, Dong-Kyun; Choi, Seongim; Hyuck Kwon, Jang
2015-01-01
The diagonally implicit harmonic balance method is developed in an overset mesh topology and applied to unsteady rotor flows analysis. Its efficiency is by reducing the complexity of a fully implicit harmonic balance method which becomes more flexible in handling the higher harmonics of the flow solutions. Applied to the overset mesh topology, the efficiency of the method becomes greater by reducing the number of solution interpolations required during the entire solution procedure as the method reduces the unsteady computation into periodic steady state. To verify the accuracy and efficiency of the method, both hovering and unsteady forward flight of Caradonna and Tung and AH-1G rotors are solved. Compared with wind-tunnel experiments, the numerical results demonstrate good agreements at computational cost an order of magnitude more efficient than the conventional time-accurate computation method. The proposed method has great potential in other engineering applications, including flapping wing vehicles, turbo-machinery, wind-turbines, etc.
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Rossow, C.-C.
2008-01-01
A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.
Multigrid diagonal implicit solutions for compressible turbulent flows and their evaluation
NASA Astrophysics Data System (ADS)
Varma, Rama Rajaraja
A numerical scheme to solve the two dimensional Navier-Stokes equations is developed and applied to several compressible turbulent flows over airfoils. A method for evaluating the quality of these solutions is then developed and illustrated with representative examples. The distinguishing features of the numerical scheme are its implicitness for improving stability, the diagonalization of the matrices in the implicit operator for computational efficiency, and the implementation within a multigrid procedure for convergence acceleration. A finite volume approximation is used for spatial discretization of the governing equations to handle complicated geometries. Artificial dissipation is added in the form of an adaptive blend of second and fourth differences of the solution to maintain robustness and stability. The viscous terms are treated explicitly to maintain the diagonal form. Results of simulations of viscous transonic flows past airfoils are presented. The computed flow field quantities are compared with those from other computations and experiments to confirm the accuracy of the method. Comparisons of convergence rates are made to demonstrate the efficiency of the method. In solutions to the Navier-Stokes equations it is important that the added numerical dissipation does not overwhelm the real viscous dissipation. In order to verify this, it is necessary to be able to estimate quantitatively the effect of numerical dissipation. A method for estimating the integrated effect of numerical dissipation on solutions to the Navier-Stokes equations is developed in this dissertation. The method is based on integration of the momentum equations and the computation of corrections due to numerical dissipation to the drag integral. These corrections can then be considered as estimates of the error due to dissipation. Solutions to the Navier-Stokes equations for laminar and turbulent flows over airfoils are used to illustrate the method. The errors due to numerical
An implicit-explicit finite-difference lattice Boltzmann subgrid method on nonuniform meshes
NASA Astrophysics Data System (ADS)
Qiu, Ruofan; Chen, Rongqian; You, Yancheng
In this paper, an implicit-explicit finite-difference lattice Boltzmann method with subgrid model on nonuniform meshes is proposed. The implicit-explicit Runge-Kutta scheme, which has good convergence rate, is used for the time discretization and a mixed difference scheme, which combines the upwind scheme with the central scheme, is adopted for the space discretization. Meanwhile, the standard Smagorinsky subgrid model is incorporated into the finite-difference lattice Boltzmann scheme. The effects of implicit-explicit Runge-Kutta scheme and nonuniform meshes of present lattice Boltzmann method are discussed through simulations of a two-dimensional lid-driven cavity flow on nonuniform meshes. Moreover, the comparison simulations of the present method and multiple relaxation time lattice Boltzmann subgrid method are conducted qualitatively and quantitatively.
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-15
The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the
NASA Astrophysics Data System (ADS)
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-01
The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the
NASA Astrophysics Data System (ADS)
Cinnella, P.; Content, C.
2016-12-01
Restrictions on the maximum allowable time step of explicit time integration methods for direct and large eddy simulations of compressible turbulent flows at high Reynolds numbers can be very severe, because of the extremely small space steps used close to solid walls to capture tiny and elongated boundary layer structures. A way of increasing stability limits is to use implicit time integration schemes. However, the price to pay is a higher computational cost per time step, higher discretization errors and lower parallel scalability. In quest for an implicit time scheme for scale-resolving simulations providing the best possible compromise between these opposite requirements, we develop a Runge-Kutta implicit residual smoothing (IRS) scheme of fourth-order accuracy, based on a bilaplacian operator. The implicit operator involves the inversion of scalar pentadiagonal systems, for which efficient parallel algorithms are available. The proposed method is assessed against two explicit and two implicit time integration techniques in terms of computational cost required to achieve a threshold level of accuracy. Precisely, the proposed time scheme is compared to four-stages and six-stages low-storage Runge-Kutta method, to the second-order IRS and to a second-order backward scheme solved by means of matrix-free quasi-exact Newton subiterations. Numerical results show that the proposed IRS scheme leads to reductions in computational time by a factor 3 to 5 for an accuracy comparable to that of the corresponding explicit Runge-Kutta scheme.
NASA Astrophysics Data System (ADS)
Dehghan, Mehdi; Mohammadi, Vahid
2017-08-01
In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.
NASA Technical Reports Server (NTRS)
Chen, Shu-Cheng; Liu, Nan-Suey; Kim, Hyun Dae
1991-01-01
Presented here is an algorithm for solving the multidimensional unsteady Navier-Stokes equations for compressible flows. It is based on a diagonally-dominant approximate factorization procedure. The factorization error and the timewise linearization error associated with this procedure are reduced by performing Newton-type inner iterations at each time step. The inviscid fluxes are evaluated by the fourth-order central differencing scheme amended with a numerical dissipation directly proportional to the entire dissipative part of the truncation error intrinsic to the third order biased upwind scheme. The important features of the proposed solution are elucidated by the numerical results of the convection of a vortex and the backward-facing step flows.
Acceleration on stretched meshes with line-implicit LU-SGS in parallel implementation
NASA Astrophysics Data System (ADS)
Otero, Evelyn; Eliasson, Peter
2015-02-01
The implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver is combined with the line-implicit technique to improve convergence on the very anisotropic grids necessary for resolving the boundary layers. The computational fluid dynamics code used is Edge, a Navier-Stokes flow solver for unstructured grids based on a dual grid and edge-based formulation. Multigrid acceleration is applied with the intention to accelerate the convergence to steady state. LU-SGS works in parallel and gives better linear scaling with respect to the number of processors, than the explicit scheme. The ordering techniques investigated have shown that node numbering does influence the convergence and that the orderings from Delaunay and advancing front generation were among the best tested. 2D Reynolds-averaged Navier-Stokes computations have clearly shown the strong efficiency of our novel approach line-implicit LU-SGS which is four times faster than implicit LU-SGS and line-implicit Runge-Kutta. Implicit LU-SGS for Euler and line-implicit LU-SGS for Reynolds-averaged Navier-Stokes are at least twice faster than explicit and line-implicit Runge-Kutta, respectively, for 2D and 3D cases. For 3D Reynolds-averaged Navier-Stokes, multigrid did not accelerate the convergence and therefore may not be needed.
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1988-01-01
An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.
A fifth order implicit method for the numerical solution of differential-algebraic equations
NASA Astrophysics Data System (ADS)
Skvortsov, L. M.
2015-06-01
An implicit two-step Runge-Kutta method of fifth order is proposed for the numerical solution of differential and differential-algebraic equations. The location of nodes in this method makes it possible to estimate the values of higher derivatives at the initial and terminal points of an integration step. Consequently, the proposed method can be regarded as a finite-difference analog of the Obrechkoff method. Numerical results, some of which are presented in this paper, show that our method preserves its order while solving stiff equations and equations of indices two and three. This is the main advantage of the proposed method as compared with the available ones.
Implicit compressible flow solvers on unstructured meshes
NASA Astrophysics Data System (ADS)
Nagaoka, Makoto; Horinouchi, Nariaki
1993-09-01
An implicit solver for compressible flows using Bi-CGSTAB method is proposed. The Euler equations are discretized with the delta-form by the finite volume method on the cell-centered triangular unstructured meshes. The numerical flux is calculated by Roe's upwind scheme. The linearized simultaneous equations with the irregular nonsymmetric sparse matrix are solved by the Bi-CGSTAB method with the preconditioner of incomplete LU factorization. This method is also vectorized by the multi-colored ordering. Although the solver requires more computational memory, it shows faster and more robust convergence than the other conventional methods: three-stage Runge-Kutta method, point Gauss-Seidel method, and Jacobi method for two-dimensional inviscid steady flows.
Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning
Ghosh, Debojyoti; Constantinescu, Emil M.
2016-06-23
Here, this paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time scale is significantly faster than the advective scale, yet it is typically not relevant to atmospheric and weather phenomena. The acoustic and advective components of the hyperbolic flux are separated in the characteristic space. High-order, conservative additive Runge-Kutta methods are applied to the partitioned equations so that the acoustic component is integrated in time implicitly with an unconditionally stable method, while the advective component is integrated explicitly. The time step ofmore » the overall algorithm is thus determined by the advective scale. Benchmark flow problems are used to demonstrate the accuracy, stability, and convergence of the proposed algorithm. The computational cost of the partitioned semi-implicit approach is compared with that of explicit time integration.« less
Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning
Ghosh, Debojyoti; Constantinescu, Emil M.
2016-06-23
Here, this paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time scale is significantly faster than the advective scale, yet it is typically not relevant to atmospheric and weather phenomena. The acoustic and advective components of the hyperbolic flux are separated in the characteristic space. High-order, conservative additive Runge-Kutta methods are applied to the partitioned equations so that the acoustic component is integrated in time implicitly with an unconditionally stable method, while the advective component is integrated explicitly. The time step of the overall algorithm is thus determined by the advective scale. Benchmark flow problems are used to demonstrate the accuracy, stability, and convergence of the proposed algorithm. The computational cost of the partitioned semi-implicit approach is compared with that of explicit time integration.
Semi-implicit spectral deferred correction methods for ordinary differential equations
Minion, Michael L.
2002-10-06
A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. The stability and accuracy of the resulting ODE methods are explored analytically and numerically. The SISDC methods are intended to be combined with the method of lines approach to yield a flexible framework for creating higher-order semi-implicit methods for partial differential equations. A discussion and numerical examples of the SISDC method applied to advection-diffusion type equations are included. The results suggest that higher-order SISDC methods are more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.
Global Asymptotic Behavior of Iterative Implicit Schemes
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.
1994-01-01
The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.
Parallel implicit unstructured grid Euler solvers
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.
1994-01-01
A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on an MIMD (multiple instruction/multiple data stream) parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed, one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the iPSC/860.
Parallel implicit unstructured grid Euler solvers
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.
1994-01-01
A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.
Implicit integration methods for dislocation dynamics
Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; ...
2015-01-20
In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a waymore » of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.« less
Implicit integration methods for dislocation dynamics
Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; Hommes, G.; Aubry, S.; Arsenlis, A.
2015-01-20
In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.
Implicit integration methods for dislocation dynamics
NASA Astrophysics Data System (ADS)
Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; Hommes, G.; Aubry, S.; Arsenlis, A.
2015-03-01
In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. This paper investigates the viability of high-order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.
High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs
NASA Technical Reports Server (NTRS)
Nielsen, Tanner B.; Carpenter, Mark H.; Fisher, Travis C.; Frankel, Steven H.
2014-01-01
This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.
A combined explicit-implicit method for high accuracy reaction path integration.
Burger, Steven K; Yang, Weitao
2006-06-14
We present the use of an optimal combined explicit-implicit method for following the reaction path to high accuracy. This is in contrast to most purely implicit reaction path integration algorithms, which are only efficient on stiff ordinary differential equations. The defining equation for the reaction path is considered to be stiff, however, we show here that the reaction path is not uniformly stiff and instead is only stiff near stationary points. The optimal algorithm developed in this work is a combination of explicit and implicit methods with a simple criterion to switch between the two. Using three different chemical reactions, we combine and compare three different integration methods: the implicit trapezoidal method, an explicit stabilized third order algorithm implemented in the code DUMKA3 and the traditional explicit fourth order Runge-Kutta method written in the code RKSUITE. The results for high accuracy show that when the implicit trapezoidal method is combined with either explicit method the number of energy and gradient calculations can potentially be reduced by almost a half compared with integrating either method alone. Finally, to explain the improvements of the combined method we expand on the concepts of stability and stiffness and relate them to the efficiency of integration methods.
Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids
NASA Astrophysics Data System (ADS)
Otero, Evelyn; Eliasson, Peter
2015-03-01
An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.
Semi-Implicit Reversible Algorithms for Rigid Body Rotational Dynamics
Nukala, Phani K; Shelton Jr, William Allison
2006-09-01
This paper presents two semi-implicit algorithms based on splitting methodology for rigid body rotational dynamics. The first algorithm is a variation of partitioned Runge-Kutta (PRK) methodology that can be formulated as a splitting method. The second algorithm is akin to a multiple time stepping scheme and is based on modified Crouch-Grossman (MCG) methodology, which can also be expressed as a splitting algorithm. These algorithms are second-order accurate and time-reversible; however, they are not Poisson integrators, i.e., non-symplectic. These algorithms conserve some of the first integrals of motion, but some others are not conserved; however, the fluctuations in these invariants are bounded over exponentially long time intervals. These algorithms exhibit excellent long-term behavior because of their reversibility property and their (approximate) Poisson structure preserving property. The numerical results indicate that the proposed algorithms exhibit superior performance compared to some of the currently well known algorithms such as the Simo-Wong algorithm, Newmark algorithm, discrete Moser-Veselov algorithm, Lewis-Simo algorithm, and the LIEMID[EA] algorithm.
Semi-implicit time integration for P{sub N} thermal radiative transfer
McClarren, Ryan G. Evans, Thomas M.; Lowrie, Robert B.; Densmore, Jeffery D.
2008-08-10
Implicit time integration involving the solution of large systems of equations is the current paradigm for time-dependent radiative transfer. In this paper we present a semi-implicit, linear discontinuous Galerkin method for the spherical harmonics (P{sub N}) equations for thermal radiative transfer in planar geometry. Our method is novel in that the material coupling terms are treated implicitly (via linearizing the emission source) and the streaming operator is treated explicitly using a second-order accurate Runge-Kutta method. The benefit of this approach is that each time step only involves the solution of equations that are local to each cell. This benefit comes at the cost of having the time step limited by a CFL condition based on the speed of light. To guarantee positivity and avoid artificial oscillations, we use a slope-limiting technique. We present analysis and numerical results that show the method is robust in the diffusion limit when the photon mean-free path is not resolved by the spatial mesh. Also, in the diffusion limit the time step restriction relaxes to a less restrictive explicit diffusion CFL condition. We demonstrate with numerical results that away from the diffusion limit our method demonstrates second-order error convergence as the spatial mesh is refined with a fixed CFL number.
An implicit and adaptive nonlinear frequency domain approach for periodic viscous flows
NASA Astrophysics Data System (ADS)
Mosahebi, A.; Nadarajah, S.
2014-12-01
An implicit nonlinear Lower-Upper symmetric Gauss-Seidel (LU-SGS) solver has been extended to the adaptive Nonlinear Frequency Domain method (adaptive NLFD) for periodic viscous flows. The discretized equations are linearized in both spatial and temporal directions, yielding an innovative segregate approach, where the effects of the neighboring cells are transferred to the right-hand-side and are updated iteratively. This property of the solver is aligned with the adaptive NLFD concept, in which different cells have different number of modes; hence, should be treated individually. The segregate analysis of the modal equations prevents assembling and inversion of a large left-hand-side matrix, when high number of modes are involved. This is an important characteristic for a selected flow solver of the adaptive NLFD method, where a high modal content may be required in highly unsteady parts of the flow field. The implicit nonlinear LU-SGS solver has demonstrated to be both robust and computationally efficient as the number of modes is increased. The developed solver is thoroughly validated for the laminar vortex shedding behind a stationary cylinder, high angle of attack NACA0012 airfoil, and a plunging NACA0012 airfoil. An order of magnitude improvement in the computational time is observed through the developed implicit approach over the classical modified 5-stage Runge-Kutta method.
NASA Astrophysics Data System (ADS)
Borazjani, Iman; Asgharzadeh, Hafez
2015-11-01
Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.
A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics
NASA Technical Reports Server (NTRS)
Iannelli, G. S.; Baker, A. J.
1992-01-01
A generalized curvilinear coordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modeled as a mixture of five perfect gases, i.e., molecular and atomic oxygen and nitrogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semidiscretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed 'companion conservation law system', permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then nonlinearly stable, and second-order accurate in space and time on arbitrary curvilinear coordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially nonoscillatory numerical solutions in the presence of strong detached shocks and boundary layer-inviscid flow interactions.
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
Hykes, J. M.; Ferrer, R. M.
2013-07-01
The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)
NASA Astrophysics Data System (ADS)
Caplan, R. M.; Mikić, Z.; Linker, J. A.; Lionello, R.
2017-05-01
We explore the performance and advantages/disadvantages of using unconditionally stable explicit super time-stepping (STS) algorithms versus implicit schemes with Krylov solvers for integrating parabolic operators in thermodynamic MHD models of the solar corona. Specifically, we compare the second-order Runge-Kutta Legendre (RKL2) STS method with the implicit backward Euler scheme computed using the preconditioned conjugate gradient (PCG) solver with both a point-Jacobi and a non-overlapping domain decomposition ILU0 preconditioner. The algorithms are used to integrate anisotropic Spitzer thermal conduction and artificial kinematic viscosity at time-steps much larger than classic explicit stability criteria allow. A key component of the comparison is the use of an established MHD model (MAS) to compute a real-world simulation on a large HPC cluster. Special attention is placed on the parallel scaling of the algorithms. It is shown that, for a specific problem and model, the RKL2 method is comparable or surpasses the implicit method with PCG solvers in performance and scaling, but suffers from some accuracy limitations. These limitations, and the applicability of RKL methods are briefly discussed.
High-Order Methods For Wave Propagation
2008-01-01
typically combined with high-order explicit time-integration methods such as the multi-stage Runge - Kutta procedure. In addition to the spatial and temporal... methods include both an explicit Runge - Kutta fourth- order temporally accurate scheme as well as an implicit, approximately factored Beam-Warming scheme of...12]. 3.2.3 Time Integration The equations are integrated in time with the classical fourth-order four-stage Runge - Kutta method . With R denoting the
Open issues in devising software for the numerical solution of implicit delay differential equations
NASA Astrophysics Data System (ADS)
Guglielmi, Nicola
2006-01-01
We consider initial value problems for systems of implicit delay differential equations of the formMy'(t)=f(t,y(t),y([alpha]1(t,y(t))),...,y([alpha]m(t,y(t)))),where M is a constant square matrix (with arbitrary rank) and [alpha]i(t,y(t))[less-than-or-equals, slant]t for all t and i.For a numerical treatment of this kind of problems, a software tool has been recently developed [6]; this code is called RADAR5 and is based on a suitable extension to delay equations of the 3-stage Radau IIA Runge-Kutta method.The aim of this work is that of illustrating some important topics which are being investigated in order to increase the efficiency of the code. They are mainly relevant to(i) the error control strategies in relation to derivative discontinuities arising in the solutions of delay equations;(ii) the integration of problems with unbounded delays (like the pantograph equation);(iii) the applications to problems with special structure (as those arising from spatial discretization of evolutions PDEs with delays).Several numerical examples will also be shown in order to illustrate some of the topics discussed in the paper.
Efficiency and flexibility using implicit methods within atmosphere dycores
NASA Astrophysics Data System (ADS)
Evans, K. J.; Archibald, R.; Norman, M. R.; Gardner, D. J.; Woodward, C. S.; Worley, P.; Taylor, M.
2016-12-01
A suite of explicit and implicit methods are evaluated for a range of configurations of the shallow water dynamical core within the spectral-element Community Atmosphere Model (CAM-SE) to explore their relative computational performance. The configurations are designed to explore the attributes of each method under different but relevant model usage scenarios including varied spectral order within an element, static regional refinement, and scaling to large problem sizes. The limitations and benefits of using explicit versus implicit, with different discretizations and parameters, are discussed in light of trade-offs such as MPI communication, memory, and inherent efficiency bottlenecks. For the regionally refined shallow water configurations, the implicit BDF2 method is about the same efficiency as an explicit Runge-Kutta method, without including a preconditioner. Performance of the implicit methods with the residual function executed on a GPU is also presented; there is speed up for the residual relative to a CPU, but overwhelming transfer costs motivate moving more of the solver to the device. Given the performance behavior of implicit methods within the shallow water dynamical core, the recommendation for future work using implicit solvers is conditional based on scale separation and the stiffness of the problem. The strong growth of linear iterations with increasing resolution or time step size is the main bottleneck to computational efficiency. Within the hydrostatic dynamical core, of CAM-SE, we present results utilizing approximate block factorization preconditioners implemented using the Trilinos library of solvers. They reduce the cost of linear system solves and improve parallel scalability. We provide a summary of the remaining efficiency considerations within the preconditioner and utilization of the GPU, as well as a discussion about the benefits of a time stepping method that provides converged and stable solutions for a much wider range of time
Implicit methods for computing chemically reacting flow
NASA Astrophysics Data System (ADS)
Li, C. P.
size of the sparse block matrix equations. The implementation of an implicit method in the solution procedure could be as prohibitively expensive as a modified Runge-Kutta method.(2)
Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations
2015-06-23
Outline: Introduction; Governing Equations- Spatial Discretizations, Temporal Discretizations; Von Neumann Analysis; Computational Results- One-dimensional Wave, Three-dimensional Vortex ; Conclusions and Future Work.
A symplectic Runge Kutta Nyström method with minimal phase-lag
NASA Astrophysics Data System (ADS)
van de Vyver, H.
2007-07-01
In this Letter we introduce a symplectic explicit RKN method for Hamiltonian systems with periodical solutions. The method has algebraic order three and phase-lag order six at a cost of three function evaluations per step. Numerical experiments show the relevance of the developed algorithm. It is found that the new method is much more efficient than the standard symplectic fourth-order method [M.P. Calvo, J.M. Sanz-Serna, SIAM J. Sci. Comput. 14 (1993) 936].
Chen, Zhaoxia; Li, Juan; Zhang, Ruqiang; You, Xiong
2015-01-01
Oscillation is one of the most important phenomena in the chemical reaction systems in living cells. The general purpose simulation algorithms fail to take into account this special character and produce unsatisfying results. In order to enhance the accuracy of the integrator, the second-order derivative is incorporated in the scheme. The oscillatory feature of the solution is captured by the integrators with an exponential fitting property. Three practical exponentially fitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRK methods, the two-gene system with cross-regulation and the circadian oscillation of the period protein in Drosophila are simulated. Each EFTDRK method has the best fitting frequency which minimizes the global error. The numerical results show that the new EFTDRK methods are more accurate and more efficient than their prototype TDRK methods or RK methods of the same order and the traditional exponentially fitted RK method in the literature. PMID:26633991
Chen, Zhaoxia; Li, Juan; Zhang, Ruqiang; You, Xiong
2015-01-01
Oscillation is one of the most important phenomena in the chemical reaction systems in living cells. The general purpose simulation algorithms fail to take into account this special character and produce unsatisfying results. In order to enhance the accuracy of the integrator, the second-order derivative is incorporated in the scheme. The oscillatory feature of the solution is captured by the integrators with an exponential fitting property. Three practical exponentially fitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRK methods, the two-gene system with cross-regulation and the circadian oscillation of the period protein in Drosophila are simulated. Each EFTDRK method has the best fitting frequency which minimizes the global error. The numerical results show that the new EFTDRK methods are more accurate and more efficient than their prototype TDRK methods or RK methods of the same order and the traditional exponentially fitted RK method in the literature.
Analysis of numerical stability and amplification matrices: Fourth-order Runge-Kutta methods
NASA Technical Reports Server (NTRS)
Kennedy, E. W.
1979-01-01
Amplification matrices, numerical kernels, stable, and exponentially stable numerical solutions are examined. The various techniques involved in these concepts are applied to certain systems that have Jordan forms, which are nondiagonal, with particular interest in the case of imaginary or zero eigenvalues.
Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations
2015-06-23
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Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations
2015-06-22
tia l D is cr et iz at io ns – Te...se w ith hi gh -o rd er s pa tia l d is cr et iz at io ns 3 D is tr ib ut io n A – A pp ro ve d fo r p ub lic re le as e; D is tr ib ut io...or s fo r 5 th -o rd er sp at ia l s ch em es a re in ad eq ua te – Th e sa m e or de r o f s pa tia l a nd te m po ra l d is cr et iz
NASA Astrophysics Data System (ADS)
Asgharzadeh, Hafez; Borazjani, Iman
2014-11-01
Time step-size restrictions and low convergence rates are major bottle necks for implicit solution of the Navier-Stokes in simulations involving complex geometries with moving boundaries. Newton-Krylov method (NKM) is a combination of a Newton-type method for super-linearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations, which can theoretically address both bottle necks. The efficiency of this method vastly depends on the Jacobian forming scheme e.g. automatic differentiation is very expensive and Jacobian-free methods slow down as the mesh is refined. A novel, computationally efficient analytical Jacobian for NKM was developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered curvilinear grids with immersed boundaries. The NKM was validated and verified against Taylor-Green vortex and pulsatile flow in a 90 degree bend and efficiently handles complex geometries such as an intracranial aneurysm with multiple overset grids, pulsatile inlet flow and immersed boundaries. The NKM method is shown to be more efficient than the semi-implicit Runge-Kutta methods and Jabobian-free Newton-Krylov methods. We believe NKM can be applied to many CFD techniques to decrease the computational cost. This work was supported partly by the NIH Grant R03EB014860, and the computational resources were partly provided by Center for Computational Research (CCR) at University at Buffalo.
Mark, V.; Heilman, K.
1998-01-01
OBJECTIVE—To determine whether stroke patients with diagonal neglect on cancellation may show diagonal neglect on line bisection, and hence to indicate whether diagonal neglect may be related solely to the type of test used or whether instead it may reflect a fundamental spatial disorder. METHODS—Nine patients with subacute right hemispheric stroke who neglected targets primarily in the near left direction on line cancellation bisected diagonal lines of two opposing orientations: near left to far right and far left to near right. The errors were assessed to determine whether line orientation significantly affected bisection error. RESULTS—Eight patients had significant bisection errors. One of these showed no effect of line orientation on error, consistent with lateral neglect. The remaining seven patients had a line orientation effect, indicating a net diagonal spatial bias. For the group, cancellation errors were significantly correlated with the line orientation effect on bisection errors. CONCLUSIONS—A significant diagonal bias on two tests of spatial attention may appear in stroke patients, although the directions of the biases may differ within individual patients. None the less, diagonal neglect may be a fundamental spatial attentional disturbance of right hemispheric stroke. Greater severity of stroke deficit as indicated by cancellation error score may be associated with a greater degree of diagonal neglect on line bisection. PMID:9728947
A variational implementation of the implicit particle filter for the shallow water equations
NASA Astrophysics Data System (ADS)
Souopgui, I.; Morzfeld, M.; Hussaini, M.; Chorin, A. J.
2013-12-01
The estimation of initial conditions for shallow water equations is a well known test problem for operational data assimilation techniques. The state-of-the-art approach to this problem is the variational method (4D-Var), i.e. the computation of the mode of the posterior probability density function (pdf) via the adjoint technique. We add a sampling step to the variational method, thus turning a computation of the conditional mode (a biased estimator) into a computation of the conditional mean (the minimum least square error estimator). Our implementation relies on implicit sampling, which is a Monte Carlo (MC) sampling scheme. The idea in implicit sampling is to first search for the high-probability region of the posterior pdf and then to find samples in this region. Because the samples are concentrated in the high-probability region, fewer samples are required than with competing MC schemes and, thus, implicit sampling can be more efficient than other MC schemes. The search for the high-probability region can be done via a numerical minimization that is very similar to the minimization in 4D-Var. Here, we use existing 4D-Var code to implement the implicit sampling scheme. Once the minimization problem is solved, we obtain samples by solving algebraic equations with a random right-hand-side. These equations can be solved efficiently, so that the additional cost of our approach, compared to 4D-Var, is small. We present numerical experiments to demonstrate the applicability and efficiency of our approach. These numerical experiments mimic physical experiments done with the CORIOLIS turntable in Grenoble (France), which are used to study the drift of a vortex. In particular we consider shallow water equations on a square domain (2.5m x 2.5m) with open boundary conditions and discretize the equations with finite differences on a staggered grid of size 256 x 256 and a fourth order Runge-Kutta time integrator. Our goal is to estimate the initial state (velocities and
Lanczos diagonalization using GPUs
NASA Astrophysics Data System (ADS)
Brouwer, William; J, Sreejith G.; Spiga, Filippo
2013-03-01
Lanczos diagonalization (LD) is an important algorithm for calculating eigenvalues and eigenvectors of large matrices, used in many aspects of condensed matter physics. This presentation details work devoted to exploiting the massive parallelism and scalability of GPUs, in order to enhance LD. One significant application area is the diagonalization of the Hamiltonian for matrices encountered in studies of the fractional quantum Hall effect. A second application discussed in this work is to the Self Consistent Field (SCF) cycle of a Density Functional Theory (DFT) code, Quantum Espresso. Initial results are promising, demonstrating a 18x speedup using GPU, over an optimized CPU implementation.
An improved semi-implicit method for structural dynamics analysis
NASA Technical Reports Server (NTRS)
Park, K. C.
1982-01-01
A semi-implicit algorithm is presented for direct time integration of the structural dynamics equations. The algorithm avoids the factoring of the implicit difference solution matrix and mitigates the unacceptable accuracy losses which plagued previous semi-implicit algorithms. This substantial accuracy improvement is achieved by augmenting the solution matrix with two simple diagonal matrices of the order of the integration truncation error.
NASA Astrophysics Data System (ADS)
Kifonidis, K.; Müller, E.
2012-08-01
Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a
NASA Technical Reports Server (NTRS)
Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.
1994-01-01
It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.
Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows
HyeongKae Park; Robert Nourgaliev; Vincent Mousseau; Dana Knoll
2008-07-01
A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” family of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.
NASA Astrophysics Data System (ADS)
Xia, Yidong
The objective this work is to develop a parallel, implicit reconstructed discontinuous Galerkin (RDG) method using Taylor basis for the solution of the compressible Navier-Stokes equations on 3D hybrid grids. This third-order accurate RDG method is based on a hierarchical weighed essentially non- oscillatory reconstruction scheme, termed as HWENO(P1P 2) to indicate that a quadratic polynomial solution is obtained from the underlying linear polynomial DG solution via a hierarchical WENO reconstruction. The HWENO(P1P2) is designed not only to enhance the accuracy of the underlying DG(P1) method but also to ensure non-linear stability of the RDG method. In this reconstruction scheme, a quadratic polynomial (P2) solution is first reconstructed using a least-squares approach from the underlying linear (P1) discontinuous Galerkin solution. The final quadratic solution is then obtained using a Hermite WENO reconstruction, which is necessary to ensure the linear stability of the RDG method on 3D unstructured grids. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the non-linear stability of the RDG method. The parallelization in the RDG method is based on a message passing interface (MPI) programming paradigm, where the METIS library is used for the partitioning of a mesh into subdomain meshes of approximately the same size. Both multi-stage explicit Runge-Kutta and simple implicit backward Euler methods are implemented for time advancement in the RDG method. In the implicit method, three approaches: analytical differentiation, divided differencing (DD), and automatic differentiation (AD) are developed and implemented to obtain the resulting flux Jacobian matrices. The automatic differentiation is a set of techniques based on the mechanical application of the chain rule to obtain derivatives of a function given as
Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li
2016-01-01
We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. PMID:26911250
Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method (I-SIM)
Robert Nourgaliev; Theo Theofanous; HyeongKae Park; Vincent Mousseau; Dana Knoll
2008-01-01
In recent work (Nourgaliev, Liou, Theofanous, JCP in press) we demonstrated that numerical simulations of interfacial flows in the presence of strong shear must be cast in dynamically sharp terms (sharp interface treatment or SIM), and that moreover they must meet stringent resolution requirements (i.e., resolving the critical layer). The present work is an outgrowth of that work aiming to overcome consequent limitations on the temporal treatment, which become still more severe in the presence of phase change. The key is to avoid operator splitting between interface motion, fluid convection, viscous/heat diffusion and reactions; instead treating all these non-linear operators fully-coupled within a Newton iteration scheme. To this end, the SIM’s cut-cell meshing is combined with the high-orderaccurate implicit Runge-Kutta and the “recovery” Discontinuous Galerkin methods along with a Jacobian-free, Krylov subspace iteration algorithm and its physics-based preconditioning. In particular, the interfacial geometry (i.e., marker’s positions and volumes of cut cells) is a part of the Newton-Krylov solution vector, so that the interface dynamics and fluid motions are fully-(non-linearly)-coupled. We show that our method is: (a) robust (L-stable) and efficient, allowing to step over stability time steps at will while maintaining high-(up to the 5th)-order temporal accuracy; (b) fully conservative, even near multimaterial contacts, without any adverse consequences (pressure/velocity oscillations); and (c) highorder-accurate in spatial discretization (demonstrated here up to the 12th-order for smoothin-the-bulk-fluid flows), capturing interfacial jumps sharply, within one cell. Performance is illustrated with a variety of test problems, including low-Mach-number “manufactured” solutions, shock dynamics/tracking with slow dynamic time scales, and multi-fluid, highspeed shock-tube problems. We briefly discuss preconditioning, and we introduce two physics
NASA Astrophysics Data System (ADS)
Baird, Henry S.; Bentley, Jon L.
2004-12-01
We propose a design methodology for "implicit" CAPTCHAs to relieve drawbacks of present technology. CAPTCHAs are tests administered automatically over networks that can distinguish between people and machines and thus protect web services from abuse by programs masquerading as human users. All existing CAPTCHAs' challenges require a significant conscious effort by the person answering them -- e.g. reading and typing a nonsense word -- whereas implicit CAPTCHAs may require as little as a single click. Many CAPTCHAs distract and interrupt users, since the challenge is perceived as an irrelevant intrusion; implicit CAPTCHAs can be woven into the expected sequence of browsing using cues tailored to the site. Most existing CAPTCHAs are vulnerable to "farming-out" attacks in which challenges are passed to a networked community of human readers; by contrast, implicit CAPTCHAs are not "fungible" (in the sense of easily answerable in isolation) since they are meaningful only in the specific context of the website that is protected. Many existing CAPTCHAs irritate or threaten users since they are obviously tests of skill: implicit CAPTCHAs appear to be elementary and inevitable acts of browsing. It can often be difficult to detect when CAPTCHAs are under attack: implicit CAPTCHAs can be designed so that certain failure modes are correlated with failed bot attacks. We illustrate these design principles with examples.
NASA Astrophysics Data System (ADS)
Baird, Henry S.; Bentley, Jon L.
2005-01-01
We propose a design methodology for "implicit" CAPTCHAs to relieve drawbacks of present technology. CAPTCHAs are tests administered automatically over networks that can distinguish between people and machines and thus protect web services from abuse by programs masquerading as human users. All existing CAPTCHAs' challenges require a significant conscious effort by the person answering them -- e.g. reading and typing a nonsense word -- whereas implicit CAPTCHAs may require as little as a single click. Many CAPTCHAs distract and interrupt users, since the challenge is perceived as an irrelevant intrusion; implicit CAPTCHAs can be woven into the expected sequence of browsing using cues tailored to the site. Most existing CAPTCHAs are vulnerable to "farming-out" attacks in which challenges are passed to a networked community of human readers; by contrast, implicit CAPTCHAs are not "fungible" (in the sense of easily answerable in isolation) since they are meaningful only in the specific context of the website that is protected. Many existing CAPTCHAs irritate or threaten users since they are obviously tests of skill: implicit CAPTCHAs appear to be elementary and inevitable acts of browsing. It can often be difficult to detect when CAPTCHAs are under attack: implicit CAPTCHAs can be designed so that certain failure modes are correlated with failed bot attacks. We illustrate these design principles with examples.
Numerical experiments with an implicit particle filter for the shallow water equations
NASA Astrophysics Data System (ADS)
Souopgui, I.; Chorin, A. J.; Hussaini, M.
2012-12-01
The estimation of initial conditions for the shallow water equations for a given set of later data is a well known test problem for data assimilation codes. A popular approach to this problem is the variational method (4D-Var), i.e. the computation of the mode of the posterior probability density function (pdf) via the adjoint technique. Here, we improve on 4D-Var by computing the conditional mean (the minimum least square error estimator) rather than the mode (a biased estimator) and we do so with implicit sampling, a Monte Carlo (MC) importance sampling method. The idea in implicit sampling is to first search for the high-probability region of the posterior pdf and then to find samples in this region. Because the samples are concentrated in the high-probability region, fewer samples are required than with competing MC schemes. The search for the high-probability region can be implemented by a minimization that is very similar to the minimization in 4D-Var, and we make use of a 4D-Var code in our implementation. The samples are obtained by solving algebraic equations with a random right-hand-side. These equations can be solved efficiently, so that the additional cost of our approach, compared to traditional 4D-Var, is small. The long-term goal is to assimilate experimental data, obtained with the CORIOLIS turntable in Grenoble (France), to study the drift of a vortex. We present results from numerical twin experiments as a first step towards our long-term goal. We discretize the shallow water equations on a square domain (2.5m× 2.5m) using finite differences on a staggered grid of size 28× 28 and a fourth order Runge-Kutta. We assume open boundary conditions and estimate the initial state (velocities and surface height) given noisy observations of the state. We solve the optimization problem using a 4D-Var code that relies on a L-BFGS method; the random algebraic equations are solved with random maps, i.e. we look for solutions in given, but random, directions
Nondestructive identification of the Bell diagonal state
Jin Jiasen; Yu Changshui; Song Heshan
2011-03-15
We propose a scheme for identifying an unknown Bell diagonal state. In our scheme the measurements are performed on the probe qubits instead of the Bell diagonal state. The distinct advantage is that the quantum state of the evolved Bell diagonal state ensemble plus probe states will still collapse on the original Bell diagonal state ensemble after the measurement on probe states; i.e., our identification is quantum state nondestructive. How to realize our scheme in the framework of cavity electrodynamics is also shown.
NASA Technical Reports Server (NTRS)
Rogers, S. E.; Kwak, D.; Chang, J. L. C.
1986-01-01
The method of pseudocompressibility has been shown to be an efficient method for obtaining a steady-state solution to the incompressible Navier-Stokes equations. Recent improvements to this method include the use of a diagonal scheme for the inversion of the equations at each iteration. The necessary transformations have been derived for the pseudocompressibility equations in generalized coordinates. The diagonal algorithm reduces the computing time necessary to obtain a steady-state solution by a factor of nearly three. Implicit viscous terms are maintained in the equations, and it has become possible to use fourth-order implicit dissipation. The steady-state solution is unchanged by the approximations resulting from the diagonalization of the equations. Computed results for flow over a two-dimensional backward-facing step and a three-dimensional cylinder mounted normal to a flat plate are presented for both the old and new algorithms. The accuracy and computing efficiency of these algorithms are compared.
The delayed coupling method: An algorithm for solving banded diagonal matrix problems in parallel
Mattor, N.; Williams, T.J.; Hewett, D.W.; Dimits, A.M.
1997-09-01
We present a new algorithm for solving banded diagonal matrix problems efficiently on distributed-memory parallel computers, designed originally for use in dynamic alternating-direction implicit partial differential equation solvers. The algorithm optimizes efficiency with respect to the number of numerical operations and to the amount of interprocessor communication. This is called the ``delayed coupling method`` because the communication is deferred until needed. We focus here on tridiagonal and periodic tridiagonal systems.
A note on generalized nonlinear diagonal dominance
NASA Astrophysics Data System (ADS)
Gan, Tai-Bin; Huang, Ting-Zhu; Gao, Jian
2006-01-01
In this paper, an open problem, proposed by A. Frommer, about nonlinear generalized diagonal dominance, is solved on some weak restriction, a counterexample is presented if such a restriction is omitted, and some new properties of nonlinear generalized diagonally dominant functions are investigated.
Parallelization of implicit finite difference schemes in computational fluid dynamics
NASA Technical Reports Server (NTRS)
Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel
1990-01-01
Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.
Implicit solvers for unstructured meshes
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, Dimitri J.
1991-01-01
Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.
Diagonal symmetries beyond the standard model
NASA Astrophysics Data System (ADS)
Batra, Puneet
We use diagonal symmetries to address experimental and conceptual shortcomings of theories "Beyond the Standard Model". We first show that embedding the Weak gauge group, SU(2)W, as the diagonal subgroup of a gauged SU(2) x SU(2) symmetry can open up dramatic new regions of parameter space for Supersymmetric models: regions where the CP-even Higgs mass is as large as ˜350 GeV (Chapter 2), where tan beta < 1 (Chapter 3), and where the lightest Higgs state is charged (Chapter 3). In Chapter 4 we show that a Little Higgs theory (with a gauged SU(12) diagonal symmetry) can form the Ultraviolet completion for another Little Higgs theory (with a gauged SU(4) diagonal symmetry). This theory remains perturbative up to 100 TeV and allows for further structural extensions to yet higher cutoffs---all without introducing quadratic instability in the Weak scale.
30. BEARING SHOE / VERTICAL / DIAGONAL / UPPER AND ...
30. BEARING SHOE / VERTICAL / DIAGONAL / UPPER AND LOWER CHORD DETAIL OF DECK TRUSS. VIEW TO NORTHEAST. - Abraham Lincoln Memorial Bridge, Spanning Missouri River on Highway 30 between Nebraska & Iowa, Blair, Washington County, NE
23. INCLINED END POST / VERTICAL / DIAGONAL / PORTAL ...
23. INCLINED END POST / VERTICAL / DIAGONAL / PORTAL BRACING DETAIL. VIEW TO SOUTHEAST. - Abraham Lincoln Memorial Bridge, Spanning Missouri River on Highway 30 between Nebraska & Iowa, Blair, Washington County, NE
Multigrid calculation of three-dimensional turbomachinery flows
NASA Technical Reports Server (NTRS)
Caughey, David A.
1989-01-01
Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.
NASA Astrophysics Data System (ADS)
Graham Hoover, William; Clinton Sprott, Julien; Griswold Hoover, Carol
2016-10-01
We describe the application of adaptive (variable time step) integrators to stiff differential equations encountered in many applications. Linear harmonic oscillators subject to nonlinear thermal constraints can exhibit either stiff or smooth dynamics. Two closely related examples, Nosé's dynamics and Nosé-Hoover dynamics, are both based on Hamiltonian mechanics and generate microstates consistent with Gibbs' canonical ensemble. Nosé's dynamics is stiff and can present severe numerical difficulties. Nosé-Hoover dynamics, although it follows exactly the same trajectory, is smooth and relatively trouble-free. We emphasize the power of adaptive integrators to resolve stiff problems such as the Nosé dynamics for the harmonic oscillator. The solutions also illustrate the power of computer graphics to enrich numerical solutions.
1980-10-01
shortcut is available; note that on the right-hand side of Equation (26) the first term leads to Eular Convolution and the second to Mean Value...Convolution. Eular Convolution and Mean Value Convolution are just special cases of R-K(2,a) Convolution (see Table 2). TABLE 2. SPECIAL CASES OF R-K(2,a)C...Convolution Eular 0 Mean Value for 1/2 1/2 Trapezoidal I For a single real pole filter, F(s) - 1 (28) and any input, G(s), the approximation using R-K(2
Implicit Causality, Implicit Consequentiality and Semantic Roles
ERIC Educational Resources Information Center
Crinean, Marcelle; Garnham, Alan
2006-01-01
Stewart, Pickering, and Sanford (1998) reported a new type of semantic inference, implicit consequentiality, which they suggest is comparable to, although not directly related to, the well-documented phenomenon of implicit causality. It is our contention that there is a direct relation between these two semantic phenomena but that this relation…
Implicit Causality, Implicit Consequentiality and Semantic Roles
ERIC Educational Resources Information Center
Crinean, Marcelle; Garnham, Alan
2006-01-01
Stewart, Pickering, and Sanford (1998) reported a new type of semantic inference, implicit consequentiality, which they suggest is comparable to, although not directly related to, the well-documented phenomenon of implicit causality. It is our contention that there is a direct relation between these two semantic phenomena but that this relation…
NASA Astrophysics Data System (ADS)
Wu, Lingfei; Laeuchli, Jesse; Kalantzis, Vassilis; Stathopoulos, Andreas; Gallopoulos, Efstratios
2016-12-01
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the evaluation of the function is expensive, the task is computationally challenging because the standard approach is based on a Monte Carlo method which converges slowly. We present a different approach that exploits the pattern correlation, if present, between the diagonal of the inverse of the matrix and the diagonal of some approximate inverse that can be computed inexpensively. We leverage various sampling and fitting techniques to fit the diagonal of the approximation to the diagonal of the inverse. Depending on the quality of the approximate inverse, our method may serve as a standalone kernel for providing a fast trace estimate with a small number of samples. Furthermore, the method can be used as a variance reduction method for Monte Carlo in some cases. This is decided dynamically by our algorithm. An extensive set of experiments with various technique combinations on several matrices from some real applications demonstrate the potential of our method.
Diagonal chromatography to study plant protein modifications.
Walton, Alan; Tsiatsiani, Liana; Jacques, Silke; Stes, Elisabeth; Messens, Joris; Van Breusegem, Frank; Goormachtig, Sofie; Gevaert, Kris
2016-08-01
An interesting asset of diagonal chromatography, which we have introduced for contemporary proteome research, is its high versatility concerning proteomic applications. Indeed, the peptide modification or sorting step that is required between consecutive peptide separations can easily be altered and thereby allows for the enrichment of specific, though different types of peptides. Here, we focus on the application of diagonal chromatography for the study of modifications of plant proteins. In particular, we show how diagonal chromatography allows for studying proteins processed by proteases, protein ubiquitination, and the oxidation of protein-bound methionines. We discuss the actual sorting steps needed for each of these applications and the obtained results. This article is part of a Special Issue entitled: Plant Proteomics--a bridge between fundamental processes and crop production, edited by Dr. Hans-Peter Mock. Copyright © 2016 Elsevier B.V. All rights reserved.
Diagonal piezoelectric sensors on cylindrical shells
NASA Astrophysics Data System (ADS)
Li, Hua; Zhang, Xufang; Tzou, Hornsen
2017-07-01
Piezoelectric sensors are effective for distributed health monitoring and sensing of structures. The signals of piezoelectric sensors are related to the orientation of the sensors. In this study, a diagonal piezoelectric sensor is proposed for cylindrical shells. The sensor is made of a rectangular piezoelectric patch and diagonally attached on the shell surface; and piezoelectric actuators are used for excitation. An analytical model of the sensor is derived based on thin shell assumption with simply-supported boundary conditions. The orientation angle of the piezoelectric sensor is introduced as an independent variable. The proposed model consists of an integral term over the electrode area, which is divided into three regions for calculation. The sensing signal is decomposed into six components to evaluate the contributions of the strain components. Case studies on signals with respect to the orientation and aspect ratios are accomplished. The cylindrical shell with piezoelectric actuators and diagonal sensors is fabricated and tested under laboratory condition. Comparison of theoretical results with experimental data is conducted, and the model of the diagonal sensors is validated. The errors between the predictions and experimental results are less than 10% for all evaluated modes.
Time integration algorithms for the two-dimensional Euler equations on unstructured meshes
NASA Technical Reports Server (NTRS)
Slack, David C.; Whitaker, D. L.; Walters, Robert W.
1994-01-01
Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.
Time integration algorithms for the two-dimensional Euler equations on unstructured meshes
NASA Astrophysics Data System (ADS)
Slack, David C.; Whitaker, D. L.; Walters, Robert W.
1994-06-01
Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.
The diagonal and off-diagonal quark number susceptibility of high temperature and finite density QCD
NASA Astrophysics Data System (ADS)
Hietanen, A.; Rummukainen, K.
2008-04-01
We study the quark number susceptibility of the hot quark-gluon plasma at zero and non-zero quark number density, using lattice Monte Carlo simulations of an effective theory of QCD, electrostatic QCD (EQCD). Analytic continuation is used to obtain results at non-zero quark chemical potential μ. We measure both flavor singlet (diagonal) and non-singlet (off-diagonal) quark number susceptibilities. The diagonal susceptibility approaches the perturbative result above ~ 20Tc, but below that temperature we observe significant deviations. The results agree well with 4d lattice data down to temperatures ~ 2Tc. The off-diagonal susceptibility is more prone to statistical and systematic errors, but the results are consistent with perturbation theory already at 10Tc.
Diagonalizing sensing matrix of broadband RSE
NASA Astrophysics Data System (ADS)
Sato, Shuichi; Kokeyama, Keiko; Kawazoe, Fumiko; Somiya, Kentaro; Kawamura, Seiji
2006-03-01
For a broadband-operated RSE interferometer, a simple and smart length sensing and control scheme was newly proposed. The sensing matrix could be diagonal, owing to a simple allocation of two RF modulations and to a macroscopic displacement of cavity mirrors, which cause a detuning of the RF modulation sidebands. In this article, the idea of the sensing scheme and an optimization of the relevant parameters will be described.
Spontaneous inferences, implicit impressions, and implicit theories.
Uleman, James S; Adil Saribay, S; Gonzalez, Celia M
2008-01-01
People make social inferences without intentions, awareness, or effort, i.e., spontaneously. We review recent findings on spontaneous social inferences (especially traits, goals, and causes) and closely related phenomena. We then describe current thinking on some of the most relevant processes, implicit knowledge, and theories. These include automatic and controlled processes and their interplay; embodied cognition, including mimicry; and associative versus rule-based processes. Implicit knowledge includes adult folk theories, conditions of personhood, self-knowledge to simulate others, and cultural and social class differences. Implicit theories concern Bayesian networks, recent attribution research, and questions about the utility of the disposition-situation dichotomy. Developmental research provides new insights. Spontaneous social inferences include a growing array of phenomena, but they have been insufficiently linked to other phenomena and theories. We hope the links suggested in this review begin to remedy this.
Langdon, A.B.
1985-03-03
Implicit time integration methods have been used extensively in numerical modelling of slowly varying phenomena in systems that also support rapid variation. Examples include diffusion, hydrodynamics and reaction kinetics. This article discussed implementation of implicit time integration in plasma codes of the ''particle-in-cell'' family, and the benefits to be gained.
Investigations on the Incompletely Developed Plane Diagonal-Tension Field
NASA Technical Reports Server (NTRS)
Kuhn, Paul
1940-01-01
This report presents the results of an investigation on the incompletely developed diagonal-tension field. Actual diagonal-tension beams work in an intermediate stage between pure shear and pure diagonal tension; the theory developed by wagner for diagonal tension is not directly applicable. The first part of the paper reviews the most essential items of the theory of pure diagonal tension as well as previous attempts to formulate a theory of incomplete diagonal tension. The second part of the paper describes strain measurement made by the N. A. C. A. to obtain the necessary coefficients for the proposed theory. The third part of the paper discusses the stress analysis of diagonal-tension beams by means of the proposed theory.
NASA Technical Reports Server (NTRS)
Skliar, M.; Ramirez, W. F.
1997-01-01
For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.
NASA Astrophysics Data System (ADS)
Chen, Yang; Zou, Ling; Zhou, Bin
2017-07-01
The high mounting precision of the fiber underwater acoustic array leads to an array manifold without perturbation. Besides, the targets are either static or slowly moving in azimuth in underwater acoustic array signal processing. Therefore, the covariance matrix can be estimated accurately by prolonging the observation time. However, this processing is limited to poor bearing resolution due to small aperture, low SNR and strong interferences. In this paper, diagonal rejection (DR) technology for Minimum Variance Distortionless Response (MVDR) was developed to enhance the resolution performance. The core idea of DR is rejecting the main diagonal elements of the covariance matrix to improve the output signal to interference and noise ratio (SINR). The definition of SINR here implicitly assumes independence between the spatial filter and the received observations at which the SINR is measured. The power of noise converges on the diagonal line in the covariance matrix and then it is integrated into the output beams. With the diagonal noise rejected by a factor smaller than 1, the array weights of MVDR will concentrate on interference suppression, leading to a better resolution capability. The algorithm was theoretically proved with optimal rejecting coefficient derived under both infinite and finite snapshots scenarios. Numerical simulations were conducted with an example of a linear array with eight elements half-wavelength spaced. Both resolution and Direction-of-Arrival (DOA) performances of MVDR and DR-based MVDR (DR-MVDR) were compared under different SNR and snapshot numbers. A conclusion can be drawn that with the covariance matrix accurately estimated, DR-MVDR can provide a lower sidelobe output level and a better bearing resolution capacity than MVDR without harming the DOA performance.
Diagonal gates in the Clifford hierarchy
NASA Astrophysics Data System (ADS)
Cui, Shawn X.; Gottesman, Daniel; Krishna, Anirudh
2017-01-01
The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characterization of the diagonal gates in the Clifford hierarchy for prime-dimensional qudits. They turn out to be pmth roots of unity raised to polynomial functions of the basis state to which they are applied, and we determine which level of the Clifford hierarchy a given gate sits in based on m and the degree of the polynomial.
Awareness of Implicit Attitudes
Hahn, Adam; Judd, Charles M.; Hirsh, Holen K.; Blair, Irene V.
2013-01-01
Research on implicit attitudes has raised questions about how well people know their own attitudes. Most research on this question has focused on the correspondence between measures of implicit attitudes and measures of explicit attitudes, with low correspondence interpreted as showing that people have little awareness of their implicit attitudes. We took a different approach and directly asked participants to predict their results on upcoming IAT measures of implicit attitudes toward five different social groups. We found that participants were surprisingly accurate in their predictions. Across four studies, predictions were accurate regardless of whether implicit attitudes were described as true attitudes or culturally learned associations (Studies 1 and 2), regardless of whether predictions were made as specific response patterns (Study 1) or as conceptual responses (Studies 2–4), and regardless of how much experience or explanation participants received before making their predictions (Study 4). Study 3 further suggested that participants’ predictions reflected unique insight into their own implicit responses, beyond intuitions about how people in general might respond. Prediction accuracy occurred despite generally low correspondence between implicit and explicit measures of attitudes, as found in prior research. All together, the research findings cast doubt on the belief that attitudes or evaluations measured by the IAT necessarily reflect unconscious attitudes. PMID:24294868
NASA Astrophysics Data System (ADS)
Zainuddin, N.; Ibrahim, Z. B.; Othman, K. I.
2014-10-01
The three point block method for solving second order ordinary differential equations (ODEs) directly using constant step size is derived. The reliability of this new method is verified in the numerical results with the improved performance in terms of computation time while maintaining the accuracy. The comparison is presented between the new method and classical backward differentiation formulas (BDF) of order 3.
A Finite-Element Approach for Modeling Inviscid and Viscous Compressible Flows using Prismatic Grids
NASA Technical Reports Server (NTRS)
Pandya, S. A.; Hefez, M.
2000-01-01
The Galerkin finite-element method is used to solve the Euler and Navier-Stokes equations on prismatic meshes. It is shown that the prismatic grid is advantageous for correctly and efficiently capturing the boundary layers in high Reynolds number flows. It can be captured accurately because of the ability to cluster grid points normal to the body. The efficiency derives from the implicit treatment of the normal direction. To treat the normal direction implicitly, a semi-implicit Runge-Kutta time stepping scheme is developed. The semi-implicit algorithm is validated on simple geometries for inviscid and viscous flows and its convergence history is compared to that of the explicit Runge-Kutta scheme. The semi-implicit scheme is shown to be a factor of 3 to 4 faster in terms of CPU time to convergence.
Implicit Cognition and Spelling Development.
ERIC Educational Resources Information Center
Steffler, Dorothy J.
2001-01-01
Addresses how existing theories of implicit cognition may contribute to the understanding of spelling development. Reviews adult literature on implicit memory and implicit learning that may be applied to spelling development. Presents a multilevel model of representational redescription from which to investigate the interrelation of implicit and…
Electromagnetic direct implicit PIC simulation
Langdon, A.B.
1983-03-29
Interesting modelling of intense electron flow has been done with implicit particle-in-cell simulation codes. In this report, the direct implicit PIC simulation approach is applied to simulations that include full electromagnetic fields. The resulting algorithm offers advantages relative to moment implicit electromagnetic algorithms and may help in our quest for robust and simpler implicit codes.
An Ancient Egyptian Diagonal Star Table in Mallawi, Egypt
NASA Astrophysics Data System (ADS)
Symons, Sarah; Cockcroft, Robert
2013-11-01
A coffin belonging to an Egyptian Middle Kingdom official Hor-em-hetepu, on public display in the Mallawi Monuments Museum, Egypt, contains a previously-unpublished diagonal star table (or "diagonal star clock"). This table adds to the other twenty-four examples of this type of astronomical record or calendar from around 2100 B.C. The table displays a regular diagonal pattern of decan (star or asterism) names, with some interesting points of content, epigraphy, and typology.
Probabilities in implicit learning.
Tseng, Philip; Hsu, Tzu-Yu; Tzeng, Ovid J L; Hung, Daisy L; Juan, Chi-Hung
2011-01-01
The visual system possesses a remarkable ability in learning regularities from the environment. In the case of contextual cuing, predictive visual contexts such as spatial configurations are implicitly learned, retained, and used to facilitate visual search-all without one's subjective awareness and conscious effort. Here we investigated whether implicit learning and its facilitatory effects are sensitive to the statistical property of such implicit knowledge. In other words, are highly probable events learned better than less probable ones even when such learning is implicit? We systematically varied the frequencies of context repetition to alter the degrees of learning. Our results showed that search efficiency increased consistently as contextual probabilities increased. Thus, the visual contexts, along with their probability of occurrences, were both picked up by the visual system. Furthermore, even when the total number of exposures was held constant between each probability, the highest probability still enjoyed a greater cuing effect, suggesting that the temporal aspect of implicit learning is also an important factor to consider in addition to the effect of mere frequency. Together, these findings suggest that implicit learning, although bypassing observers' conscious encoding and retrieval effort, behaves much like explicit learning in the sense that its facilitatory effect also varies as a function of its associative strengths.
Diagonal-norm upwind SBP operators
NASA Astrophysics Data System (ADS)
Mattsson, Ken
2017-04-01
High-order accurate first derivative finite difference operators are derived that naturally introduce artificial dissipation. The boundary closures are based on the diagonal-norm summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability for a large class of initial boundary value problems. These novel first derivative SBP operators have a non-central difference stencil in the interior, and come in pairs (for each order of accuracy). The resulting SBP-SAT approximations lead to fully explicit ODE systems. The accuracy and stability properties are demonstrated for linear first- and second-order hyperbolic problems in 1D, and for the compressible Euler equations in 2D. The newly derived first derivative SBP operators lead to significantly more robust and accurate numerical approximations, compared with the exclusive usage of (previously derived central) non-dissipative first derivative SBP operators.
Universal single level implicit algorithm for gasdynamics
NASA Technical Reports Server (NTRS)
Lombard, C. K.; Venkatapthy, E.
1984-01-01
A single level effectively explicit implicit algorithm for gasdynamics is presented. The method meets all the requirements for unconditionally stable global iteration over flows with mixed supersonic and supersonic zones including blunt body flow and boundary layer flows with strong interaction and streamwise separation. For hyperbolic (supersonic flow) regions the method is automatically equivalent to contemporary space marching methods. For elliptic (subsonic flow) regions, rapid convergence is facilitated by alternating direction solution sweeps which bring both sets of eigenvectors and the influence of both boundaries of a coordinate line equally into play. Point by point updating of the data with local iteration on the solution procedure at each spatial step as the sweeps progress not only renders the method single level in storage but, also, improves nonlinear accuracy to accelerate convergence by an order of magnitude over related two level linearized implicit methods. The method derives robust stability from the combination of an eigenvector split upwind difference method (CSCM) with diagonally dominant ADI(DDADI) approximate factorization and computed characteristic boundary approximations.
7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL ...
7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 522 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV
6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...
6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2502 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV
4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...
4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 270t EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV
3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...
3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 2742 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV
2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 ...
2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2932 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV
5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...
5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 323' EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV
1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 ...
1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE WEST GATE ROAD CULVERT, LOOKING 3052 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV
15. View showing junction of compression diagonal, vertical member, tension ...
15. View showing junction of compression diagonal, vertical member, tension diagonal, and lower chord members between 5th and 6th panels from north end of north span, looking from the east - Bridge No. 4900, Spanning Root River at Trunk Highway 16, Rushford, Fillmore County, MN
Optimization of fuzzy logic analysis by diagonals for pattern recognition
NASA Astrophysics Data System (ADS)
Habiballa, Hashim; Hires, Matej
2017-07-01
The article presents an optimization of the fuzzy logic analysis method for pattern recognition. The enhancements of the original method through the usage of additional two types of pattern components - leftwise diagonal and rightwise diagonal ones. The method is described in theoretical background and further articles show the implementation and experimental verification of the approach.
Panel Post & Diagonal Brace Joint Detail; Crossbracing Center Joint ...
Panel Post & Diagonal Brace Joint Detail; Crossbracing Center Joint Detail; Chord, Panel Post, Tie Bar, & Diagonal Brace Joint Detail; Chord, Tie Bar, & Crossbracing Joint Detail - Medora Bridge, Spanning East Fork of White River at State Route 235, Medora, Jackson County, IN
16. View of riveted gusset plate connection between compression diagonal, ...
16. View of riveted gusset plate connection between compression diagonal, tension diagonal, and lateral brace at center of 4th panel from north end of west truss of north span, looking from the east - Bridge No. 4900, Spanning Root River at Trunk Highway 16, Rushford, Fillmore County, MN
NASA Technical Reports Server (NTRS)
Bardina, Jorge; Lombard, C. K.
1987-01-01
The Bardina and Lombard (1985) three-dimensional CSCM Navier-Stokes method is presently extended to the simulation of complex hypersonic reentry vehicle external flows at angle of attack. The robust stability of the method derives from the combination of conservative implicit upwind flux difference splitting with a three-dimensional diagonally-dominant approximate factorization and relaxation scheme and characteristic-based implicit boundary approximations. The method's efficiency derives from an implicit symmetric Gauss-Seidel 'method of planes' relaxation scheme with alternating directional space marching sweeps along the flow coordinate direction.
Implicit Attitudes in Prosopagnosia
Knutson, Kristine M.; DeTucci, Karen A.; Grafman, Jordan
2011-01-01
We studied a male with acquired prosopagnosia using a battery of implicit association tests (IATs) to investigate whether observing faces varying by social category would activate the patient’s implicit social biases. We also asked him to categorize faces explicitly by race, gender, and political party. The patient, G.B., was marginally slower to categorize black compared to white faces. He showed congruency effects in the race and celebrity IATs, but not in the gender or political IATs. These results indicate that G.B. possesses an implicit social sensitivity to certain facial stimuli despite an inability to overtly recognize familiar faces. The results demonstrate that social biases can be retrieved based on facial stimuli via pathways bypassing the fusiform gyri. Thus the IAT effect can be added to the list of covert recognition effects found in prosopagnosia. PMID:21414330
Devos, Thierry; Banaji, Mahzarin R
2003-10-01
Recent advances in research on implicit social cognition offer an opportunity to challenge common assumptions about self and identity. In the present article, we critically review a burgeoning line of research on self-related processes known to occur outside conscious awareness or conscious control. Our discussion focuses on these implicit self-related processes as they unfold in the context of social group memberships. That is, we show that group memberships can shape thoughts, preferences, motives, goals, or behaviors without the actor's being aware of such an influence or having control over such expressions. As such, this research brings to the fore facets of the self that often contrast with experiences of reflexive consciousness and introspection. Far from being rigid or monolithic, these processes are highly flexible, context-sensitive, and deeply rooted in socio-structural realities. As such, work on implicit self and identity renew thinking about the interplay between the individual and the collective.
Solving block linear systems with low-rank off-diagonal blocks is easily parallelizable
Menkov, V.
1996-12-31
An easily and efficiently parallelizable direct method is given for solving a block linear system Bx = y, where B = D + Q is the sum of a non-singular block diagonal matrix D and a matrix Q with low-rank blocks. This implicitly defines a new preconditioning method with an operation count close to the cost of calculating a matrix-vector product Qw for some w, plus at most twice the cost of calculating Qw for some w. When implemented on a parallel machine the processor utilization can be as good as that of those operations. Order estimates are given for the general case, and an implementation is compared to block SSOR preconditioning.
Adventures with Implicit Methods
NASA Technical Reports Server (NTRS)
Warming, Robert F.; Beam, Richard M.; Kwak, Dochan (Technical Monitor)
1997-01-01
In this lecture we trace the historical developments of alternating direction implicit methods. In particular, we emphasize contributions originating in the Computational Fluid Dynamics Branch at Ames Research Center in the 1970's and early 1980's. Joe Steger played a seminal role in demonstrating the practicality of using an efficient, vectorized, implicit code for solving the compressible Navier-Stokes equations. Numerous discussions with Joe had a significant impact on our own research and it is a pleasure to dedicate this lecture to honor his memory.
Numerical Aspects of Atomic Physics: Helium Basis Sets and Matrix Diagonalization
NASA Astrophysics Data System (ADS)
Jentschura, Ulrich; Noble, Jonathan
2014-03-01
We present a matrix diagonalization algorithm for complex symmetric matrices, which can be used in order to determine the resonance energies of auto-ionizing states of comparatively simple quantum many-body systems such as helium. The algorithm is based in multi-precision arithmetic and proceeds via a tridiagonalization of the complex symmetric (not necessarily Hermitian) input matrix using generalized Householder transformations. Example calculations involving so-called PT-symmetric quantum systems lead to reference values which pertain to the imaginary cubic perturbation (the imaginary cubic anharmonic oscillator). We then proceed to novel basis sets for the helium atom and present results for Bethe logarithms in hydrogen and helium, obtained using the enhanced numerical techniques. Some intricacies of ``canned'' algorithms such as those used in LAPACK will be discussed. Our algorithm, for complex symmetric matrices such as those describing cubic resonances after complex scaling, is faster than LAPACK's built-in routines, for specific classes of input matrices. It also offer flexibility in terms of the calculation of the so-called implicit shift, which is used in order to ``pivot'' the system toward the convergence to diagonal form. We conclude with a wider overview.
Implicit Understanding of Belief.
ERIC Educational Resources Information Center
Clements, Wendy A.; Perner, Josef
1994-01-01
Implicit understanding of false belief was investigated by monitoring where preschoolers looked in anticipation of a protagonist reappearing, when the protagonist mistakenly thinks that his desired object is in a different place from where it really is. Two-year olds erroneously looked at the object's real location whereas most older children…
Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes
NASA Technical Reports Server (NTRS)
Marx, Yves P.
1990-01-01
An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.
A multigrid nonoscillatory method for computing high speed flows
NASA Technical Reports Server (NTRS)
Li, C. P.; Shieh, T. H.
1993-01-01
A multigrid method using different smoothers has been developed to solve the Euler equations discretized by a nonoscillatory scheme up to fourth order accuracy. The best smoothing property is provided by a five-stage Runge-Kutta technique with optimized coefficients, yet the most efficient smoother is a backward Euler technique in factored and diagonalized form. The singlegrid solution for a hypersonic, viscous conic flow is in excellent agreement with the solution obtained by the third order MUSCL and Roe's method. Mach 8 inviscid flow computations for a complete entry probe have shown that the accuracy is at least as good as the symmetric TVD scheme of Yee and Harten. The implicit multigrid method is four times more efficient than the explicit multigrid technique and 3.5 times faster than the single-grid implicit technique. For a Mach 8.7 inviscid flow over a blunt delta wing at 30 deg incidence, the CPU reduction factor from the three-level multigrid computation is 2.2 on a grid of 37 x 41 x 73 nodes.
Implicit Learning as an Ability
ERIC Educational Resources Information Center
Kaufman, Scott Barry; DeYoung, Caroline G.; Gray, Jeremy R.; Jimenez, Luis; Brown, Jamie; Mackintosh, Nicholas
2010-01-01
The ability to automatically and implicitly detect complex and noisy regularities in the environment is a fundamental aspect of human cognition. Despite considerable interest in implicit processes, few researchers have conceptualized implicit learning as an ability with meaningful individual differences. Instead, various researchers (e.g., Reber,…
Implicit Learning as an Ability
ERIC Educational Resources Information Center
Kaufman, Scott Barry; DeYoung, Caroline G.; Gray, Jeremy R.; Jimenez, Luis; Brown, Jamie; Mackintosh, Nicholas
2010-01-01
The ability to automatically and implicitly detect complex and noisy regularities in the environment is a fundamental aspect of human cognition. Despite considerable interest in implicit processes, few researchers have conceptualized implicit learning as an ability with meaningful individual differences. Instead, various researchers (e.g., Reber,…
Diagonal dominance using function minimization algorithms. [multivariable control system design
NASA Technical Reports Server (NTRS)
Leininger, G. G.
1977-01-01
A new approach to the design of multivariable control systems using the inverse Nyquist array method is proposed. The technique utilizes a conjugate direction function minimization algorithm to achieve dominance over a specified frequency range by minimizing the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal term of the inverse open loop transfer function matrix. The technique is easily implemented in either a batch or interactive computer mode and will yield diagonalization when previously suggested methods fail. The proposed method has been successfully applied to design a control system for a sixteenth order state model of the F-100 turbofan engine with three inputs.
Separability of three qubit Greenberger–Horne–Zeilinger diagonal states
NASA Astrophysics Data System (ADS)
Han, Kyung Hoon; Kye, Seung-Hyeok
2017-04-01
We characterize the separability of three qubit GHZ diagonal states in terms of entries. This enables us to check separability of GHZ diagonal states without decomposition into the sum of pure product states. In the course of discussion, we show that the necessary criterion of Gühne (2011 Entanglement criteria and full separability of multi-qubit quantum states Phys. Lett. A 375 406–10) for (full) separability of three qubit GHZ diagonal states is sufficient with a simpler formula. The main tool is to use entanglement witnesses which are tri-partite Choi matrices of positive bi-linear maps.
Classical limit of diagonal form factors and HHL correlators
NASA Astrophysics Data System (ADS)
Bajnok, Zoltan; Janik, Romuald A.
2017-01-01
We propose an expression for the classical limit of diagonal form factors in which we integrate the corresponding observable over the moduli space of classical solutions. In infinite volume the integral has to be regularized by proper subtractions and we present the one, which corresponds to the classical limit of the connected diagonal form factors. In finite volume the integral is finite and can be expressed in terms of the classical infinite volume diagonal form factors and subvolumes of the moduli space. We analyze carefully the periodicity properties of the finite volume moduli space and found a classical analogue of the Bethe-Yang equations. By applying the results to the heavy-heavy-light three point functions we can express their strong coupling limit in terms of the classical limit of the sine-Gordon diagonal form factors.
33. Coal Fuel Elevator (diagonal in foreground), Fuel Elevator (left), ...
33. Coal Fuel Elevator (diagonal in foreground), Fuel Elevator (left), Fuel Storage Bins (center), and Power Plant (right) Photographs taken by Joseph E.B. Elliot - Huber Coal Breaker, 101 South Main Street, Ashley, Luzerne County, PA
21. DIAGONAL VIEW OF THE 48' MILL STEAM ENGINE. SPARE ...
21. DIAGONAL VIEW OF THE 48' MILL STEAM ENGINE. SPARE VERTICAL ROLLS ARE VISIBLE TO THE LEFT AND RIGHT OF THE ENGINE. - U.S. Steel Homestead Works, 48" Plate Mill, Along Monongahela River, Homestead, Allegheny County, PA
31. DETAIL OF DIAGONAL REINFORCING RODS TYPICAL OF FLOORS IN ...
31. DETAIL OF DIAGONAL REINFORCING RODS TYPICAL OF FLOORS IN CLASSROOMS AT NORTH PORTIONS OF EAST AND WEST WINGS - Frederika Bremer Intermediate School, 1214 Lowry Avenue North, Minneapolis, Hennepin County, MN
19. Typical lower chord tension member, vertical lattice and diagonal ...
19. Typical lower chord tension member, vertical lattice and diagonal eye bat pinning. View is at north side of 3rd span looking west. - Cleves Bridge, Spanning Great Miami River on U.S. Highway 50, Cleves, Hamilton County, OH
4. LOOKING SOUTHWEST AT LATTICED GUARDRAIL, DIAGONALS, ASPHALT DECK AND ...
4. LOOKING SOUTHWEST AT LATTICED GUARDRAIL, DIAGONALS, ASPHALT DECK AND LACED ANGLES ON VERTICALS - Wayne County Bridge No. 122, Spanning West Fork Whitewater River at Main Street, Milton, Wayne County, IN
Detail view of turnbuckle in diagonal member, with kodachrome film ...
Detail view of turnbuckle in diagonal member, with kodachrome film box on right turnbuckle for scale. - Pennsylvania Railroad, Whitford Bridge, Spanning Amtrak tracks at Whitford Road, Whitford, Chester County, PA
52. Fixed Span, Top Chord at Panel Point 6; diagonal ...
52. Fixed Span, Top Chord at Panel Point 6; diagonal member goes to intermediate connection 7 & then to bottom chord at 8; looking ESE. - Pacific Shortline Bridge, U.S. Route 20,spanning Missouri River, Sioux City, Woodbury County, IA
8. DETAIL VIEW OF TOP CHORD, DIAGONALS, VERTICAL MEMBERS, BOTTOM ...
8. DETAIL VIEW OF TOP CHORD, DIAGONALS, VERTICAL MEMBERS, BOTTOM CHORD, FLOOR BEAMS AND STRINGERS - Northfield Parker Truss Bridge, Over tracks of Central Vermont Railroad, Northfield, Washington County, VT
11. DETAIL OF BRIDGE DECK, SHOWING UPPER CHORDS, VERTICALS, DIAGONALS ...
11. DETAIL OF BRIDGE DECK, SHOWING UPPER CHORDS, VERTICALS, DIAGONALS AND GUARDRAILS. VIEW TO WEST. - Whispering Pines Bridge, Spanning East Verde River at Forest Service Control Road, Payson, Gila County, AZ
28. DETAIL OF DOUBLE DOORS SHOWING CROSS BRACING AND DIAGONAL ...
28. DETAIL OF DOUBLE DOORS SHOWING CROSS BRACING AND DIAGONAL TONGUE AND GROOVE SHEATHING; NOTE PILOT DOOR AT LOWER RIGHTHAND CORNER - Fort Lewis, Locomotive Shelter, South side of South Drive, DuPont, Pierce County, WA
13. Detail of connection of end portal, top chord, diagonal, ...
13. Detail of connection of end portal, top chord, diagonal, vertical and portal strut. Looking at east end, north side of east span. - Boomershine Bridge, Spanning Twin Creek, Farmersville, Montgomery County, OH
15. VIEW NORTHWEST, WEST TRUSS, DETAIL OF TOP CHORD, DIAGONAL ...
15. VIEW NORTHWEST, WEST TRUSS, DETAIL OF TOP CHORD, DIAGONAL MEMBER, AND VERTICAL MEMBER - Osborn Avenue Bridge, Spanning New Jersey Transit Raritan Valley Line at Tuttle Parkway (formerly Osborn Avenue), Westfield, Union County, NJ
13. VIEW OF TOP CHORD CONNECTION, SHOWING DIAGONAL AND VERTICAL ...
13. VIEW OF TOP CHORD CONNECTION, SHOWING DIAGONAL AND VERTICAL WEB MEMBERS AND TOP LATERAL BRACING, SOUTHEAST SPAN, LOOKING NORTHEAST - Linden Avenue Bridge, Spanning Purgatoire River on Linden Avenue, Trinidad, Las Animas County, CO
Detail of diagonal end post support bracket mounted to east ...
Detail of diagonal end post support bracket mounted to east face of track girder, east span. View south - New York, New Haven & Hartford Railroad, Fort Point Channel Rolling Lift Bridge, Spanning Fort Point Channel, Boston, Suffolk County, MA
15. DETAIL OF TOP CHORD, SECONDARY VERTICAL POST, DIAGONAL MEMBERS, ...
15. DETAIL OF TOP CHORD, SECONDARY VERTICAL POST, DIAGONAL MEMBERS, AND TOP LATERAL CONNECTION ON WEST SIDE OF TRUSS, VIEW NORTHWEST - Shaytown Road Bridge, Spanning Thornapple River, Vermontville, Eaton County, MI
Discriminative Block-Diagonal Representation Learning for Image Recognition.
Zhang, Zheng; Xu, Yong; Shao, Ling; Yang, Jian
2017-07-04
Existing block-diagonal representation studies mainly focuses on casting block-diagonal regularization on training data, while only little attention is dedicated to concurrently learning both block-diagonal representations of training and test data. In this paper, we propose a discriminative block-diagonal low-rank representation (BDLRR) method for recognition. In particular, the elaborate BDLRR is formulated as a joint optimization problem of shrinking the unfavorable representation from off-block-diagonal elements and strengthening the compact block-diagonal representation under the semisupervised framework of LRR. To this end, we first impose penalty constraints on the negative representation to eliminate the correlation between different classes such that the incoherence criterion of the extra-class representation is boosted. Moreover, a constructed subspace model is developed to enhance the self-expressive power of training samples and further build the representation bridge between the training and test samples, such that the coherence of the learned intraclass representation is consistently heightened. Finally, the resulting optimization problem is solved elegantly by employing an alternative optimization strategy, and a simple recognition algorithm on the learned representation is utilized for final prediction. Extensive experimental results demonstrate that the proposed method achieves superb recognition results on four face image data sets, three character data sets, and the 15 scene multicategories data set. It not only shows superior potential on image recognition but also outperforms the state-of-the-art methods.
Implicit learning as an ability.
Kaufman, Scott Barry; Deyoung, Colin G; Gray, Jeremy R; Jiménez, Luis; Brown, Jamie; Mackintosh, Nicholas
2010-09-01
The ability to automatically and implicitly detect complex and noisy regularities in the environment is a fundamental aspect of human cognition. Despite considerable interest in implicit processes, few researchers have conceptualized implicit learning as an ability with meaningful individual differences. Instead, various researchers (e.g., Reber, 1993; Stanovich, 2009) have suggested that individual differences in implicit learning are minimal relative to individual differences in explicit learning. In the current study of English 16-17year old students, we investigated the association of individual differences in implicit learning with a variety of cognitive and personality variables. Consistent with prior research and theorizing, implicit learning, as measured by a probabilistic sequence learning task, was more weakly related to psychometric intelligence than was explicit associative learning, and was unrelated to working memory. Structural equation modeling revealed that implicit learning was independently related to two components of psychometric intelligence: verbal analogical reasoning and processing speed. Implicit learning was also independently related to academic performance on two foreign language exams (French, German). Further, implicit learning was significantly associated with aspects of self-reported personality, including intuition, Openness to Experience, and impulsivity. We discuss the implications of implicit learning as an ability for dual-process theories of cognition, intelligence, personality, skill learning, complex cognition, and language acquisition.
Auditory spatial resolution in horizontal, vertical, and diagonal planes
NASA Astrophysics Data System (ADS)
Grantham, D. Wesley; Hornsby, Benjamin W. Y.; Erpenbeck, Eric A.
2003-08-01
Minimum audible angle (MAA) and minimum audible movement angle (MAMA) thresholds were measured for stimuli in horizontal, vertical, and diagonal (60°) planes. A pseudovirtual technique was employed in which signals were recorded through KEMAR's ears and played back to subjects through insert earphones. Thresholds were obtained for wideband, high-pass, and low-pass noises. Only 6 of 20 subjects obtained wideband vertical-plane MAAs less than 10°, and only these 6 subjects were retained for the complete study. For all three filter conditions thresholds were lowest in the horizontal plane, slightly (but significantly) higher in the diagonal plane, and highest for the vertical plane. These results were similar in magnitude and pattern to those reported by Perrott and Saberi [J. Acoust. Soc. Am. 87, 1728-1731 (1990)] and Saberi and Perrott [J. Acoust. Soc. Am. 88, 2639-2644 (1990)], except that these investigators generally found that thresholds for diagonal planes were as good as those for the horizontal plane. The present results are consistent with the hypothesis that diagonal-plane performance is based on independent contributions from a horizontal-plane system (sensitive to interaural differences) and a vertical-plane system (sensitive to pinna-based spectral changes). Measurements of the stimuli recorded through KEMAR indicated that sources presented from diagonal planes can produce larger interaural level differences (ILDs) in certain frequency regions than would be expected based on the horizontal projection of the trajectory. Such frequency-specific ILD cues may underlie the very good performance reported in previous studies for diagonal spatial resolution. Subjects in the present study could apparently not take advantage of these cues in the diagonal-plane condition, possibly because they did not externalize the images to their appropriate positions in space or possibly because of the absence of a patterned visual field.
Implicit and explicit representations.
Rougier, Nicolas P
2009-03-01
During the past decades, the symbol grounding problem, as has been identified by Harnard [Harnard, S. (1990). The symbol grounding problem. Physica D: Nonlinear Phenomena, 42, 335-346], became a prominent problem in the cognitive science society. The idea that a symbol is much more than a mere meaningless token that can be processed through some algorithm, sheds new light on higher brain functions such as language and cognition. We present in this article a computational framework that may help in our understanding of the nature of grounded representations. Two models are briefly introduced that aim at emphasizing the difference we make between implicit and explicit representations.
Hassin, Ran R; Bargh, John A; Engell, Andrew D; McCulloch, Kathleen C
2009-09-01
Working Memory (WM) plays a crucial role in many high-level cognitive processes (e.g., reasoning, decision making, goal pursuit and cognitive control). The prevalent view holds that active components of WM are predominantly intentional and conscious. This conception is oftentimes expressed explicitly, but it is best reflected in the nature of major WM tasks: All of them are blatantly explicit. We developed two new WM paradigms that allow for an examination of the role of conscious awareness in WM. Results from five studies show that WM can operate unintentionally and outside of conscious awareness, thus suggesting that the current view should be expanded to include implicit WM.
Hassin, Ran R.; Bargh, John A.; Engell, Andrew D.; McCulloch, Kathleen C.
2009-01-01
Working Memory (WM) plays a crucial role in many high-level cognitive processes (e.g., reasoning, decision making, goal pursuit and cognitive control). The prevalent view holds that active components of WM are predominantly intentional and conscious. This conception is oftentimes expressed explicitly, but it is best reflected in the nature of major WM tasks: All of them are blatantly explicit. We developed two new WM paradigms that allow for an examination of the role of conscious awareness in WM. Results from five studies show that WM can operate unintentionally and outside of conscious awareness, thus suggesting that the current view should be expanded to include implicit WM. PMID:19442537
The efficient calculation of chemically reacting flow
NASA Technical Reports Server (NTRS)
Eklund, D. R.; Hassan, H. A.; Drummond, J. P.
1986-01-01
A semi-implicit finite volume formulation is used to study flows with chemical reactions. In this formulation the source terms resulting from the chemical reactions are treated implicitly and the resulting system of partial differential equations is solved using two time-stepping schemes. The first is based on the Runge-Kutta method while the second is based on an Adams predictor-corrector method. Results show that improvements in computational efficiency depend to a large extent on the manner in which the source term is treated. Further, analysis and computation indicate that the Runge-Kutta method is more efficient than the Adams methods. Finally, an adaptive time stepping scheme is developed to study problems involving shock ignition. Calculations for a hydrogen-air system agree well with other methods.
Correlations and diagonal entropy after quantum quenches in XXZ chains
NASA Astrophysics Data System (ADS)
Piroli, Lorenzo; Vernier, Eric; Calabrese, Pasquale; Rigol, Marcos
2017-02-01
We study quantum quenches in the XXZ spin-1 /2 Heisenberg chain from families of ferromagnetic and antiferromagnetic initial states. Using Bethe ansatz techniques, we compute short-range correlators in the complete generalized Gibbs ensemble (GGE), which takes into account all local and quasilocal conservation laws. We compare our results to exact diagonalization and numerical linked cluster expansion calculations for the diagonal ensemble, finding excellent agreement and thus providing a very accurate test for the validity of the complete GGE. Furthermore, we use exact diagonalization to compute the diagonal entropy in the postquench steady state. We show that the Yang-Yang entropy for the complete GGE is consistent with twice the value of the diagonal entropy in the largest chains or the extrapolated result in the thermodynamic limit. Finally, the complete GGE is quantitatively contrasted with the GGE built using only the local conserved charges (local GGE). The predictions of the two ensembles are found to differ significantly in the case of ferromagnetic initial states. Such initial states are better suited than others considered in the literature to experimentally test the validity of the complete GGE and contrast it to the failure of the local GGE.
Improving DTI Tractography by including Diagonal Tract Propagation
Taylor, Paul A.; Cho, Kuan-Hung; Lin, Ching-Po; Biswal, Bharat B.
2012-01-01
Tractography algorithms have been developed to reconstruct likely WM pathways in the brain from diffusion tensor imaging (DTI) data. In this study, an elegant and simple means for improving existing tractography algorithms is proposed by allowing tracts to propagate through diagonal trajectories between voxels, instead of only rectilinearly to their facewise neighbors. A series of tests (using both real and simulated data sets) are utilized to show several benefits of this new approach. First, the inclusion of diagonal tract propagation decreases the dependence of an algorithm on the arbitrary orientation of coordinate axes and therefore reduces numerical errors associated with that bias (which are also demonstrated here). Moreover, both quantitatively and qualitatively, including diagonals decreases overall noise sensitivity of results and leads to significantly greater efficiency in scanning protocols; that is, the obtained tracts converge much more quickly (i.e., in a smaller amount of scanning time) to those of data sets with high SNR and spatial resolution. Importantly, the inclusion of diagonal propagation adds essentially no appreciable time of calculation or computational costs to standard methods. This study focuses on the widely-used streamline tracking method, FACT (fiber assessment by continuous tracking), and the modified method is termed “FACTID” (FACT including diagonals). PMID:22970125
Development of Implicit Methods in CFD NASA Ames Research Center 1970's - 1980's
NASA Technical Reports Server (NTRS)
Pulliam, Thomas H.
2010-01-01
The focus here is on the early development (mid 1970's-1980's) at NASA Ames Research Center of implicit methods in Computational Fluid Dynamics (CFD). A class of implicit finite difference schemes of the Beam and Warming approximate factorization type will be addressed. The emphasis will be on the Euler equations. A review of material pertinent to the solution of the Euler equations within the framework of implicit methods will be presented. The eigensystem of the equations will be used extensively in developing a framework for various methods applied to the Euler equations. The development and analysis of various aspects of this class of schemes will be given along with the motivations behind many of the choices. Various acceleration and efficiency modifications such as matrix reduction, diagonalization and flux split schemes will be presented.
Critical range evaluation using a diagonal flat plate
NASA Technical Reports Server (NTRS)
Lee, Teh-Hong; Clark, Tony L.; Burnside, Walter D.; Gupta, Inder J.
1992-01-01
A novel technique is presented to image stray signals in RCS measurement ranges. In this technique, the scattered fields of a flat plate in the diagonal plane are measured in a range for various frequencies and look angles. The scattered field data is then processed to generate an inverse synthetic aperture radar (ISAR) image of the diagonal flat plate. It is shown that scattering mechanisms associated with various stray signals can be identified by using the ISAR image. This leads to better understanding of the range and possible chamber improvements. Scattering mechanisms as small as 90 dB below the plate broadside scattered field level have been observed in the image domain due to the high directivity and low sidelobe characteristics associated with the diagonal flat plate backscattered fields. The results obtained from evaluating the two compact range facilities at The Ohio State University ElectroScience Laboratory are presented to illustrate the virtues of this new range evaluation technique.
Entanglement and nonlocality in diagonal symmetric states of N qubits
NASA Astrophysics Data System (ADS)
Quesada, Ruben; Rana, Swapan; Sanpera, Anna
2017-04-01
We analyze entanglement and nonlocal properties of the convex set of symmetric N -qubit states which are diagonal in the Dicke basis. First, we demonstrate that within this set, semidefinite positivity of partial transposition (PPT) is necessary and sufficient for separability—which has also been reported recently by Yu [Phys. Rev. A 94, 060101(R) (2016), 10.1103/PhysRevA.94.060101]. Furthermore, we show which states among the entangled diagonal symmetric are nonlocal under two-body Bell inequalities. The diagonal symmetric convex set contains a simple and extended family of states that violate the weak Peres conjecture, being PPT with respect to one partition but violating a Bell inequality in such partition. Our method opens directions to address entanglement and nonlocality on higher dimensional symmetric states, where presently very few results are available.
Using off-diagonal confinement as a cooling method
Rousseau, V. G.; Hettiarachchilage, K.; Jarrell, M.; Moreno, J.; Sheehy, D. E.
2010-12-15
In a recent letter [Phys. Rev. Lett. 104, 167201 (2010)] we proposed a new confining method for ultracold atoms on optical lattices, which is based on off-diagonal confinement (ODC). This method was shown to have distinct advantages over the conventional diagonal confinement (DC), which makes use of a trapping potential, such as the existence of pure Mott phases and highly populated condensates. In this manuscript we show that the ODC method can also lead to lower temperatures than the DC method for a wide range of control parameters. Using exact diagonalization we determine this range of parameters for the hard-core case and then we extend our results to the soft-core case by performing quantum Monte Carlo (QMC) simulations for both DC and ODC systems at fixed temperature and analyzing the corresponding entropies. We also propose a method for measuring the entropy in QMC simulations.
Multigrid time-accurate integration of Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.
1993-01-01
Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.
Stiff modes in spinvalve simulations with OOMMF
NASA Astrophysics Data System (ADS)
Mitropoulos, Spyridon; Tsiantos, Vassilis; Ovaliadis, Kyriakos; Kechrakos, Dimitris; Donahue, Michael
2016-04-01
Micromagnetic simulations are an important tool for the investigation of magnetic materials. Micromagnetic software uses various techniques to solve differential equations, partial or ordinary, involved in the dynamic simulations. Euler, Runge-Kutta, Adams, and BDF (Backward Differentiation Formulae) are some of the methods used for this purpose. In this paper, spinvalve simulations are investigated. Evidence is presented showing that these systems have stiff modes, and that implicit methods such as BDF are more effective than explicit methods in such cases.
A Computational Model of the Eye for Primary and Secondary Blast Injury
2012-10-01
difference scheme [18] and integrated in time using a four-stage Runge - Kutta method . An eight-order implicit spatial filtering proposed by Gaintonde et...each 9 time step (Figure 4A). In general, there are two coupling methods used in fluid structure interaction algorithms— explicit (or weak, one... method . Prentice-Hall. Englewood Cliffs, NJ, Chapter 9. 25Zygote Media Group , Inc is a developer company for computer-generated 3D graphical
Multigrid time-accurate integration of Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.
1993-01-01
Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.
Axisymmetric fully spectral code for hyperbolic equations
NASA Astrophysics Data System (ADS)
Panosso Macedo, Rodrigo; Ansorg, Marcus
2014-11-01
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge-Kutta (“SDIRK”-) method. In this paper, the SDIRK-method is also used to solve issue (ii). The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hole space-time in so-called hyperboloidal slices and reproduce some recent results available in the literature.
Quantum Discord of 2 n -Dimensional Bell-Diagonal States
NASA Astrophysics Data System (ADS)
Jafarizadeh, M. A.; Karimi, N.; Amidi, D.; Zahir Olyaei, H.
2016-03-01
In this study, using the concept of relative entropy as a distance measure of correlations we investigate the important issue of evaluating quantum correlations such as entanglement, dissonance and classical correlations for 2 n -dimensional Bell-diagonal states. We provide an analytical technique, which describes how we find the closest classical states(CCS) and the closest separable states(CSS) for these states. Then analytical results are obtained for quantum discord of 2 n -dimensional Bell-diagonal states. As illustration, some special cases are examined. Finally, we investigate the additivity relation between the different correlations for the separable generalized Bloch sphere states.
Neural network based diagonal decoupling control of powered wheelchair systems.
Nguyen, Tuan Nghia; Su, Steven; Nguyen, Hung T
2014-03-01
This paper proposes an advanced diagonal decoupling control method for powered wheelchair systems. This control method is based on a combination of the systematic diagonalization technique and the neural network control design. As such, this control method reduces coupling effects on a multivariable system, leading to independent control design procedures. Using an obtained dynamic model, the problem of the plant's Jacobian calculation is eliminated in a neural network control design. The effectiveness of the proposed control method is verified in a real-time implementation on a powered wheelchair system. The obtained results confirm that robustness and desired performance of the overall system are guaranteed, even under parameter uncertainty effects.
Implicit Theories of Peer Relationships
ERIC Educational Resources Information Center
Rudolph, Karen D.
2010-01-01
This research investigated the role of children's implicit theories of peer relationships in their psychological, emotional, and behavioral adjustment. Participants included 206 children (110 girls; 96 boys; M age = 10.13 years, SD = 1.16) who reported on their implicit theories of peer relationships, social goal orientation, need for approval,…
The neuropharmacology of implicit learning.
Uddén, Julia; Folia, Vasiliki; Petersson, Karl Magnus
2010-12-01
Two decades of pharmacologic research on the human capacity to implicitly acquire knowledge as well as cognitive skills and procedures have yielded surprisingly few conclusive insights. We review the empirical literature of the neuropharmacology of implicit learning. We evaluate the findings in the context of relevant computational models related to neurotransmittors such as dopamine, serotonin, acetylcholine and noradrenalin. These include models for reinforcement learning, sequence production, and categorization. We conclude, based on the reviewed literature, that one can predict improved implicit acquisition by moderately elevated dopamine levels and impaired implicit acquisition by moderately decreased dopamine levels. These effects are most prominent in the dorsal striatum. This is supported by a range of behavioral tasks in the empirical literature. Similar predictions can be made for serotonin, although there is yet a lack of support in the literature for serotonin involvement in classical implicit learning tasks. There is currently a lack of evidence for a role of the noradrenergic and cholinergic systems in implicit and related forms of learning. GABA modulators, including benzodiazepines, seem to affect implicit learning in a complex manner and further research is needed. Finally, we identify allosteric AMPA receptors modulators as a potentially interesting target for future investigation of the neuropharmacology of procedural and implicit learning.
Implicit Theories of Peer Relationships
ERIC Educational Resources Information Center
Rudolph, Karen D.
2010-01-01
This research investigated the role of children's implicit theories of peer relationships in their psychological, emotional, and behavioral adjustment. Participants included 206 children (110 girls; 96 boys; M age = 10.13 years, SD = 1.16) who reported on their implicit theories of peer relationships, social goal orientation, need for approval,…
The repressed and implicit knowledge.
Talvitie, Vesa; Ihanus, Juhani
2002-12-01
The distinction between implicit (non-conscious) and explicit (conscious) knowledge made by cognitive scientists is applied to the psychoanalytic idea of repressed contents. The consequences of repression are suggested to have been caused by implicit representations. Repressed memories can also be treated in terms of explicit representations, which are prevented from becoming activated. Implicit knowledge cannot, however, be made conscious, and thus the idea of becoming conscious of the repressed desires and fears that have never been conscious is contradictory. This tension may be relieved by reconceptualising the idea of becoming conscious of the repressed. It is suggested that this could be seen as creating explicit knowledge about the effects of implicit representations. By applying the implicit/explicit knowledge distinction, psychoanalytic ideas concerning the repressed could be connected to current views in the domain of cognitive orientation.
NASA Astrophysics Data System (ADS)
Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.
2014-03-01
A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.
On stability of diagonal actions and tensor invariants
Anisimov, Artem B
2012-04-30
For a connected simply connected semisimple algebraic group G we prove the existence of invariant tensors in certain tensor powers of rational G-modules and establish relations between the existence of such invariant tensors and stability of diagonal actions of G on affine algebraic varieties. Bibliography: 12 titles.
1. Aerial view of turnpike path running diagonally up from ...
1. Aerial view of turnpike path running diagonally up from lower left (present-day Orange Turnpike alignment) and containing on towards upper right through tree clump in center of the bare spot on the landscape, and on through the trees. View looking south. - Orange Turnpike, Parallel to new Orange Turnpike, Monroe, Orange County, NY
7. View from oiler's platform showing diagonal top bracing rods, ...
7. View from oiler's platform showing diagonal top bracing rods, tension members of eye-bars, sway bracing, upper struts, bottom (roadway) chord, decorative railing, and drum girder below. (Nov. 25, 1988) - University Heights Bridge, Spanning Harlem River at 207th Street & West Harlem Road, New York County, NY
14. Typical pin connection of eye bars, diagonal tension members ...
14. Typical pin connection of eye bars, diagonal tension members and vertical beam found at 2nd and 3rd spans. View is of north side of 2nd span. - Cleves Bridge, Spanning Great Miami River on U.S. Highway 50, Cleves, Hamilton County, OH
Penguins and Pandas: A Note on Teaching Cantor's Diagonal Argument
ERIC Educational Resources Information Center
Rauff, James V.
2008-01-01
Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…
Understanding of Prospective Mathematics Teachers of the Concept of Diagonal
ERIC Educational Resources Information Center
Ayvaz, Ülkü; Gündüz, Nazan; Bozkus, Figen
2017-01-01
This study aims to investigate the concept images of prospective mathematics teachers about the concept of diagonal. With this aim, case study method was used in the study. The participants of the study were consisted of 7 prospective teachers educating at the Department of Mathematics Education. Criterion sampling method was used to select the…
Penguins and Pandas: A Note on Teaching Cantor's Diagonal Argument
ERIC Educational Resources Information Center
Rauff, James V.
2008-01-01
Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…
Why the South Pacific Convergence Zone is diagonal
NASA Astrophysics Data System (ADS)
van der Wiel, Karin; Matthews, Adrian J.; Joshi, Manoj M.; Stevens, David P.
2016-03-01
During austral summer, the majority of precipitation over the Pacific Ocean is concentrated in the South Pacific Convergence Zone (SPCZ). The surface boundary conditions required to support the diagonally (northwest-southeast) oriented SPCZ are determined through a series of experiments with an atmospheric general circulation model. Continental configuration and orography do not have a significant influence on SPCZ orientation and strength. The key necessary boundary condition is the zonally asymmetric component of the sea surface temperature (SST) distribution. This leads to a strong subtropical anticyclone over the southeast Pacific that, on its western flank, transports warm moist air from the equator into the SPCZ region. This moisture then intensifies (diagonal) bands of convection that are initiated by regions of ascent and reduced static stability ahead of the cyclonic vorticity in Rossby waves that are refracted toward the westerly duct over the equatorial Pacific. The climatological SPCZ is comprised of the superposition of these diagonal bands of convection. When the zonally asymmetric SST component is reduced or removed, the subtropical anticyclone and its associated moisture source is weakened. Despite the presence of Rossby waves, significant moist convection is no longer triggered; the SPCZ disappears. The diagonal SPCZ is robust to large changes (up to ±6 °C) in absolute SST (i.e. where the SST asymmetry is preserved). Extreme cooling (change <-6 °C) results in a weaker and more zonal SPCZ, due to decreasing atmospheric temperature, moisture content and convective available potential energy.
View, from south showing verticals, diagonals, and overhead bracing of ...
View, from south showing verticals, diagonals, and overhead bracing of south span Pratt through trusses, south portal of north span, pipe rails and posts, and concrete deck with bituminous wearing surface - Castle Garden Bridge, Township Route 343 over Bennetts Branch of Sinnemahoning Creek, Driftwood, Cameron County, PA
Improving stochastic estimates with inference methods: Calculating matrix diagonals
NASA Astrophysics Data System (ADS)
Selig, Marco; Oppermann, Niels; Enßlin, Torsten A.
2012-02-01
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image reconstruction and statistical inference. Here, methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals. In particular, the generalized Wiener filter methodology, as developed within information field theory, is shown to significantly improve estimates based on only a few sampling probes, in cases in which some form of continuity of the solution can be assumed. The strength, length scale, and precise functional form of the exploited autocorrelation function of the matrix diagonal is determined from the probes themselves. The developed algorithm is successfully applied to mock and real world problems. These performance tests show that, in situations where a matrix diagonal has to be calculated from only a small number of computationally expensive probes, a speedup by a factor of 2 to 10 is possible with the proposed method.
34. Coal Fuel Elevator (diagonal in foreground), Fuel Elevator (left), ...
34. Coal Fuel Elevator (diagonal in foreground), Fuel Elevator (left), Fuel Storage Bins (center), and Power Plant (far center), and Retail Coal Storage Bins (right) Photograph taken by George Harven - Huber Coal Breaker, 101 South Main Street, Ashley, Luzerne County, PA
35. Coal Fuel Elevator (diagonal in center), Fuel Elevator (left), ...
35. Coal Fuel Elevator (diagonal in center), Fuel Elevator (left), Fuel Storage Bins (center), and Power Plant (far center), and Retail Coal Storage Bins (right) Photograph taken by George Harven - Huber Coal Breaker, 101 South Main Street, Ashley, Luzerne County, PA
Implicit Self-Evaluations Predict Changes in Implicit Partner Evaluations
McNulty, James K.; Baker, Levi R.; Olson, Michael A.
2014-01-01
Do people who feel good about themselves have better relations with others? Although the notion that they do is central to both classic and modern theories, there is little strong evidence to support it. We argue that one reason for the lack of evidence is that prior research has relied exclusively on explicit measures of self- and relationship evaluations. The current longitudinal study of newlywed couples used explicit measures of self-, relationship, and partner evaluations as well as implicit measures of self- and partner evaluations to examine the link between self-evaluations and changes in relationship evaluations over the first three years of marriage. Whereas explicit self-evaluations were unrelated to changes in all interpersonal measures, implicit self-evaluations positively predicted changes in implicit partner evaluations. This finding joins others in highlighting the importance of automatic processes and implicit measures to the study of close interpersonal relationships. PMID:24958686
Implicit self-evaluations predict changes in implicit partner evaluations.
McNulty, James K; Baker, Levi R; Olson, Michael A
2014-08-01
Do people who feel good about themselves have better relations with others? Although the notion that they do is central to both classic and modern theories, there is little strong evidence to support it. We argue that one reason for the lack of evidence is that prior research has relied exclusively on explicit measures of self- and relationship evaluation. The current longitudinal study of newlywed couples used implicit measures of self- and partner evaluation, as well as explicit measures of self-, relationship, and partner evaluation, to examine the link between self-evaluations and changes in relationship evaluations over the first 3 years of marriage. Whereas explicit self-evaluations were unrelated to changes in all interpersonal measures, implicit self-evaluations positively predicted changes in implicit partner evaluations. This finding adds to previous research by highlighting the importance of automatic processes and implicit measures in the study of close interpersonal relationships. © The Author(s) 2014.
Semi-implicit finite difference methods for three-dimensional shallow water flow
Casulli, Vincenzo; Cheng, Ralph T.
1992-01-01
A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.
Implicit Numerical Methods in Meteorology
NASA Technical Reports Server (NTRS)
Augenbaum, J.
1984-01-01
The development of a fully implicit finite-difference model, whose time step is chosen solely to resolve accurately the physical flow of interest is discussed. The method is based on an operator factorization which reduces the dimensionality of the implicit approach: at each time step only (spatially) one-dimensional block-tridiagonal linear systems must be solved. The scheme uses two time levels and is second-order accurate in time. Compact implicit spatial differences are used, yielding fourth-order accuracy both vertically and horizontally. In addition, the development of a fully interactive computer code is discussed. With this code the user will have a choice of models, with various levels of accuracy and sophistication, which are imbedded, as subsets of the fully implicit 3D code.
NASA Astrophysics Data System (ADS)
Klaij, C. M.; van der Vegt, J. J. W.; van der Ven, H.
2006-12-01
The space-time discontinuous Galerkin discretization of the compressible Navier-Stokes equations results in a non-linear system of algebraic equations, which we solve with pseudo-time stepping methods. We show that explicit Runge-Kutta methods developed for the Euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality. To evaluate its effectiveness, we compare with an implicit-explicit Runge-Kutta method which does not suffer from the viscous stability constraint. We analyze the stability of the methods and illustrate their performance by computing the flow around a 2D airfoil and a 3D delta wing at low and moderate Reynolds numbers.
Navier-Stokes cascade analysis with a stiff Kappa-Epsilon turbulence solver
NASA Technical Reports Server (NTRS)
Liu, Jong-Shang; Sockol, Peter M.; Prahl, Joseph M.
1987-01-01
The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.
Navier-Stokes cascade analysis with a stiff k-epsilon turbulence solver
NASA Technical Reports Server (NTRS)
Liu, Jong-Shang; Sockol, Peter M.; Prahl, Joseph M.
1988-01-01
The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.
NASA Astrophysics Data System (ADS)
Geiser, Jürgen
2008-07-01
In this paper we design higher-order time integrators for systems of stiff ordinary differential equations. We combine implicit Runge-Kutta and BDF methods with iterative operator-splitting methods to obtain higher-order methods. The idea of decoupling each complicated operator in simpler operators with an adapted time scale allows to solve the problems more efficiently. We compare our new methods with the higher-order fractional-stepping Runge-Kutta methods, developed for stiff ordinary differential equations. The benefit is the individual handling of each operator with adapted standard higher-order time integrators. The methods are applied to equations for convection-diffusion reactions and we obtain higher-order results. Finally we discuss the applications of the iterative operator-splitting methods to multi-dimensional and multi-physical problems.
A brief introduction to symplectic integrators and recent results
Channell, P.J.
1994-02-01
The author begins with a brief synopsis about Hamiltonian systems and symplectic maps. A symplectic integrator is a symplectic map {phi}(q,p;t) that systematically approximates the time t flow of a Hamiltonian system. Systematic means: (1) in time step, t, i.e. the error should vanish as some power of the time step, and (2) in order of approximation, i.e. one would like a hierarchy of such {phi} that have errors that vanish as successively higher powers of the time step. At present the authors known two general types of symplectic integrators: (1) implicit integrators that are derived from a generating function or from algebraic conditions on Runge-Kutta schemes, and (2) explicit integrators that are derived from integrable Hamiltonians or from algebraic conditions on Runge-Kutta schemes.
NASA Technical Reports Server (NTRS)
Atkins, Harold
1991-01-01
A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.
NASA Technical Reports Server (NTRS)
Atkins, H. L.
1991-01-01
A multi-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell-vertex method which employs central-difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques, and variable-coefficient numerical smoothing results in an efficient and robust scheme. The multi-block strategy places the block loop within the Runge-Kutta loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one- and two-block calculations in which the two-block grid is generated by splitting the one-block grid. Results are presented for both Euler and Navier-Stokes computations of wings and wing-fuselage combinations.
NASA Astrophysics Data System (ADS)
Bidadi, Shreyas; Rani, Sarma L.
2016-01-01
The authors regret that in Fig. 8(c) of the paper, the labels for the dimensionless time t* and flatness S4, as well as the plot legend are incorrect. In place of the original figure, the following figure should be used.
Block-bordered diagonalization and parallel iterative solvers
Alvarado, F.; Dag, H.; Bruggencate, M. ten
1994-12-31
One of the most common techniques for enhancing parallelism in direct sparse matrix methods is the reorganization of a matrix into a blocked-bordered structure. Incomplete LDU factorization is a very good preconditioner for PCG in serial environments. However, the inherent sequential nature of the preconditioning step makes it less desirable in parallel environments. This paper explores the use of BBD (Blocked Bordered Diagonalization) in connection with ILU preconditioners. The paper shows that BBD-based ILU preconditioners are quite amenable to parallel processing. Neglecting entries from the entire border can result in a blocked diagonal matrix. The result is a great increase in parallelism at the expense of additional iterations. Experiments on the Sequent Symmetry shared memory machine using (mostly) power system that matrices indicate that the method is generally better than conventional ILU preconditioners and in many cases even better than partitioned inverse preconditioners, without the initial setup disadvantages of partitioned inverse preconditioners.
Off-diagonal Jacobian support for Nodal BCs
Peterson, John W.; Andrs, David; Gaston, Derek R.; Permann, Cody J.; Slaughter, Andrew E.
2015-01-01
In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite element codes in general: 1. The ability to zero out entire Jacobian matrix rows after \
Density of states for almost-diagonal random matrices
NASA Astrophysics Data System (ADS)
Yevtushenko, Oleg; Kravtsov, Vladimir E.
2004-02-01
We study the density of states (DOS) for disordered systems whose spectral statistics can be described by a Gaussian ensemble of almost-diagonal Hermitian random matrices. The matrices have independent random entries Hi⩾j with small off-diagonal elements: <|Hi≠j|2>≪<|Hii|2>˜1. Using the recently suggested method of a virial expansion in the number of interacting energy levels [J. Phys. A 36, 8265 (2003)], we calculate the leading correction to the Poissonian DOS in the cases of the Gaussian orthogonal and unitary ensembles. We apply the general formula to the critical power-law banded random matrices and the unitary Moshe-Neuberger-Shapiro model and compare the DOS’s of these models.
Lee, Jun Chang; Nam, Kyoung Won; Jang, Dong Pyo; Kim, In Young
2015-12-01
Previously suggested diagonal-steering algorithms for binaural hearing support devices have commonly assumed that the direction of the speech signal is known in advance, which is not always the case in many real circumstances. In this study, a new diagonal-steering-based binaural speech localization (BSL) algorithm is proposed, and the performances of the BSL algorithm and the binaural beamforming algorithm, which integrates the BSL and diagonal-steering algorithms, were evaluated using actual speech-in-noise signals in several simulated listening scenarios. Testing sounds were recorded in a KEMAR mannequin setup and two objective indices, improvements in signal-to-noise ratio (SNRi ) and segmental SNR (segSNRi ), were utilized for performance evaluation. Experimental results demonstrated that the accuracy of the BSL was in the 90-100% range when input SNR was -10 to +5 dB range. The average differences between the γ-adjusted and γ-fixed diagonal-steering algorithms (for -15 to +5 dB input SNR) in the talking in the restaurant scenario were 0.203-0.937 dB for SNRi and 0.052-0.437 dB for segSNRi , and in the listening while car driving scenario, the differences were 0.387-0.835 dB for SNRi and 0.259-1.175 dB for segSNRi . In addition, the average difference between the BSL-turned-on and the BSL-turned-off cases for the binaural beamforming algorithm in the listening while car driving scenario was 1.631-4.246 dB for SNRi and 0.574-2.784 dB for segSNRi . In all testing conditions, the γ-adjusted diagonal-steering and BSL algorithm improved the values of the indices more than the conventional algorithms. The binaural beamforming algorithm, which integrates the proposed BSL and diagonal-steering algorithm, is expected to improve the performance of the binaural hearing support devices in noisy situations.
Diagonalization and representation results for nonpositive sesquilinear form measures
NASA Astrophysics Data System (ADS)
Hytönen, Tuomas; Pellonpää, Juha-Pekka; Ylinen, Kari
2008-02-01
We study decompositions of operator measures and more general sesquilinear form measures E into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent E as a trace class valued measure of bounded variation on a new Hilbert space related to E. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals.
A Summary of Diagonal Tension Part I : Methods of Analysis
NASA Technical Reports Server (NTRS)
Kuhn, Paul; Peterson, James P; Levin, L Ross
1952-01-01
Previously published methods for stress and strength analysis of plane and curved shear webs working in diagonal tension are presented as a unified method. The treatment is sufficiently comprehensive and detailed to make the paper self-contained. Part 1 discusses the theory and methods for calculating the stresses and shear deflections of web systems as well as the strengths of the web, the stiffeners, and the riveting. Part 2, published separately, presents the experimental evidence. (author)
INTERIOR OF HOG BARN SHOWING MILKING STANCHIONS AND DIAGONAL SHEATHING, ...
INTERIOR OF HOG BARN SHOWING MILKING STANCHIONS AND DIAGONAL SHEATHING, LOOKING EAST. (In the 1940s the hog barn was converted to a calf barn to service the growing dairy. After a fire on the property took the Engles main barn in 1954, the building was converted into a milking parlor.) - Engle Farm, Barn, 89 South Ebey Road, Coupeville, Island County, WA
Efficient variational diagonalization of fully many-body localized Hamiltonians
NASA Astrophysics Data System (ADS)
Pollmann, Frank; Khemani, Vedika; Cirac, J. Ignacio; Sondhi, S. L.
2016-07-01
We introduce a variational unitary matrix product operator based variational method that approximately finds all the eigenstates of fully many-body localized one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed depth of the UTN ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.
Diagonal dominance for the multivariable Nyquist array using function minimization
NASA Technical Reports Server (NTRS)
Leininger, G. G.
1977-01-01
A new technique for the design of multivariable control systems using the multivariable Nyquist array method was developed. A conjugate direction function minimization algorithm is utilized to achieve a diagonal dominant condition over the extended frequency range of the control system. The minimization is performed on the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal terms of either the inverse or direct open loop transfer function matrix. Several new feedback design concepts were also developed, including: (1) dominance control parameters for each control loop; (2) compensator normalization to evaluate open loop conditions for alternative design configurations; and (3) an interaction index to determine the degree and type of system interaction when all feedback loops are closed simultaneously. This new design capability was implemented on an IBM 360/75 in a batch mode but can be easily adapted to an interactive computer facility. The method was applied to the Pratt and Whitney F100 turbofan engine.
Block diagonal representations for covariance based anomalous change detectors
Matsekh, Anna; Theiler, James
2009-01-01
Change detection methods are of crucial importance in many remote sensing applications such as monitoring and surveillance, where the goal is to identify and separate changes of interest from pervasive changes inevitably present in images taken at different times and in different environmental and illumination conditions. Anomalous change detection (ACD) methods aim to identify rare, unusual, or anomalous changes among the changes of interest. Covariance-based ACD methods provide a powerful tool for detection of unusual changes in hyper-spectral images. In this paper we study the properties of the eigenvalue spectra of a family of ACD matrices in order to better understand the algebraic and numerical behavior of the covariance-based quadratic ACD methods. We propose to use singular vectors of covariance matrices of two hyper-spectral images in whitened coordinates for obtaining block-diagonal representations of the matrices of quadratic ACD methods. SVD transformation gives an equivalent representation of ACD matrices in compact block-diagonal form. In the paper we show that the eigenvalue spectrum of a block-diagonal ACD matrix can be identified analytically as a function of the singular value spectrum of the corresponding covariance matrix in whitened coordinates.
Off-Diagonal Decay of Toric Bergman Kernels
NASA Astrophysics Data System (ADS)
Zelditch, Steve
2016-12-01
We study the off-diagonal decay of Bergman kernels {Π_{h^k}(z,w)} and Berezin kernels {P_{h^k}(z,w)} for ample invariant line bundles over compact toric projective kähler manifolds of dimension m. When the metric is real analytic, {P_{h^k}(z,w) ˜eq k^m exp - k D(z,w)} where {D(z,w)} is the diastasis. When the metric is only {C^{∞}} this asymptotic cannot hold for all {(z,w)} since the diastasis is not even defined for all {(z,w)} close to the diagonal. Our main result is that for general toric {C^{∞}} metrics, {P_{h^k}(z,w) ˜eq k^m exp - k D(z,w)} as long as w lies on the {R_+^m}-orbit of z, and for general {(z,w)}, {lim sup_{k to ∞} 1/k log P_{h^k}(z,w) ≤ - D(z^*,w^*)} where {D(z, w^*)} is the diastasis between z and the translate of w by {(S^1)^m} to the {R_+^m} orbit of z. These results are complementary to Mike Christ's negative results showing that {P_{h^k}(z,w)} does not have off-diagonal exponential decay at "speed" k if {(z,w)} lies on the same {(S^1)^m}-orbit.
Quantum Diagonalization Method in the TAVIS-CUMMINGS Model
NASA Astrophysics Data System (ADS)
Fujii, Kazuyuki; Higashida, Kyoko; Kato, Ryosuke; Suzuki, Tatsuo; Wada, Yukako
2005-06-01
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\\otimes a+S_{-}\\otimes a^{\\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\\equiv S_{+}\\otimes a+S_{-}\\otimes a^{\\dagger}$ diagonal to calculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint to an application to a noncommutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the noncommutativity of operators in quantum physics. Our method may open a new point of view in Mathematical Physics or Quantum Physics.
Ordered Subspace Clustering With Block-Diagonal Priors.
Wu, Fei; Hu, Yongli; Gao, Junbin; Sun, Yanfeng; Yin, Baocai
2016-12-01
Many application scenarios involve sequential data, but most existing clustering methods do not well utilize the order information embedded in sequential data. In this paper, we study the subspace clustering problem for sequential data and propose a new clustering method, namely ordered sparse clustering with block-diagonal prior (BD-OSC). Instead of using the sparse normalizer in existing sparse subspace clustering methods, a quadratic normalizer for the data sparse representation is adopted to model the correlation among the data sparse coefficients. Additionally, a block-diagonal prior for the spectral clustering affinity matrix is integrated with the model to improve clustering accuracy. To solve the proposed BD-OSC model, which is a complex optimization problem with quadratic normalizer and block-diagonal prior constraint, an efficient algorithm is proposed. We test the proposed clustering method on several types of databases, such as synthetic subspace data set, human face database, video scene clips, motion tracks, and dynamic 3-D face expression sequences. The experiments show that the proposed method outperforms state-of-the-art subspace clustering methods.
[Using the Implicit Association Test (IAT) to measure implicit shyness].
Aikawa, Atsushi; Fujii, Tsutomu
2011-04-01
Previous research has shown that implicitly measured shyness predicted spontaneous shy behavior in social situations, while explicit self-ratings of shyness predicted controlled shy behavior (Asendorpf, Banse, & Mücke, 2002). The present study examined whether these same results would be replicated in Japan. In Study 1, college students (N=47) completed a shyness Implicit Association Test (IAT for shyness) and explicit self-ratings of shyness. In Study 2, friends (N=69) of the Study 1 participants rated those participants on various personality scales. Covariance structure analysis, revealed that only implicit self-concept measured by the shyness IAT predicted other-rated high interpersonal tension (spontaneous shy behavior). Also, only explicit self-concept predicted other-rated low praise seeking (controlled shy behavior). The results of this study are similar to the findings of the previous research.
Yao, Yao; Zhou, Nengji; Prior, Javier; Zhao, Yang
2015-01-01
It has long been a puzzle on what drives charge separation in artificial polymeric solar cells as a consensus has yet to emerge among rivaling theories based upon electronic localization and delocalization pictures. Here we propose an alternative using the two-bath spin-boson model with simultaneous diagonal and off-diagonal coupling: the critical phase, which is born out of the competition of the two coupling types, and is neither localized nor delocalized. The decoherence-free feature of the critical phase also helps explain sustained coherence of the charge-transfer state. Exploiting Hamiltonian symmetries in an enhanced algorithm of density-matrix renormalization group, we map out boundaries of the critical phase to a precision previously unattainable, and determine the bath spectral densities inducive to the existence of the charge-transfer state. PMID:26412693
Posture modulates implicit hand maps.
Longo, Matthew R
2015-11-01
Several forms of somatosensation require that afferent signals be informed by stored representations of body size and shape. Recent results have revealed that position sense relies on a highly distorted body representation. Changes of internal hand posture produce plastic alterations of processing in somatosensory cortex. This study therefore investigated how such postural changes affect implicit body representations underlying position sense. Participants localised the knuckles and tips of each finger in external space in two postures: the fingers splayed (Apart posture) or pressed together (Together posture). Comparison of the relative locations of the judgments of each landmark were used to construct implicit maps of represented hand structure. Spreading the fingers apart produced increases in the implicit representation of hand size, with no apparent effect on hand shape. Thus, changes of internal hand posture produce rapid modulation of how the hand itself is represented, paralleling the known effects on somatosensory cortical processing. Copyright © 2015 Elsevier Inc. All rights reserved.
Implicit emotional awareness in frontotemporal dementia.
Ibáñez, Agustín; Velásquez, María Marcela; Caro, Miguel Martorell; Manes, Facundo
2013-01-01
The preserved "implicit awareness" in patients with Alzheimer disease (AD) presenting anosognosia has opened a new branch of research regarding explicit-implicit integration. The behavioral variant of frontotemporal dementia (bvFTD), contrary to AD, would present impaired anosognosia-related implicit awareness due to a dysfunctional implicit integration of contextual information caused by an abnormal fronto-insular-temporal network. Loss of insight and anosognosia are pervasive in bvFTD, but no reports have assessed the implicit emotional awareness in this condition. We emphasize the need to investigate and extend our knowledge of implicit contextual integration impairments and their relation with anosognosia in bvFTD vs AD.
Parallel, Implicit, Finite Element Solver
NASA Astrophysics Data System (ADS)
Lowrie, Weston; Shumlak, Uri; Meier, Eric; Marklin, George
2007-11-01
A parallel, implicit, finite element solver is described for solutions to the ideal MHD equations and the Pseudo-1D Euler equations. The solver uses the conservative flux source form of the equations. This helps simplify the discretization of the finite element method by keeping the specification of the physics separate. An implicit time advance is used to allow sufficiently large time steps. The Portable Extensible Toolkit for Scientific Computation (PETSc) is implemented for parallel matrix solvers and parallel data structures. Results for several test cases are described as well as accuracy of the method.
Diagonal queue medical image steganography with Rabin cryptosystem.
Jain, Mamta; Lenka, Saroj Kumar
2016-03-01
The main purpose of this work is to provide a novel and efficient method to the image steganography area of research in the field of biomedical, so that the security can be given to the very precious and confidential sensitive data of the patient and at the same time with the implication of the highly reliable algorithms will explode the high security to the precious brain information from the intruders. The patient information such as patient medical records with personal identification information of patients can be stored in both storage and transmission. This paper describes a novel methodology for hiding medical records like HIV reports, baby girl fetus, and patient's identity information inside their Brain disease medical image files viz. scan image or MRI image using the notion of obscurity with respect to a diagonal queue least significant bit substitution. Data structure queue plays a dynamic role in resource sharing between multiple communication parties and when secret medical data are transferred asynchronously (secret medical data not necessarily received at the same rate they were sent). Rabin cryptosystem is used for secret medical data writing, since it is computationally secure against a chosen-plaintext attack and shows the difficulty of integer factoring. The outcome of the cryptosystem is organized in various blocks and equally distributed sub-blocks. In steganography process, various Brain disease cover images are organized into various blocks of diagonal queues. The secret cipher blocks and sub-blocks are assigned dynamically to selected diagonal queues for embedding. The receiver gets four values of medical data plaintext corresponding to one ciphertext, so only authorized receiver can identify the correct medical data. Performance analysis was conducted using MSE, PSNR, maximum embedding capacity as well as by histogram analysis between various Brain disease stego and cover images.
Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition
Weinstein, Marvin; Auerbach, Assa; Chandra, V.Ravi; /Technion
2011-11-04
We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. The lattice of size N is partitioned into two subclusters. At each iteration the Lanczos vector is projected into a set of n{sub svd} smaller subcluster vectors using singular value decomposition. For low entanglement entropy S{sub ee}, (satisfied by short range Hamiltonians), we expect the truncation error to vanish as exp(-n{sup 1/S{sub ee}}{sub svd}). Convergence is tested for the Heisenberg model on Kagome clusters of up to 36 sites, with no symmetries exploited, using less than 15GB of memory. Generalization to multiple partitioning is discussed.
Non-Diagonal Flavour Observables in B and Collider Physics
Hurth, Tobias
2003-11-11
Until now the focus within the direct search for supersymmetry has mainly been on flavour diagonal observables. Recently lepton flavour violating signals at future electron positron colliders have been studied. There is now an opportunity to analyze the relations between collider observables and low-energy observables in the hadronic sector. In a first work in this direction, we study flavour violation in the squark decays of the second and third generations taking into account results from B physics, in particular from the rare decay b {yields} s gamma. Correlations between various squark decay modes can be used to get more precise information on various flavour violating parameters.
Performance Theory of Diagonal Conducting Wall MHD Accelerators
NASA Technical Reports Server (NTRS)
Litchford, R. J.
2003-01-01
The theoretical performance of diagonal conducting wall crossed field accelerators is examined on the basis of an infinite segmentation assumption using a cross-plane averaged generalized Ohm's law for a partially ionized gas, including ion slip. The desired accelerator performance relationships are derived from the cross-plane averaged Ohm's law by imposing appropriate configuration and loading constraints. A current dependent effective voltage drop model is also incorporated to account for cold-wall boundary layer effects including gasdynamic variations, discharge constriction, and electrode falls. Definition of dimensionless electric fields and current densities lead to the construction of graphical performance diagrams, which further illuminate the rudimentary behavior of crossed field accelerator operation.
Diagonal-Axes Stage for Pointing an Optical Communications Transceiver
NASA Technical Reports Server (NTRS)
Regehr, Martin W.; Garkanian, Vachik
2011-01-01
Traditional azimuth-elevation ("az-el") stages are used to point a variety of devices ranging from large optical telescopes to tank guns. Such a stage typically has an elevation stage having a horizontal axis mounted on an azimuth stage with a vertical axis. Both stages are often motorized. Optical communications transceivers often require two-axis motorized control, as when the communications link is between a ground station and an aircraft or satellite. In such applications, the traditional azimuth-elevation stage has two important drawbacks: a gimbal lock exclusion zone at zenith and susceptibility to pointing errors caused by backlash. Az-el stages in which the azimuth stage cannot rotate a full 360deg have the additional drawback of an azimuth exclusion zone. The diagonal-axes stage described here mitigates or eliminates all of these problems. Instead of one vertical axis and one horizontal axis, a diagonal-axes stage has two horizontal axes, both oriented at 45 to the trajectory of the target. For example, a ground station located on the equator tracking a satellite with an equatorial orbit would have one axis parallel to northeast and southwest, and the other axis parallel to northwest and southeast. The diagonal-axes stage is considerably less vulnerable to backlash. If it is correctly oriented, its axes rotate in only one direction during an overhead pass by a satellite. As a result, the effects of backlash may be inherently eliminated. If the gravity-induced torque on either axis changes during the pass, then backlash may become important during the part of the pass where the gravity torque, instead of opposing the motion of the stage, pushes the stage in the direction of motion. This can result in the loss of gear-to-gear contact in one or more stages of the gear reduction mechanism. In this case, a preload spring used to eliminate backlash need only be sufficiently strong to overcome the gravity torque, i.e. it need not overcome friction in the gear
Anharmonicity and NLO responses: an exact diagonalization study
NASA Astrophysics Data System (ADS)
Freo, Luca Del; Painelli, Anna
2001-04-01
We present the exact numerical diagonalization of the Mulliken donor-acceptor (DA) dimer with Holstein coupling. The resulting eigenstates are introduced in sum-over-states expressions of static optical susceptibilities. The careful partitioning of the sum, and the comparison with spectral properties give important clues on the role of electron-phonon (e-ph) coupling. Anharmonicity does not appreciably affect vibrational spectra, nor linear electronic spectra, and is irrelevant for the static linear polarizability. By contrast, huge anharmonic contributions to hyperpolarizabilities are found: the harmonic approximation is unreliable for the calculation of non-linear responses, even for systems where it hardly affects linear optical spectra.
Applications and accuracy of the parallel diagonal dominant algorithm
NASA Technical Reports Server (NTRS)
Sun, Xian-He
1993-01-01
The Parallel Diagonal Dominant (PDD) algorithm is a highly efficient, ideally scalable tridiagonal solver. In this paper, a detailed study of the PDD algorithm is given. First the PDD algorithm is introduced. Then the algorithm is extended to solve periodic tridiagonal systems. A variant, the reduced PDD algorithm, is also proposed. Accuracy analysis is provided for a class of tridiagonal systems, the symmetric, and anti-symmetric Toeplitz tridiagonal systems. Implementation results show that the analysis gives a good bound on the relative error, and the algorithm is a good candidate for the emerging massively parallel machines.
Convergence to Diagonal Form of Block Jacobi-type Processes
NASA Astrophysics Data System (ADS)
Hari, Vjeran
2008-09-01
The main result of recent research on convergence to diagonal form of block Jacobi-type processes is presented. For this purpose, all notions needed to describe the result are introduced. In particular, elementary block transformation matrices, simple and non-simple algorithms, block pivot strategies together with the appropriate equivalence relations are defined. The general block Jacobi-type process considered here can be specialized to take the form of almost any known Jacobi-type method for solving the ordinary or the generalized matrix eigenvalue and singular value problems. The assumptions used in the result are satisfied by many concrete methods.
Dynamical dimer-dimer correlation functions from exact diagonalization
Werner, Ralph
2001-05-01
A regularization method is presented to deduce dynamic correlation functions from exact diagonalization calculations. It is applied to dimer-dimer correlation functions in quantum spin chains relevant for the description of spin-Peierls systems. Exact results for the XY model are presented. The analysis draws into doubt that the dimer-dimer correlation functions show the same scale invariance as spin-spin correlation functions. The results are applied to describe the quasielastic scattering in CuGeO{sub 3} and the hardening of the Peierls-active phonons.
Neutrino beam constraints on flavor-diagonal Lorentz violation
NASA Astrophysics Data System (ADS)
Altschul, Brett
2013-05-01
Breaking of isotropy and Lorentz boost invariance in the dynamics of second-generation leptons would lead to direction-dependent changes in the lifetimes of charged pions. This would make the intensity of a neutrino beam produced via pion decay a function of the beam orientation. The experimental signature of this phenomenon—sidereal variations in the event rate at a downstream neutrino detector—has already been studied, in searches for Lorentz-violating neutrino oscillations. Existing analyses of MINOS near detector data can be used to constrain the flavor-diagonal Lorentz violation coefficients affecting muon neutrino speeds at roughly the 10-5 level.
Media multitasking and implicit learning.
Edwards, Kathleen S; Shin, Myoungju
2017-07-01
Media multitasking refers to the simultaneous use of different forms of media. Previous research comparing heavy media multitaskers and light media multitaskers suggests that heavy media multitaskers have a broader scope of attention. The present study explored whether these differences in attentional scope would lead to a greater degree of implicit learning for heavy media multitaskers. The study also examined whether media multitasking behaviour is associated with differences in visual working memory, and whether visual working memory differentially affects the ability to process contextual information. In addition to comparing extreme groups (heavy and light media multitaskers) the study included analysis of people who media multitask in moderation (intermediate media multitaskers). Ninety-four participants were divided into groups based on responses to the media use questionnaire, and completed the contextual cueing and n-back tasks. Results indicated that the speed at which implicit learning occurred was slower in heavy media multitaskers relative to both light and intermediate media multitaskers. There was no relationship between working memory performance and media multitasking group, and no relationship between working memory and implicit learning. There was also no evidence for superior performance of intermediate media multitaskers. A deficit in implicit learning observed in heavy media multitaskers is consistent with previous literature, which suggests that heavy media multitaskers perform more poorly than light media multitaskers in attentional tasks due to their wider attentional scope.
Learning in Autism: Implicitly Superb
Londe, Zsuzsa; Mingesz, Robert; Fazekas, Marta; Jambori, Szilvia; Danyi, Izabella; Vetro, Agnes
2010-01-01
Background Although autistic people have shown impairments in various learning and memory tasks, recent studies have reported mixed findings concerning implicit learning in ASD. Implicit skill learning, with its unconscious and statistical properties, underlies not only motor but also cognitive and social skills, and it therefore plays an important role from infancy to old age. Methodology/Principal Findings We investigated probabilistic implicit sequence learning and its consolidation in Autism Spectrum Disorder (ASD). Three groups of children participated: thirteen with high-functioning ASD, 14 age-matched controls, and 13 IQ-matched controls. All were tested on the Alternating Serial Reaction Time Task (ASRT), making it possible to separate general skill learning from sequence-specific learning. The ASRT task was repeated after 16 hours. We found that control and ASD children showed similar sequence-specific and general skill learning in the learning phase. Consolidation of skill learning and sequence-specific learning were also intact in the ASD compared to the control groups. Conclusions/Significance These results suggest that autistic children can use the effects/results of implicit learning not only for a short period, but also for a longer stretch of time. Using these findings, therapists can design more effective educational and rehabilitation programs. PMID:20661300
Implicit meshes for surface reconstruction.
Ilic, Slobodan; Fua, Pascal
2006-02-01
Deformable 3D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, but fitting them involves minimizing a nondifferentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiable algebraic distance, but are harder to meaningfully deform and render. Here, we propose a method that combines the strength of both approaches. It relies on a technique that can turn a completely arbitrary triangulated mesh, such as one taken from the Web, into an implicit surface that closely approximates it and can deform in tandem with it. This allows both automated algorithms to take advantage of the attractive properties of implicit surfaces for fitting purposes and people to use standard deformation tools they feel comfortable for interaction and animation purposes. We demonstrate the applicability of our technique to modeling the human upper-body, including face, neck, shoulders, and ears, from noisy stereo and silhouette data.
Ego depletion impairs implicit learning.
Thompson, Kelsey R; Sanchez, Daniel J; Wesley, Abigail H; Reber, Paul J
2014-01-01
Implicit skill learning occurs incidentally and without conscious awareness of what is learned. However, the rate and effectiveness of learning may still be affected by decreased availability of central processing resources. Dual-task experiments have generally found impairments in implicit learning, however, these studies have also shown that certain characteristics of the secondary task (e.g., timing) can complicate the interpretation of these results. To avoid this problem, the current experiments used a novel method to impose resource constraints prior to engaging in skill learning. Ego depletion theory states that humans possess a limited store of cognitive resources that, when depleted, results in deficits in self-regulation and cognitive control. In a first experiment, we used a standard ego depletion manipulation prior to performance of the Serial Interception Sequence Learning (SISL) task. Depleted participants exhibited poorer test performance than did non-depleted controls, indicating that reducing available executive resources may adversely affect implicit sequence learning, expression of sequence knowledge, or both. In a second experiment, depletion was administered either prior to or after training. Participants who reported higher levels of depletion before or after training again showed less sequence-specific knowledge on the post-training assessment. However, the results did not allow for clear separation of ego depletion effects on learning versus subsequent sequence-specific performance. These results indicate that performance on an implicitly learned sequence can be impaired by a reduction in executive resources, in spite of learning taking place outside of awareness and without conscious intent.
NASA Astrophysics Data System (ADS)
Jiang, Zhen-Hua; Yan, Chao; Yu, Jian
2013-08-01
Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.
Implicit Learning of Nonlocal Musical Rules: Implicitly Learning More Than Chunks
ERIC Educational Resources Information Center
Kuhn, Gustav; Dienes, Zoltan
2005-01-01
Dominant theories of implicit learning assume that implicit learning merely involves the learning of chunks of adjacent elements in a sequence. In the experiments presented here, participants implicitly learned a nonlocal rule, thus suggesting that implicit learning can go beyond the learning of chunks. Participants were exposed to a set of…
Implicit Learning of Nonlocal Musical Rules: Implicitly Learning More Than Chunks
ERIC Educational Resources Information Center
Kuhn, Gustav; Dienes, Zoltan
2005-01-01
Dominant theories of implicit learning assume that implicit learning merely involves the learning of chunks of adjacent elements in a sequence. In the experiments presented here, participants implicitly learned a nonlocal rule, thus suggesting that implicit learning can go beyond the learning of chunks. Participants were exposed to a set of…
Integrating Implicit Bias into Counselor Education
ERIC Educational Resources Information Center
Boysen, Guy A.
2010-01-01
The author reviews the empirical and theoretical literature on implicit bias as it relates to counselor education. Counselor educators can integrate implicit bias into the concepts of multicultural knowledge, awareness, and skill. Knowledge about implicit bias includes its theoretical explanation, measurement, and impact on counseling. Awareness…
Semantic Generalization in Implicit Language Learning
ERIC Educational Resources Information Center
Paciorek, Albertyna; Williams, John N.
2015-01-01
Despite many years of investigation into implicit learning in nonlinguistic domains, the potential for implicit learning to deliver the kinds of generalizations that underlie natural language competence remains unclear. In a series of experiments, we investigated implicit learning of the semantic preferences of novel verbs, specifically, whether…
Semantic Generalization in Implicit Language Learning
ERIC Educational Resources Information Center
Paciorek, Albertyna; Williams, John N.
2015-01-01
Despite many years of investigation into implicit learning in nonlinguistic domains, the potential for implicit learning to deliver the kinds of generalizations that underlie natural language competence remains unclear. In a series of experiments, we investigated implicit learning of the semantic preferences of novel verbs, specifically, whether…
Permuting sparse rectangular matrices into block-diagonal form
Aykanat, Cevdet; Pinar, Ali; Catalyurek, Umit V.
2002-12-09
This work investigates the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for the solution of the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Besides proposing the models to represent sparse matrices and investigating related combinatorial problems, we provide a detailed survey of relevant literature to bridge the gap between different societies, investigate existing techniques for partitioning and propose new ones, and finally present a thorough empirical study of these techniques. Our experiments on a wide range of matrices, using state-of-the-art graph and hypergraph partitioning tools MeTiS and PaT oH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and run time.
Distributions of off-diagonal scattering matrix elements: Exact results
Nock, A. Kumar, S. Sommers, H.-J. Guhr, T.
2014-03-15
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process. The universal features of scattering in chaotic systems is most generally modeled by the Heidelberg approach which introduces stochasticity to the scattering matrix at the level of the Hamiltonian describing the scattering center. The statistics of the scattering matrix is obtained by averaging over the ensemble of random Hamiltonians of appropriate symmetry. We derive exact results for the distributions of the real and imaginary parts of the off-diagonal scattering matrix elements applicable to orthogonally-invariant and unitarily-invariant Hamiltonians, thereby solving a long standing problem. -- Highlights: •Scattering problem in complex or chaotic systems. •Heidelberg approach to model the chaotic nature of the scattering center. •A novel route to the nonlinear sigma model based on the characteristic function. •Exact results for the distributions of off-diagonal scattering-matrix elements. •Universal aspects of the scattering-matrix fluctuations.
Effect of Off-Diagonal Exciton-Phonon Coupling on Intramolecular Singlet Fission.
Huang, Zhongkai; Fujihashi, Yuta; Zhao, Yang
2017-07-20
Intramolecular singlet fission (iSF) materials provide remarkable advantages in terms of tunable electronic structures, and quantum chemistry studies have indicated strong electronic coupling modulation by high frequency phonon modes. In this work, we formulate a microscopic model of iSF with simultaneous diagonal and off-diagonal coupling to high-frequency modes. A nonperturbative treatment, the Dirac-Frenkel time-dependent variational approach is adopted using the multiple Davydov trial states. It is shown that both diagonal and off-diagonal coupling can aid efficient singlet fission if excitonic coupling is weak, and fission is only facilitated by diagonal coupling if excitonic coupling is strong. In the presence of off-diagonal coupling, it is found that high frequency modes create additional fission channels for rapid iSF. Results presented here may help provide guiding principles for design of efficient singlet fission materials by directly tuning singlet-triplet interstate coupling.
Lin, W.L.; Carlson, K.D.; Chen, C.J. |
1999-05-01
In this study, a diagonal Cartesian method for thermal analysis is developed for simulation of conjugate heat transfer over complex boundaries. This method uses diagonal line segments in addition to Cartesian coordinates. The velocity fields are also modeled using the diagonal Cartesian method. The transport equations are discretized with the finite analytic (FA) method. The current work is validated by simulating a rotated lid-driven cavity flow with conjugate heat transfer, and accurate results are obtained.
Flatness characteristics for diagonal scans from Varian and Siemens linear accelerators.
Dawson, J; Kahler, D; Gu, J; McDonald, B; Abrath, F; Kopecky, W
1996-09-01
The advent of 3D treatment planning systems whose algorithms utilize diagonal scan data to perform dose calculations has made the collection of diagonal profile data essential. Manufacturers' specifications (MS) on beam flatness and symmetry apply to both the radial and transverse axes of all square field sizes from 10 X 10 cm2 to the largest field available. Beam profile measurements were obtained for both diagonal axes over a range of field sizes and depths for two units, a Varian 2100C and a Siemens KD. In this note the International Electrotechnical Commission (IEC) flatness definition was used to characterize the diagonal flatness of each beam.
Implicit Theories of Peer Relationships
Rudolph, Karen D.
2009-01-01
This research investigated the role of children’s implicit theories of peer relationships in their psychological, emotional, and behavioral adjustment. Participants included 206 children (110 girls; 96 boys; M age = 10.13 years, SD = 1.16) who reported on their implicit theories of peer relationships, social goal orientation, need for approval, depressive and aggressive symptoms, and exposure to peer victimization. Parents also provided reports on aggressive symptoms. Results confirmed that holding an entity theory of peer relationships was associated with a greater tendency to endorse performance-oriented social goals and to evaluate oneself negatively in the face of peer disapproval. Moreover, entity theorists were more likely than incremental theorists to demonstrate depressive and aggressive symptoms when victimized. These findings contribute to social-cognitive theories of motivation and personality, and have practical implications for children exposed to peer victimization and associated difficulties. PMID:20396649
Revealing children's implicit spelling representations.
Critten, Sarah; Pine, Karen J; Messer, David J
2013-06-01
Conceptualizing the underlying representations and cognitive mechanisms of children's spelling development is a key challenge for literacy researchers. Using the Representational Redescription model (Karmiloff-Smith), Critten, Pine and Steffler (2007) demonstrated that the acquisition of phonological and morphological knowledge may be underpinned by increasingly explicit levels of spelling representation. However, their proposal that implicit representations may underlie early 'visually based' spelling remains unresolved. Children (N = 101, aged 4-6 years) were given a recognition task (Critten et al., 2007) and a novel production task, both involving verbal justifications of why spellings are correct/incorrect, strategy use and word pattern similarity. Results for both tasks supported an implicit level of spelling characterized by the ability to correctly recognize/produce words but the inability to explain operational strategies or generalize knowledge. Explicit levels and multiple representations were also in evidence across the two tasks. Implications for cognitive mechanisms underlying spelling development are discussed.
NASA Astrophysics Data System (ADS)
Ha, Sanghyun; You, Donghyun
2015-11-01
Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of both incompressible and compressible Navier-Stokes equations. A semi-implicit ADI finite-volume method for integration of the incompressible and compressible Navier-Stokes equations, which are discretized on a structured arbitrary grid, is parallelized for GPU computations using CUDA (Compute Unified Device Architecture). In the semi-implicit ADI finite-volume method, the nonlinear convection terms and the linear diffusion terms are integrated in time using a combination of an explicit scheme and an ADI scheme. Inversion of multiple tri-diagonal matrices is found to be the major challenge in GPU computations of the present method. Some of the algorithms for solving tri-diagonal matrices on GPUs are evaluated and optimized for GPU-acceleration of the present semi-implicit ADI computations of incompressible and compressible Navier-Stokes equations. Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning Grant NRF-2014R1A2A1A11049599.
Ego Depletion Impairs Implicit Learning
Thompson, Kelsey R.; Sanchez, Daniel J.; Wesley, Abigail H.; Reber, Paul J.
2014-01-01
Implicit skill learning occurs incidentally and without conscious awareness of what is learned. However, the rate and effectiveness of learning may still be affected by decreased availability of central processing resources. Dual-task experiments have generally found impairments in implicit learning, however, these studies have also shown that certain characteristics of the secondary task (e.g., timing) can complicate the interpretation of these results. To avoid this problem, the current experiments used a novel method to impose resource constraints prior to engaging in skill learning. Ego depletion theory states that humans possess a limited store of cognitive resources that, when depleted, results in deficits in self-regulation and cognitive control. In a first experiment, we used a standard ego depletion manipulation prior to performance of the Serial Interception Sequence Learning (SISL) task. Depleted participants exhibited poorer test performance than did non-depleted controls, indicating that reducing available executive resources may adversely affect implicit sequence learning, expression of sequence knowledge, or both. In a second experiment, depletion was administered either prior to or after training. Participants who reported higher levels of depletion before or after training again showed less sequence-specific knowledge on the post-training assessment. However, the results did not allow for clear separation of ego depletion effects on learning versus subsequent sequence-specific performance. These results indicate that performance on an implicitly learned sequence can be impaired by a reduction in executive resources, in spite of learning taking place outside of awareness and without conscious intent. PMID:25275517
[Psychological theory and implicit sociology.].
Sévigny, R
1983-01-01
This text is based on the hypothesis that every theory on the psychology of personality must inevitably, in one manner or another, have a sociological referent, that is to say, it must refer to a body of knowledge which deals with a diversity of social contexts and their relations to individuals. According to this working hypothesis, such a sociology is implicit. This text then discusses a group of theoretical approaches in an effort to verify this hypothesis. This approach allows the extrication of diverse forms or diverse expressions of this implicit sociology within this context several currents are rapidly explored : psychoanalysis, behaviorism, gestalt, classical theory of needs. The author also comments on the approach, inspired by oriental techniques or philosophies, which employs the notion of myth to deepen self awareness. Finally, from the same perspective, he comments at greater length on the work of Carl Rogers, highlighting the diverse form of implicit sociology. In addition to Carl Rogers, this text refers to Freud, Jung, Adler, Reich, Perls, Goodman, Skinner as well as to Ginette Paris and various analysts of Taoism. In conclusion, the author indicates the significance of his analysis from double viewpoint of psychological theory and practice.
Impaired Implicit Learning in Schizophrenia
Horan, William P.; Green, Michael F.; Knowlton, Barbara J.; Wynn, Jonathan K.; Mintz, Jim; Nuechterlein, Keith H.
2008-01-01
Schizophrenia patients consistently show deficits on tasks of explicit learning and memory. In contrast, their performance on implicit processing tasks often appears to be relatively intact, though most studies have focused on implicit learning of motor skills. This study evaluated implicit learning in 59 medicated schizophrenia outpatients and 43 healthy controls using two different cognitive skill tasks. Participants completed a Probabilistic Classification task to assess procedural habit learning and an Artificial Grammar task to assess incidental learning of complex rule-based knowledge, as well as an explicit verbal learning and memory task. In addition to performing worse than controls on the explicit learning task, patients showed worse overall performance on the Probabilistic Classification task, which involves gradual learning through trial-by-trial performance feedback. However, patients and controls showed similar levels of learning on the Artificial Grammar task, suggesting a preserved ability to acquire complex rule-based knowledge in the absence of performance feedback. Discussion focuses on possible explanations for schizophrenia patients’ poor Probabilistic Classification task performance. PMID:18763880
Coordinate Bethe ANSÄTZE for Non-Diagonal Boundaries
NASA Astrophysics Data System (ADS)
Ragoucy, Eric
2013-11-01
Bethe ansatz goes back to 1931, when H. Bethe invented it to solve some one-dimensional models, such as XXX spin chain, proposed by W. Heisenberg in 1928. Although it is a very powerful method to compute eigenvalues and eigenvectors of the corresponding Hamiltonian, it can be applied only for very specific boundary conditions: periodic boundary ones, and so-called open-diagonal boundary ones. After reviewing this method, we will present a generalization of it that applies also to open-triangular boundary conditions. This short note presents only the basic ideas of the technique, and does not attend to give a general overview of the subject. Interested readers should refer to the original papers and references therein.
Diagonalizing controller for a superconducting six-axis accelerometer
NASA Astrophysics Data System (ADS)
Bachrach, B.; Canavan, E. R.; Levine, W. S.
A relatively simple MIMO (multiple input, multiple output) controller which converts an instrument with a nondiagonally dominant transfer function matrix into a strongly diagonally dominant device is developed. The instrument, which uses inductance bridges to sense the position of a magnetically levitated superconducting mass, has very lightly damped resonances and fairly strong cross coupling. By taking advantage of the particular structure of the instrument's transfer function matrix, it is possible to develop a relatively simple controller which achieves the desired decoupling. This controller consists of two parts. The first part cancels the nondiagonal terms of the open-loop transfer function matrix, while the second part is simply a set of SISO (single input, single output) controllers. The stability of the closed-loop system is studied using Rosenbrock's INA (inverse Nyguist array) technique, which produces a simple set of conditions guaranteeing stability. Simulation of the closed-loop system indicates that it should easily achieve its performance goals.
Diagnosis of Interaction-driven Topological Phase via Exact Diagonalization
NASA Astrophysics Data System (ADS)
Wu, Han-Qing; He, Yuan-Yao; Fang, Chen; Meng, Zi Yang; Lu, Zhong-Yi
2016-08-01
We propose a general scheme for diagnosing interaction-driven topological phases in the weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition.
Performance Theory of Diagonal Conducting Wall Magnetohydrodynamic Accelerators
NASA Technical Reports Server (NTRS)
Litchford, R. J.
2004-01-01
The theoretical performance of diagonal conducting wall crossed-field accelerators is examined on the basis of an infinite segmentation assumption using a cross-plane averaged generalized Ohm s law for a partially ionized gas, including ion slip. The desired accelerator performance relationships are derived from the cross-plane averaged Ohm s law by imposing appropriate configuration and loading constraints. A current-dependent effective voltage drop model is also incorporated to account for cold-wall boundary layer effects, including gasdynamic variations, discharge constriction, and electrode falls. Definition of dimensionless electric fields and current densities leads to the construction of graphical performance diagrams, which further illuminate the rudimentary behavior of crossed-field accelerator operation.
Diagonal ordering operation technique applied to Morse oscillator
Popov, Dušan; Dong, Shi-Hai; Popov, Miodrag
2015-11-15
We generalize the technique called as the integration within a normally ordered product (IWOP) of operators referring to the creation and annihilation operators of the harmonic oscillator coherent states to a new operatorial approach, i.e. the diagonal ordering operation technique (DOOT) about the calculations connected with the normally ordered product of generalized creation and annihilation operators that generate the generalized hypergeometric coherent states. We apply this technique to the coherent states of the Morse oscillator including the mixed (thermal) state case and get the well-known results achieved by other methods in the corresponding coherent state representation. Also, in the last section we construct the coherent states for the continuous dynamics of the Morse oscillator by using two new methods: the discrete–continuous limit, respectively by solving a finite difference equation. Finally, we construct the coherent states corresponding to the whole Morse spectrum (discrete plus continuous) and demonstrate their properties according the Klauder’s prescriptions.
Diagonal composite order in a two-channel Kondo lattice.
Hoshino, Shintaro; Otsuki, Junya; Kuramoto, Yoshio
2011-12-09
A novel type of symmetry breaking is reported for the two-channel Kondo lattice where conduction electrons have spin and orbital (channel) degrees of freedom. Using the continuous-time quantum Monte Carlo and the dynamical mean-field theory, a spontaneous breaking of the orbital symmetry is observed. The tiny breakdown of orbital occupation number, however, vanishes if the conduction electrons have the particle-hole symmetry. The proper order parameter instead is identified as a composite quantity representing the orbital-selective Kondo effect. The single-particle spectrum of the selected orbital shows insulating property, while the other orbital behaves as a Fermi liquid. This composite order is the first example of odd-frequency order other than off-diagonal order (superconductivity), and is a candidate of hidden order in f-electron systems.
Cold bosons in optical lattices: a tutorial for exact diagonalization
NASA Astrophysics Data System (ADS)
Raventós, David; Graß, Tobias; Lewenstein, Maciej; Juliá-Díaz, Bruno
2017-06-01
Exact diagonalization (ED) techniques are a powerful method for studying many-body problems. Here, we apply this method to systems of few bosons in an optical lattice, and use it to demonstrate the emergence of interesting quantum phenomena such as fragmentation and coherence. Starting with a standard Bose-Hubbard Hamiltonian, we first revise the characterisation of the superfluid to Mott insulator (MI) transitions. We then consider an inhomogeneous lattice, where one potential minimum is made much deeper than the others. The MI phase due to repulsive on-site interactions then competes with the trapping of all atoms in the deep potential. Finally, we turn our attention to attractively interacting systems, and discuss the appearance of strongly correlated phases and the onset of localisation for a slightly biased lattice. The article is intended to serve as a tutorial for ED of Bose-Hubbard models.
Diagnosis of Interaction-driven Topological Phase via Exact Diagonalization.
Wu, Han-Qing; He, Yuan-Yao; Fang, Chen; Meng, Zi Yang; Lu, Zhong-Yi
2016-08-05
We propose a general scheme for diagnosing interaction-driven topological phases in the weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition.
Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition
NASA Astrophysics Data System (ADS)
Weinstein, Marvin; Chandra, Ravi; Auerbach, Assa
2012-02-01
We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. In contrast to variational approaches and most implementations of DMRG, Lanczos rotations towards the ground state do not involve incremental minimizations, (e.g. sweeping procedures) which may get stuck in false local minima. The lattice of size N is partitioned into two subclusters. At each iteration the rotating Lanczos vector is compressed into two sets of nsvd small subcluster vectors using singular value decomposition. For low entanglement entropy See, (satisfied by short range Hamiltonians), the truncation error is bounded by (-nsvd^1/See). Convergence is tested for the Heisenberg model on Kagom'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given. Reference: arXiv:1105.0007
Filter diagonalization method for processing PFG NMR data.
Martini, Beau R; Mandelshtam, Vladimir A; Morris, Gareth A; Colbourne, Adam A; Nilsson, Mathias
2013-09-01
Obtaining diffusion coefficients from PFG NMR diffusion (a.k.a DOSY) data is, in the general case, an ill-posed problem. Numerous methods for processing such data have therefore been developed, each with different constraints and assumptions. The Regularized Resolvent Transform (RRT) is a proven and robust method for spectral inversion. In earlier papers RRT, albeit very slow, was argued to be superior for DOSY processing to a related algorithm, the Filter Diagonalization Method (FDM). Here FDM is revisited and a new regularization method is implemented, which drastically improves the performance and provides spectra of comparable or better quality to those provided by RRT. Both the RRT and the FDM for DOSY processing have been implemented as options in the free and open source DOSY Toolbox. Copyright © 2013 Elsevier Inc. All rights reserved.
Reducing memory cost of exact diagonalization using singular value decomposition.
Weinstein, Marvin; Auerbach, Assa; Chandra, V Ravi
2011-11-01
We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, without restricting to variational ansatzes. The lattice of size N is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of n(svd) smaller subcluster vectors using singular value decomposition. For low entanglement entropy S(ee), (satisfied by short-range Hamiltonians), the truncation error is expected to vanish as exp(-n(svd)(1/S(ee))). Convergence is tested for the Heisenberg model on Kagomé clusters of 24, 30, and 36 sites, with no lattice symmetries exploited, using less than 15 GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.
Exact Diagonalization of Heisenberg SU(N) models.
Nataf, Pierre; Mila, Frédéric
2014-09-19
Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on n sites increases very fast with N, this formulation allows us to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).
Protein folding in HP model on hexagonal lattices with diagonals
2014-01-01
Three dimensional structure prediction of a protein from its amino acid sequence, known as protein folding, is one of the most studied computational problem in bioinformatics and computational biology. Since, this is a hard problem, a number of simplified models have been proposed in literature to capture the essential properties of this problem. In this paper we introduce the hexagonal lattices with diagonals to handle the protein folding problem considering the well researched HP model. We give two approximation algorithms for protein folding on this lattice. Our first algorithm is a 53-approximation algorithm, which is based on the strategy of partitioning the entire protein sequence into two pieces. Our next algorithm is also based on partitioning approaches and improves upon the first algorithm. PMID:24564789
Exact-diagonalization study of exciton condensation in electron bilayers
NASA Astrophysics Data System (ADS)
Kaneko, T.; Ejima, S.; Fehske, H.; Ohta, Y.
2013-07-01
We report on small-cluster exact-diagonalization calculations which prove the formation of electron-hole pairs (excitons) as a prerequisite for spontaneous interlayer phase coherence in double-layer systems described by the extended Falicov-Kimball model. Evaluating the anomalous Green's function and momentum distribution function of the pairs, and thereby analyzing the dependence of the exciton binding energy, condensation amplitude, and coherence length on the Coulomb interaction strength, we demonstrate a crossover between a BCS-like electron-hole pairing transition and a Bose-Einstein condensation of tightly bound preformed excitons. We furthermore show that a mass imbalance between electrons and holes tends to suppress the condensation of excitons.
Quantum transport in chains with noisy off-diagonal couplings.
Pereverzev, Andrey; Bittner, Eric R
2005-12-22
We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time evolution of the system reduces to the [Lindblad, Commun. Math. Phys. 48, 119 (1976)] equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfies discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.
Eye movements during mental time travel follow a diagonal line.
Hartmann, Matthias; Martarelli, Corinna S; Mast, Fred W; Stocker, Kurt
2014-11-01
Recent research showed that past events are associated with the back and left side, whereas future events are associated with the front and right side of space. These spatial-temporal associations have an impact on our sensorimotor system: thinking about one's past and future leads to subtle body sways in the sagittal dimension of space (Miles, Nind, & Macrae, 2010). In this study we investigated whether mental time travel leads to sensorimotor correlates in the horizontal dimension of space. Participants were asked to mentally displace themselves into the past or future while measuring their spontaneous eye movements on a blank screen. Eye gaze was directed more rightward and upward when thinking about the future than when thinking about the past. Our results provide further insight into the spatial nature of temporal thoughts, and show that not only body, but also eye movements follow a (diagonal) "time line" during mental time travel.
Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
NASA Astrophysics Data System (ADS)
Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
2013-10-01
Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T-Q relation and the Bethe ansatz equations are derived.
Diagonalization and Jordan Normal Form--Motivation through "Maple"[R
ERIC Educational Resources Information Center
Glaister, P.
2009-01-01
Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…
Diagonalization and Jordan Normal Form--Motivation through "Maple"[R
ERIC Educational Resources Information Center
Glaister, P.
2009-01-01
Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…
Implicit Social Biases in People With Autism.
Birmingham, Elina; Stanley, Damian; Nair, Remya; Adolphs, Ralph
2015-11-01
Implicit social biases are ubiquitous and are known to influence social behavior. A core diagnostic criterion of autism spectrum disorders (ASD) is abnormal social behavior. We investigated the extent to which individuals with ASD might show a specific attenuation of implicit social biases, using Implicit Association Tests (IATs) involving social (gender, race) and nonsocial (nature, shoes) categories. High-functioning adults with ASD showed intact but reduced IAT effects relative to healthy control participants. We observed no selective attenuation of implicit social (vs. nonsocial) biases in our ASD population. To extend these results, we supplemented our healthy control data with data collected from a large online sample from the general population and explored correlations between autistic traits and IAT effects. We observed no systematic relationship between autistic traits and implicit social biases in our online and control samples. Taken together, these results suggest that implicit social biases, as measured by the IAT, are largely intact in ASD. © The Author(s) 2015.
The Dynamics of Some Iterative Implicit Schemes
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.
1994-01-01
The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations is analyzed using the theory of dynamical systems. With the aid of parallel Connection Machines (CM-2 and CM-5), the associated bifurcation diagrams as a function of the time step, and the complex behavior of the associated 'numerical basins of attraction' of these iterative implicit schemes are revealed and compared. Studies showed that all of the four implicit LMMs exhibit a drastic distortion and segmentation but less shrinkage of the basin of attraction of the true solution than standard explicit methods. The numerical basins of attraction of a noniterative implicit procedure mimic more closely the basins of attraction of the differential equations than the iterative implicit procedures for the four implicit LMMs.
An implicit Smooth Particle Hydrodynamic code
Knapp, Charles E.
2000-05-01
An implicit version of the Smooth Particle Hydrodynamic (SPH) code SPHINX has been written and is working. In conjunction with the SPHINX code the new implicit code models fluids and solids under a wide range of conditions. SPH codes are Lagrangian, meshless and use particles to model the fluids and solids. The implicit code makes use of the Krylov iterative techniques for solving large linear-systems and a Newton-Raphson method for non-linear corrections. It uses numerical derivatives to construct the Jacobian matrix. It uses sparse techniques to save on memory storage and to reduce the amount of computation. It is believed that this is the first implicit SPH code to use Newton-Krylov techniques, and is also the first implicit SPH code to model solids. A description of SPH and the techniques used in the implicit code are presented. Then, the results of a number of tests cases are discussed, which include a shock tube problem, a Rayleigh-Taylor problem, a breaking dam problem, and a single jet of gas problem. The results are shown to be in very good agreement with analytic solutions, experimental results, and the explicit SPHINX code. In the case of the single jet of gas case it has been demonstrated that the implicit code can do a problem in much shorter time than the explicit code. The problem was, however, very unphysical, but it does demonstrate the potential of the implicit code. It is a first step toward a useful implicit SPH code.
A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation
Smith, Peter E.
2006-01-01
A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.
O'Shea, Brian; Watson, Derrick G; Brown, Gordon D A
2016-02-01
How can implicit attitudes best be measured? The Implicit Relational Assessment Procedure (IRAP), unlike the Implicit Association Test (IAT), claims to measure absolute, not just relative, implicit attitudes. In the IRAP, participants make congruent (Fat Person-Active: false; Fat Person-Unhealthy: true) or incongruent (Fat Person-Active: true; Fat Person-Unhealthy: false) responses in different blocks of trials. IRAP experiments have reported positive or neutral implicit attitudes (e.g., neutral attitudes toward fat people) in cases in which negative attitudes are normally found on explicit or other implicit measures. It was hypothesized that these results might reflect a positive framing bias (PFB) that occurs when participants complete the IRAP. Implicit attitudes toward categories with varying prior associations (nonwords, social systems, flowers and insects, thin and fat people) were measured. Three conditions (standard, positive framing, and negative framing) were used to measure whether framing influenced estimates of implicit attitudes. It was found that IRAP scores were influenced by how the task was framed to the participants, that the framing effect was modulated by the strength of prior stimulus associations, and that a default PFB led to an overestimation of positive implicit attitudes when measured by the IRAP. Overall, the findings question the validity of the IRAP as a tool for the measurement of absolute implicit attitudes. A new tool (Simple Implicit Procedure:SIP) for measuring absolute, not just relative, implicit attitudes is proposed. (PsycINFO Database Record
Using Implicit Measures to Highlight Science Teachers' Implicit Theories of Intelligence
ERIC Educational Resources Information Center
Mascret, Nicolas; Roussel, Peggy; Cury, François
2015-01-01
Using an innovative method, a Single-Target Implicit Association Test (ST-IAT) was created to explore the implicit theories of intelligence among science and liberal arts teachers and their relationships with their gender. The results showed that for science teachers--especially for male teachers--there was a negative implicit association between…
Using Implicit Measures to Highlight Science Teachers' Implicit Theories of Intelligence
ERIC Educational Resources Information Center
Mascret, Nicolas; Roussel, Peggy; Cury, François
2015-01-01
Using an innovative method, a Single-Target Implicit Association Test (ST-IAT) was created to explore the implicit theories of intelligence among science and liberal arts teachers and their relationships with their gender. The results showed that for science teachers--especially for male teachers--there was a negative implicit association between…
Metrology target design (MTD) solution for diagonally orientated DRAM layer
NASA Astrophysics Data System (ADS)
Lee, Myungjun; Smith, Mark D.; Adel, Michael E.; Chen, Chia-Hung; Huang, Chin-Chang; Huang, Hao-Lun; Tsai, Hsueh-Jen; Wang, I.-Lin; Huang, Jen-Chou; Chin, Jo-Lan; Chou, Kuo-Yao; Lan, Yuan-Ku; Lung, Hsien-Yen; Yang, Jui-Chin; Itzkovich, Tal; Huang, Healthy; Abramovitz, Yaniv; Song, Jinyan; Dror, Chen; Cheng, Harvey; Levy, Ady
2016-03-01
We present a novel metrology target design framework using the scanner exit pupil wavefront analysis together with Zernike sensitivity analysis (ZSA) based on the Monte-Carlo technique. The proposed method enables the design of robust metrology targets that maximize target process window (PW) while minimizing placement error discrepancies with device features in the presence of spatial and temporal variation of the aberration characteristics of an exposure tool. Knowing the limitations of lithography systems, design constraints, and detailed lithography information including illumination, mask type, etc., we can successfully design an optimal metrology target. We have validated our new metrology target design (MTD) method for one of the challenging DRAM active layer consisting of diagonal line and space patterns illuminated by a rotated extreme dipole source. We find that an optimal MTD target gives the maximized PW and the strong device correlation, resulting in the dramatic improvement of overall overlay performance. The proposed target design framework is completely general and can be used to optimize targets for different lithography conditions. The results from our analysis are both physically sensible and in good agreement with experimental results.
Microscopic diagonal entropy and its connection to basic thermodynamic relations
Polkovnikov, Anatoli
2011-02-15
We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as S{sub d}=-{Sigma}{sub n{rho}nn}ln{rho}{sub nn} with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy S{sub n} = -Tr{rho} ln {rho}. However, in contrast to S{sub n}, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy distribution function and thus it is measurable, at least in principle. Under very generic assumptions of the locality of the Hamiltonian and non-integrability the d-entropy becomes a unique function of the average energy in large systems and automatically satisfies the fundamental thermodynamic relation. This relation reduces to the first law of thermodynamics for quasi-static processes. The d-entropy is also automatically conserved for adiabatic processes. We illustrate our results with explicit examples and show that S{sub d} behaves consistently with expectations from thermodynamics.
Exact Diagonalization studies of frustrated AFM Heisenberg polytopes
NASA Astrophysics Data System (ADS)
Rousochatzakis, Ioannis; Laeuchli, Andreas; Mila, Frederic
2007-03-01
We explore the low energy physics of the AFM s=1/2 Heisenberg model on a number of frustrated magnetic molecule systems using exact diagonalization (ED). Particular emphasis is given to molecules with spins occupying the vertices of symmetric polyhedra. To this end, we have extended the standard ED technique in order to exploit the full point group (permutation) symmetry, thus including higher than one-dimensional irreducible representations. Apart from classifying the energy spectra according to both spin and permutation symmetries, our method provides the exact level degeneracies. In particular, for large frustrated polytopes, we find the existence of an accordingly large number of low-lying singlets below the first triplet, similarly to the case of frustrated 2D magnets. We also study the properties of the local spectral density functions, in view of interpreting recent neutron scattering experiments in Fe30, one of the biggest AFM frustrated molecule available (comprising 30 spins 5/2 mounted on the vertices of a icosidodecahedron).
Significance of matrix diagonalization in modelling inelastic electron scattering.
Lee, Z; Hambach, R; Kaiser, U; Rose, H
2016-11-21
Electron scattering is always applied as one of the routines to investigate nanostructures. Nowadays the development of hardware offers more and more prospect for this technique. For example imaging nanostructures with inelastic scattered electrons may allow to produce component-sensitive images with atomic resolution. Modelling inelastic electron scattering is therefore essential for interpreting these images. The main obstacle to study inelastic scattering problem is its complexity. During inelastic scattering, incident electrons entangle with objects, and the description of this process involves a multidimensional array. Since the simulation usually involves fourdimensional Fourier transforms, the computation is highly inefficient. In this work we have offered one solution to handle the multidimensional problem. By transforming a high dimensional array into twodimensional array, we are able to perform matrix diagonalization and approximate the original multidimensional array with its twodimensional eigenvectors. Our procedure reduces the complicated multidimensional problem to a twodimensional problem. In addition, it minimizes the number of twodimensional problems. This method is very useful for studying multiple inelastic scattering.
Development of precise off-diagonal magnetoimpedance gradiometer for magnetocardiography
NASA Astrophysics Data System (ADS)
Uchiyama, Tsuyoshi; Takiya, Takashi
2017-05-01
We have developed a precise off-diagonal magnetoimpedance (MI) gradiometer that can operate in an unshielded environment and at room temperature with 200 pT root-mean-square noise in a 100 Hz bandwidth. The MI sensor probe is compact and easy to handle. The achieved noise level corresponds approximately to the maximum magnetocardiography (MCG) signal reported so far. We have performed MCG measurements using the developed gradiometer system in an unshielded environment, and a real-time signal like MCG can be identified by the MI gradiometer when the distance between the sensor head and chest surface is less than 3 mm. However, the signal seems to be affected by the movement of the chest surface caused by the heartbeat. A peak magnetic signal of 100 pT (corresponding to conventional MCG) was observed when the sensor head was set 10 mm apart from the chest surface to avoid the influence of the chest movement. Under such conditions, the signal needed to be averaged over more than 50 cycles to identify the peak magnetic signal.
Power take-off analysis for diagonally connected MHD channels
Pan, Y C; Doss, E D
1980-01-01
The electrical loading of the power take-off region of diagonally connected MHD channels is investigated by a two-dimensional model. The study examines the loading schemes typical of those proposed for the U-25 and U-25 Bypass channels. The model is applicable for the following four cases: (1) connection with diodes only, (2) connection with diodes and equal resistors, (3) connection with diodes and variable resistances to obtain a given current distribution, and (4) connection with diodes and variable resistors under changing load. The analysis is applicable for the power take-off regions of single or multiple-output systems. The general behaviors of the current and the potential distributions in all four cases are discussed. The analytical results are in good agreement with the experimental data. It is found possible to design the electrical circuit of the channel in the take-off region so as to achieve a fairly even load current output under changing total load current.
Improvement of child survival in Mexico: the diagonal approach.
Sepúlveda, Jaime; Bustreo, Flavia; Tapia, Roberto; Rivera, Juan; Lozano, Rafael; Oláiz, Gustavo; Partida, Virgilio; García-García, Lourdes; Valdespino, José Luis
2006-12-02
Public health interventions aimed at children in Mexico have placed the country among the seven countries on track to achieve the goal of child mortality reduction by 2015. We analysed census data, mortality registries, the nominal registry of children, national nutrition surveys, and explored temporal association and biological plausibility to explain the reduction of child, infant, and neonatal mortality rates. During the past 25 years, child mortality rates declined from 64 to 23 per 1000 livebirths. A dramatic decline in diarrhoea mortality rates was recorded. Polio, diphtheria, and measles were eliminated. Nutritional status of children improved significantly for wasting, stunting, and underweight. A selection of highly cost-effective interventions bridging clinics and homes, what we called the diagonal approach, were central to this progress. Although a causal link to the reduction of child mortality was not possible to establish, we saw evidence of temporal association and biological plausibility to the high level of coverage of public health interventions, as well as significant association to the investments in women education, social protection, water, and sanitation. Leadership and continuity of public health policies, along with investments on institutions and human resources strengthening, were also among the reasons for these achievements.
Implicit bias, awareness and imperfect cognitions.
Holroyd, Jules
2015-05-01
Are individuals responsible for behaviour that is implicitly biased? Implicitly biased actions are those which manifest the distorting influence of implicit associations. That they express these 'implicit' features of our cognitive and motivational make up has been appealed to in support of the claim that, because individuals lack the relevant awareness of their morally problematic discriminatory behaviour, they are not responsible for behaving in ways that manifest implicit bias. However, the claim that such influences are implicit is, in fact, not straightforwardly related to the claim that individuals lack awareness of the morally problematic dimensions of their behaviour. Nor is it clear that lack of awareness does absolve from responsibility. This may depend on whether individuals culpably fail to know something that they should know. I propose that an answer to this question, in turn, depends on whether other imperfect cognitions are implicated in any lack of the relevant kind of awareness. In this paper I clarify our understanding of 'implicitly biased actions' and then argue that there are three different dimensions of awareness that might be at issue in the claim that individuals lack awareness of implicit bias. Having identified the relevant sense of awareness I argue that only one of these senses is defensibly incorporated into a condition for responsibility, rejecting recent arguments from Washington & Kelly for an 'externalist' epistemic condition. Having identified what individuals should - and can - know about their implicitly biased actions, I turn to the question of whether failures to know this are culpable. This brings us to consider the role of implicit biases in relation to other imperfect cognitions. I conclude that responsibility for implicitly biased actions may depend on answers to further questions about their relationship to other imperfect cognitions.
Early LLNL Application Scaling Results on BlueGene/L
Cook, A W; Greenough, J A; Gygi, F; Streitz, F H; Kubota, A; Bulatov, V V; Louis, S
2004-11-01
Miranda is a high order hydrodynamics code for computing fluid instabilities and turbulent mixing. It employs FFTs and band-diagonal matrix solvers for computing spectrally-accurate derivatives, combined with high-order integration methods for time advancement; e.g., fourth-order Runge-Kutta. Fluid properties, i.e., viscosity, diffusivity and thermal conductivity, are computed from kinetic theory. The code contains solvers for both compressible and incompressible flows. It has been used primarily for studying Rayleigh-Taylor (R-T) and Richtmyer-Meshkov (R-M) instabilities, which occur in supernovae and Inertial Confinement Fusion (ICF).
Understanding Implicit Bias: What Educators Should Know
ERIC Educational Resources Information Center
Staats, Cheryl
2016-01-01
The desire to ensure the best for children is precisely why educators should become aware of the concept of implicit bias: the attitudes or stereotypes that affect our understanding, actions, and decisions in an unconscious manner. Operating outside of our conscious awareness, implicit biases are pervasive, and they can challenge even the most…
Implicit Relational Effects in Associative Recognition
ERIC Educational Resources Information Center
Algarabel, S.; Pitarque, A.; Combita, L. M.; Rodriguez, L. A.
2013-01-01
We study the contribution of implicit relatedness to associative recognition in two experiments. In the first experiment, we showed an implicit improvement in recognition when the stimulus elements of each word pair shared common letters and they were unpaired at test. Moreover, when asked to study the stimuli under divided attention, recollection…
Evidence for Implicit Learning in Syntactic Comprehension
ERIC Educational Resources Information Center
Fine, Alex B.; Jaeger, T. Florian
2013-01-01
This study provides evidence for implicit learning in syntactic comprehension. By reanalyzing data from a syntactic priming experiment (Thothathiri & Snedeker, 2008), we find that the error signal associated with a syntactic prime influences comprehenders' subsequent syntactic expectations. This follows directly from error-based implicit learning…
Implicit and Explicit Learning of Languages.
ERIC Educational Resources Information Center
McDermott, James E.
1999-01-01
Discusses theoretical and practical issues connected with implicit and explicit learning of languages. Explicit learning is knowledge expressed in the form of rules or definitions; implicit knowledge can be inferred to exist because of observed performance but cannot be clearly described. Hypothesizes why explicit learning can lead to implicit…
Why Explicit Knowledge Cannot Become Implicit Knowledge
ERIC Educational Resources Information Center
VanPatten, Bill
2016-01-01
In this essay, I review one of the conclusions in Lindseth (2016) published in "Foreign Language Annals." That conclusion suggests that explicit learning and practice (what she called form-focused instruction) somehow help the development of implicit knowledge (or might even become implicit knowledge). I argue for a different…
Why Explicit Knowledge Cannot Become Implicit Knowledge
ERIC Educational Resources Information Center
VanPatten, Bill
2016-01-01
In this essay, I review one of the conclusions in Lindseth (2016) published in "Foreign Language Annals." That conclusion suggests that explicit learning and practice (what she called form-focused instruction) somehow help the development of implicit knowledge (or might even become implicit knowledge). I argue for a different…
Evidence for Implicit Learning in Syntactic Comprehension
ERIC Educational Resources Information Center
Fine, Alex B.; Jaeger, T. Florian
2013-01-01
This study provides evidence for implicit learning in syntactic comprehension. By reanalyzing data from a syntactic priming experiment (Thothathiri & Snedeker, 2008), we find that the error signal associated with a syntactic prime influences comprehenders' subsequent syntactic expectations. This follows directly from error-based implicit learning…
Psychometric Intelligence Dissociates Implicit and Explicit Learning
ERIC Educational Resources Information Center
Gebauer, Guido F.; Mackintosh, Nicholas J.
2007-01-01
The hypothesis that performance on implicit learning tasks is unrelated to psychometric intelligence was examined in a sample of 605 German pupils. Performance in artificial grammar learning, process control, and serial learning did not correlate with various measures of intelligence when participants were given standard implicit instructions.…
Implicit and Explicit Exercise and Sedentary Identity
ERIC Educational Resources Information Center
Berry, Tanya R.; Strachan, Shaelyn M.
2012-01-01
We examined the relationship between implicit and explicit "exerciser" and "sedentary" self-identity when activated by stereotypes. Undergraduate participants (N = 141) wrote essays about university students who either liked to exercise or engage in sedentary activities. This was followed by an implicit identity task and an explicit measure of…
Implicit and Explicit Instruction of Spelling Rules
ERIC Educational Resources Information Center
Kemper, M. J.; Verhoeven, L.; Bosman, A. M. T.
2012-01-01
The study aimed to compare the differential effectiveness of explicit and implicit instruction of two Dutch spelling rules. Students with and without spelling disabilities were instructed a spelling rule either implicitly or explicitly in two experiments. Effects were tested in a pretest-intervention-posttest control group design. Experiment 1…
Implicit and Explicit Instruction of Spelling Rules
ERIC Educational Resources Information Center
Kemper, M. J.; Verhoeven, L.; Bosman, A. M. T.
2012-01-01
The study aimed to compare the differential effectiveness of explicit and implicit instruction of two Dutch spelling rules. Students with and without spelling disabilities were instructed a spelling rule either implicitly or explicitly in two experiments. Effects were tested in a pretest-intervention-posttest control group design. Experiment 1…
Altered Implicit Category Learning in Anorexia Nervosa
Shott, Megan E.; Filoteo, J. Vincent; Jappe, Leah M.; Pryor, Tamara; Maddox, W. Todd; Rollin, Michael D.H.; Hagman, Jennifer O.; Frank, Guido K.W.
2012-01-01
Objective Recent research has identified specific cognitive deficits in patients with anorexia nervosa (AN), including impairment in executive functioning and attention. Another such cognitive process, implicit category learning has been less studied in AN. This study examined whether implicit category learning is impaired in AN. Method Twenty-one women diagnosed with AN and 19 control women (CW) were administered an implicit category learning task in which they were asked to categorize simple perceptual stimuli (Gabor patches) into one of two categories. Category membership was based on a linear integration (i.e., an implicit task) of two stimulus dimensions (orientation and spatial frequency of the stimulus). Results AN individuals were less accurate on implicit category learning relative to age-matched CW. Model-based analyses indicated that, even when AN individuals used the appropriate (i.e., implicit) strategy they were still impaired relative to CW who also used the same strategy. In addition, task performance in AN patients was worse the higher they were in self-reported novelty seeking and the lower they were in sensitivity to punishment. Conclusions These results indicate that AN patients have implicit category learning deficits, and given this type of learning is thought to be mediated by striatal dopamine pathways, AN patients may have deficits in these neural systems. The finding of significant correlations with novelty seeking and sensitivity to punishment suggests that feedback sensitivity is related to implicit learning in AN. PMID:22201300
Implicit social cognition: From measures to mechanisms
Nosek, Brian A.; Hawkins, Carlee Beth; Frazier, Rebecca S.
2011-01-01
Most of human cognition occurs outside of conscious awareness or conscious control. Some of these implicit processes influence social perception, judgment and action. The last fifteen years of research in implicit social cognition can be characterized as the Age of Measurement because of a proliferation of measurement methods and research evidence demonstrating their practical value for predicting human behavior. Implicit measures assess constructs that are distinct, but related, to self-report assessments, and predict variation in behavior that is not accounted for by those explicit measures. The present state of knowledge provides a foundation for the next age of implicit social cognition – clarification of the mechanisms underlying implicit measurement and how the measured constructs influence behavior. PMID:21376657
Implicit sequence learning with competing explicit cues.
Jiménez, L; Méndez, C
2001-05-01
Previous research has shown that the expression of implicit sequence learning is eliminated in a choice reaction time task when an explicit cue allows participants to accurately predict the next stimulus (Cleeremans, 1997), but that two contingencies predicting the same outcome can be learned and expressed simultaneously when both of them remain implicit (Jiménez & Méndez, 1999). Two experiments tested the hypothesis that it is the deliberate use of explicit knowledge that produces the inhibitory effects over the expression of implicit sequence learning. However, the results of these experiments do not support this hypothesis, rather showing that implicit learning is acquired and expressed regardless of the influence of explicit knowledge. These results are interpreted as reinforcing the thesis about the automatic nature of both the acquisition and the expression of implicit sequence learning. The contradictory results reported by Cleeremans are attributed to a floor effect derived from the use of a special type of explicit cue.
Implicit restart Lanczos as an eigensolver
NASA Astrophysics Data System (ADS)
Rajaie Khorasani, Reza; Dumont, Randall S.
2009-03-01
This paper investigates the efficiency of the implicit restart Lanczos and simple (without reorthogonalization) Lanczos algorithms, as eigensolvers for large scale computations in molecular and chemical physics. Using the cardioid billiard and the hydrogen cyanide/hydrogen isocyanide (HCN/HNC) molecule as model systems we demonstrate superior efficiency of implicit restart Lanczos compared to the simple Lanczos algorithm. A modified implementation of implicit restart Lanczos is also presented which works with a smaller Krylov space—with associated savings in memory—and can handle larger basis sets than the usual implicit restart Lanczos. It also enables getting all eigenpairs of a matrix, or all eigenvalues below a threshold (where the number of such is not known before hand), which is more difficult with the usual implicit restart algorithm.
Sequential congruency effects in implicit sequence learning.
Jiménez, Luis; Lupiáñez, Juan; Vaquero, Joaquín M M
2009-09-01
We deal with situations incongruent with our automatic response tendencies much better right after having done so on a previous trial than after having reacted to a congruent trial. The nature of the mechanisms responsible for these sequential congruency effects is currently a hot topic of debate. According to the conflict monitoring model these effects depend on the adjustment of control triggered by the detection of conflict on the preceding situation. We tested whether these conflict monitoring processes can operate implicitly in an implicit learning procedure, modulating the expression of knowledge of which participants are not aware. We reanalyze recently published data, and present an experiment with a probabilistic sequence learning procedure, both showing consistent effects of implicit sequence learning. Despite being implicit, the expression of learning was reduced or completely eliminated right after trials incongruent with the learned sequence, thus showing that sequential congruency effects can be obtained even when the source of congruency itself remains implicit.
Implicit Social Biases in People with Autism
Birmingham, Elina; Stanley, Damian; Nair, Remya; Adolphs, Ralph
2015-01-01
Implicit social biases are ubiquitous and are known to influence social behavior. A core diagnostic criterion of Autism Spectrum Disorder (ASD) is abnormal social behavior. Here we investigated the extent to which individuals with ASD might show a specific attenuation of implicit social biases, using the Implicit Association Test (IAT) across Social (gender, race) and Nonsocial (flowers/insect, shoes) categories. High-functioning adults with ASD showed intact but reduced IAT effects relative to healthy controls. Importantly, we observed no selective attenuation of implicit social (vs. nonsocial) biases in our ASD population. To extend these results, we collected data from a large online sample of the general population, and explored correlations between autistic traits and IAT effects. No associations were found between autistic traits and IAT effects for any of the categories tested in our online sample. Taken together, these results suggest that implicit social biases, as measured by the IAT, are largely intact in ASD. PMID:26386014
Implicit measures: A normative analysis and review.
De Houwer, Jan; Teige-Mocigemba, Sarah; Spruyt, Adriaan; Moors, Agnes
2009-05-01
Implicit measures can be defined as outcomes of measurement procedures that are caused in an automatic manner by psychological attributes. To establish that a measurement outcome is an implicit measure, one should examine (a) whether the outcome is causally produced by the psychological attribute it was designed to measure, (b) the nature of the processes by which the attribute causes the outcome, and (c) whether these processes operate automatically. This normative analysis provides a heuristic framework for organizing past and future research on implicit measures. The authors illustrate the heuristic function of their framework by using it to review past research on the 2 implicit measures that are currently most popular: effects in implicit association tests and affective priming tasks. (PsycINFO Database Record (c) 2009 APA, all rights reserved).
Implicit social cognition: from measures to mechanisms.
Nosek, Brian A; Hawkins, Carlee Beth; Frazier, Rebecca S
2011-04-01
Most human cognition occurs outside conscious awareness or conscious control. Some of these implicit processes influence social perception, judgment and action. The past 15 years of research in implicit social cognition can be characterized as the Age of Measurement because of a proliferation of measurement methods and research evidence demonstrating their practical value for predicting human behavior. Implicit measures assess constructs that are distinct, but related, to self-report assessments, and predict variation in behavior that is not accounted for by those explicit measures. The present state of knowledge provides a foundation for the next age of implicit social cognition: clarification of the mechanisms underlying implicit measurement and how the measured constructs influence behavior.
Scroggins, W Anthony; Mackie, Diane M; Allen, Thomas J; Sherman, Jeffrey W
2016-02-01
In three experiments, we used a novel Implicit Association Test procedure to investigate the impact of group memberships on implicit bias and implicit group boundaries. Results from Experiment 1 indicated that categorizing targets using a shared category reduced implicit bias by increasing the extent to which positivity was associated with Blacks. Results from Experiment 2 revealed that shared group membership, but not mere positivity of a group membership, was necessary to reduce implicit bias. Quadruple process model analyses indicated that changes in implicit bias caused by shared group membership are due to changes in the way that targets are evaluated, not to changes in the regulation of evaluative bias. Results from Experiment 3 showed that categorizing Black targets into shared group memberships expanded implicit group boundaries.
Comparative study on diagonal equivalent methods of masonry infill panel
NASA Astrophysics Data System (ADS)
Amalia, Aniendhita Rizki; Iranata, Data
2017-06-01
ratio of height to width of 1 to 1.5. Load used in the experiment was based on Uniform Building Code (UBC) 1991. Every method compared was calculated first to get equivalent diagonal strut width. The second step was modelling method using structure analysis software as a frame with a diagonal in a linear mode. The linear mode was chosen based on structure analysis commonly used by structure designers. The frame was loaded and for every model, its load and deformation values were identified. The values of load - deformation of every method were compared to those of experimental test specimen by Mehrabi and open frame. From comparative study performed, Holmes' and Bazan-Meli's equations gave results the closest to the experimental test specimen by Mehrabi. Other equations that gave close values within the limit (by comparing it to the open frame) are Saneinejad-Hobbs, Stafford-Smith, Bazan-Meli, Liauw Kwan, Paulay and Priestley, FEMA 356, Durani Luo, Hendry, Papia and Chen-Iranata.
GRIM: General Relativistic Implicit Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Chandra, Mani; Foucart, Francois; Gammie, Charles F.
2017-02-01
GRIM (General Relativistic Implicit Magnetohydrodynamics) evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal magnetohydrodynamics. Non-ideal effects are modeled through heat conduction along magnetic field lines and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) instabilities. GRIM, which runs on CPUs as well as on GPUs, combines time evolution and primitive variable inversion needed for conservative schemes into a single step using only the residuals of the governing equations as inputs. This enables the code to be physics agnostic as well as flexible regarding time-stepping schemes.
Lanczos diagonalizations of the 1-D Peierls-Hubbard model
Loh, E.Y.; Campbell, D.K.; Gammel, J.T.
1989-01-01
In studies of interacting electrons in reduced dimensions'' one is trapped between the Scylla of exponential growth of the number of states in any exact many-body basis and the Charybdis of the failure of mean-field theories to capture adequately the effects of interactions. In the present article we focus on one technique -- the Lanczos method -- which, at least in the case of the 1-D Peierls-Hubbard model, appears to allow us to sail the narrow channel between these two hazards. In contrast to Quantum Monte Carlo methods, which circumvent the exponential growth of states by statistical techniques and importance sampling, the Lanczos approach attacks this problem head-on by diagonalizing the full Hamiltonian. Given the restrictions of present computers, this approach is thus limited to studying finite clusters of roughly 12--14 sites. Fortunately, in one dimension, such clusters are usually sufficient for extracting many of the properties of the infinite system provided that one makes full use of the ability to vary the boundary conditions. In this article we shall apply the Lanczos methodology and novel phase randomization'' techniques to study the 1-D Peierls-Hubbard model, with particular emphasis on the optical absorption properties, including the spectrum of absorptions as a function of photon energy. Despite the discreteness of the eigenstates in our finite clusters, we are able to obtain optical spectra that, in cases where independent tests can be made, agree well with the known exact results for the infinite system. Thus we feel that this combination of techniques represents an important and viable means of studying many interesting novel materials involving strongly correlated electrons. 26 refs., 6 figs.
Pediatric Extracorporeal Life Support Using a Third Generation Diagonal Pump.
Speth, Marlene; Münch, Frank; Purbojo, Ariawan; Glöckler, Martin; Toka, Okan; Cesnjevar, Robert A; Rüffer, André
2016-01-01
This study reports a single-centre experience of the Medos Deltastream diagonal-pump (DP3) for extracorporeal cardiac, pulmonary, or combined support in a single-center pediatric cohort. Twenty-seven consecutive patients with 28 runs of the DP3 between January 2013 and June 2014 were included for analysis. Median patient age, weight, and duration of support were 278 days (range: 0 days-14.2 years), 7.2 kg (range: 2.5-39 kg), and 8 days (range: 2-69 days). Midline sternotomy (n = 20, 71.4%) or cervical approaches (n = 8, 28.6%) were used for cannulation. The DP3 was employed for either veno-arterial extracorporeal life support (ECLS, n = 16), veno-venous extracorporeal membrane oxygenation (ECMO, n = 5), or ventricular assist devices (right ventricular assist device [RVAD], n = 1; left ventricular assist device [LVAD], n = 1; and univentricular assist device [UNIVAD], n = 5). Three patients initially supported with ECLS were switched to UNIVAD and one patient with UNIVAD was changed to ECLS. Required flow for neonates (n = 8) ranged between 0.2 and 0.75 L/min. Irreversible pump damage occurred in one patient during deairing after air block. Successful weaning, 30 day and hospital survival were 89.3% (n = 25), 85.7% (n = 24), and 71.4% (n = 20). All patients on UNIVAD, who did not require further extracorporeal respiratory assist, survived. In conclusion, the DP3 can be used for individual patient demands and adapted to their most suitable method of support. Meticulous flow adjustments render this pump highly effective for extracorporeal support particularly in pediatric patients.
Parallel Implicit Algorithms for CFD
NASA Technical Reports Server (NTRS)
Keyes, David E.
1998-01-01
The main goal of this project was efficient distributed parallel and workstation cluster implementations of Newton-Krylov-Schwarz (NKS) solvers for implicit Computational Fluid Dynamics (CFD.) "Newton" refers to a quadratically convergent nonlinear iteration using gradient information based on the true residual, "Krylov" to an inner linear iteration that accesses the Jacobian matrix only through highly parallelizable sparse matrix-vector products, and "Schwarz" to a domain decomposition form of preconditioning the inner Krylov iterations with primarily neighbor-only exchange of data between the processors. Prior experience has established that Newton-Krylov methods are competitive solvers in the CFD context and that Krylov-Schwarz methods port well to distributed memory computers. The combination of the techniques into Newton-Krylov-Schwarz was implemented on 2D and 3D unstructured Euler codes on the parallel testbeds that used to be at LaRC and on several other parallel computers operated by other agencies or made available by the vendors. Early implementations were made directly in Massively Parallel Integration (MPI) with parallel solvers we adapted from legacy NASA codes and enhanced for full NKS functionality. Later implementations were made in the framework of the PETSC library from Argonne National Laboratory, which now includes pseudo-transient continuation Newton-Krylov-Schwarz solver capability (as a result of demands we made upon PETSC during our early porting experiences). A secondary project pursued with funding from this contract was parallel implicit solvers in acoustics, specifically in the Helmholtz formulation. A 2D acoustic inverse problem has been solved in parallel within the PETSC framework.
NASA Technical Reports Server (NTRS)
Farhat, Charbel; Crivelli, Luis
1993-01-01
Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.
A transient FETI methodology for large-scale parallel implicit computations in structural mechanics
NASA Technical Reports Server (NTRS)
Farhat, Charbel; Crivelli, Luis; Roux, Francois-Xavier
1992-01-01
Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.
NASA Astrophysics Data System (ADS)
Zahr, M. J.; Persson, P.-O.
2016-12-01
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian-Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge-Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space-time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization. The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier-Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.
16. DIAGONAL VIEW TO NORTHWEST OF 1895 ENGINE/PUMP HOUSE SHOWING ...
16. DIAGONAL VIEW TO NORTHWEST OF 1895 ENGINE/PUMP HOUSE SHOWING REPLACEMENT DIESEL ENGINE LOCATIONS AND ASSOCIATED COOLING EQUIPMENT WITH PIPING - Deer Island Pumping Station, Boston, Suffolk County, MA
Localization in band random matrix models with and without increasing diagonal elements.
Wang, Wen-ge
2002-06-01
It is shown that localization of eigenfunctions in the Wigner band random matrix model with increasing diagonal elements can be related to localization in a band random matrix model with random diagonal elements. The relation is obtained by making use of a result of a generalization of Brillouin-Wigner perturbation theory, which shows that reduced Hamiltonian matrices with relatively small dimensions can be introduced for nonperturbative parts of eigenfunctions, and by employing intermediate basis states, which can improve the method of the reduced Hamiltonian matrix. The latter model deviates from the standard band random matrix model mainly in two aspects: (i) the root mean square of diagonal elements is larger than that of off-diagonal elements within the band, and (ii) statistical distributions of the matrix elements are close to the Lévy distribution in their central parts, except in the high top regions.
A Summary of Design Formulas for Beams Having Thin Webs in Diagonal Tension
NASA Technical Reports Server (NTRS)
Kuhn, Paul
1933-01-01
This report presents an explanation of the fundamental principles and a summary of the essential formulas for the design of diagonal-tension field beams, i.e. beams with very thin webs, as developed by Professor Wagner of Germany.
A Fast Method for Solving a Class of Tri-Diagonal Linear Systems
It is proved that the diagonals of the LU decomposition of the coefficient matrix rapidly converge to full floating - point precision. It is also proved...that the computed LU decomposition converges when floating - point arithmetic is used and that the limits of the LU diagonals using floating point are...roughly within machine precision of the limits using real arithmetic. This fact is exploited to reduce the number of floating - point operations required
Taking correlations in GPS least squares adjustments into account with a diagonal covariance matrix
NASA Astrophysics Data System (ADS)
Kermarrec, Gaël; Schön, Steffen
2016-09-01
Based on the results of Luati and Proietti (Ann Inst Stat Math 63:673-686, 2011) on an equivalence for a certain class of polynomial regressions between the diagonally weighted least squares (DWLS) and the generalized least squares (GLS) estimator, an alternative way to take correlations into account thanks to a diagonal covariance matrix is presented. The equivalent covariance matrix is much easier to compute than a diagonalization of the covariance matrix via eigenvalue decomposition which also implies a change of the least squares equations. This condensed matrix, for use in the least squares adjustment, can be seen as a diagonal or reduced version of the original matrix, its elements being simply the sums of the rows elements of the weighting matrix. The least squares results obtained with the equivalent diagonal matrices and those given by the fully populated covariance matrix are mathematically strictly equivalent for the mean estimator in terms of estimate and its a priori cofactor matrix. It is shown that this equivalence can be empirically extended to further classes of design matrices such as those used in GPS positioning (single point positioning, precise point positioning or relative positioning with double differences). Applying this new model to simulated time series of correlated observations, a significant reduction of the coordinate differences compared with the solutions computed with the commonly used diagonal elevation-dependent model was reached for the GPS relative positioning with double differences, single point positioning as well as precise point positioning cases. The estimate differences between the equivalent and classical model with fully populated covariance matrix were below the mm for all simulated GPS cases and below the sub-mm for the relative positioning with double differences. These results were confirmed by analyzing real data. Consequently, the equivalent diagonal covariance matrices, compared with the often used elevation
Implicit training of nonnative speech stimuli.
Vlahou, Eleni L; Protopapas, Athanassios; Seitz, Aaron R
2012-05-01
Learning nonnative speech contrasts in adulthood has proven difficult. Standard training methods have achieved moderate effects using explicit instructions and performance feedback. In this study, the authors question preexisting assumptions by demonstrating a superiority of implicit training procedures. They trained 3 groups of Greek adults on a difficult Hindi contrast (a) explicitly, with feedback (Experiment 1), or (b) implicitly, unaware of the phoneme distinctions, with (Experiment 2) or without (Experiment 3) feedback. Stimuli were natural recordings of consonant-vowel syllables with retroflex and dental unvoiced stops by a native Hindi speaker. On each trial, participants heard pairs of tokens from both categories and had to identify the retroflex sounds (explicit condition) or the sounds differing in intensity (implicit condition). Unbeknownst to participants, in the implicit conditions, target sounds were always retroflex, and distractor sounds were always dental. Post-training identification and discrimination tests showed improved performance of all groups, compared with a baseline of untrained Greek listeners. Learning was most robust for implicit training without feedback. It remains to be investigated whether implicitly trained skills can generalize to linguistically relevant phonetic categories when appropriate variability is introduced. These findings challenge traditional accounts on the role of feedback in phonetic training and highlight the importance of implicit, reward-based mechanisms.
Haptics-based dynamic implicit solid modeling.
Hua, Jing; Qin, Hong
2004-01-01
This paper systematically presents a novel, interactive solid modeling framework, Haptics-based Dynamic Implicit Solid Modeling, which is founded upon volumetric implicit functions and powerful physics-based modeling. In particular, we augment our modeling framework with a haptic mechanism in order to take advantage of additional realism associated with a 3D haptic interface. Our dynamic implicit solids are semi-algebraic sets of volumetric implicit functions and are governed by the principles of dynamics, hence responding to sculpting forces in a natural and predictable manner. In order to directly manipulate existing volumetric data sets as well as point clouds, we develop a hierarchical fitting algorithm to reconstruct and represent discrete data sets using our continuous implicit functions, which permit users to further design and edit those existing 3D models in real-time using a large variety of haptic and geometric toolkits, and visualize their interactive deformation at arbitrary resolution. The additional geometric and physical constraints afford more sophisticated control of the dynamic implicit solids. The versatility of our dynamic implicit modeling enables the user to easily modify both the geometry and the topology of modeled objects, while the inherent physical properties can offer an intuitive haptic interface for direct manipulation with force feedback.
In Vivo Imaging Reveals Composite Coding for Diagonal Motion in the Drosophila Visual System
Zhou, Wei; Chang, Jin
2016-01-01
Understanding information coding is important for resolving the functions of visual neural circuits. The motion vision system is a classic model for studying information coding as it contains a concise and complete information-processing circuit. In Drosophila, the axon terminals of motion-detection neurons (T4 and T5) project to the lobula plate, which comprises four regions that respond to the four cardinal directions of motion. The lobula plate thus represents a topographic map on a transverse plane. This enables us to study the coding of diagonal motion by investigating its response pattern. By using in vivo two-photon calcium imaging, we found that the axon terminals of T4 and T5 cells in the lobula plate were activated during diagonal motion. Further experiments showed that the response to diagonal motion is distributed over the following two regions compared to the cardinal directions of motion—a diagonal motion selective response region and a non-selective response region—which overlap with the response regions of the two vector-correlated cardinal directions of motion. Interestingly, the sizes of the non-selective response regions are linearly correlated with the angle of the diagonal motion. These results revealed that the Drosophila visual system employs a composite coding for diagonal motion that includes both independent coding and vector decomposition coding. PMID:27695103
Distilling perfect GHZ states from two copies of non-GHZ-diagonal mixed states
NASA Astrophysics Data System (ADS)
Wang, Xin-Wen; Tang, Shi-Qing; Yuan, Ji-Bing; Zhang, Deng-Yu
2017-06-01
It has been shown that a nearly pure Greenberger-Horne-Zeilinger (GHZ) state could be distilled from a large (even infinite) number of GHZ-diagonal states that can be obtained by depolarizing general multipartite mixed states (non-GHZ-diagonal states) through sequences of (probabilistic) local operations and classical communications. We here demonstrate that perfect GHZ states can be extracted, with certain probabilities, from two copies of non-GHZ-diagonal mixed states when some conditions are satisfied. This result implies that it is not necessary to depolarize these entangled mixed states to the GHZ-diagonal type, and that they are better than GHZ-diagonal states for distillation of pure GHZ states. We find a wide class of multipartite entangled mixed states that fulfill the requirements. Moreover, we display that the obtained result can be applied to practical noisy environments, e.g., amplitude-damping channels. Our findings provide an important complementarity to conventional GHZ-state distillation protocols (designed for GHZ-diagonal states) in theory, as well as having practical applications.
Implicit access to semantic information.
Young, A W; Newcombe, F; Hellawell, D; De Haan, E
1989-11-01
Three experiments investigating the patient M.S.'s semantic memory are reported. Experiments 1 and 2 involved a category-membership decision task, in which M.S. was asked to determine whether a noun was a member of a specified semantic category. His performance in Experiment 1 was impaired for nouns from living categories in comparison with nouns from nonliving categories, and this impairment was especially marked for nouns of low typicality. Experiment 2 demonstrated an equivalent pattern of very poor performance to nouns of low familiarity from living categories. In Experiment 3 the effect of a category label on lexical decision was examined, using category labels as primes preceding nouns or pronounceable nonwords. Facilitation from related category label primes was found for typical and untypical members of living and nonliving semantic categories. These findings demonstrate that M.S. has impaired knowledge of the structure of living semantic categories when explicit access to this information is required (Experiments 1 and 2), but that some form of preserved category structure can be demonstrated in tasks which assess this implicitly (Experiment 3).
Implicit learning and acquisition of music.
Rohrmeier, Martin; Rebuschat, Patrick
2012-10-01
Implicit learning is a core process for the acquisition of a complex, rule-based environment from mere interaction, such as motor action, skill acquisition, or language. A body of evidence suggests that implicit knowledge governs music acquisition and perception in nonmusicians and musicians, and that both expert and nonexpert participants acquire complex melodic, harmonic, and other features from mere exposure. While current findings and computational modeling largely support the learning of chunks, some results indicate learning of more complex structures. Despite the body of evidence, more research is required to support the cross-cultural validity of implicit learning and to show that core and more complex music theoretical features are acquired implicitly. Copyright © 2012 Cognitive Science Society, Inc.
Parallelizing alternating direction implicit solver on GPUs
USDA-ARS?s Scientific Manuscript database
We present a parallel Alternating Direction Implicit (ADI) solver on GPUs. Our implementation significantly improves existing implementations in two aspects. First, we address the scalability issue of existing Parallel Cyclic Reduction (PCR) implementations by eliminating their hardware resource con...
Psychometric intelligence dissociates implicit and explicit learning.
Gebauer, Guido F; Mackintosh, Nicholas J
2007-01-01
The hypothesis that performance on implicit learning tasks is unrelated to psychometric intelligence was examined in a sample of 605 German pupils. Performance in artificial grammar learning, process control, and serial learning did not correlate with various measures of intelligence when participants were given standard implicit instructions. Under an explicit rule discovery instruction, however, a significant relationship between performance on the learning tasks and intelligence appeared. This finding provides support for Reber's hypothesis that implicit learning, in contrast to explicit learning, is independent of intelligence, and confirms thereby the distinction between the 2 modes of learning. However, because there were virtually no correlations among the 3 learning tasks, the assumption of a unitary ability of implicit learning was not supported.
Kim, Kyungjoo; Parks, Michael L.; Perego, Mauro; Trask, Nathanial; Pan, Wenxiao
2016-11-09
ISPH code is developed to solve multi-physics meso-scale flow problems using implicit SPH method. In particular, the code can provides solutions for incompressible, multi phase flow and electro-kinetic flows.
Implicit memory function in fibromyalgia syndrome.
Duschek, Stefan; Werner, Natalie S; Winkelmann, Andreas; Wankner, Sarah
2013-01-01
The study investigated implicit memory function in fibromyalgia syndrome (FMS) and its association with clinical parameters. Implicit memory refers to the influence of past experience on current behavior without conscious awareness of these experiences. Eighteen FMS patients and 25 healthy individuals accomplished a word-stem completion task. As possible factors mediating the expected impairment, pain severity, emotional disorders, and medication were taken into account. The patients displayed markedly reduced task performance and higher levels of depression and anxiety. Among the clinical features, pain severity was most closely associated with performance, whereas depression, anxiety, and medication showed only a minor impact. The study documented reduced implicit memory function in FMS. In contrast to former findings on impaired performance of FMS patients on classical memory tests, lower implicit memory function cannot be ascribed to motivational deficits. Instead, the aberrances may relate to functional inference between central nervous nociceptive activity and cognitive processing.
Gifted Students' Implicit Beliefs about Intelligence and Giftedness
ERIC Educational Resources Information Center
Makel, Matthew C.; Snyder, Kate E.; Thomas, Chandler; Malone, Patrick S.; Putallaz, Martha
2015-01-01
Growing attention is being paid to individuals' implicit beliefs about the nature of intelligence. However, implicit beliefs about giftedness are currently underexamined. In the current study, we examined academically gifted adolescents' implicit beliefs about both intelligence and giftedness. Overall, participants' implicit beliefs about…
Unconscious Motivation. Part I: Implicit Attitudes toward L2 Speakers
ERIC Educational Resources Information Center
Al-Hoorie, Ali H.
2016-01-01
This paper reports the first investigation in the second language acquisition field assessing learners' implicit attitudes using the Implicit Association Test, a computerized reaction-time measure. Examination of the explicit and implicit attitudes of Arab learners of English (N = 365) showed that, particularly for males, implicit attitudes toward…
Implicit Association Tests of Attitudes toward Persons with Disabilities
ERIC Educational Resources Information Center
Thomas, Adrian; Vaughn, Edwin D.; Doyle, Andrea; Bubb, Robert
2014-01-01
The authors assessed 3 of the currently available implicit association tests designed to measure attitudes toward persons with disabilities. The Revised Multiple Disability Implicit Association Test, the Implicit Association Test for Attitudes Toward Athletes With Disabilities, and the Disability Attitude Implicit Association Test were related to…
Implicit Association Tests of Attitudes toward Persons with Disabilities
ERIC Educational Resources Information Center
Thomas, Adrian; Vaughn, Edwin D.; Doyle, Andrea; Bubb, Robert
2014-01-01
The authors assessed 3 of the currently available implicit association tests designed to measure attitudes toward persons with disabilities. The Revised Multiple Disability Implicit Association Test, the Implicit Association Test for Attitudes Toward Athletes With Disabilities, and the Disability Attitude Implicit Association Test were related to…
Gifted Students' Implicit Beliefs about Intelligence and Giftedness
ERIC Educational Resources Information Center
Makel, Matthew C.; Snyder, Kate E.; Thomas, Chandler; Malone, Patrick S.; Putallaz, Martha
2015-01-01
Growing attention is being paid to individuals' implicit beliefs about the nature of intelligence. However, implicit beliefs about giftedness are currently underexamined. In the current study, we examined academically gifted adolescents' implicit beliefs about both intelligence and giftedness. Overall, participants' implicit beliefs about…
Implicit measures of association in psychopathology research.
Roefs, Anne; Huijding, Jorg; Smulders, Fren T Y; MacLeod, Colin M; de Jong, Peter J; Wiers, Reinout W; Jansen, Anita T M
2011-01-01
Studies obtaining implicit measures of associations in Diagnostic and Statistical Manual of Mental Disorders (4th ed., Text Revision; American Psychiatric Association, 2000) Axis I psychopathology are organized into three categories: (a) studies comparing groups having a disorder with controls, (b) experimental validity studies, and (c) incremental and predictive validity studies. In the first category, implicit measures of disorder-relevant associations were consistent with explicit beliefs for some disorders (e.g., specific phobia), but for other disorders evidence was either mixed (e.g., panic disorder) or inconsistent with explicit beliefs (e.g., pain disorder). For substance use disorders and overeating, expected positive and unexpected negative associations with craved substances were found consistently. Contrary to expectation, implicit measures of self-esteem were consistently positive for patients with depressive disorder, social phobia, and body dysmorphic disorder. In the second category, short-term manipulations of disorder-relevant states generally affected implicit measures as expected. Therapeutic interventions affected implicit measures for one type of specific phobia, social phobia, and panic disorder, but not for alcohol use disorders or obesity. In the third category, implicit measures had predictive value for certain psychopathological behaviors, sometimes moderated by the availability of cognitive resources (e.g., for alcohol and food, only when cognitive resources were limited). The strengths of implicit measures include (a) converging evidence for dysfunctional beliefs regarding certain disorders and consistent new insights for other disorders and (b) prediction of some psychopathological behaviors that explicit measures cannot explain. Weaknesses include (a) that findings were inconsistent for some disorders, raising doubts about the validity of the measures, and (b) that understanding of the concept "implicit" is incomplete.
Implicit attitudes in sexuality: gender differences.
Geer, James H; Robertson, Gloria G
2005-12-01
This study examined the role of gender in both implicit and explicit attitudes toward sexuality. Implicit attitudes are judgments or evaluations of social objects that are automatically activated, often without the individual's conscious awareness of the causation. In contrast, explicit attitudes are judgments or evaluations that are well established in awareness. As described in Oliver and Hyde's (1993) meta-analysis of self-report (explicit) data, women report greater negative attitudes toward sexuality than do men. In the current study, we used the Sexual Opinion Survey (SOS) developed by Fisher, Byrne, White, and Kelley (1988) to index explicit attitudes and the Implicit Association Test (IAT) developed by Greenwald, McGhee, and Schwartz (1998) to index implicit attitudes. Research has demonstrated that the IAT reveals attitudes that participants may be reluctant to express. Independent variables examined were participant gender, social acceptability of sexual words, and order of associated evaluations in the IAT (switching from positive to negative evaluations or the reverse). The IAT data revealed a significant Order x Gender interaction that showed that women had more negative implicit attitudes toward sexuality than did men. There was also a significant Order x Acceptability interaction, indicating that implicit attitudes were more strongly revealed when the sexual words used in the IAT were more socially unacceptable. As expected, on the SOS, women had more negative explicit attitudes toward sexuality. There was no significant correlation between explicit and implicit attitudes. These data suggest that at both automatic (implicit) and controlled (explicit) levels of attitudes, women harbor more negative feelings toward sex than do men.
Convergence speeding up in the calculation of the viscous flow about an airfoil
NASA Technical Reports Server (NTRS)
Radespiel, R.; Rossow, C.
1988-01-01
A finite volume method to solve the three dimensional Navier-Stokes equations was developed. It is based on a cell-vertex scheme with central differences and explicit Runge-Kutta time steps. A good convergence for a stationary solution was obtained by the use of local time steps, implicit smoothing of the residues, a multigrid algorithm, and a carefully controlled artificial dissipative term. The method is illustrated by results for transonic profiles and airfoils. The method allows a routine solution of the Navier-Stokes equations.
NASA Technical Reports Server (NTRS)
Jentink, Thomas Neil; Usab, William J., Jr.
1990-01-01
An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.
NASA Technical Reports Server (NTRS)
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
Speeding up Newton-type iterations for stiff problems
NASA Astrophysics Data System (ADS)
Gonzalez-Pinto, S.; Rojas-Bello, R.
2005-09-01
Iterative schemes based on the Cooper and Butcher iteration [5] are considered, in order to implement highly implicit Runge-Kutta methods on stiff problems. By introducing two appropriate parameters in the scheme, a new iteration making use of the last two iterates, is proposed. Specific schemes of this type for the Gauss, Radau IA-IIA and Lobatto IIIA-B-C processes are developed. It is also shown that in many situations the new iteration presents a faster convergence than the original.
A Navier-Stokes solver for cascade flows
NASA Technical Reports Server (NTRS)
Arnone, A.; Swanson, R. C.
1988-01-01
A computer code for solving the Reynolds averaged full Navier-Stokes equations has been developed and applied using sheared H-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady state calculations. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications in less than 100 multigrid cycles on the finest mesh.
Accuracy of schemes for the Euler equations with non-uniform meshes
NASA Technical Reports Server (NTRS)
Turkel, E.; Yaniv, S.; Landau, U.
1985-01-01
The effect of non-uniform grids on the solution of the Euler equations is analyzed. A Runge-Kutta type scheme based on a finite volume formulation is considered. It is shown that for arbitrary grids the scheme can be inconsistent even though it is second-order accurate for uniform grids. An improvement is suggested which leads to at least first-order accuracy for general grids. Test cases are presented in both two- and three-space dimensions. Applications to finite difference and implicit algorithms are also given.
Propulsion-related flowfields using the preconditioned Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Venkateswaran, S.; Weiss, J. M.; Merkle, C. L.; Choi, Y.-H.
1992-01-01
A previous time-derivative preconditioning procedure for solving the Navier-Stokes is extended to the chemical species equations. The scheme is implemented using both the implicit ADI and the explicit Runge-Kutta algorithms. A new definition for time-step is proposed to enable grid-independent convergence. Several examples of both reacting and non-reacting propulsion-related flowfields are considered. In all cases, convergence that is superior to conventional methods is demonstrated. Accuracy is verified using the example of a backward facing step. These results demonstrate that preconditioning can enhance the capability of density-based methods over a wide range of Mach and Reynolds numbers.
Mixed collocation methods for y''=f(x,y)
NASA Astrophysics Data System (ADS)
Coleman, John P.; Duxbury, Suzanne C.
2000-12-01
The collocation methods introduced here are based on linear combinations of trigonometric functions and powers. The motivation is to provide better approximations for oscillatory solutions of initial-value problems for differential equations of the special form y''=f(x,y). The resulting methods, for two or more collocation points, are implicit Runge-Kutta-Nyström methods with coefficients which depend on both the fitted angular frequency and the steplength. Algebraic and trigonometric order conditions are considered and the stability properties of some methods are examined. Particular mixed collocation methods, and other methods for the same class of problems, are compared by applying them to a variety of test problems.
Xia, Yidong; Liu, Xiaodong; Luo, Hong; ...
2015-06-01
Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time,more » while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.« less
Xia, Yidong; Liu, Xiaodong; Luo, Hong; Nourgaliev, Robert
2015-06-01
Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time, while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.
Retroactive interference effects in implicit memory.
Eakin, Deborah K; Smith, Robert
2012-09-01
One source of evidence for separate explicit and implicit memory systems is that explicit but not implicit memory is impacted by interference (e.g., Graf & Schacter, 1987). The present experiment examined whether retroactive interference (RI) effects could be obtained in implicit memory when a strong test of RI was used. People studied an original list of word pairs (e.g., COTTON-PRIZE) using the typical RI paradigm. During the interpolated phase, participants studied either interference pairs for which the same cue was re-paired with a different target (e.g., COTTON-PRINT) or novel pairs (e.g., HOST-VASE). RI was tested with the modified opposition cued recall test (Eakin, Schreiber, & Sergent-Marshall, 2003). The original-list cue was presented along with the beginning stem of its target (e.g., COTTON-PRI-) and a hint (e.g., not PRINT). RI effects were obtained for explicit and implicit memory. Taken together with prior research finding proactive interference effects in implicit memory, the findings indicate that implicit memory is not immune from retroactive interference. PsycINFO Database Record (c) 2012 APA, all rights reserved.
Measurement of off-diagonal transport coefficients in two-phase flow in porous media.
Ramakrishnan, T S; Goode, P A
2015-07-01
The prevalent description of low capillary number two-phase flow in porous media relies on the independence of phase transport. An extended Darcy's law with a saturation dependent effective permeability is used for each phase. The driving force for each phase is given by its pressure gradient and the body force. This diagonally dominant form neglects momentum transfer from one phase to the other. Numerical and analytical modeling in regular geometries have however shown that while this approximation is simple and acceptable in some cases, many practical problems require inclusion of momentum transfer across the interface. Its inclusion leads to a generalized form of extended Darcy's law in which both the diagonal relative permeabilities and the off-diagonal terms depend not only on saturation but also on the viscosity ratio. Analogous to application of thermodynamics to dynamical systems, any of the extended forms of Darcy's law assumes quasi-static interfaces of fluids for describing displacement problems. Despite the importance of the permeability coefficients in oil recovery, soil moisture transport, contaminant removal, etc., direct measurements to infer the magnitude of the off-diagonal coefficients have been lacking. The published data based on cocurrent and countercurrent displacement experiments are necessarily indirect. In this paper, we propose a null experiment to measure the off-diagonal term directly. For a given non-wetting phase pressure-gradient, the null method is based on measuring a counter pressure drop in the wetting phase required to maintain a zero flux. The ratio of the off-diagonal coefficient to the wetting phase diagonal coefficient (relative permeability) may then be determined. The apparatus is described in detail, along with the results obtained. We demonstrate the validity of the experimental results and conclude the paper by comparing experimental data to numerical simulation.
Convergence Acceleration for Multistage Time-Stepping Schemes
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Turkel, Eli L.; Rossow, C-C; Vasta, V. N.
2006-01-01
The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.
IMEX time marching for discontinuous Galerkin methods
NASA Astrophysics Data System (ADS)
Shu, Chi-Wang
2017-07-01
In this talk we give a short summary of our recent work [9, 10, 11, 7], jointly with H. Wang, Q. Zhang, S. Wang and Y. Liu, on the development, analysis and application of implicit-explicit (IMEX) Runge-Kutta or multi-step time marching methods for discontinuous Galerkin (DG) methods approximating convection diffusion equations. For such DG methods, explicit time marching is expensive since the time step is restricted by the square of the spatial mesh size, while fully implicit methods would require the solution of a non-symmetric, non-positive definite and possibly nonlinear system in each time step. The high order accurate IMEX Runge-Kutta or multi-step time marching would treat the diffusion term implicitly (which is often linear, resulting in a linear positive-definite solver) and the convection term (often nonlinear) explicitly, hence it can greatly improve computational efficiency. We prove that certain IMEX time discretizations, up to third order accuracy, coupled with local DG (LDG) method for the diffusion term treated implicitly, and regular DG method for the convection term treated explicitly, are unconditionally stable (the time step is upper bounded only by a constant depending on the diffusion coefficient but not on the spatial mesh size) and optimally convergent. The results also hold for drift-diffusion model in semiconductor device simulations, where a convection diffusion equation is coupled with an electrical potential equation. Numerical experiments confirm the good performance of such schemes.
A diagonal landing task to assess dynamic postural stability in ACL reconstructed females.
Patterson, Matthew R; Delahunt, Eamonn
2013-12-01
Previous research has used time to stabilization (TTS) from forward landing tasks to assess dynamic postural stability in ACL reconstructed (ACLR) athletes in order to identify impaired sensorimotor control and mechanical stability. This may not be an appropriate test due to the fact that research has suggested that ACL injury has a multi-planar mechanism of injury. The purpose of the present study was to compare TTS values from a forward land and a diagonal land to determine if diagonal landing TTS values are more sensitive to dynamic postural stability deficits in female ACLR athletes. A group of ACL reconstructed female athletes and a group of female control athletes performed three forward lands and three diagonal lands onto a force-plate and remained still on one foot for 15s. TTS was calculated for the anterior-posterior and medial-lateral ground reaction forces as well as the resultant vector of both forces. All three TTS values were significantly increased in the ACLR group from the control group for the diagonal landing task. There was no difference in TTS values between the groups for the forward landing task. TTS values from a diagonal landing are more sensitive at detecting impaired dynamic postural stability in a group of female ACLR athletes compared to TTS values from a forward land. III - Casecontrolled study. Copyright © 2013 Elsevier B.V. All rights reserved.
Volume localized spin echo correlation spectroscopy with suppression of ‘diagonal' peaks
NASA Astrophysics Data System (ADS)
Banerjee, Abhishek; Chandrakumar, N.
2014-02-01
Two dimensional homonuclear 1H correlation spectroscopy is of considerable interest for volume localized spectral studies, both in vivo and in vitro, of biological as well as material objects. The information principally sought from correlation spectra resides in the cross-peaks, which are often masked however by the presence of diagonal peaks in COSY, or ‘pseudo-diagonal' peaks at F1 = 0 in SECSY. It has therefore been a concern to suppress these diagonal or ‘pseudo-diagonal' peaks, in order to ensure that cross-peak information is fully discernible. We present here a report of our work on volume localized DIagonal Suppressed Spin Echo Correlation specTroscopy (LDISSECT) and demonstrate its performance in comparison to the standard volume localized SECSY experiment, employing brain metabolite phantoms in a gel. The sequence works in the inhomogeneous, multi-component environment by exploiting the short acquisition time to suppress undesired information by employing an additional rf pulse. A brief description of the pulse sequence, its theory, and simulations are also included, besides experimental benchmarking on two brain metabolite phantoms in gel phase.
Volume localized spin echo correlation spectroscopy with suppression of 'diagonal' peaks.
Banerjee, Abhishek; Chandrakumar, N
2014-02-01
Two dimensional homonuclear (1)H correlation spectroscopy is of considerable interest for volume localized spectral studies, both in vivo and in vitro, of biological as well as material objects. The information principally sought from correlation spectra resides in the cross-peaks, which are often masked however by the presence of diagonal peaks in COSY, or 'pseudo-diagonal' peaks at F1=0 in SECSY. It has therefore been a concern to suppress these diagonal or 'pseudo-diagonal' peaks, in order to ensure that cross-peak information is fully discernible. We present here a report of our work on volume localized DIagonal Suppressed Spin Echo Correlation specTroscopy (LDISSECT) and demonstrate its performance in comparison to the standard volume localized SECSY experiment, employing brain metabolite phantoms in a gel. The sequence works in the inhomogeneous, multi-component environment by exploiting the short acquisition time to suppress undesired information by employing an additional rf pulse. A brief description of the pulse sequence, its theory, and simulations are also included, besides experimental benchmarking on two brain metabolite phantoms in gel phase. Copyright © 2013 Elsevier Inc. All rights reserved.
An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows
NASA Technical Reports Server (NTRS)
Gnoffo, Peter A.
1990-01-01
An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, compressible, perfect-gas flows is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Viscous terms are discretized using central differences. The relaxation strategy is well suited for computers employing either vector or parallel architectures. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. Convergence rates and grid refinement studies are conducted for Mach 5 flow through an inlet with a 10 deg compression ramp and Mach 14 flow over a 15 deg ramp. Predictions for pressure distributions, surface heating, and aerodynamics coefficients compare well with experiment data for Mach 10 flow over a blunt body.
ERIC Educational Resources Information Center
Power, Patricia; Barnes-Holmes, Dermot; Barnes-Holmes, Yvonne; Stewart, Ian
2009-01-01
The Implicit Relational Assessment Procedure (IRAP) was designed to examine implicit beliefs or attitudes. In Experiment 1, response latencies obtained from Irish participants on the IRAP showed a strong preference for Irish over Scottish and American over African. In contrast, responses to explicit Likert measures diverged from the IRAP…
ERIC Educational Resources Information Center
Power, Patricia; Barnes-Holmes, Dermot; Barnes-Holmes, Yvonne; Stewart, Ian
2009-01-01
The Implicit Relational Assessment Procedure (IRAP) was designed to examine implicit beliefs or attitudes. In Experiment 1, response latencies obtained from Irish participants on the IRAP showed a strong preference for Irish over Scottish and American over African. In contrast, responses to explicit Likert measures diverged from the IRAP…
Using the Implicit Association Test to Assess Children's Implicit Attitudes toward Smoking
Andrews, Judy A.; Hampson, Sarah E.; Greenwald, Anthony G.; Gordon, Judith; Widdop, Chris
2009-01-01
The development and psychometric properties of an Implicit Association Test (IAT) measuring implicit attitude toward smoking among fifth grade children were described. The IAT with “sweets” as the contrast category resulted in higher correlations with explicit attitudes than did the IAT with “healthy foods” as the contrast category. Children with family members who smoked (versus non-smoking) and children who were high in sensation seeking (versus low) had a significantly more favorable implicit attitude toward smoking. Further, implicit attitudes became less favorable after engaging in tobacco prevention activities targeting risk perceptions of addiction. Results support the reliability and validity of this version of the IAT and illustrate its usefulness in assessing young children's implicit attitude toward smoking. PMID:21566676
Using the Implicit Association Test to Assess Children's Implicit Attitudes toward Smoking.
Andrews, Judy A; Hampson, Sarah E; Greenwald, Anthony G; Gordon, Judith; Widdop, Chris
2010-09-01
The development and psychometric properties of an Implicit Association Test (IAT) measuring implicit attitude toward smoking among fifth grade children were described. The IAT with "sweets" as the contrast category resulted in higher correlations with explicit attitudes than did the IAT with "healthy foods" as the contrast category. Children with family members who smoked (versus non-smoking) and children who were high in sensation seeking (versus low) had a significantly more favorable implicit attitude toward smoking. Further, implicit attitudes became less favorable after engaging in tobacco prevention activities targeting risk perceptions of addiction. Results support the reliability and validity of this version of the IAT and illustrate its usefulness in assessing young children's implicit attitude toward smoking.
How Explicit and Implicit Test Instructions in an Implicit Learning Task Affect Performance
Witt, Arnaud; Puspitawati, Ira; Vinter, Annie
2013-01-01
Typically developing children aged 5 to 8 years were exposed to artificial grammar learning. Following an implicit exposure phase, half of the participants received neutral instructions at test while the other half received instructions making a direct, explicit reference to the training phase. We first aimed to assess whether implicit learning operated in the two test conditions. We then evaluated the differential impact of age on learning performances as a function of test instructions. The results showed that performance did not vary as a function of age in the implicit instructions condition, while age effects emerged when explicit instructions were employed at test. However, performance was affected differently by age and the instructions given at test, depending on whether the implicit learning of short or long units was assessed. These results suggest that the claim that the implicit learning process is independent of age needs to be revised. PMID:23326409