New algorithms for solving third- and fifth-order two point boundary value problems based on nonsymmetric generalized Jacobi Petrov–Galerkin method

PubMed Central

Doha, E.H.; Abd-Elhameed, W.M.; Youssri, Y.H.

2014-01-01

Two families of certain nonsymmetric generalized Jacobi polynomials with negative integer indexes are employed for solving third- and fifth-order two point boundary value problems governed by homogeneous and nonhomogeneous boundary conditions using a dual Petrov–Galerkin method. The idea behind our method is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The resulting linear systems from the application of our method are specially structured and they can be efficiently inverted. The use of generalized Jacobi polynomials simplify the theoretical and numerical analysis of the method and also leads to accurate and efficient numerical algorithms. The presented numerical results indicate that the proposed numerical algorithms are reliable and very efficient. PMID:26425358

Scalar conservation and boundedness in simulations of compressible flow

NASA Astrophysics Data System (ADS)

Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.

2017-11-01

With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variables are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. We present methods for passive and active scalars, and demonstrate their effectiveness with several examples.

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

Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.

With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g.passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variablesmore » are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. As a result, we present methods for passive and active scalars, and demonstrate their effectiveness with several examples.« less

Least-squares finite element method for fluid dynamics

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1989-01-01

An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

PubMed

Khader, M M

2013-10-01

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

NASA Astrophysics Data System (ADS)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

Onset of detachment in adhesive contact of an elastic half-space and flat-ended punches with non-circular shape: analytic estimates and comparison with numeric analysis

NASA Astrophysics Data System (ADS)

Li, Qiang; Argatov, Ivan; Popov, Valentin L.

2018-04-01

A recent paper by Popov, Pohrt and Li (PPL) in Friction investigated adhesive contacts of flat indenters in unusual shapes using numerical, analytical and experimental methods. Based on that paper, we analyze some special cases for which analytical solutions are known. As in the PPL paper, we consider adhesive contact in the Johnson-Kendall-Roberts approximation. Depending on the energy balance, different upper and lower estimates are obtained in terms of certain integral characteristics of the contact area. The special cases of an elliptical punch as well as a system of two circular punches are considered. Theoretical estimations for the first critical force (force at which the detachment process begins) are confirmed by numerical simulations using the adhesive boundary element method. It is shown that simpler approximations for the pull-off force, based both on the Holm radius of contact and the contact area, substantially overestimate the maximum adhesive force.

Representation of DNA sequences in genetic codon context with applications in exon and intron prediction.

PubMed

Yin, Changchuan

2015-04-01

To apply digital signal processing (DSP) methods to analyze DNA sequences, the sequences first must be specially mapped into numerical sequences. Thus, effective numerical mappings of DNA sequences play key roles in the effectiveness of DSP-based methods such as exon prediction. Despite numerous mappings of symbolic DNA sequences to numerical series, the existing mapping methods do not include the genetic coding features of DNA sequences. We present a novel numerical representation of DNA sequences using genetic codon context (GCC) in which the numerical values are optimized by simulation annealing to maximize the 3-periodicity signal to noise ratio (SNR). The optimized GCC representation is then applied in exon and intron prediction by Short-Time Fourier Transform (STFT) approach. The results show the GCC method enhances the SNR values of exon sequences and thus increases the accuracy of predicting protein coding regions in genomes compared with the commonly used 4D binary representation. In addition, this study offers a novel way to reveal specific features of DNA sequences by optimizing numerical mappings of symbolic DNA sequences.

Factorization and reduction methods for optimal control of distributed parameter systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Powers, R. K.

1985-01-01

A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.

Scalar conservation and boundedness in simulations of compressible flow

DOE PAGES

Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.

2017-08-07

With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g.passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variablesmore » are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. As a result, we present methods for passive and active scalars, and demonstrate their effectiveness with several examples.« less

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Numerical investigations of two-phase flow with dynamic capillary pressure in porous media via a moving mesh method

NASA Astrophysics Data System (ADS)

Zhang, Hong; Zegeling, Paul Andries

2017-09-01

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow in porous media incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. The traveling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behavior. Special attention is paid to the non-monotonic profiles. The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.

Behaviors of printed circuit boards due to microwave supported curing process of coating materials.

PubMed

Bremerkamp, Felix; Nowottnick, Mathias; Seehase, Dirk; Bui, Trinh Dung

2012-01-01

The Application of a microwave supported curing process for coatings in the field of electronic industry poses a challenge. Here the implementation of this technology is represented. Within the scope of the investigation special PCB Test Layouts were designed and the polymer curing process examined by the method of dielectric analysis. Furthermore the coupling of microwave radiation with conductive PCB structures was analyzed experimentally by means of special test boards. The formation of standing waves and regular heating distribution along the conductive wires on the PCB could be observed. The experimental results were compared with numerical simulation. In this context the numerical analysis of microwave PCB interaction led to important findings concerning wave propagation on wired PCB. The final valuation demonstrated a substantial similarity between numerical simulations and experimental results.

Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit

NASA Technical Reports Server (NTRS)

Barry, B. F.; Pimm, R. S.; Rowe, C. K.

1971-01-01

In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

PubMed

Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo

2016-05-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

PubMed Central

Sun, Hui; Zhou, Shenggao; Moore, David K.; Cheng, Li-Tien; Li, Bo

2015-01-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems. PMID:27365866

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

On a new iterative method for solving linear systems and comparison results

NASA Astrophysics Data System (ADS)

Jing, Yan-Fei; Huang, Ting-Zhu

2008-10-01

In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

Numerical methods for the inverse problem of density functional theory

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

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Making it Easy to Construct Accurate Hydrological Models that Exploit High Performance Computers (Invited)

NASA Astrophysics Data System (ADS)

Kees, C. E.; Farthing, M. W.; Terrel, A.; Certik, O.; Seljebotn, D.

2013-12-01

This presentation will focus on two barriers to progress in the hydrological modeling community, and research and development conducted to lessen or eliminate them. The first is a barrier to sharing hydrological models among specialized scientists that is caused by intertwining the implementation of numerical methods with the implementation of abstract numerical modeling information. In the Proteus toolkit for computational methods and simulation, we have decoupled these two important parts of computational model through separate "physics" and "numerics" interfaces. More recently we have begun developing the Strong Form Language for easy and direct representation of the mathematical model formulation in a domain specific language embedded in Python. The second major barrier is sharing ANY scientific software tools that have complex library or module dependencies, as most parallel, multi-physics hydrological models must have. In this setting, users and developer are dependent on an entire distribution, possibly depending on multiple compilers and special instructions depending on the environment of the target machine. To solve these problem we have developed, hashdist, a stateless package management tool and a resulting portable, open source scientific software distribution.

Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel

NASA Astrophysics Data System (ADS)

Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-12-01

Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.

Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

NASA Astrophysics Data System (ADS)

Wu, Fang-Xiang; Mu, Lei; Shi, Zhong-Ke

2010-01-01

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.

Dual number algebra method for Green's function derivatives in 3D magneto-electro-elasticity

NASA Astrophysics Data System (ADS)

Dziatkiewicz, Grzegorz

2018-01-01

The Green functions are the basic elements of the boundary element method. To obtain the boundary integral formulation the Green function and its derivative should be known for the considered differential operator. Today the interesting group of materials are electronic composites. The special case of the electronic composite is the magnetoelectroelastic continuum. The mentioned continuum is a model of the piezoelectric-piezomagnetic composites. The anisotropy of their physical properties makes the problem of Green's function determination very difficult. For that reason Green's functions for the magnetoelectroelastic continuum are not known in the closed form and numerical methods should be applied to determine such Green's functions. These means that the problem of the accurate and simply determination of Green's function derivatives is even harder. Therefore in the present work the dual number algebra method is applied to calculate numerically the derivatives of 3D Green's functions for the magnetoelectroelastic materials. The introduced method is independent on the step size and it can be treated as a special case of the automatic differentiation method. Therefore, the dual number algebra method can be applied as a tool for checking the accuracy of the well-known finite difference schemes.

Computation of Nonlinear Backscattering Using a High-Order Numerical Method

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2001-01-01

The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

Numerical simulation of the cavitation characteristics of a mixed-flow pump

NASA Astrophysics Data System (ADS)

Chen, T.; Li, S. R.; Li, W. Z.; Liu, Y. L.; Wu, D. Z.; Wang, L. Q.

2013-12-01

As a kind of general equipment for fluid transportation, pumps were widely used in industry which includes many applications of high pressure, temperature and toxic fluids transportations. Performances of pumps affect the safety and reliability of the whole special equipment system. Cavitation in pumps cause the loss of performance and erosion of the blade, which could affect the running stability and reliability of the pump system. In this paper, a kind of numerical method for cavitaion performance prediction was presented. In order to investigate the accuracy of the method, CFD flow analysis and cavitation performance predictions of a mixed-flow pump were carried out. The numerical results were compared with the test results.

Numerical integration of discontinuous functions: moment fitting and smart octree

NASA Astrophysics Data System (ADS)

Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander

2017-11-01

A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.

Comment on "Applications of homogenous balanced principle on investigating exact solutions to a series of time fractional nonlinear PDEs", [Commun Nonlinear Sci Numer Simulat 47 (2017) 253-266

NASA Astrophysics Data System (ADS)

Li, Xiangzheng

2018-06-01

A counterexample is given to show that the product rule of the Caputo fractional derivatives does not hold except on a special point. The function-expansion method of separation variable proposed by Rui[Commun Nonlinear Sci Numer Simulat 47 (2017) 253-266] based on the product rule must be modified.

Applications of Massive Mathematical Computations

DTIC Science & Technology

1990-04-01

particles from the first principles of QCD . This problem is under intensive numerical study 11-6 using special purpose parallel supercomputers in...several places around the world. The method used here is the Monte Carlo integration for a fixed 3-D plus time lattices . Reliable results are still years...mathematical and theoretical physics, but its most promising applications are in the numerical realization of QCD computations. Our programs for the solution

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2000-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented. Supplementary material is available for this article at 10.12942/lrr-2000-2.

The wood cylinder method of measuring forest inflammability

Treesearch

H. T. Gisborne

1933-01-01

The best test of the practicability of any new method or device is the actual trial by numerous users who are interested only in the end product, and who have no special interest in the means employed to reach that end. Such users are not inclined to give the new method the advantage of any doubts, and they are particularly critical of the method or device insofar as...

Topography Modeling in Atmospheric Flows Using the Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Ackerman, A. S.; Senocak, I.; Mansour, N. N.; Stevens, D. E.

2004-01-01

Numerical simulation of flow over complex geometry needs accurate and efficient computational methods. Different techniques are available to handle complex geometry. The unstructured grid and multi-block body-fitted grid techniques have been widely adopted for complex geometry in engineering applications. In atmospheric applications, terrain fitted single grid techniques have found common use. Although these are very effective techniques, their implementation, coupling with the flow algorithm, and efficient parallelization of the complete method are more involved than a Cartesian grid method. The grid generation can be tedious and one needs to pay special attention in numerics to handle skewed cells for conservation purposes. Researchers have long sought for alternative methods to ease the effort involved in simulating flow over complex geometry.

Surface critical behavior of thin Ising films at the ‘special point’

NASA Astrophysics Data System (ADS)

Moussa, Najem; Bekhechi, Smaine

2003-03-01

The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, js= Js/ J, the phase diagram exhibits a special surface coupling jsp at which all the films have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.

Simulation of random road microprofile based on specified correlation function

NASA Astrophysics Data System (ADS)

Rykov, S. P.; Rykova, O. A.; Koval, V. S.; Vlasov, V. G.; Fedotov, K. V.

2018-03-01

The paper aims to develop a numerical simulation method and an algorithm for a random microprofile of special roads based on the specified correlation function. The paper used methods of correlation, spectrum and numerical analysis. It proves that the transfer function of the generating filter for known expressions of spectrum input and output filter characteristics can be calculated using a theorem on nonnegative and fractional rational factorization and integral transformation. The model of the random function equivalent of the real road surface microprofile enables us to assess springing system parameters and identify ranges of variations.

Variational data assimilation system "INM RAS - Black Sea"

NASA Astrophysics Data System (ADS)

Parmuzin, Eugene; Agoshkov, Valery; Assovskiy, Maksim; Giniatulin, Sergey; Zakharova, Natalia; Kuimov, Grigory; Fomin, Vladimir

2013-04-01

Development of Informational-Computational Systems (ICS) for Data Assimilation Procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The problems discussed above are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for Personal Computers (PC). Special problems and questions arise while effective ICS versions for PC are being developed. These problems and questions can be solved with applying modern methods of numerical mathematics and by solving "parallelism problem" using OpenMP technology and special linear algebra packages. In this work the results on the ICS development for PC-ICS "INM RAS - Black Sea" are presented. In the work the following problems and questions are discussed: practical problems that can be studied by ICS; parallelism problems and their solutions with applying of OpenMP technology and the linear algebra packages used in ICS "INM - Black Sea"; Interface of ICS. The results of ICS "INM RAS - Black Sea" testing are presented. Efficiency of technologies and methods applied are discussed. The work was supported by RFBR, grants No. 13-01-00753, 13-05-00715 and by The Ministry of education and science of Russian Federation, project 8291, project 11.519.11.1005 References: [1] V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 5-31 [2] E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 69-94 [3] V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 95-111 [4] V.I. Agoshkov, S.V. Giniatulin, G.V. Kuimov. OpenMP technology and linear algebra packages in the variation data assimilation systems. - Abstracts of the 1-st China-Russia Conference on Numerical Algebra with Applications in Radiactive Hydrodynamics, Beijing, China, October 16-18, 2012. [5] Zakharova N.B., Agoshkov V.I., Parmuzin E.I., The new method of ARGO buoys system observation data interpolation. Russian Journal of Numerical Analysis and Mathematical Modelling. Vol. 28, Issue 1, 2013.

Finite element solutions of free convective Casson fluid flow past a vertically inclined plate submitted in magnetic field in presence of heat and mass transfer

NASA Astrophysics Data System (ADS)

Raju, R. Srinivasa; Reddy, B. Mahesh; Reddy, G. Jithender

2017-09-01

The aim of this research work is to study the influence of thermal radiation on steady magnetohydrodynamic-free convective Casson fluid flow of an optically thick fluid over an inclined vertical plate with heat and mass transfer. Combined phenomenon of heat and mass transfer is considered. Numerical solutions in general form are obtained by using the finite element method. The sum of thermal and mechanical parts is expressed as velocity of fluid. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained numerical solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Numerical results for the controlling flow parameters are drawn graphically and discussed in detail. In some special cases, the obtained numerical results are compared and found to be in good agreement with the previously published results which are available in literature. Applications of this study includes laminar magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics, etc.

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

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

Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution ofmore » dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.« less

Formal Solutions for Polarized Radiative Transfer. I. The DELO Family

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

Janett, Gioele; Carlin, Edgar S.; Steiner, Oskar

The discussion regarding the numerical integration of the polarized radiative transfer equation is still open and the comparison between the different numerical schemes proposed by different authors in the past is not fully clear. Aiming at facilitating the comprehension of the advantages and drawbacks of the different formal solvers, this work presents a reference paradigm for their characterization based on the concepts of order of accuracy , stability , and computational cost . Special attention is paid to understand the numerical methods belonging to the Diagonal Element Lambda Operator family, in an attempt to highlight their specificities.

A practical introduction to tensor networks: Matrix product states and projected entangled pair states

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

Orús, Román, E-mail: roman.orus@uni-mainz.de

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems aremore » also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.« less

Error Analysis of p-Version Discontinuous Galerkin Method for Heat Transfer in Built-up Structures

NASA Technical Reports Server (NTRS)

Kaneko, Hideaki; Bey, Kim S.

2004-01-01

The purpose of this paper is to provide an error analysis for the p-version of the discontinuous Galerkin finite element method for heat transfer in built-up structures. As a special case of the results in this paper, a theoretical error estimate for the numerical experiments recently conducted by James Tomey is obtained.

Numerical calculation of primary slot leakage inductance of a Single-sided HTS linear induction motor used for linear metro

NASA Astrophysics Data System (ADS)

Li, Dong; Wen, Yinghong; Li, Weili; Fang, Jin; Cao, Junci; Zhang, Xiaochen; Lv, Gang

2017-03-01

In the paper, the numerical method calculating asymmetric primary slot leakage inductances of Single-sided High-Temperature Superconducting (HTS) Linear Induction Motor (HTS LIM) is presented. The mathematical and geometric models of three-dimensional nonlinear transient electromagnetic field are established and the boundary conditions are also given. The established model is solved by time-stepping Finite Element Method (FEM). Then, the three-phase asymmetric primary slot leakage inductances under different operation conditions are calculated by using the obtained electromagnetic field distribution. The influences of the special effects such as longitudinal end effects, transversal edge effects, etc. on the primary slot leakage inductance are investigated. The presented numerical method is validated by experiments carried out on a 3.5 kW prototype with copper wires which has the same structures with the HTS LIM.

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

Upwind and symmetric shock-capturing schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.

1987-01-01

The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis is on the construction of the basic nonlinear scalar second-order schemes and the methods of extending these nonlinear scalar schemes to nonlinear systems via the extact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows is discussed. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas dynamics problems.

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy (Editor); Deconinck, Herman (Editor)

1999-01-01

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

A 1D radiative transfer benchmark with polarization via doubling and adding

NASA Astrophysics Data System (ADS)

Ganapol, B. D.

2017-11-01

Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to seven places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

Special data base of Informational - Computational System 'INM RAS - Black Sea' for solving inverse and data assimilation problems

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Piskovatsky, Nicolay; Gusev, Anatoly

2014-05-01

Development of Informational-Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The above problems are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for personal computers. In this work the results on the Special data base development for ICS "INM RAS - Black Sea" are presented. In the presentation the input information for ICS is discussed, some special data processing procedures are described. In this work the results of forecast using ICS "INM RAS - Black Sea" with operational observation data assimilation are presented. This study was supported by the Russian Foundation for Basic Research (project No 13-01-00753) and by Presidium Program of Russian Academy of Sciences (project P-23 "Black sea as an imitational ocean model"). References 1. V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 5-31. 2. E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 69-94. 3. V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 95-111. 4. Agoshkov V.I.,Assovsky M.B., Giniatulin S. V., Zakharova N.B., Kuimov G.V., Parmuzin E.I., Fomin V.V. Informational Computational system of variational assimilation of observation data "INM RAS - Black sea"// Ecological safety of coastal and shelf zones and complex use of shelf resources: Collection of scientific works. Issue 26, Volume 2. - National Academy of Sciences of Ukraine, Marine Hydrophysical Institute, Sebastopol, 2012. Pages 352-360. (In russian)

Constructing exact symmetric informationally complete measurements from numerical solutions

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

Towards a rational theory for CFD global stability

NASA Technical Reports Server (NTRS)

Baker, A. J.; Iannelli, G. S.

1989-01-01

The fundamental notion of the consistent stability of semidiscrete analogues of evolution PDEs is explored. Lyapunov's direct method is used to develop CFD semidiscrete algorithms which yield the TVD constraint as a special case. A general formula for supplying dissipation parameters for arbitrary multidimensional conservation law systems is proposed. The reliability of the method is demonstrated by the results of two numerical tests for representative Euler shocked flows.

Numerical study of drop spreading on a flat surface

NASA Astrophysics Data System (ADS)

Wang, Sheng; Desjardins, Olivier

2017-11-01

In this talk, we perform a numerical study of a droplet on a flat surface with special emphasis on capturing the spreading dynamics. The computational methodology employed is tailored for simulating large-scale two-phase flows within complex geometries. It combines a conservative level-set method to capture the liquid-gas interface, a conservative immersed boundary method to represent the solid-fluid interface, and a sub-grid curvature model at the triple-point to implicitly impose the contact angle of the liquid-gas interface. The performance of the approach is assessed in the inertial droplet spreading regime, the viscous spreading regime of high viscosity drops, and with the capillary oscillation of low viscosity droplets.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Symplectic molecular dynamics simulations on specially designed parallel computers.

PubMed

Borstnik, Urban; Janezic, Dusanka

2005-01-01

We have developed a computer program for molecular dynamics (MD) simulation that implements the Split Integration Symplectic Method (SISM) and is designed to run on specialized parallel computers. The MD integration is performed by the SISM, which analytically treats high-frequency vibrational motion and thus enables the use of longer simulation time steps. The low-frequency motion is treated numerically on specially designed parallel computers, which decreases the computational time of each simulation time step. The combination of these approaches means that less time is required and fewer steps are needed and so enables fast MD simulations. We study the computational performance of MD simulation of molecular systems on specialized computers and provide a comparison to standard personal computers. The combination of the SISM with two specialized parallel computers is an effective way to increase the speed of MD simulations up to 16-fold over a single PC processor.

Radar studies of the atmosphere using spatial and frequency diversity

NASA Astrophysics Data System (ADS)

Yu, Tian-You

This work provides results from a thorough investigation of atmospheric radar imaging including theory, numerical simulations, observational verification, and applications. The theory is generalized to include the existing imaging techniques of coherent radar imaging (CRI) and range imaging (RIM), which are shown to be special cases of three-dimensional imaging (3D Imaging). Mathematically, the problem of atmospheric radar imaging is posed as an inverse problem. In this study, the Fourier, Capon, and maximum entropy (MaxEnt) methods are proposed to solve the inverse problem. After the introduction of the theory, numerical simulations are used to test, validate, and exercise these techniques. Statistical comparisons of the three methods of atmospheric radar imaging are presented for various signal-to-noise ratio (SNR), receiver configuration, and frequency sampling. The MaxEnt method is shown to generally possess the best performance for low SNR. The performance of the Capon method approaches the performance of the MaxEnt method for high SNR. In limited cases, the Capon method actually outperforms the MaxEnt method. The Fourier method generally tends to distort the model structure due to its limited resolution. Experimental justification of CRI and RIM is accomplished using the Middle and Upper (MU) Atmosphere Radar in Japan and the SOUnding SYstem (SOUSY) in Germany, respectively. A special application of CRI to the observation of polar mesosphere summer echoes (PMSE) is used to show direct evidence of wave steepening and possibly explain gravity wave variations associated with PMSE.

Approximation Methods for Inverse Problems Governed by Nonlinear Parabolic Systems

DTIC Science & Technology

1999-12-17

We present a rigorous theoretical framework for approximation of nonlinear parabolic systems with delays in the context of inverse least squares...numerical results demonstrating the convergence are given for a model of dioxin uptake and elimination in a distributed liver model that is a special case of the general theoretical framework .

A Network Analysis of the American Library Association: Defining a Profession

ERIC Educational Resources Information Center

Battleson, Brenda L.

2010-01-01

The term "librarianship" is a generic one, suggesting one overarching discipline despite the numerous specializations and areas of research within the profession. While many disciplines use bibliometric analysis of their literature to define subfields of study within, such methods are not appropriate to librarianship due to the nature of…

Comparison of four stable numerical methods for Abel's integral equation

NASA Technical Reports Server (NTRS)

Murio, Diego A.; Mejia, Carlos E.

1991-01-01

The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.

Experimental and simulation flow rate analysis of the 3/2 directional pneumatic valve

NASA Astrophysics Data System (ADS)

Blasiak, Slawomir; Takosoglu, Jakub E.; Laski, Pawel A.; Pietrala, Dawid S.; Zwierzchowski, Jaroslaw; Bracha, Gabriel; Nowakowski, Lukasz; Blasiak, Malgorzata

The work includes a study on the comparative analysis of two test methods. The first method - numerical method, consists in determining the flow characteristics with the use of ANSYS CFX. A modeled poppet directional valve 3/2 3D CAD software - SolidWorks was used for this purpose. Based on the solid model that was developed, simulation studies of the air flow through the way valve in the software for computational fluid dynamics Ansys CFX were conducted. The second method - experimental, entailed conducting tests on a specially constructed test stand. The comparison of the test results obtained on the basis of both methods made it possible to determine the cross-correlation. High compatibility of the results confirms the usefulness of the numerical procedures. Thus, they might serve to determine the flow characteristics of directional valves as an alternative to a costly and time-consuming test stand.

Numerical Modelling of Foundation Slabs with use of Schur Complement Method

NASA Astrophysics Data System (ADS)

Koktan, Jiří; Brožovský, Jiří

2017-10-01

The paper discusses numerical modelling of foundation slabs with use of advanced numerical approaches, which are suitable for parallel processing. The solution is based on the Finite Element Method with the slab-type elements. The subsoil is modelled with use of Winklertype contact model (as an alternative a multi-parameter model can be used). The proposed modelling approach uses the Schur Complement method to speed-up the computations of the problem. The method is based on a special division of the analyzed model to several substructures. It adds some complexity to the numerical procedures, especially when subsoil models are used inside the finite element method solution. In other hand, this method makes possible a fast solution of large models but it introduces further problems to the process. Thus, the main aim of this paper is to verify that such method can be successfully used for this type of problem. The most suitable finite elements will be discussed, there will be also discussion related to finite element mesh and limitations of its construction for such problem. The core approaches of the implementation of the Schur Complement Method for this type of the problem will be also presented. The proposed approach was implemented in the form of a computer program, which will be also briefly introduced. There will be also presented results of example computations, which prove the speed-up of the solution - there will be shown important speed-up of solution even in the case of on-parallel processing and the ability of bypass size limitations of numerical models with use of the discussed approach.

Modeling of aerodynamic heat flux and thermoelastic behavior of nose caps of hypersonic vehicles

NASA Astrophysics Data System (ADS)

Persova, Marina G.; Soloveichik, Yury G.; Belov, Vasiliy K.; Kiselev, Dmitry S.; Vagin, Denis V.; Domnikov, Petr A.; Patrushev, Ilya I.; Kurskiy, Denis N.

2017-07-01

In this paper, the problem of numerical modeling of thermoelastic behavior of nose caps of hypersonic vehicles at different angles of attack is considered. 3D finite element modeling is performed by solving the coupled heat and elastic problems taking into account thermal and mechanical properties variations with temperature. A special method for calculating the aerodynamic heat flux entering the nose cap from its surface is proposed. This method is characterized by very low computational costs and allows calculating the aerodynamic heat flux at different values of the Mach number and angles of attack which may vary during the aerodynamic heating. The numerical results obtained by the proposed approach are compared with the numerical results and experimental data obtained by other authors. The developed approach has been used for studying the impact of the angle of attack on the thermoelastic behavior of nose caps main components.

The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

1998-01-01

Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

Use of various versions of Schwarz method for solving the problem of contact interaction of elastic bodies

NASA Astrophysics Data System (ADS)

Galanin, M. P.; Lukin, V. V.; Rodin, A. S.

2018-04-01

A definition of a sufficiently common problem of mechanical contact interaction in a system of elastic bodies is given. Various versions of realization of the Schwarz method for solving the contact problem numerically are described and the results of solution of a number of problems are presented. Special attention is paid to calculations where the grids in the bodies significantly differ in steps.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

NASA Technical Reports Server (NTRS)

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

Hybrid transfer-matrix FDTD method for layered periodic structures.

PubMed

Deinega, Alexei; Belousov, Sergei; Valuev, Ilya

2009-03-15

A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.

WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

Generalized self-consistent method for predicting the effective elastic properties of composites with random hybrid structures

NASA Astrophysics Data System (ADS)

Pan'kov, A. A.

1997-05-01

The feasibility of using a generalized self-consistent method for predicting the effective elastic properties of composites with random hybrid structures has been examined. Using this method, the problem is reduced to solution of simpler special averaged problems for composites with single inclusions and corresponding transition layers in the medium examined. The dimensions of the transition layers are defined by correlation radii of the composite random structure of the composite, while the heterogeneous elastic properties of the transition layers take account of the probabilities for variation of the size and configuration of the inclusions using averaged special indicator functions. Results are given for a numerical calculation of the averaged indicator functions and analysis of the effect of the micropores in the matrix-fiber interface region on the effective elastic properties of unidirectional fiberglass—epoxy using the generalized self-consistent method and compared with experimental data and reported solutions.

NASA Glenn Research Center Overview

NASA Technical Reports Server (NTRS)

Sehra, Arun K.

2002-01-01

This viewgraph presentation provides information on the NASA Glenn Research Center. The presentation is a broad overview, including the chain of command at the center, its aeronautics facilities, and the factors which shape aerospace product line integration at the center. Special attention is given to the future development of high fidelity probabilistic methods, and NPSS (Numerical Propulsion System Simulation).

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

Exact special twist method for quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Dagrada, Mario; Karakuzu, Seher; Vildosola, Verónica Laura; Casula, Michele; Sorella, Sandro

2016-12-01

We present a systematic investigation of the special twist method introduced by Rajagopal et al. [Phys. Rev. B 51, 10591 (1995), 10.1103/PhysRevB.51.10591] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure "exact special twist" (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the three-dimensional electron gas. Afterwards, we test its efficiency within ab initio quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost since it involves the evaluation of just one wave function. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations; our method will be particularly relevant when the physical problem under consideration requires large periodic cells.

Computation of viscous flows over airfoils, including separation, with a coupling approach

NASA Technical Reports Server (NTRS)

Leballeur, J. C.

1983-01-01

Viscous incompressible flows over single or multiple airfoils, with or without separation, were computed using an inviscid flow calculation, with modified boundary conditions, and by a method providing calculation and coupling for boundary layers and wakes, within conditions of strong viscous interaction. The inviscid flow is calculated with a method of singularities, the numerics of which were improved by using both source and vortex distributions over profiles, associated with regularity conditions for the fictitious flows inside of the airfoils. The viscous calculation estimates the difference between viscous flow and inviscid interacting flow, with a direct or inverse integral method, laminar or turbulent, with or without reverse flow. The numerical method for coupling determines iteratively the boundary conditions for the inviscid flow. For attached viscous layers regions, an underrelaxation is locally calculated to insure stability. For separated or separating regions, a special semi-inverse algorithm is used. Comparisons with experiments are presented.

Introducing a new family of short-range potentials and their numerical solutions using the asymptotic iteration method

NASA Astrophysics Data System (ADS)

Assi, I. A.; Sous, A. J.

2018-05-01

The goal of this work is to derive a new class of short-range potentials that could have a wide range of physical applications, specially in molecular physics. The tridiagonal representation approach has been developed beyond its limitations to produce new potentials by requiring the representation of the Schrödinger wave operator to be multidiagonal and symmetric. This produces a family of Hulthén potentials that has a specific structure, as mentioned in the introduction. As an example, we have solved the nonrelativistic wave equation for the new four-parameter short-range screening potential numerically using the asymptotic iteration method, where we tabulated the eigenvalues for both s -wave and arbitrary l -wave cases in tables.

Flow Applications of the Least Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1998-01-01

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

Optimization of droplets for UV-NIL using coarse-grain simulation of resist flow

NASA Astrophysics Data System (ADS)

Sirotkin, Vadim; Svintsov, Alexander; Zaitsev, Sergey

2009-03-01

A mathematical model and numerical method are described, which make it possible to simulate ultraviolet ("step and flash") nanoimprint lithography (UV-NIL) process adequately even using standard Personal Computers. The model is derived from 3D Navier-Stokes equations with the understanding that the resist motion is largely directed along the substrate surface and characterized by ultra-low values of the Reynolds number. By the numerical approximation of the model, a special finite difference method is applied (a coarse-grain method). A coarse-grain modeling tool for detailed analysis of resist spreading in UV-NIL at the structure-scale level is tested. The obtained results demonstrate the high ability of the tool to calculate optimal dispensing for given stamp design and process parameters. This dispensing provides uniform filled areas and a homogeneous residual layer thickness in UV-NIL.

Dundee Biennial Conference on Numerical Analysis held at Dundee Univ (United Kingdom) on 23-26 June 1977

DTIC Science & Technology

1987-06-26

a related class of implicit Runge-Kutta-Nystrom methods. The talk will conclude with a look at some ongoing work...formulae with deferred corrections. In order to perform the deferred correction stage efficiently, a special class of formulae, known as Mono-Implicit... of this type ( termed "CBS methods") have been developed which permit a wide variety of convergent interpolations, many of which are unstable in

Fluid Stochastic Petri Nets: Theory, Applications, and Solution

NASA Technical Reports Server (NTRS)

Horton, Graham; Kulkarni, Vidyadhar G.; Nicol, David M.; Trivedi, Kishor S.

1996-01-01

In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

A Fast Numerical Method for Max-Convolution and the Application to Efficient Max-Product Inference in Bayesian Networks.

PubMed

Serang, Oliver

2015-08-01

Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in log-transformed form and denoted as "infimal convolution," "min-convolution," or "convolution on the tropical semiring"), for which no O(k log(k)) method is currently known. Presented here is an O(k log(k)) numerical method for estimating the max-convolution of two nonnegative vectors (e.g., two probability mass functions), where k is the length of the larger vector. This numerical max-convolution method is then demonstrated by performing fast max-product inference on a convolution tree, a data structure for performing fast inference given information on the sum of n discrete random variables in O(nk log(nk)log(n)) steps (where each random variable has an arbitrary prior distribution on k contiguous possible states). The numerical max-convolution method can be applied to specialized classes of hidden Markov models to reduce the runtime of computing the Viterbi path from nk(2) to nk log(k), and has potential application to the all-pairs shortest paths problem.

A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Special Year on Numerical Linear Algebra

DTIC Science & Technology

1988-09-01

ORNL) Worley, Pat (ORNL) A special acknowledgement should go to Mary Drake (UT) and Mitzy Denson (ORNL) who carried the burden of making the innumerable...a time step appropriate for the regular cells with no stability restriction. Entrance to Y-12 requires a pass. Contact Mitzy Denson (615) 574-3125 to...requires a pass. Contact Mitzy Denson (615) 574-3125 to obtain one. ’This seminar is part of the Special Year on Numerical Linear Algebra sponsored by the

Long-term Stable Conservative Multiscale Methods for Vortex Flows

DTIC Science & Technology

2017-10-31

Computational and Applied Mathematics and Engeneering, Eccomas 2016 (Crete, June, 2016) - M. A. Olshanskii, Scientific computing seminar of Math ...UMass Dartmouth (October 2015) - L. Rebholz, Applied Math Seminar Talk, University of Alberta (October 2015) - L. Rebholz, Colloquium Talk, Scientific...Colloquium, (November 2016) - L. Rebholz, Joint Math Meetings 2017, Special session on recent advances in numerical analysis of PDEs, Atlanta GA

The Benefits of Supporting the Autonomy of Individuals with Mild Intellectual Disabilities: An Experimental Study

ERIC Educational Resources Information Center

Emond Pelletier, Julie; Joussemet, Mireille

2017-01-01

Background: The benefits of autonomy support with the general population have been demonstrated numerous times. However, little research has been conducted to verify if these benefits apply to people with special needs. Methods: The goal of the study was to examine whether autonomy support (AS) can foster the sense of autonomy of people with a…

On the probability of exceeding allowable leak rates through degraded steam generator tubes

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

Cizelj, L.; Sorsek, I.; Riesch-Oppermann, H.

1997-02-01

This paper discusses some possible ways of predicting the behavior of the total leak rate through the damaged steam generator tubes. This failure mode is of special concern in cases where most through-wall defects may remain In operation. A particular example is the application of alternate (bobbin coil voltage) plugging criterion to Outside Diameter Stress Corrosion Cracking at the tube support plate intersections. It is the authors aim to discuss some possible modeling options that could be applied to solve the problem formulated as: Estimate the probability that the sum of all individual leak rates through degraded tubes exceeds themore » predefined acceptable value. The probabilistic approach is of course aiming at reliable and computationaly bearable estimate of the failure probability. A closed form solution is given for a special case of exponentially distributed individual leak rates. Also, some possibilities for the use of computationaly efficient First and Second Order Reliability Methods (FORM and SORM) are discussed. The first numerical example compares the results of approximate methods with closed form results. SORM in particular shows acceptable agreement. The second numerical example considers a realistic case of NPP in Krsko, Slovenia.« less

PREFACE: Special section on Computational Fluid Dynamics—in memory of Professor Kunio Kuwahara Special section on Computational Fluid Dynamics—in memory of Professor Kunio Kuwahara

NASA Astrophysics Data System (ADS)

Ishii, Katsuya

2011-08-01

This issue includes a special section on computational fluid dynamics (CFD) in memory of the late Professor Kunio Kuwahara, who passed away on 15 September 2008, at the age of 66. In this special section, five articles are included that are based on the lectures and discussions at `The 7th International Nobeyama Workshop on CFD: To the Memory of Professor Kuwahara' held in Tokyo on 23 and 24 September 2009. Professor Kuwahara started his research in fluid dynamics under Professor Imai at the University of Tokyo. His first paper was published in 1969 with the title 'Steady Viscous Flow within Circular Boundary', with Professor Imai. In this paper, he combined theoretical and numerical methods in fluid dynamics. Since that time, he made significant and seminal contributions to computational fluid dynamics. He undertook pioneering numerical studies on the vortex method in 1970s. From then to the early nineties, he developed numerical analyses on a variety of three-dimensional unsteady phenomena of incompressible and compressible fluid flows and/or complex fluid flows using his own supercomputers with academic and industrial co-workers and members of his private research institute, ICFD in Tokyo. In addition, a number of senior and young researchers of fluid mechanics around the world were invited to ICFD and the Nobeyama workshops, which were held near his villa, and they intensively discussed new frontier problems of fluid physics and fluid engineering at Professor Kuwahara's kind hospitality. At the memorial Nobeyama workshop held in 2009, 24 overseas speakers presented their papers, including the talks of Dr J P Boris (Naval Research Laboratory), Dr E S Oran (Naval Research Laboratory), Professor Z J Wang (Iowa State University), Dr M Meinke (RWTH Aachen), Professor K Ghia (University of Cincinnati), Professor U Ghia (University of Cincinnati), Professor F Hussain (University of Houston), Professor M Farge (École Normale Superieure), Professor J Y Yong (National Taiwan University), and Professor H S Kwak (Kumoh National Institute of Technology). For his contributions to CFD, Professor Kuwahara received Awards from the Japan Society of Automobile Engineers and the Japan Society of Mechanical Engineers in 1992, the Computational Mechanics Achievement Award from the Japan Society of Mechanical Engineers in 1993, and the Max Planck Research Award in 1993. He received the Computational Mechanics Award from the Japan Society of Mechanical Engineers again in 2008. Professor Kuwahara also supported the development of the Japan Society of Fluid Mechanics, whose office is located in the same building as ICFD. In the proceedings of the 6th International Nobeyama Workshop on CFD to commemorate the 60th birthday of Professor Kuwahara, Professor Jae Min Hyun of KAIST wrote 'The major professional achievement of Professor Kuwahara may be compressed into two main categories. First and foremost, Professor Kuwahara will long be recorded as the front-line pioneer in using numerical computations to tackle complex problems in fluid mechanics. ...Another important contribution of Professor Kuwahara was in the training and fostering of talented manpower of computational mechanics research.'[1] Among the various topics of the five papers in this special section are examples of Professor Kuwahara's works mentioned by Professor Hyun. The main authors of all papers have grown up in the research circle of Professor Kuwahara. All the papers demostrate the challenge of new aspects of computational fluid dynamics; a new numerical method for compressible flows, thermo-acoustic flows of helium gas in a small tube, electro-osmic flows in a micro/nano channel, MHD flows over a wavy disk, and a new extraction method of multi-object aircraft design rules. Last but not least, this special section is cordially dedicated to the late Professor Kuwahara and his family. Reference [1] Hyun J M 2005 Preface of New Developments in Computational Fluid Dynamics vol 90 Notes on Numerical Fluid Mechanics and Multidisciplinary Design ed K Fujii et al (Berlin: Springer)

Quadratic RK shooting solution for a environmental parameter prediction boundary value problem

NASA Astrophysics Data System (ADS)

Famelis, Ioannis Th.; Tsitouras, Ch.

2014-10-01

Using tools of Information Geometry, the minimum distance between two elements of a statistical manifold is defined by the corresponding geodesic, e.g. the minimum length curve that connects them. Such a curve, where the probability distribution functions in the case of our meteorological data are two parameter Weibull distributions, satisfies a 2nd order Boundary Value (BV) system. We study the numerical treatment of the resulting special quadratic form system using Shooting method. We compare the solutions of the problem when we employ a classical Singly Diagonally Implicit Runge Kutta (SDIRK) 4(3) pair of methods and a quadratic SDIRK 5(3) pair . Both pairs have the same computational costs whereas the second one attains higher order as it is specially constructed for quadratic problems.

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2003-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them. Supplementary material is available for this article at 10.12942/lrr-2003-4.

A radial basis function Galerkin method for inhomogeneous nonlocal diffusion

DOE PAGES

Lehoucq, Richard B.; Rowe, Stephen T.

2016-02-01

We introduce a discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. The stiffness matrix entries are assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. As a result, we explore approximating the solution to anisotropic differential equations by solving anisotropic nonlocal integral equations using the radial basis function method.

Exponential Methods for the Time Integration of Schroedinger Equation

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

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

Committee Opinion No 707: Access to Emergency Contraception.

PubMed

2017-07-01

Emergency contraception refers to contraceptive methods used to prevent pregnancy in the first few days after unprotected intercourse, sexual assault, or contraceptive failure. Although the U.S. Food and Drug Administration approved the first dedicated product for emergency contraception in 1998, numerous barriers to emergency contraception remain. The purpose of this Committee Opinion is to examine barriers to the use of emergency contraception, emphasize the importance of increasing access, and review new methods of emergency contraception and limitations in efficacy in special populations.

Committee Opinion No. 707 Summary: Access to Emergency Contraception.

PubMed

2017-07-01

Emergency contraception refers to contraceptive methods used to prevent pregnancy in the first few days after unprotected intercourse, sexual assault, or contraceptive failure. Although the U.S. Food and Drug Administration approved the first dedicated product for emergency contraception in 1998, numerous barriers to emergency contraception remain. The purpose of this Committee Opinion is to examine barriers to the use of emergency contraception, emphasize the importance of increasing access, and review new methods of emergency contraception and limitations in efficacy in special populations.

On a numerical solving of random generated hexamatrix games

NASA Astrophysics Data System (ADS)

Orlov, Andrei; Strekalovskiy, Alexander

2016-10-01

In this paper, we develop a global search method for finding a Nash equilibrium in a hexamatrix game (polymatrix game of three players). The method, on the one hand, is based on the equivalence theorem of the problem of finding a Nash equilibrium in the game and a special mathematical optimization problem, and, on the other hand, on the usage of Global Search Theory for solving the latter problem. The efficiency of this approach is demonstrated by the results of computational testing.

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov-Uvarov Method

NASA Astrophysics Data System (ADS)

Akpan, N. Ikot; Hassan, Hassanabadi; Tamunoimi, M. Abbey

2015-12-01

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseudospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore » methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.« less

Analysis and algorithms for a regularized Cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

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

Cameron, M.K.; Fomel, S.B.; Sethian, J.A.

2009-01-01

In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approachmore » is a spectral Chebyshev method with truncated series. We show that our schemes work because of (1) the special input corresponding to a positive finite seismic velocity, (2) special initial conditions corresponding to the image rays, (3) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (4) the need to compute the solution only for a short interval of time. We test our numerical scheme on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.« less

Two dimensional fully nonlinear numerical wave tank based on the BEM

NASA Astrophysics Data System (ADS)

Sun, Zhe; Pang, Yongjie; Li, Hongwei

2012-12-01

The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.

Two Legendre-Dual-Petrov-Galerkin Algorithms for Solving the Integrated Forms of High Odd-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, Waleed M.; Doha, Eid H.; Bassuony, Mahmoud A.

2014-01-01

Two numerical algorithms based on dual-Petrov-Galerkin method are developed for solving the integrated forms of high odd-order boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made. PMID:24616620

General Potential Theory of Arbitrary Wing Sections

NASA Technical Reports Server (NTRS)

Theodorsen, T.; Garrick, I. E.

1979-01-01

The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.

A three-dimensional Dirichlet-to-Neumann operator for water waves over topography

NASA Astrophysics Data System (ADS)

Andrade, D.; Nachbin, A.

2018-06-01

Surface water waves are considered propagating over highly variable non-smooth topographies. For this three dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modeling and evolution to the two dimensional free surface. The corresponding Fourier-type operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care and a Galerkin method is provided accordingly. One dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large amplitude, rapidly varying topography. An alternative, conformal mapping based, method is used for benchmarking. A two dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three dimensional DtN operator.

A boundary integral method for numerical computation of radar cross section of 3D targets using hybrid BEM/FEM with edge elements

NASA Astrophysics Data System (ADS)

Dodig, H.

2017-11-01

This contribution presents the boundary integral formulation for numerical computation of time-harmonic radar cross section for 3D targets. Method relies on hybrid edge element BEM/FEM to compute near field edge element coefficients that are associated with near electric and magnetic fields at the boundary of the computational domain. Special boundary integral formulation is presented that computes radar cross section directly from these edge element coefficients. Consequently, there is no need for near-to-far field transformation (NTFFT) which is common step in RCS computations. By the end of the paper it is demonstrated that the formulation yields accurate results for canonical models such as spheres, cubes, cones and pyramids. Method has demonstrated accuracy even in the case of dielectrically coated PEC sphere at interior resonance frequency which is common problem for computational electromagnetic codes.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Immunomagnetic separation for MEMS-based biosensor of waterborne pathogens detection

NASA Astrophysics Data System (ADS)

Guo, Jianjiang; Zhang, Rongbiao

2017-07-01

Rapid isolation and detection of special pathogens present in environmental drinking water is critical for water quality monitoring. Numerical analysis and experimental investigations on immunomagnetic capture and isolation of waterborne pathogens with magnetic nanoparticles (MNPs) in microfluidic channel are performed. A finite-element COMSOL-based model is established to demonstrate the novel method of on-chip capturing pathogens using MNPs together with periodic pulse magnetic field. Simulation results determine the optimum magnetic pole current and switching frequency for magnetic separation. With the magnetic isolation experiment platform built up, as a pathogen example of Escherichia coli O157:H7, the performance of the method is experimentally verified. Both numerical and experimental results are found to agree reasonably well. Results of these investigations show that the capture efficiency of the immunomagnetic separation method is more than 92%, which could be encouraging for the design and optimization of MEMS-based biosensor of waterborne pathogen detection.

Flow field predictions for a slab delta wing at incidence

NASA Technical Reports Server (NTRS)

Conti, R. J.; Thomas, P. D.; Chou, Y. S.

1972-01-01

Theoretical results are presented for the structure of the hypersonic flow field of a blunt slab delta wing at moderately high angle of attack. Special attention is devoted to the interaction between the boundary layer and the inviscid entropy layer. The results are compared with experimental data. The three-dimensional inviscid flow is computed numerically by a marching finite difference method. Attention is concentrated on the windward side of the delta wing, where detailed comparisons are made with the data for shock shape and surface pressure distributions. Surface streamlines are generated, and used in the boundary layer analysis. The three-dimensional laminar boundary layer is computed numerically using a specially-developed technique based on small cross-flow in streamline coordinates. In the rear sections of the wing the boundary layer decreases drastically in the spanwise direction, so that it is still submerged in the entropy layer at the centerline, but surpasses it near the leading edge. Predicted heat transfer distributions are compared with experimental data.

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Accuracy Study of the Space-Time CE/SE Method for Computational Aeroacoustics Problems Involving Shock Waves

NASA Technical Reports Server (NTRS)

Wang, Xiao Yen; Chang, Sin-Chung; Jorgenson, Philip C. E.

1999-01-01

The space-time conservation element and solution element(CE/SE) method is used to study the sound-shock interaction problem. The order of accuracy of numerical schemes is investigated. The linear model problem.govemed by the 1-D scalar convection equation, sound-shock interaction problem governed by the 1-D Euler equations, and the 1-D shock-tube problem which involves moving shock waves and contact surfaces are solved to investigate the order of accuracy of numerical schemes. It is concluded that the accuracy of the CE/SE numerical scheme with designed 2nd-order accuracy becomes 1st order when a moving shock wave exists. However, the absolute error in the CE/SE solution downstream of the shock wave is on the same order as that obtained using a fourth-order accurate essentially nonoscillatory (ENO) scheme. No special techniques are used for either high-frequency low-amplitude waves or shock waves.

Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

NASA Technical Reports Server (NTRS)

Deavours, Daniel D.; Qureshi, M. Akber; Sanders, William H.

1997-01-01

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure.

Numerical Technology for Large-Scale Computational Electromagnetics

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

Sharpe, R; Champagne, N; White, D

The key bottleneck of implicit computational electromagnetics tools for large complex geometries is the solution of the resulting linear system of equations. The goal of this effort was to research and develop critical numerical technology that alleviates this bottleneck for large-scale computational electromagnetics (CEM). The mathematical operators and numerical formulations used in this arena of CEM yield linear equations that are complex valued, unstructured, and indefinite. Also, simultaneously applying multiple mathematical modeling formulations to different portions of a complex problem (hybrid formulations) results in a mixed structure linear system, further increasing the computational difficulty. Typically, these hybrid linear systems aremore » solved using a direct solution method, which was acceptable for Cray-class machines but does not scale adequately for ASCI-class machines. Additionally, LLNL's previously existing linear solvers were not well suited for the linear systems that are created by hybrid implicit CEM codes. Hence, a new approach was required to make effective use of ASCI-class computing platforms and to enable the next generation design capabilities. Multiple approaches were investigated, including the latest sparse-direct methods developed by our ASCI collaborators. In addition, approaches that combine domain decomposition (or matrix partitioning) with general-purpose iterative methods and special purpose pre-conditioners were investigated. Special-purpose pre-conditioners that take advantage of the structure of the matrix were adapted and developed based on intimate knowledge of the matrix properties. Finally, new operator formulations were developed that radically improve the conditioning of the resulting linear systems thus greatly reducing solution time. The goal was to enable the solution of CEM problems that are 10 to 100 times larger than our previous capability.« less

Plans for wind energy system simulation

NASA Technical Reports Server (NTRS)

Dreier, M. E.

1978-01-01

A digital computer code and a special purpose hybrid computer, were introduced. The digital computer program, the Root Perturbation Method or RPM, is an implementation of the classic floquet procedure which circumvents numerical problems associated with the extraction of Floquet roots. The hybrid computer, the Wind Energy System Time domain simulator (WEST), yields real time loads and deformation information essential to design and system stability investigations.

Static Methods in the Design of Nonlinear Automatic Control Systems,

DTIC Science & Technology

1984-06-27

227 Chapter VI. Ways of Decrease of the Number of Statistical Nodes During the Research of Nonlinear Systems...at present occupies the central place. This region of research was called the statistical dynamics of nonlinear H automatic control systems...receives further development in the numerous research of Soviet and C foreign scientists. Special role in the development of the statistical dynamics of

The Effects of Co-Teaching on Regular Education and Special Education Students' Standardized Communication Arts Test Scores in a Suburban Midwest Middle School

ERIC Educational Resources Information Center

O'Neal, Angeline N.

2013-01-01

In response to numerous mandates in the field of education, schools have found it imperative to ensure that teachers are incorporating effective instructional methods which meet the diverse needs of student populations within a single classroom. The co-teaching model of instruction is just one way educators have chosen to lead classroom…

Some special solutions to the Hyperbolic NLS equation

NASA Astrophysics Data System (ADS)

Vuillon, Laurent; Dutykh, Denys; Fedele, Francesco

2018-04-01

The Hyperbolic Nonlinear SCHRöDINGER equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The PETVIASHVILI method is then exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly accurate FOURIER solver.

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

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.

A new method for extracting near-surface mass-density anomalies from land-based gravity data, based on a special case of Poisson's PDE at the Earth's surface: A case study of salt diapirs in the south of Iran

NASA Astrophysics Data System (ADS)

AllahTavakoli, Y.; Safari, A.; Ardalan, A.; Bahroudi, A.

2015-12-01

The current research provides a method for tracking near-surface mass-density anomalies via using only land-based gravity data, which is based on a special version of Poisson's Partial Differential Equation (PDE) of the gravitational field at Earth's surface. The research demonstrates how the Poisson's PDE can provide us with a capability to extract the near-surface mass-density anomalies from land-based gravity data. Herein, this version of the Poisson's PDE is mathematically introduced to the Earth's surface and then it is used to develop the new method for approximating the mass-density via derivatives of the Earth's gravitational field (i.e. via the gradient tensor). Herein, the author believes that the PDE can give us new knowledge about the behavior of the Earth's gravitational field at the Earth's surface which can be so useful for developing new methods of Earth's mass-density determination. In a case study, the proposed method is applied to a set of gravity stations located in the south of Iran. The results were numerically validated via certain knowledge about the geological structures in the area of the case study. Also, the method was compared with two standard methods of mass-density determination. All the numerical experiments show that the proposed approach is well-suited for tracking near-surface mass-density anomalies via using only the gravity data. Finally, the approach is also applied to some petroleum exploration studies of salt diapirs in the south of Iran.

A new dipolar potential for numerical simulations of polar fluids on the 4D hypersphere

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

Caillol, Jean-Michel, E-mail: Jean-Michel.Caillol@th.u-psud.fr; Trulsson, Martin, E-mail: martin.trulsson@lptms.u-psud.fr

2014-09-28

We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three-dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions: when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all themore » formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.« less

A new dipolar potential for numerical simulations of polar fluids on the 4D hypersphere

NASA Astrophysics Data System (ADS)

Caillol, Jean-Michel; Trulsson, Martin

2014-09-01

We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three-dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions: when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all the formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.

Gradient-based stochastic estimation of the density matrix

NASA Astrophysics Data System (ADS)

Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D.; Barros, Kipton

2018-03-01

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S-(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

Tapered fiber optical tweezers for microscopic particle trapping: fabrication and application

NASA Astrophysics Data System (ADS)

Liu, Zhihai; Guo, Chengkai; Yang, Jun; Yuan, Libo

2006-12-01

A novel single tapered fiber optical tweezers is proposed and fabricated by heating and drawing technology. The microscopic particle tapping performance of this special designed tapered fiber probe is demonstrated and investigated. The distribution of the optical field emerging from the tapered fiber tip is numerically calculated based on the beam propagation method. The trapping force FDTD analysis results, both axial and transverse, are also given.

An optimization method for the problems of thermal cloaking of material bodies

NASA Astrophysics Data System (ADS)

Alekseev, G. V.; Levin, V. A.

2016-11-01

Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

Finite-Element Analysis of Residual Stresses Generated Under Nitriding Process: a Three-Dimensional Model

NASA Astrophysics Data System (ADS)

Sawicki, J.; Siedlaczek, P.; Staszczyk, A.

2018-03-01

A numerical three-dimensional model for computing residual stresses generated in cross section of steel 42CrMo4 after nitriding is presented. The diffusion process is analyzed by the finite-element method. The internal stresses are computed using the obtained profile of the distribution of the nitrogen concentration. The special features of the intricate geometry of the treated articles including edges and angles are considered. Comparative analysis of the results of the simulation and of the experimental measurement of residual stresses is performed by the Waisman-Philips method.

Chemical vapor deposition fluid flow simulation modelling tool

NASA Technical Reports Server (NTRS)

Bullister, Edward T.

1992-01-01

Accurate numerical simulation of chemical vapor deposition (CVD) processes requires a general purpose computational fluid dynamics package combined with specialized capabilities for high temperature chemistry. In this report, we describe the implementation of these specialized capabilities in the spectral element code NEKTON. The thermal expansion of the gases involved is shown to be accurately approximated by the low Mach number perturbation expansion of the incompressible Navier-Stokes equations. The radiative heat transfer between multiple interacting radiating surfaces is shown to be tractable using the method of Gebhart. The disparate rates of reaction and diffusion in CVD processes are calculated via a point-implicit time integration scheme. We demonstrate the use above capabilities on prototypical CVD applications.

DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-06-01

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

Systems of Inhomogeneous Linear Equations

NASA Astrophysics Data System (ADS)

Scherer, Philipp O. J.

Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

The application of the mesh-free method in the numerical simulations of the higher-order continuum structures

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

Sun, Yuzhou, E-mail: yuzhousun@126.com; Chen, Gensheng; Li, Dongxia

2016-06-08

This paper attempts to study the application of mesh-free method in the numerical simulations of the higher-order continuum structures. A high-order bending beam considers the effect of the third-order derivative of deflections, and can be viewed as a one-dimensional higher-order continuum structure. The moving least-squares method is used to construct the shape function with the high-order continuum property, the curvature and the third-order derivative of deflections are directly interpolated with nodal variables and the second- and third-order derivative of the shape function, and the mesh-free computational scheme is establish for beams. The coupled stress theory is introduced to describe themore » special constitutive response of the layered rock mass in which the bending effect of thin layer is considered. The strain and the curvature are directly interpolated with the nodal variables, and the mesh-free method is established for the layered rock mass. The good computational efficiency is achieved based on the developed mesh-free method, and some key issues are discussed.« less

Method of moments comparison for soot population modeling in turbulent combustion

NASA Astrophysics Data System (ADS)

Chong, Shao Teng; Im, Hong; Raman, Venkat

2017-11-01

Representation of soot population is an important component in the efficient computational prediction of particulate emissions. However, there are a number of moments-based techniques with varying numerical complexity. In the past, development of such methods has been principally carried out on canonical laminar and 0-D flows. However, their applications in realistic solvers developed for turbulent combustion may face challenges from turbulence closure to selection of moment sets. In this work, the accuracy and relative computational expense of a few common soot method of moments are tested in canonical turbulent flames for different configurations. Large eddy simulation (LES) will be used as the turbulence modeling framework. In grid-filtered LES, the interaction of numerical and modeling errors is a first-order problem that can undermine the accuracy of soot predictions. In the past, special moments-based methods for solvers that transport high frequency content fluid with ability to reconstruct particle size distribution have been developed. Here, a similar analysis will be carried out for the moment-based soot modeling approaches above. Specifically, realizability of moments methods with nonlinear advection schemes will be discussed.

Human-computer interfaces applied to numerical solution of the Plateau problem

NASA Astrophysics Data System (ADS)

Elias Fabris, Antonio; Soares Bandeira, Ivana; Ramos Batista, Valério

2015-09-01

In this work we present a code in Matlab to solve the Problem of Plateau numerically, and the code will include human-computer interface. The Problem of Plateau has applications in areas of knowledge like, for instance, Computer Graphics. The solution method will be the same one of the Surface Evolver, but the difference will be a complete graphical interface with the user. This will enable us to implement other kinds of interface like ocular mouse, voice, touch, etc. To date, Evolver does not include any graphical interface, which restricts its use by the scientific community. Specially, its use is practically impossible for most of the Physically Challenged People.

The Lyapunov dimension and its estimation via the Leonov method

NASA Astrophysics Data System (ADS)

Kuznetsov, N. V.

2016-06-01

Along with widely used numerical methods for estimating and computing the Lyapunov dimension there is an effective analytical approach, proposed by G.A. Leonov in 1991. The Leonov method is based on the direct Lyapunov method with special Lyapunov-like functions. The advantage of the method is that it allows one to estimate the Lyapunov dimension of invariant sets without localization of the set in the phase space and, in many cases, to get effectively an exact Lyapunov dimension formula. In this work the invariance of the Lyapunov dimension with respect to diffeomorphisms and its connection with the Leonov method are discussed. For discrete-time dynamical systems an analog of Leonov method is suggested. In a simple but rigorous way, here it is presented the connection between the Leonov method and the key related works: Kaplan and Yorke (the concept of the Lyapunov dimension, 1979), Douady and Oesterlé (upper bounds of the Hausdorff dimension via the Lyapunov dimension of maps, 1980), Constantin, Eden, Foiaş, and Temam (upper bounds of the Hausdorff dimension via the Lyapunov exponents and Lyapunov dimension of dynamical systems, 1985-90), and the numerical calculation of the Lyapunov exponents and dimension.

A method for screening of plant species for space use

NASA Technical Reports Server (NTRS)

Goeschl, J. D.; Sauer, R. L.; Scheld, H. W.

1986-01-01

A cost-effective methodology which monitors numerous dynamic aspects of carbon assimilation and allocation kinetics in live, intact plants is discussed. Analogous methods can apply to nitrogen uptake and allocation. This methodology capitalizes on the special properties of the short-lived, positron-gamma emitting isotope C-11 especially when applied as CO2-11 in a special extended square wave (ESW) pattern. The 20.4 minute half-life allows for repeated or continuous experiments on the same plant over periods of minutes, hours, days, or weeks. The steady-state isotope equilibrium approached during the ESW experiments, and the parameters which can be analyzed by this technique are also direct results of that short half-life. Additionally, the paired .511 MeV gamma rays penetrate any amount of tissue and their 180 deg opposite orientation provides good collimation and allows coincidence counting which nearly eliminates background.

Enhancing predictive accuracy and reproducibility in clinical evaluation research: Commentary on the special section of the Journal of Evaluation in Clinical Practice.

PubMed

Bryant, Fred B

2016-12-01

This paper introduces a special section of the current issue of the Journal of Evaluation in Clinical Practice that includes a set of 6 empirical articles showcasing a versatile, new machine-learning statistical method, known as optimal data (or discriminant) analysis (ODA), specifically designed to produce statistical models that maximize predictive accuracy. As this set of papers clearly illustrates, ODA offers numerous important advantages over traditional statistical methods-advantages that enhance the validity and reproducibility of statistical conclusions in empirical research. This issue of the journal also includes a review of a recently published book that provides a comprehensive introduction to the logic, theory, and application of ODA in empirical research. It is argued that researchers have much to gain by using ODA to analyze their data. © 2016 John Wiley & Sons, Ltd.

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

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving schememore » we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.« less

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics.

PubMed

Brocchini, Maurizio

2013-12-08

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

PubMed Central

Brocchini, Maurizio

2013-01-01

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention. PMID:24353475

Stability and Drag Reduction in a Boundary Layer with Microbubbles.

DTIC Science & Technology

1988-02-01

order accurate. .’ Since the numerical methods are not the object of this % dissertation, we decline from including the finite difference equations...previous appendix must be the special case of zero pressure gradient. Some entries of the matrices of the block tridiagonal system will be different ...of the wall mean velocity gradient was observed to be associated with the migration of the bubbles away from the boundary layer. The time scale of the

Discrete mathematical model of wave diffraction on pre-fractal impedance strips. TM mode case

NASA Astrophysics Data System (ADS)

Nesvit, K. V.

2013-10-01

In this paper a transverse magnetic (TM) wave diffraction problem on pre-fractal impedance strips is considered. The overall aim of this work is to develop a discrete mathematical model of the boundary integral equations (IEs) with the help of special quadrature formulas with the nodes in the zeros of Chebyshev polynomials and to perform a numerical experiments with the help of an efficient discrete singularities method (DSM).

SENS-5D trajectory and wind-sensitivity calculations for unguided rockets

NASA Technical Reports Server (NTRS)

Singh, R. P.; Huang, L. C. P.; Cook, R. A.

1975-01-01

A computational procedure is described which numerically integrates the equations of motion of an unguided rocket. Three translational and two angular (roll discarded) degrees of freedom are integrated through the final burnout; and then, through impact, only three translational motions are considered. Input to the routine is: initial time, altitude and velocity, vehicle characteristics, and other defined options. Input format has a wide range of flexibility for special calculations. Output is geared mainly to the wind-weighting procedure, and includes summary of trajectory at burnout, apogee and impact, summary of spent-stage trajectories, detailed position and vehicle data, unit-wind effects for head, tail and cross winds, coriolis deflections, range derivative, and the sensitivity curves (the so called F(Z) and DF(Z) curves). The numerical integration procedure is a fourth-order, modified Adams-Bashforth Predictor-Corrector method. This method is supplemented by a fourth-order Runge-Kutta method to start the integration at t=0 and whenever error criteria demand a change in step size.

A numerical solution method for acoustic radiation from axisymmetric bodies

NASA Technical Reports Server (NTRS)

Caruthers, John E.; Raviprakash, G. K.

1995-01-01

A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.

Time is Money

NASA Astrophysics Data System (ADS)

Ausloos, Marcel; Vandewalle, Nicolas; Ivanova, Kristinka

Specialized topics on financial data analysis from a numerical and physical point of view are discussed when pertaining to the analysis of coherent and random sequences in financial fluctuations within (i) the extended detrended fluctuation analysis method, (ii) multi-affine analysis technique, (iii) mobile average intersection rules and distributions, (iv) sandpile avalanches models for crash prediction, (v) the (m,k)-Zipf method and (vi) the i-variability diagram technique for sorting out short range correlations. The most baffling result that needs further thought from mathematicians and physicists is recalled: the crossing of two mobile averages is an original method for measuring the "signal" roughness exponent, but why it is so is not understood up to now.

Structural optimization by multilevel decomposition

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, J.; James, B.; Dovi, A.

1983-01-01

A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem.

Study of Dynamic Characteristics of Aeroelastic Systems Utilizing Randomdec Signatures

NASA Technical Reports Server (NTRS)

Chang, C. S.

1975-01-01

The feasibility of utilizing the random decrement method in conjunction with a signature analysis procedure to determine the dynamic characteristics of an aeroelastic system for the purpose of on-line prediction of potential on-set of flutter was examined. Digital computer programs were developed to simulate sampled response signals of a two-mode aeroelastic system. Simulated response data were used to test the random decrement method. A special curve-fit approach was developed for analyzing the resulting signatures. A number of numerical 'experiments' were conducted on the combined processes. The method is capable of determining frequency and damping values accurately from randomdec signatures of carefully selected lengths.

Analysis and Assessment of Environmental Load of Vending Machines by a LCA Method, and Eco-Improvement Effect

NASA Astrophysics Data System (ADS)

Kimura, Yukio; Sadamichi, Yucho; Maruyama, Naoki; Kato, Seizo

These days the environmental impact due to vending machines'(VM) diffusion has greatly been discussed. This paper describes the numerical evaluation of the environmental impact by using the LCA (Life Cycle Assessment) scheme and then proposes eco-improvements' strategy toward environmentally conscious products(ECP). A new objective and universal consolidated method for the LCA-evaluation, so-called LCA-NETS(Numerical Eco-load Standardization ) developed by the authors is applied to the present issue. As a result, the environmental loads at the 5years' operation and the material procurement stages are found to dominate others over the life cycle. Further eco-improvement is realized by following the order of the LCA-NETS magnitude; namely, energy saving, materials reducing, parts' re-using, and replacing with low environmental load material. Above all, parts' re-using is specially recommendable for significant reduction of the environmental loads toward ECP.

Experiments and Dynamic Finite Element Analysis of a Wire-Rope Rockfall Protective Fence

NASA Astrophysics Data System (ADS)

Tran, Phuc Van; Maegawa, Koji; Fukada, Saiji

2013-09-01

The imperative need to protect structures in mountainous areas against rockfall has led to the development of various protection methods. This study introduces a new type of rockfall protection fence made of posts, wire ropes, wire netting and energy absorbers. The performance of this rock fence was verified in both experiments and dynamic finite element analysis. In collision tests, a reinforced-concrete block rolled down a natural slope and struck the rock fence at the end of the slope. A specialized system of measuring instruments was employed to accurately measure the acceleration of the block without cable connection. In particular, the performance of two energy absorbers, which contribute also to preventing wire ropes from breaking, was investigated to determine the best energy absorber. In numerical simulation, a commercial finite element code having explicit dynamic capabilities was employed to create models of the two full-scale tests. To facilitate simulation, certain simplifying assumptions for mechanical data of each individual component of the rock fence and geometrical data of the model were adopted. Good agreement between numerical simulation and experimental data validated the numerical simulation. Furthermore, the results of numerical simulation helped highlight limitations of the testing method. The results of numerical simulation thus provide a deeper understanding of the structural behavior of individual components of the rock fence during rockfall impact. More importantly, numerical simulations can be used not only as supplements to or substitutes for full-scale tests but also in parametric study and design.

Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

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

Azarnykh, Dmitrii, E-mail: d.azarnykh@tum.de; Litvinov, Sergey; Adams, Nikolaus A.

2016-06-01

A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solvedmore » by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.« less

Adaptive numerical algorithms to simulate the dynamical Casimir effect in a closed cavity with different boundary conditions

NASA Astrophysics Data System (ADS)

Villar, Paula I.; Soba, Alejandro

2017-07-01

We present an alternative numerical approach to compute the number of particles created inside a cavity due to time-dependent boundary conditions. The physical model consists of a rectangular cavity, where a wall always remains still while the other wall of the cavity presents a smooth movement in one direction. The method relies on the setting of the boundary conditions (Dirichlet and Neumann) and the following resolution of the corresponding equations of modes. By a further comparison between the ground state before and after the movement of the cavity wall, we finally compute the number of particles created. To demonstrate the method, we investigate the creation of particle production in vibrating cavities, confirming previously known results in the appropriate limits. Within this approach, the dynamical Casimir effect can be investigated, making it possible to study a variety of scenarios where no analytical results are known. Of special interest is, of course, the realistic case of the electromagnetic field in a three-dimensional cavity, with transverse electric (TE)-mode and transverse magnetic (TM)-mode photon production. Furthermore, with our approach we are able to calculate numerically the particle creation in a tuneable resonant superconducting cavity by the use of the generalized Robin boundary condition. We compare the numerical results with analytical predictions as well as a different numerical approach. Its extension to three dimensions is also straightforward.

Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

NASA Astrophysics Data System (ADS)

Quy Muoi, Pham; Nho Hào, Dinh; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong

2018-05-01

In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.

Numerical study of steady dissipative mixed convection optically-thick micropolar flow with thermal radiation effects

NASA Astrophysics Data System (ADS)

Gupta, Diksha; Kumar, Lokendra; Bég, O. Anwar; Singh, Bani

2017-10-01

The objective of this paper is to study theoretically and numerically the effect of thermal radiation on mixed convection boundary layer flow of a dissipative micropolar non-Newtonian fluid from a continuously moving vertical porous sheet. The governing partial differential equations are transformed into a set of non-linear differential equations by using similarity transformations. These equations are solved iteratively with the Bellman-Kalaba quasi-linearization algorithm. This method converges quadratically and the solution is valid for a large range of parameters. The effects of transpiration (suction or injection) parameter, buoyancy parameter, radiation parameter and Eckert number on velocity, microrotation and temperature functions have been studied. Under a special case comparison of the present numerical results is made with the results available in the literature and an excellent agreement is found. Additionally skin friction and rate of heat transfer have also been computed. The study has applications in polymer processing.

Editing of EIA coded, numerically controlled, machine tool tapes

NASA Technical Reports Server (NTRS)

Weiner, J. M.

1975-01-01

Editing of numerically controlled (N/C) machine tool tapes (8-level paper tape) using an interactive graphic display processor is described. A rapid technique required for correcting production errors in N/C tapes was developed using the interactive text editor on the IMLAC PDS-ID graphic display system and two special programs resident on disk. The correction technique and special programs for processing N/C tapes coded to EIA specifications are discussed.

Dynamical topology and statistical properties of spatiotemporal chaos.

PubMed

Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli

2012-12-01

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.

Teaching Square Roots: Conceptual Complexity in Mathematics Language

ERIC Educational Resources Information Center

Gough, John

2007-01-01

Mathematics is an "artificial" deliberately constructed language, supported crucially by: (1) special alpha-numeric characters and usages; (2) extra-special non-alphanumeric symbols; (3) special written formats within a single line, such as superscripts and subscripts; (4) grouping along a line, including bracketing using round brackets,…

A methodology for analysing lateral coupled behavior of high speed railway vehicles and structures

NASA Astrophysics Data System (ADS)

Antolín, P.; Goicolea, J. M.; Astiz, M. A.; Alonso, A.

2010-06-01

Continuous increment of the speed of high speed trains entails the increment of kinetic energy of the trains. The main goal of this article is to study the coupled lateral behavior of vehicle-structure systems for high speed trains. Non linear finite element methods are used for structures whereas multibody dynamics methods are employed for vehicles. Special attention must be paid when dealing with contact rolling constraints for coupling bridge decks and train wheels. The dynamic models must include mixed variables (displacements and creepages). Additionally special attention must be paid to the contact algorithms adequate to wheel-rail contact. The coupled vehicle-structure system is studied in a implicit dynamic framework. Due to the presence of very different systems (trains and bridges), different frequencies are involved in the problem leading to stiff systems. Regarding to contact methods, a main branch is studied in normal contact between train wheels and bridge decks: penalty method. According to tangential contact FastSim algorithm solves the tangential contact at each time step solving a differential equation involving relative displacements and creepage variables. Integration for computing the total forces in the contact ellipse domain is performed for each train wheel and each solver iteration. Coupling between trains and bridges requires a special treatment according to the kinetic constraints imposed in the wheel-rail pair and the load transmission. A numerical example is performed.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

NASA Astrophysics Data System (ADS)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

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

Meyers, M.D., E-mail: mdmeyers@physics.ucla.edu; Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095; Huang, C.-K., E-mail: huangck@lanl.gov

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTDmore » scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.« less

Equivalent orthotropic elastic moduli identification method for laminated electrical steel sheets

NASA Astrophysics Data System (ADS)

Saito, Akira; Nishikawa, Yasunari; Yamasaki, Shintaro; Fujita, Kikuo; Kawamoto, Atsushi; Kuroishi, Masakatsu; Nakai, Hideo

2016-05-01

In this paper, a combined numerical-experimental methodology for the identification of elastic moduli of orthotropic media is presented. Special attention is given to the laminated electrical steel sheets, which are modeled as orthotropic media with nine independent engineering elastic moduli. The elastic moduli are determined specifically for use with finite element vibration analyses. We propose a three-step methodology based on a conventional nonlinear least squares fit between measured and computed natural frequencies. The methodology consists of: (1) successive augmentations of the objective function by increasing the number of modes, (2) initial condition updates, and (3) appropriate selection of the natural frequencies based on their sensitivities on the elastic moduli. Using the results of numerical experiments, it is shown that the proposed method achieves more accurate converged solution than a conventional approach. Finally, the proposed method is applied to measured natural frequencies and mode shapes of the laminated electrical steel sheets. It is shown that the method can successfully identify the orthotropic elastic moduli that can reproduce the measured natural frequencies and frequency response functions by using finite element analyses with a reasonable accuracy.

Mode Identification of High-Amplitude Pressure Waves in Liquid Rocket Engines

NASA Astrophysics Data System (ADS)

EBRAHIMI, R.; MAZAHERI, K.; GHAFOURIAN, A.

2000-01-01

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure amplitude histories and phase diagrams along the tube are computed. To determine the validity of the presented method for steep non-linear waves, the Euler equations are numerically solved for non-linear waves, and negligible interactions between these waves are observed. To show the applicability of this method, other's experimental results in which modes were identified are used. Results indicate that this simple method can be used in analyzing complicated pressure signal measurements.

a Numerical Method for Stability Analysis of Pinned Flexible Mechanisms

NASA Astrophysics Data System (ADS)

Beale, D. G.; Lee, S. W.

1996-05-01

A technique is presented to investigate the stability of mechanisms with pin-jointed flexible members. The method relies on a special floating frame from which elastic link co-ordinates are defined. Energies are easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equations of motion with constraints. Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotational speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bending mode is employed to develop resonance curves and stability boundaries in the crank length-crank speed parameter plane. Flip and fold bifurcations are common occurrences in both mechanisms. The accuracy of the proposed method was also verified by comparison with previous experimental results [1].

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

On the Hosoya index of a family of deterministic recursive trees

NASA Astrophysics Data System (ADS)

Chen, Xufeng; Zhang, Jingyuan; Sun, Weigang

2017-01-01

In this paper, we calculate the Hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule. We then obtain a recursive solution of the Hosoya index based on the operations of a determinant. The computational complexity of our proposed algorithm is O(log2 n) with n being the network size, which is lower than that of the existing numerical methods. Finally, we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the Hosoya index.

New wrinkles on black hole perturbations: Numerical treatment of acoustic and gravitational waves

NASA Astrophysics Data System (ADS)

Tenyotkin, Valery

2009-06-01

This thesis develops two main topics. A full relativistic calculation of quasinormal modes of an acoustic black hole is carried out. The acoustic black hole is formed by a perfect, inviscid, relativistic, ideal gas that is spherically accreting onto a Schwarzschild black hole. The second major part is the calculation of sourceless vector (electromagnetic) and tensor (gravitational) covariant field evolution equations for perturbations on a Schwarzschild background using the relatively recent [Special characters omitted.] decomposition method. Scattering calculations are carried out in Schwarzschild coordinates for electromagnetic and gravitational cases as validation of the method and the derived equations.

Accurate evaluation of exchange fields in finite element micromagnetic solvers

NASA Astrophysics Data System (ADS)

Chang, R.; Escobar, M. A.; Li, S.; Lubarda, M. V.; Lomakin, V.

2012-04-01

Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

Asynchronous collision integrators: Explicit treatment of unilateral contact with friction and nodal restraints

PubMed Central

Wolff, Sebastian; Bucher, Christian

2013-01-01

This article presents asynchronous collision integrators and a simple asynchronous method treating nodal restraints. Asynchronous discretizations allow individual time step sizes for each spatial region, improving the efficiency of explicit time stepping for finite element meshes with heterogeneous element sizes. The article first introduces asynchronous variational integration being expressed by drift and kick operators. Linear nodal restraint conditions are solved by a simple projection of the forces that is shown to be equivalent to RATTLE. Unilateral contact is solved by an asynchronous variant of decomposition contact response. Therein, velocities are modified avoiding penetrations. Although decomposition contact response is solving a large system of linear equations (being critical for the numerical efficiency of explicit time stepping schemes) and is needing special treatment regarding overconstraint and linear dependency of the contact constraints (for example from double-sided node-to-surface contact or self-contact), the asynchronous strategy handles these situations efficiently and robust. Only a single constraint involving a very small number of degrees of freedom is considered at once leading to a very efficient solution. The treatment of friction is exemplified for the Coulomb model. Special care needs the contact of nodes that are subject to restraints. Together with the aforementioned projection for restraints, a novel efficient solution scheme can be presented. The collision integrator does not influence the critical time step. Hence, the time step can be chosen independently from the underlying time-stepping scheme. The time step may be fixed or time-adaptive. New demands on global collision detection are discussed exemplified by position codes and node-to-segment integration. Numerical examples illustrate convergence and efficiency of the new contact algorithm. Copyright © 2013 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd. PMID:23970806

Job Design: An Administrator's Guide to Supporting and Retaining Special Educators

ERIC Educational Resources Information Center

Bettini, Elizabeth A.; Cheyney, Kristi; Wang, Jun; Leko, Christopher

2015-01-01

Special education teacher attrition has numerous negative impacts for students and schools. Administrators play an essential role in supporting special educators, but they seldom receive adequate preparation to provide this support effectively. The authors synthesize job characteristics theory, an area of research conducted by organizational…

Bilinear Inverse Problems: Theory, Algorithms, and Applications

NASA Astrophysics Data System (ADS)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

Study on cold forming of special fasteners using finite element method

NASA Astrophysics Data System (ADS)

Hsia, Shao-Yi; Chou, Yu-Tuan; Yang, Chun-Chieh

2013-12-01

The cold forming plays an important role in the field of fasteners. It can be extended to the automotive industry, construction, aerospace and 3C products. This study used Deform-3D analysis software to investigate the effect of the preforms for standard hex nuts. The effective stress, effective strain, velocity field and other information could be obtained from the numerical simulation. The outcome was verified with the physical phenomena and experiments. Furthermore, the analytical process can also be used to explore the forming technology of the special shaped nuts. When comparing to the standard hex nuts during the different stages, the optimized cold forming parameters could be extracted from the simulation and adopted to improve the performance of manufacturing for the special shaped nuts. The results can help the multi-pass processing factory to establish a cold forming capacity in the development of new products. Consequence, the ability of self-design and self-manufacture for special shaped fasteners in Taiwan would be increased widely to enhance the international competition of domestic industries.

Determination of plasma density from data on the ion current to cylindrical and planar probes

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

Voloshin, D. G., E-mail: dvoloshin@mics.msu.su; Vasil’eva, A. N.; Kovalev, A. S.

2016-12-15

To improve probe methods of plasma diagnostics, special probe measurements were performed and numerical models describing ion transport to a probe with allowance for collisions were developed. The current–voltage characteristics of cylindrical and planar probes were measured in an RF capacitive discharge in argon at a frequency of 81 MHz and plasma densities of 10{sup 10}–10{sup 11} cm{sup –3}, typical of modern RF reactors. 1D and 2D numerical models based on the particle-in-cell method with Monte Carlo collisions for simulating ion motion and the Boltzmann equilibrium for electrons are developed to describe current collection by a probe. The models weremore » used to find the plasma density from the ion part of the current–voltage characteristic, study the effect of ion collisions, and verify simplified approaches to determining the plasma density. A 1D hydrodynamic model of the ion current to a cylindrical probe with allowance for ion collisions is proposed. For a planar probe, a method to determine the plasma density from the averaged numerical results is developed. A comparative analysis of different approaches to calculating the plasma density from the ion current to a probe is performed.« less

Pseudospectral method for gravitational wave collapse

NASA Astrophysics Data System (ADS)

Hilditch, David; Weyhausen, Andreas; Brügmann, Bernd

2016-03-01

We present a new pseudospectral code, bamps, for numerical relativity written with the evolution of collapsing gravitational waves in mind. We employ the first-order generalized harmonic gauge formulation. The relevant theory is reviewed, and the numerical method is critically examined and specialized for the task at hand. In particular, we investigate formulation parameters—gauge- and constraint-preserving boundary conditions well suited to nonvanishing gauge source functions. Different types of axisymmetric twist-free moment-of-time-symmetry gravitational wave initial data are discussed. A treatment of the axisymmetric apparent horizon condition is presented with careful attention to regularity on axis. Our apparent horizon finder is then evaluated in a number of test cases. Moving on to evolutions, we investigate modifications to the generalized harmonic gauge constraint damping scheme to improve conservation in the strong-field regime. We demonstrate strong-scaling of our pseudospectral penalty code. We employ the Cartoon method to efficiently evolve axisymmetric data in our 3 +1 -dimensional code. We perform test evolutions of the Schwarzschild spacetime perturbed by gravitational waves and by gauge pulses, both to demonstrate the use of our black-hole excision scheme and for comparison with earlier results. Finally, numerical evolutions of supercritical Brill waves are presented to demonstrate durability of the excision scheme for the dynamical formation of a black hole.

Modeling of diatomic molecule using the Morse potential and the Verlet algorithm

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

Fidiani, Elok

Performing molecular modeling usually uses special software for Molecular Dynamics (MD) such as: GROMACS, NAMD, JMOL etc. Molecular dynamics is a computational method to calculate the time dependent behavior of a molecular system. In this work, MATLAB was used as numerical method for a simple modeling of some diatomic molecules: HCl, H{sub 2} and O{sub 2}. MATLAB is a matrix based numerical software, in order to do numerical analysis, all the functions and equations describing properties of atoms and molecules must be developed manually in MATLAB. In this work, a Morse potential was generated to describe the bond interaction betweenmore » the two atoms. In order to analyze the simultaneous motion of molecules, the Verlet Algorithm derived from Newton’s Equations of Motion (classical mechanics) was operated. Both the Morse potential and the Verlet algorithm were integrated using MATLAB to derive physical properties and the trajectory of the molecules. The data computed by MATLAB is always in the form of a matrix. To visualize it, Visualized Molecular Dynamics (VMD) was performed. Such method is useful for development and testing some types of interaction on a molecular scale. Besides, this can be very helpful for describing some basic principles of molecular interaction for educational purposes.« less

A high-resolution Godunov method for compressible multi-material flow on overlapping grids

NASA Astrophysics Data System (ADS)

Banks, J. W.; Schwendeman, D. W.; Kapila, A. K.; Henshaw, W. D.

2007-04-01

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform-pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on the Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of a planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

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

Hong Luo; Yidong Xia; Robert Nourgaliev

2011-05-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison.more » Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.« less

Developmental specialization of the left parietal cortex for the semantic representation of Arabic numerals: an fMR-adaptation study.

PubMed

Vogel, Stephan E; Goffin, Celia; Ansari, Daniel

2015-04-01

The way the human brain constructs representations of numerical symbols is poorly understood. While increasing evidence from neuroimaging studies has indicated that the intraparietal sulcus (IPS) becomes increasingly specialized for symbolic numerical magnitude representation over developmental time, the extent to which these changes are associated with age-related differences in symbolic numerical magnitude representation or with developmental changes in non-numerical processes, such as response selection, remains to be uncovered. To address these outstanding questions we investigated developmental changes in the cortical representation of symbolic numerical magnitude in 6- to 14-year-old children using a passive functional magnetic resonance imaging adaptation design, thereby mitigating the influence of response selection. A single-digit Arabic numeral was repeatedly presented on a computer screen and interspersed with the presentation of novel digits deviating as a function of numerical ratio (smaller/larger number). Results demonstrated a correlation between age and numerical ratio in the left IPS, suggesting an age-related increase in the extent to which numerical symbols are represented in the left IPS. Brain activation of the right IPS was modulated by numerical ratio but did not correlate with age, indicating hemispheric differences in IPS engagement during the development of symbolic numerical representation. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Improved design of special boundary elements for T-shaped reinforced concrete walls

NASA Astrophysics Data System (ADS)

Ji, Xiaodong; Liu, Dan; Qian, Jiaru

2017-01-01

This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design method. Comparison of the design provisions of the GB 50011-2010 code and those of the American code ACI 318-14 indicates a possible deficiency in the T-shaped wall design provisions in GB 50011-2010. A case study of a typical T-shaped wall designed in accordance with GB 50011-2010 also indicates the insufficient extent of the boundary element at the non-flange end and overly conservative design of the flange end boundary element. Improved designs for special boundary elements of T-shaped walls are developed using a displacement-based method. The proposed design formulas produce a longer boundary element at the non-flange end and a shorter boundary element at the flange end, relative to those of the GB 50011-2010 provisions. Extensive numerical analysis indicates that T-shaped walls designed using the proposed formulas develop inelastic drift of 0.01 for both cases of the flange in compression and in tension.

Recent advances in numerical PDEs

NASA Astrophysics Data System (ADS)

Zuev, Julia Michelle

In this thesis, we investigate four neighboring topics, all in the general area of numerical methods for solving Partial Differential Equations (PDEs). Topic 1. Radial Basis Functions (RBF) are widely used for multi-dimensional interpolation of scattered data. This methodology offers smooth and accurate interpolants, which can be further refined, if necessary, by clustering nodes in select areas. We show, however, that local refinements with RBF (in a constant shape parameter [varepsilon] regime) may lead to the oscillatory errors associated with the Runge phenomenon (RP). RP is best known in the case of high-order polynomial interpolation, where its effects can be accurately predicted via Lebesgue constant L (which is based solely on the node distribution). We study the RP and the applicability of Lebesgue constant (as well as other error measures) in RBF interpolation. Mainly, we allow for a spatially variable shape parameter, and demonstrate how it can be used to suppress RP-like edge effects and to improve the overall stability and accuracy. Topic 2. Although not as versatile as RBFs, cubic splines are useful for interpolating grid-based data. In 2-D, we consider a patch representation via Hermite basis functions s i,j ( u, v ) = [Special characters omitted.] h mn H m ( u ) H n ( v ), as opposed to the standard bicubic representation. Stitching requirements for the rectangular non-equispaced grid yield a 2-D tridiagonal linear system AX = B, where X represents the unknown first derivatives. We discover that the standard methods for solving this NxM system do not take advantage of the spline-specific format of the matrix B. We develop an alternative approach using this specialization of the RHS, which allows us to pre-compute coefficients only once, instead of N times. MATLAB implementation of our fast 2-D cubic spline algorithm is provided. We confirm analytically and numerically that for large N ( N > 200), our method is at least 3 times faster than the standard algorithm and is just as accurate. Topic 3. The well-known ADI-FDTD method for solving Maxwell's curl equations is second-order accurate in space/time, unconditionally stable, and computationally efficient. We research Richardson extrapolation -based techniques to improve time discretization accuracy for spatially oversampled ADI-FDTD. A careful analysis of temporal accuracy, computational efficiency, and the algorithm's overall stability is presented. Given the context of wave- type PDEs, we find that only a limited number of extrapolations to the ADI-FDTD method are beneficial, if its unconditional stability is to be preserved. We propose a practical approach for choosing the size of a time step that can be used to improve the efficiency of the ADI-FDTD algorithm, while maintaining its accuracy and stability. Topic 4. Shock waves and their energy dissipation properties are critical to understanding the dynamics controlling the MHD turbulence. Numerical advection algorithms used in MHD solvers (e.g. the ZEUS package) introduce undesirable numerical viscosity. To counteract its effects and to resolve shocks numerically, Richtmyer and von Neumann's artificial viscosity is commonly added to the model. We study shock power by analyzing the influence of both artificial and numerical viscosity on energy decay rates. Also, we analytically characterize the numerical diffusivity of various advection algorithms by quantifying their diffusion coefficients e.

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

NASA Technical Reports Server (NTRS)

Sandham, N. D.; Yee, H. C.; Kwak, Dochan (Technical Monitor)

2000-01-01

A stable high order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy splitting approach splits the inviscid flux derivatives into conservative and non-conservative portions. The spatial difference operators satisfy a summation by parts condition leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier-Stokes equations is used to ensure that any tendency to odd-even decoupling associated with central schemes can be countered by the fluid viscosity. A special formulation of the continuity equation is used, based on similar arguments. The resulting methods are able to minimize spurious high frequency oscillation producing nonlinear instability associated with pure central schemes, especially for long time integration simulation such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at a friction Mach number of 0.1 where a very accurate turbulence data base exists. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with incompressible channel data, as expected at this Mach number. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

Vortex methods and vortex statistics

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

Chorin, A.J.

Vortex methods originated from the observation that in incompressible, inviscid, isentropic flow vorticity (or, more accurately, circulation) is a conserved quantity, as can be readily deduced from the absence of tangential stresses. Thus if the vorticity is known at time t = 0, one can deduce the flow at a later time by simply following it around. In this narrow context, a vortex method is a numerical method that makes use of this observation. Even more generally, the analysis of vortex methods leads, to problems that are closely related to problems in quantum physics and field theory, as well asmore » in harmonic analysis. A broad enough definition of vortex methods ends up by encompassing much of science. Even the purely computational aspects of vortex methods encompass a range of ideas for which vorticity may not be the best unifying theme. The author restricts himself in these lectures to a special class of numerical vortex methods, those that are based on a Lagrangian transport of vorticity in hydrodynamics by smoothed particles (``blobs``) and those whose understanding contributes to the understanding of blob methods. Vortex methods for inviscid flow lead to systems of ordinary differential equations that can be readily clothed in Hamiltonian form, both in three and two space dimensions, and they can preserve exactly a number of invariants of the Euler equations, including topological invariants. Their viscous versions resemble Langevin equations. As a result, they provide a very useful cartoon of statistical hydrodynamics, i.e., of turbulence, one that can to some extent be analyzed analytically and more importantly, explored numerically, with important implications also for superfluids, superconductors, and even polymers. In the authors view, vortex ``blob`` methods provide the most promising path to the understanding of these phenomena.« less

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Yu, Sheng-Tao

2001-01-01

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

Study of grid independence of finite element method on MHD free convective casson fluid flow with slip effect

NASA Astrophysics Data System (ADS)

Raju, R. Srinivasa; Ramesh, K.

2018-05-01

The purpose of this work is to study the grid independence of finite element method on MHD Casson fluid flow past a vertically inclined plate filled in a porous medium in presence of chemical reaction, heat absorption, an external magnetic field and slip effect has been investigated. For this study of grid independence, a mathematical model is developed and analyzed by using appropriate mathematical technique, called finite element method. Grid study discussed with the help of numerical values of velocity, temperature and concentration profiles in tabular form. avourable comparisons with previously published work on various special cases of the problem are obtained.

African American Learners in Special Education: A Closer Look at Milwaukee

ERIC Educational Resources Information Center

Obiakor, Festus E.; Harris, Mateba K.; Offor, MaxMary T.; Beachum, Floyd D.

2010-01-01

Problems facing African American students with special needs are numerous and complex. Although processes and procedures are in place to properly serve these students, far too many become ensnared in webs of bureaucracy and benign neglect. This article examines African American students? experiences with special education in Milwaukee Public…

On computing special functions in marine engineering

NASA Astrophysics Data System (ADS)

Constantinescu, E.; Bogdan, M.

2015-11-01

Important modeling applications in marine engineering conduct us to a special class of solutions for difficult differential equations with variable coefficients. In order to be able to solve and implement such models (in wave theory, in acoustics, in hydrodynamics, in electromagnetic waves, but also in many other engineering fields), it is necessary to compute so called special functions: Bessel functions, modified Bessel functions, spherical Bessel functions, Hankel functions. The aim of this paper is to develop numerical solutions in Matlab for the above mentioned special functions. Taking into account the main properties for Bessel and modified Bessel functions, we shortly present analytically solutions (where possible) in the form of series. Especially it is studied the behavior of these special functions using Matlab facilities: numerical solutions and plotting. Finally, it will be compared the behavior of the special functions and point out other directions for investigating properties of Bessel and spherical Bessel functions. The asymptotic forms of Bessel functions and modified Bessel functions allow determination of important properties of these functions. The modified Bessel functions tend to look more like decaying and growing exponentials.

A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification

NASA Astrophysics Data System (ADS)

Wu, Keyi; Li, Jinglai

2016-09-01

In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter y. The performance parameter y is random due to the presence of various sources of uncertainty in the system, and our goal is to estimate the probability density function (PDF) of y. We propose to use the multicanonical Monte Carlo (MMC) method, a special type of adaptive importance sampling algorithms, to compute the PDF of interest. Moreover, we develop an adaptive algorithm to construct local Gaussian process surrogates to further accelerate the MMC iterations. With numerical examples we demonstrate that the proposed method can achieve several orders of magnitudes of speedup over the standard Monte Carlo methods.

Numerical calculation on infrared characteristics of the special vehicle exhaust system

NASA Astrophysics Data System (ADS)

Feng, Yun-song; Li, Xiao-xia; Jin, Wei

2017-10-01

For mastery of infrared radiation characteristics and flow field of the special vehicle exhaust system, first, a physical model of the special vehicle exhaust system is established with the Gambit, and the mathematical model of flow field is determined. Secondly, software Fluent6.3 is used to simulated the 3-D exterior flow field of the special vehicle exhaust system, and the datum of flow field, such as temperature, pressure and density, are obtained. Thirdly, based on the plume temperature, the special vehicle exhaust space is divided. The exhaust is equivalent to a gray-body. A calculating model of the vehicle exhaust infrared radiation is established, and the exhaust infrared radiation characteristics are calculated by the software MATLAB, then the spatial distribution curves are drawn. Finally, the numerical results are analyzing, and the basic laws of the special vehicle exhaust infrared radiation are explored. The results show that with the increase of the engine speed, the temperature of the exhaust pipe wall of the special vehicle increases, and the temperature and pressure of the exhaust gas flow field increase, which leads to the enhancement of the infrared radiation intensity

Numerical modelling of thin-walled Z-columns made of general laminates subjected to uniform shortening

NASA Astrophysics Data System (ADS)

Teter, Andrzej; Kolakowski, Zbigniew

2018-01-01

The numerical modelling of a plate structure was performed with the finite element method and a one-mode approach based on Koiter's method. The first order approximation of Koiter's method enables one to solve the eigenvalue problem. The second order approximation describes post-buckling equilibrium paths. In the finite element analysis, the Lanczos method was used to solve the linear problem of buckling. Simulations of the non-linear problem were performed with the Newton-Raphson method. Detailed calculations were carried out for a short Z-column made of general laminates. Configurations of laminated layers were non-symmetric. Due to possibilities of its application, the general laminate is very interesting. The length of the samples was chosen to obtain the lowest value of local buckling load. The amplitude of initial imperfections was 10% of the wall thickness. Thin-walled structures were simply supported on both ends. The numerical results were verified in experimental tests. A strain-gauge technique was applied. A static compression test was performed on a universal testing machine and a special grip, which consisted of two rigid steel plates and clamping sleeves, was used. Specimens were obtained with an autoclave technique. Tests were performed at a constant velocity of the cross-bar equal to 2 mm/min. The compressive load was less than 150% of the bifurcation load. Additionally, soft and thin pads were used to reduce inaccuracy of the sample ends.

Approximate analytic method for high-apogee twelve-hour orbits of artificial Earth's satellites

NASA Astrophysics Data System (ADS)

Vashkovyaka, M. A.; Zaslavskii, G. S.

2016-09-01

We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth's satellites. We describe parameters of the motion model used for the artificial Earth's satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose.

Adapted all-numerical correlator for face recognition applications

NASA Astrophysics Data System (ADS)

Elbouz, M.; Bouzidi, F.; Alfalou, A.; Brosseau, C.; Leonard, I.; Benkelfat, B.-E.

2013-03-01

In this study, we suggest and validate an all-numerical implementation of a VanderLugt correlator which is optimized for face recognition applications. The main goal of this implementation is to take advantage of the benefits (detection, localization, and identification of a target object within a scene) of correlation methods and exploit the reconfigurability of numerical approaches. This technique requires a numerical implementation of the optical Fourier transform. We pay special attention to adapt the correlation filter to this numerical implementation. One main goal of this work is to reduce the size of the filter in order to decrease the memory space required for real time applications. To fulfil this requirement, we code the reference images with 8 bits and study the effect of this coding on the performances of several composite filters (phase-only filter, binary phase-only filter). The saturation effect has for effect to decrease the performances of the correlator for making a decision when filters contain up to nine references. Further, an optimization is proposed based for an optimized segmented composite filter. Based on this approach, we present tests with different faces demonstrating that the above mentioned saturation effect is significantly reduced while minimizing the size of the learning data base.

Discrete-continuous variable structural synthesis using dual methods

NASA Technical Reports Server (NTRS)

Schmit, L. A.; Fleury, C.

1980-01-01

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.

Explosive compaction of aluminum oxide modified by multiwall carbon nanotubes

NASA Astrophysics Data System (ADS)

Buzyurkin, A. E.; Kraus, E. I.; Lukyanov, Ya L.

2018-04-01

This paper presents experiments and numerical research on explosive compaction of aluminum oxide powder modified by multiwall carbon nanotubes (MWCNT) and modeling of the stress state behind the shock front at shock loading. The aim of this study was to obtain a durable low-porosity compact sample. The explosive compaction technology is used in this problem because the aluminum oxide is an extremely hard and refractory material. Therefore, its compaction by traditional methods requires special equipment and considerable expenses.

Recovery of time-dependent volatility in option pricing model

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Hon, Y. C.; Isakov, V.

2016-11-01

In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).

Numerical study of droplet evaporation in an acoustic levitator

NASA Astrophysics Data System (ADS)

Bänsch, Eberhard; Götz, Michael

2018-03-01

We present a finite element method for the simulation of all relevant processes of the evaporation of a liquid droplet suspended in an acoustic levitation device. The mathematical model and the numerical implementation take into account heat and mass transfer across the interface between the liquid and gaseous phase and the influence of acoustic streaming on this process, as well as the displacement and deformation of the droplet due to acoustic radiation pressure. We apply this numerical method to several theoretical and experimental examples and compare our results with the well-known d2-law for the evaporation of spherical droplets and with theoretical predictions for the acoustic streaming velocity. We study the influence of acoustic streaming on the distribution of water vapor and temperature in the levitation device, with special attention to the vapor distribution in the emerging toroidal vortices. We also compare the evaporation rate of a droplet with and without acoustic streaming, as well as the evaporation rates in dependence of different temperatures and sound pressure levels. Finally, a simple model of protein inactivation due to heat damage is considered and studied for different evaporation settings and their respective influence on protein damage.

Finite Element Solution of Unsteady Mixed Convection Flow of Micropolar Fluid over a Porous Shrinking Sheet

PubMed Central

Gupta, Diksha; Singh, Bani

2014-01-01

The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements. PMID:24672310

Biomedical application of hierarchically built structures based on metal oxides

NASA Astrophysics Data System (ADS)

Korovin, M. S.; Fomenko, A. N.

2017-12-01

Nowadays, the use of hierarchically built structures in biology and medicine arouses much interest. The aim of this work is to review and summarize the available literature data about hierarchically organized structures in biomedical application. Nanoparticles can serve as an example of such structures. Medicine holds a special place among various application methods of similar systems. Special attention is paid to inorganic nanoparticles based on different metal oxides and hydroxides, such as iron, zinc, copper, and aluminum. Our investigations show that low-dimensional nanostructures based on aluminum oxides and hydroxides have an inhibitory effect on tumor cells and possess an antimicrobial activity. At the same time, it is obvious that the large-scale use of nanoparticles by humans needs to thoroughly study their properties. Special attention should be paid to the study of nanoparticle interaction with living biological objects. The numerous data show that there is no clear understanding of interaction mechanisms between nanoparticles and various cell types.

Projected role of advanced computational aerodynamic methods at the Lockheed-Georgia company

NASA Technical Reports Server (NTRS)

Lores, M. E.

1978-01-01

Experience with advanced computational methods being used at the Lockheed-Georgia Company to aid in the evaluation and design of new and modified aircraft indicates that large and specialized computers will be needed to make advanced three-dimensional viscous aerodynamic computations practical. The Numerical Aerodynamic Simulation Facility should be used to provide a tool for designing better aerospace vehicles while at the same time reducing development costs by performing computations using Navier-Stokes equations solution algorithms and permitting less sophisticated but nevertheless complex calculations to be made efficiently. Configuration definition procedures and data output formats can probably best be defined in cooperation with industry, therefore, the computer should handle many remote terminals efficiently. The capability of transferring data to and from other computers needs to be provided. Because of the significant amount of input and output associated with 3-D viscous flow calculations and because of the exceedingly fast computation speed envisioned for the computer, special attention should be paid to providing rapid, diversified, and efficient input and output.

The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Hajarian, Masoud

2012-08-01

A matrix P is called a symmetric orthogonal if P = P T = P -1. A matrix X is said to be a generalised bisymmetric with respect to P if X = X T = PXP. It is obvious that any symmetric matrix is also a generalised bisymmetric matrix with respect to I (identity matrix). By extending the idea of the Jacobi and the Gauss-Seidel iterations, this article proposes two new iterative methods, respectively, for computing the generalised bisymmetric (containing symmetric solution as a special case) and skew-symmetric solutions of the generalised Sylvester matrix equation ? (including Sylvester and Lyapunov matrix equations as special cases) which is encountered in many systems and control applications. When the generalised Sylvester matrix equation has a unique generalised bisymmetric (skew-symmetric) solution, the first (second) iterative method converges to the generalised bisymmetric (skew-symmetric) solution of this matrix equation for any initial generalised bisymmetric (skew-symmetric) matrix. Finally, some numerical results are given to illustrate the effect of the theoretical results.

The Numerical Simulation of the Shock Wave of Coal Gas Explosions in Gas Pipe*

NASA Astrophysics Data System (ADS)

Chen, Zhenxing; Hou, Kepeng; Chen, Longwei

2018-03-01

For the problem of large deformation and vortex, the method of Euler and Lagrange has both advantage and disadvantage. In this paper we adopt special fuzzy interface method(volume of fluid). Gas satisfies the conditions of conservation equations of mass, momentum, and energy. Based on explosion and three-dimension fluid dynamics theory, using unsteady, compressible, inviscid hydrodynamic equations and state equations, this paper considers pressure gradient’s effects to velocity, mass and energy in Lagrange steps by the finite difference method. To minimize transport errors of material, energy and volume in Finite Difference mesh, it also considers material transport in Euler steps. Programmed with Fortran PowerStation 4.0 and visualized with the software designed independently, we design the numerical simulation of gas explosion with specific pipeline structure, check the key points of the pressure change in the flow field, reproduce the gas explosion in pipeline of shock wave propagation, from the initial development, flame and accelerate the process of shock wave. This offers beneficial reference and experience to coal gas explosion accidents or safety precautions.

Inclusive Pedagogy in Light of Social Justice. Special Educational Rights and Inclusive Classrooms: On Whose Terms? a Field Study in Stockholm Suburbs

ERIC Educational Resources Information Center

De Silva, Nilani Ljunggren

2013-01-01

The question of inclusive education is not straightforward. Despite all its good intentions, inclusive education, in practice faces numerous challenges today. This study analyses these challenges in the Swedish special education context. The author explores special educators' experiences, possibilities and challenges when applying inclusive…

Public and Private School Principals' Knowledge of Special Education Law

ERIC Educational Resources Information Center

Boyd, Marie Nicole

2018-01-01

The purpose of this study is to examine the knowledge of special education law held by public and private school principals as the law pertains to providing the appropriate services to students with disabilities. Numerous studies have investigated public school principals' level of preparation, training, and role within in special education law.…

Many Hats and a Delicate Balance: The Lives and Times of Today's Special Education Directors

ERIC Educational Resources Information Center

Thompson, James R.; O'Brian, Mary

2007-01-01

A statewide survey of special education directors revealed that director of special education preparation programs should be time limited and offered in convenient locations to recruit the best possible pool of students and future directors. Current directors have come to their positions through numerous and diverse career paths. The lack of…

26 CFR 26.2642-3 - Special rule for charitable lead annuity trusts.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 26 Internal Revenue 14 2014-04-01 2013-04-01 true Special rule for charitable lead annuity trusts... 1986 § 26.2642-3 Special rule for charitable lead annuity trusts. (a) In general. In determining the applicable fraction with respect to a charitable lead annuity trust— (1) The numerator is the adjusted...

26 CFR 26.2642-3 - Special rule for charitable lead annuity trusts.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 26 Internal Revenue 14 2011-04-01 2010-04-01 true Special rule for charitable lead annuity trusts... 1986 § 26.2642-3 Special rule for charitable lead annuity trusts. (a) In general. In determining the applicable fraction with respect to a charitable lead annuity trust— (1) The numerator is the adjusted...

26 CFR 26.2642-3 - Special rule for charitable lead annuity trusts.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 26 Internal Revenue 14 2012-04-01 2012-04-01 false Special rule for charitable lead annuity trusts... 1986 § 26.2642-3 Special rule for charitable lead annuity trusts. (a) In general. In determining the applicable fraction with respect to a charitable lead annuity trust— (1) The numerator is the adjusted...

26 CFR 26.2642-3 - Special rule for charitable lead annuity trusts.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 26 Internal Revenue 14 2013-04-01 2013-04-01 false Special rule for charitable lead annuity trusts... 1986 § 26.2642-3 Special rule for charitable lead annuity trusts. (a) In general. In determining the applicable fraction with respect to a charitable lead annuity trust— (1) The numerator is the adjusted...

Understanding Vocabulary Use by Native American Students and the Relationship with Special Education

ERIC Educational Resources Information Center

Costa-Guerra, Leslie; Costa-Guerra, Boris

2016-01-01

The Pueblo People of the Southwest face numerous challenges with reference to language issues. A substantial number of Native American students are placed into special education possibly due to different linguistic abilities. The over-identification of Native American students for special education programs may be due to the lack of knowledge as a…

What can Numerical Computation do for the History of Science? (Study of an Orbit Drawn by Newton on a Letter to Hooke)

NASA Astrophysics Data System (ADS)

Stuchi, Teresa; Cardozo Dias, P.

2013-05-01

Abstract (2,250 Maximum Characters): On a letter to Robert Hooke, Isaac Newton drew the orbit of a mass moving under a constant attracting central force. How he drew the orbit may indicate how and when he developed dynamic categories. Some historians claim that Newton used a method contrived by Hooke; others that he used some method of curvature. We prove geometrically: Hooke’s method is a second order symplectic area preserving algorithm, and the method of curvature is a first order algorithm without special features; then we integrate the hamiltonian equations. Integration by the method of curvature can also be done exploring geometric properties of curves. We compare three methods: Hooke’s method, the method of curvature and a first order method. A fourth order algorithm sets a standard of comparison. We analyze which of these methods best explains Newton’s drawing.

What can numerical computation do for the history of science? (a study of an orbit drawn by Newton in a letter to Hooke)

NASA Astrophysics Data System (ADS)

Cardozo Dias, Penha Maria; Stuchi, T. J.

2013-11-01

In a letter to Robert Hooke, Isaac Newton drew the orbit of a mass moving under a constant attracting central force. The drawing of the orbit may indicate how and when Newton developed dynamic categories. Some historians claim that Newton used a method contrived by Hooke; others that he used some method of curvature. We prove that Hooke’s method is a second-order symplectic area-preserving algorithm, and the method of curvature is a first-order algorithm without special features; then we integrate the Hamiltonian equations. Integration by the method of curvature can also be done, exploring the geometric properties of curves. We compare three methods: Hooke’s method, the method of curvature and a first-order method. A fourth-order algorithm sets a standard of comparison. We analyze which of these methods best explains Newton’s drawing.

Edge grouping combining boundary and region information.

PubMed

Stahl, Joachim S; Wang, Song

2007-10-01

This paper introduces a new edge-grouping method to detect perceptually salient structures in noisy images. Specifically, we define a new grouping cost function in a ratio form, where the numerator measures the boundary proximity of the resulting structure and the denominator measures the area of the resulting structure. This area term introduces a preference towards detecting larger-size structures and, therefore, makes the resulting edge grouping more robust to image noise. To find the optimal edge grouping with the minimum grouping cost, we develop a special graph model with two different kinds of edges and then reduce the grouping problem to finding a special kind of cycle in this graph with a minimum cost in ratio form. This optimal cycle-finding problem can be solved in polynomial time by a previously developed graph algorithm. We implement this edge-grouping method, test it on both synthetic data and real images, and compare its performance against several available edge-grouping and edge-linking methods. Furthermore, we discuss several extensions of the proposed method, including the incorporation of the well-known grouping cues of continuity and intensity homogeneity, introducing a factor to balance the contributions from the boundary and region information, and the prevention of detecting self-intersecting boundaries.

PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

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

Wu, Kailiang; Tang, Huazhong, E-mail: wukl@pku.edu.cn, E-mail: hztang@math.pku.edu.cn

The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with themore » aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L {sup 1}-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.« less

Finite element techniques in computational time series analysis of turbulent flows

NASA Astrophysics Data System (ADS)

Horenko, I.

2009-04-01

In recent years there has been considerable increase of interest in the mathematical modeling and analysis of complex systems that undergo transitions between several phases or regimes. Such systems can be found, e.g., in weather forecast (transitions between weather conditions), climate research (ice and warm ages), computational drug design (conformational transitions) and in econometrics (e.g., transitions between different phases of the market). In all cases, the accumulation of sufficiently detailed time series has led to the formation of huge databases, containing enormous but still undiscovered treasures of information. However, the extraction of essential dynamics and identification of the phases is usually hindered by the multidimensional nature of the signal, i.e., the information is "hidden" in the time series. The standard filtering approaches (like f.~e. wavelets-based spectral methods) have in general unfeasible numerical complexity in high-dimensions, other standard methods (like f.~e. Kalman-filter, MVAR, ARCH/GARCH etc.) impose some strong assumptions about the type of the underlying dynamics. Approach based on optimization of the specially constructed regularized functional (describing the quality of data description in terms of the certain amount of specified models) will be introduced. Based on this approach, several new adaptive mathematical methods for simultaneous EOF/SSA-like data-based dimension reduction and identification of hidden phases in high-dimensional time series will be presented. The methods exploit the topological structure of the analysed data an do not impose severe assumptions on the underlying dynamics. Special emphasis will be done on the mathematical assumptions and numerical cost of the constructed methods. The application of the presented methods will be first demonstrated on a toy example and the results will be compared with the ones obtained by standard approaches. The importance of accounting for the mathematical assumptions used in the analysis will be pointed up in this example. Finally, applications to analysis of meteorological and climate data will be presented.

Dimensional Metrology of Non-rigid Parts Without Specialized Inspection Fixtures =

NASA Astrophysics Data System (ADS)

Sabri, Vahid

Quality control is an important factor for manufacturing companies looking to prosper in an era of globalization, market pressures and technological advances. Functionality and product quality cannot be guaranteed without this important aspect. Manufactured parts have deviations from their nominal (CAD) shape caused by the manufacturing process. Thus, geometric inspection is a very important element in the quality control of mechanical parts. We will focus here on the geometric inspection of non-rigid (flexible) parts which are widely used in the aeronautic and automotive industries. Non-rigid parts can have different forms in a free-state condition compared with their nominal models due to residual stress and gravity loads. To solve this problem, dedicated inspection fixtures are generally used in industry to compensate for the displacement of such parts for simulating the use state in order to perform geometric inspections. These fixtures and the installation and inspection processes are expensive and time-consuming. Our aim in this thesis is therefore to develop an inspection method which eliminates the need for specialized fixtures. This is done by acquiring a point cloud from the part in a free-state condition using a contactless measuring device such as optical scanning and comparing it with the CAD model for the deviation identification. Using a non-rigid registration method and finite element analysis, we numerically inspect the profile of a non-rigid part. To do so, a simulated displacement is performed using an improved definition of displacement boundary conditions for simulating unfixed parts. In addition, we propose a numerical method for dimensional metrology of non-rigid parts in a free-state condition based on the arc length measurement by calculating the geodesic distance using the Fast Marching Method (FMM). In this thesis, we apply our developed methods on industrial non-rigid parts with free-form surfaces simulated with different types of displacement, defect, and measurement noise in order to evaluate the metrological performance of the developed methods.

Analysis of 2-spar cantilever wings with special reference to torsion and load transference

NASA Technical Reports Server (NTRS)

Kuhn, Paul

1936-01-01

This report deals with the analysis of 2-spar cantilever wings in torsion, taking cognizance of the fact that the spars are not independent, but are interconnected by ribs and other structural members. The principles of interaction are briefly explained, showing that the mutual relief action occurring depends on the "pure torsional stiffness" of the wing cross section. Various practical methods of analysis are outlined. The "Friedrichs-Von Karman equations" are shown to require the least amount of labor. Numerical examples by the several methods of analysis are given and the agreement between the calculation and experiment is shown.

Photoacoustic spectroscopy of condensed matter

NASA Technical Reports Server (NTRS)

Somoano, R. B.

1978-01-01

Photoacoustic spectroscopy is a new analytical tool that provides a simple nondestructive technique for obtaining information about the electronic absorption spectrum of samples such as powders, semisolids, gels, and liquids. It can also be applied to samples which cannot be examined by conventional optical methods. Numerous applications of this technique in the field of inorganic and organic semiconductors, biology, and catalysis have been described. Among the advantages of photoacoustic spectroscopy, the signal is almost insensitive to light scattering by the sample and information can be obtained about nonradiative deactivation processes. Signal saturation, which can modify the intensity of individual absorption bands in special cases, is a drawback of the method.

Real Time Optima Tracking Using Harvesting Models of the Genetic Algorithm

NASA Technical Reports Server (NTRS)

Baskaran, Subbiah; Noever, D.

1999-01-01

Tracking optima in real time propulsion control, particularly for non-stationary optimization problems is a challenging task. Several approaches have been put forward for such a study including the numerical method called the genetic algorithm. In brief, this approach is built upon Darwinian-style competition between numerical alternatives displayed in the form of binary strings, or by analogy to 'pseudogenes'. Breeding of improved solution is an often cited parallel to natural selection in.evolutionary or soft computing. In this report we present our results of applying a novel model of a genetic algorithm for tracking optima in propulsion engineering and in real time control. We specialize the algorithm to mission profiling and planning optimizations, both to select reduced propulsion needs through trajectory planning and to explore time or fuel conservation strategies.

Numerical analysis of whole-body cryotherapy chamber design improvement

NASA Astrophysics Data System (ADS)

Yerezhep, D.; Tukmakova, A. S.; Fomin, V. E.; Masalimov, A.; Asach, A. V.; Novotelnova, A. V.; Baranov, A. Yu

2018-05-01

Whole body cryotherapy is a state-of-the-art method that uses cold for treatment and prevention of diseases. The process implies the impact of cryogenic gas on a human body that implements in a special cryochamber. The temperature field in the chamber is of great importance since local integument over-cooling may occur. Numerical simulation of WBC has been carried out. Chamber design modification has been proposed in order to increase the uniformity of the internal temperature field. The results have been compared with the ones obtained for a standard chamber design. The value of temperature gradient formed in the chamber containing curved wall with certain height has been decreased almost twice in comparison with the results obtained for the standard design. The modification proposed may increase both safety and comfort of cryotherapy.

Numerical reconstruction of tsunami source using combined seismic, satellite and DART data

NASA Astrophysics Data System (ADS)

Krivorotko, Olga; Kabanikhin, Sergey; Marinin, Igor

2014-05-01

Recent tsunamis, for instance, in Japan (2011), in Sumatra (2004), and at the Indian coast (2004) showed that a system of producing exact and timely information about tsunamis is of a vital importance. Numerical simulation is an effective instrument for providing such information. Bottom relief characteristics and the initial perturbation data (a tsunami source) are required for the direct simulation of tsunamis. The seismic data about the source are usually obtained in a few tens of minutes after an event has occurred (the seismic waves velocity being about five hundred kilometres per minute, while the velocity of tsunami waves is less than twelve kilometres per minute). A difference in the arrival times of seismic and tsunami waves can be used when operationally refining the tsunami source parameters and modelling expected tsunami wave height on the shore. The most suitable physical models related to the tsunamis simulation are based on the shallow water equations. The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate three different inverse problems of determining a tsunami source using three different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements, satellite wave-form images and seismic data. These problems are severely ill-posed. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of singular values of an inverse problem operator which is agreed with the error level in measured data is described and analyzed. In numerical experiment we used gradient methods (Landweber iteration and conjugate gradient method) for solving inverse tsunami problems. Gradient methods are based on minimizing the corresponding misfit function. To calculate the gradient of the misfit function, the adjoint problem is solved. The conservative finite-difference schemes for solving the direct and adjoint problems in the approximation of shallow water are constructed. Results of numerical experiments of the tsunami source reconstruction are presented and discussed. We show that using a combination of three different types of data allows one to increase the stability and efficiency of tsunami source reconstruction. Non-profit organization WAPMERR (World Agency of Planetary Monitoring and Earthquake Risk Reduction) in collaboration with Informap software development department developed the Integrated Tsunami Research and Information System (ITRIS) to simulate tsunami waves and earthquakes, river course changes, coastal zone floods, and risk estimates for coastal constructions at wave run-ups and earthquakes. The special scientific plug-in components are embedded in a specially developed GIS-type graphic shell for easy data retrieval, visualization and processing. This work was supported by the Russian Foundation for Basic Research (project No. 12-01-00773 'Theory and Numerical Methods for Solving Combined Inverse Problems of Mathematical Physics') and interdisciplinary project of SB RAS 14 'Inverse Problems and Applications: Theory, Algorithms, Software'.

The Dysfunctions of Bureaucratic Structure.

ERIC Educational Resources Information Center

Duttweiler, Patricia Cloud

1988-01-01

Numerous dysfunctions result from bureaucratic school organization, including an overemphasis on specialized tasks, routine operating rules, and formal procedures for managing teaching and learning. Such schools are characterized by numerous regulations; formal communications; centralized decision making; and sharp distinctions among…

Flow and Heat Transfer in Sisko Fluid with Convective Boundary Condition

PubMed Central

Malik, Rabia; Khan, Masood; Munir, Asif; Khan, Waqar Azeem

2014-01-01

In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a non-isothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting method. Effects of different parameters like power-law index , magnetic parameter , stretching parameter , generalized Prandtl number Pr and generalized Biot number are presented graphically. It is found that temperature profile increases with the increasing value of and whereas it decreases for . Numerical values of the skin-friction coefficient and local Nusselt number are tabulated at various physical situations. In addition, a comparison between the HAM and exact solutions is also made as a special case and excellent agreement between results enhance a confidence in the HAM results. PMID:25285822

Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions

PubMed Central

Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.

2000-01-01

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickness is small. In this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm (EDRA). As an example, we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters, i.e. the convergence does not deteriorate with diminishing thickness or mesh refinement. This robustness is sine qua non for the efficient computation of large-scale eigenvalue problems for thin elastic structures. PMID:10655469

Closure of the operator product expansion in the non-unitary bootstrap

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

Esterlis, Ilya; Fitzpatrick, A. Liam; Ramirez, David M.

We use the numerical conformal bootstrap in two dimensions to search for finite, closed sub-algebras of the operator product expansion (OPE), without assuming unitarity. We find the minimal models as special cases, as well as additional lines of solutions that can be understood in the Coulomb gas formalism. All the solutions we find that contain the vacuum in the operator algebra are cases where the external operators of the bootstrap equation are degenerate operators, and we argue that this follows analytically from the expressions in arXiv:1202.4698 for the crossing matrices of Virasoro conformal blocks. Our numerical analysis is a specialmore » case of the “Gliozzi” bootstrap method, and provides a simpler setting in which to study technical challenges with the method. In the supplementary material, we provide a Mathematica notebook that automates the calculation of the crossing matrices and OPE coefficients for degenerate operators using the formulae of Dotsenko and Fateev.« less

Closure of the operator product expansion in the non-unitary bootstrap

DOE PAGES

Esterlis, Ilya; Fitzpatrick, A. Liam; Ramirez, David M.

2016-11-07

We use the numerical conformal bootstrap in two dimensions to search for finite, closed sub-algebras of the operator product expansion (OPE), without assuming unitarity. We find the minimal models as special cases, as well as additional lines of solutions that can be understood in the Coulomb gas formalism. All the solutions we find that contain the vacuum in the operator algebra are cases where the external operators of the bootstrap equation are degenerate operators, and we argue that this follows analytically from the expressions in arXiv:1202.4698 for the crossing matrices of Virasoro conformal blocks. Our numerical analysis is a specialmore » case of the “Gliozzi” bootstrap method, and provides a simpler setting in which to study technical challenges with the method. In the supplementary material, we provide a Mathematica notebook that automates the calculation of the crossing matrices and OPE coefficients for degenerate operators using the formulae of Dotsenko and Fateev.« less

Analysis of the Multiple-Solution Response of a Flexible Rotor Supported on Non-Linear Squeeze Film Dampers

NASA Astrophysics Data System (ADS)

ZHU, C. S.; ROBB, D. A.; EWINS, D. J.

2002-05-01

The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.

A multivariate quadrature based moment method for LES based modeling of supersonic combustion

NASA Astrophysics Data System (ADS)

Donde, Pratik; Koo, Heeseok; Raman, Venkat

2012-07-01

The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.

Review of Thawing Time Prediction Models Depending
on Process Conditions and Product Characteristics

PubMed Central

Kluza, Franciszek; Spiess, Walter E. L.; Kozłowicz, Katarzyna

2016-01-01

Summary Determining thawing times of frozen foods is a challenging problem as the thermophysical properties of the product change during thawing. A number of calculation models and solutions have been developed. The proposed solutions range from relatively simple analytical equations based on a number of assumptions to a group of empirical approaches that sometimes require complex calculations. In this paper analytical, empirical and graphical models are presented and critically reviewed. The conditions of solution, limitations and possible applications of the models are discussed. The graphical and semi--graphical models are derived from numerical methods. Using the numerical methods is not always possible as running calculations takes time, whereas the specialized software and equipment are not always cheap. For these reasons, the application of analytical-empirical models is more useful for engineering. It is demonstrated that there is no simple, accurate and feasible analytical method for thawing time prediction. Consequently, simplified methods are needed for thawing time estimation of agricultural and food products. The review reveals the need for further improvement of the existing solutions or development of new ones that will enable accurate determination of thawing time within a wide range of practical conditions of heat transfer during processing. PMID:27904387

Experimental testing and numerical simulation on natural composite for aerospace applications

NASA Astrophysics Data System (ADS)

Kumar, G. Raj; Vijayanandh, R.; Kumar, M. Senthil; Kumar, S. Sathish

2018-05-01

Nowadays polymers are commonly used in various applications, which make it difficult to avoid its usage even though it causes environmental problems. Natural fibers are best alternate to overcome the polymer based environmental issues. Natural fibers play an important role in developing high performing fully newline biodegradable green composites which will be a key material to solve environmental problems in future. In this paper deals the properties analysis of banana fiber is combined with epoxy resin in order to create a natural composite, which has special characteristics for aerospace applications. The objective of this paper is to investigate the characteristics of failure modes and strength of natural composite using experimental and numerical methods. The test specimen of natural composite has been fabricated as per ASTM standard, which undergoes tensile and compression tests using Tinius Olsen UTM in order to determine mechanical and physical properties. The reference model has been designed by CATIA, and then numerical simulation has been carried out by Ansys Workbench 16.2 for the given boundary conditions.

Statements of Special Educational Needs and Tribunal Appeals in England and Wales 2003-2013--In Numbers

ERIC Educational Resources Information Center

Marsh, Alan J.

2014-01-01

The study presents a statistical analysis of statements of special educational needs and Special Educational Needs and Disability (SEND) tribunal appeal rates in England and Wales. It is set against the backcloth of the 2014 Children and Families Act which replaces statements with Education, Health and Care (EHC) plans. The numerical overview…

The Boy Factor: Can Single-Gender Classes Reduce the Over-Representation of Boys in Special Education?

ERIC Educational Resources Information Center

Piechura-Couture, Kathy; Heins, Elizabeth; Tichenor, Mercedes

2013-01-01

Since the early 1990s numerous studies have concluded that there is an over-representation of males and minorities in special education. This paper examines the question if a different educational format, such as single-gender education, can help boys' behavior and thus reduce the number of special education referrals? The rationale for…

The Boy Factor: Can Single-Gender Classes Reduce the Over-Representation of Boys in Special Education?

ERIC Educational Resources Information Center

Piechura-Couture, Kathy; Heins, Elizabeth; Tichenor, Mercedes

2011-01-01

Since the early 1990s numerous studies have concluded that there is an over-representation of males and minorities in special education. This paper examines the question if a different educational format, such as single-gender education, can help boys' behavior and thus reduce the number of special education referrals? The rationale for…

The FLAME-slab method for electromagnetic wave scattering in aperiodic slabs

NASA Astrophysics Data System (ADS)

Mansha, Shampy; Tsukerman, Igor; Chong, Y. D.

2017-12-01

The proposed numerical method, "FLAME-slab," solves electromagnetic wave scattering problems for aperiodic slab structures by exploiting short-range regularities in these structures. The computational procedure involves special difference schemes with high accuracy even on coarse grids. These schemes are based on Trefftz approximations, utilizing functions that locally satisfy the governing differential equations, as is done in the Flexible Local Approximation Method (FLAME). Radiation boundary conditions are implemented via Fourier expansions in the air surrounding the slab. When applied to ensembles of slab structures with identical short-range features, such as amorphous or quasicrystalline lattices, the method is significantly more efficient, both in runtime and in memory consumption, than traditional approaches. This efficiency is due to the fact that the Trefftz functions need to be computed only once for the whole ensemble.

Investigation of cellular detonation structure formation via linear stability theory and 2D and 3D numerical simulations

NASA Astrophysics Data System (ADS)

Borisov, S. P.; Kudryavtsev, A. N.

2017-10-01

Linear and nonlinear stages of the instability of a plane detonation wave (DW) and the subsequent process of formation of cellular detonation structure are investigated. A simple model with one-step irreversible chemical reaction is used. The linear analysis is employed to predict the DW front structure at the early stages of its formation. An emerging eigenvalue problem is solved with a global method using a Chebyshev pseudospectral method and the LAPACK software library. A local iterative shooting procedure is used for eigenvalue refinement. Numerical simulations of a propagation of a DW in plane and rectangular channels are performed with a shock capturing WENO scheme of 5th order. A special method of a computational domain shift is implemented in order to maintain the DW in the domain. It is shown that the linear analysis gives certain predictions about the DW structure that are in agreement with the numerical simulations of early stages of DW propagation. However, at later stages, a merger of detonation cells occurs so that their number is approximately halved. Computations of DW propagation in a square channel reveal two different types of spatial structure of the DW front, "rectangular" and "diagonal" types. A spontaneous transition from the rectangular to diagonal type of structure is observed during propagation of the DW.

Numerical study of effect of the gas-coolant free surface on the droplet fragmentation behavior of coolants

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

Li, H.X.; Anh, B.V.; Dinh, T.N.

1999-07-01

This paper presents results of a numerical investigation on the behavior of melt drops falling in a gas (vapor) space and then penetrating into a liquid volume through the gas-liquid interface. The phenomenon studied here is, usually, observed when a liquid drop falls through air into a water pool and is, specially, of interest when a hypothetical severe reactor core meltdown accident is considered. The objective of this work is to study the effect of the gas-liquid interface on the dynamic evolution of the interaction area between the fragmenting melt drop and water. In the present study, the Navier-Stokes equationsmore » are solved for three phases (gas, liquid and melt-drop) using a higher-order, explicit, numerical method, called Cubic-Interpolated Pseudo-Particle (CIP) method, which is employed in combination with an advanced front-capturing scheme, named the Level Set Algorithm (LSA). By using this method, reasonable physical pictures of droplet deformation and fragmentation during movement in a stationary uniform water pool, and in a gas-liquid two-layer volume, is simulated. Effect of the gas-liquid interface on the drop deformation and fragmentation is analyzed by comparing the simulation results obtained for the two cases. Effects of the drop geometry, and of the flow conditions, on the behavior of the melt drop are also analyzed.« less

A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

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

Banks, J W; Schwendeman, D W; Kapila, A K

2006-02-13

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on amore » uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.« less

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

Guo, Z.; Department of Applied Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083; Lin, P.

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C{sup 0} finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy lawmore » (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C{sup 0} finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme.« less

Implementation of Rosenbrock methods

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

Shampine, L. F.

1980-11-01

Rosenbrock formulas have shown promise in research codes for the solution of initial-value problems for stiff systems of ordinary differential equations (ODEs). To help assess their practical value, the author wrote an item of mathematical software based on such a formula. This required a variety of algorithmic and software developments. Those of general interest are reported in this paper. Among them is a way to select automatically, at every step, an explicit Runge-Kutta formula or a Rosenbrock formula according to the stiffness of the problem. Solving linear systems is important to methods for stiff ODEs, and is rather special formore » Rosenbrock methods. A cheap, effective estimate of the condition of the linear systems is derived. Some numerical results are presented to illustrate the developments.« less

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

An improved K-means clustering method for cDNA microarray image segmentation.

PubMed

Wang, T N; Li, T J; Shao, G F; Wu, S X

2015-07-14

Microarray technology is a powerful tool for human genetic research and other biomedical applications. Numerous improvements to the standard K-means algorithm have been carried out to complete the image segmentation step. However, most of the previous studies classify the image into two clusters. In this paper, we propose a novel K-means algorithm, which first classifies the image into three clusters, and then one of the three clusters is divided as the background region and the other two clusters, as the foreground region. The proposed method was evaluated on six different data sets. The analyses of accuracy, efficiency, expression values, special gene spots, and noise images demonstrate the effectiveness of our method in improving the segmentation quality.

ɛ-subgradient algorithms for bilevel convex optimization

NASA Astrophysics Data System (ADS)

Helou, Elias S.; Simões, Lucas E. A.

2017-05-01

This paper introduces and studies the convergence properties of a new class of explicit ɛ-subgradient methods for the task of minimizing a convex function over a set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation concerning certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction. ES Helou was supported by FAPESP grants 2013/07375-0 and 2013/16508-3 and CNPq grant 311476/2014-7. LEA Simões was supported by FAPESP grants 2011/02219-4 and 2013/14615-7.

Efficacy and safety of tofacitinib following inadequate response to conventional synthetic or biological disease-modifying antirheumatic drugs

PubMed Central

Charles-Schoeman, Christina; Burmester, Gerd; Nash, Peter; Zerbini, Cristiano A F; Soma, Koshika; Kwok, Kenneth; Hendrikx, Thijs; Bananis, Eustratios; Fleischmann, Roy

2016-01-01

Objectives Biological disease-modifying antirheumatic drugs (bDMARDs) have shown diminished clinical response following an inadequate response (IR) to ≥1 previous bDMARD. Here, tofacitinib was compared with placebo in patients with an IR to conventional synthetic DMARDs (csDMARDs; bDMARD-naive) and in patients with an IR to bDMARDs (bDMARD-IR). Methods Data were taken from phase II and phase III studies of tofacitinib in patients with rheumatoid arthritis (RA). Patients received tofacitinib 5 or 10 mg twice daily, or placebo, as monotherapy or with background methotrexate or other csDMARDs. Efficacy endpoints and incidence rates of adverse events (AEs) of special interest were assessed. Results 2812 bDMARD-naive and 705 bDMARD-IR patients were analysed. Baseline demographics and disease characteristics were generally similar between treatment groups within subpopulations. Across subpopulations, improvements in efficacy parameters at month 3 were generally significantly greater for both tofacitinib doses versus placebo. Clinical response was numerically greater with bDMARD-naive versus bDMARD-IR patients (overlapping 95% CIs). Rates of safety events of special interest were generally similar between tofacitinib doses and subpopulations; however, patients receiving glucocorticoids had more serious AEs, discontinuations due to AEs, serious infection events and herpes zoster. Numerically greater clinical responses and incidence rates of AEs of special interest were generally reported for tofacitinib 10 mg twice daily versus tofacitinib 5 mg twice daily (overlapping 95% CIs). Conclusions Tofacitinib demonstrated efficacy in both bDMARD-naive and bDMARD-IR patients with RA. Clinical response to tofacitinib was generally numerically greater in bDMARD-naive than bDMARD-IR patients. The safety profile appeared similar between subpopulations. Trial registration numbers (NCT00413660, NCT0050446, NCT00603512, NCT00687193, NCT00960440, NCT00847613, NCT00814307, NCT00856544, NCT00853385). PMID:26275429

Numerical calculations of turbulent swirling flow

NASA Technical Reports Server (NTRS)

Kubo, I.; Gouldin, F. C.

1974-01-01

Description of a numerical technique for solving axisymmetric, incompressible, turbulent swirling flow problems. Isothermal flow calculations are presented for a coaxial flow configuration of special interest. The calculation results are discussed in regard to their implications for the design of gas turbine combustors.

Current and emerging strategies for organophosphate decontamination: special focus on hyperstable enzymes.

PubMed

Jacquet, Pauline; Daudé, David; Bzdrenga, Janek; Masson, Patrick; Elias, Mikael; Chabrière, Eric

2016-05-01

Organophosphorus chemicals are highly toxic molecules mainly used as pesticides. Some of them are banned warfare nerve agents. These compounds are covalent inhibitors of acetylcholinesterase, a key enzyme in central and peripheral nervous systems. Numerous approaches, including chemical, physical, and biological decontamination, have been considered for developing decontamination methods against organophosphates (OPs). This work is an overview of both validated and emerging strategies for the protection against OP pollution with special attention to the use of decontaminating enzymes. Considerable efforts have been dedicated during the past decades to the development of efficient OP degrading biocatalysts. Among these, the promising biocatalyst SsoPox isolated from the archaeon Sulfolobus solfataricus is emphasized in the light of recently published results. This hyperthermostable enzyme appears to be particularly attractive for external decontamination purposes with regard to both its catalytic and stability properties.

Numeric and symbolic knowledge representation of cerebral cortex anatomy: methods and preliminary results.

PubMed

Dameron, O; Gibaud, B; Morandi, X

2004-06-01

The human cerebral cortex anatomy describes the brain organization at the scale of gyri and sulci. It is used as landmarks for neurosurgery as well as localization support for functional data analysis or inter-subject data comparison. Existing models of the cortex anatomy either rely on image labeling but fail to represent variability and structural properties or rely on a conceptual model but miss the inner 3D nature and relations of anatomical structures. This study was therefore conducted to propose a model of sulco-gyral anatomy for the healthy human brain. We hypothesized that both numeric knowledge (i.e., image-based) and symbolic knowledge (i.e., concept-based) have to be represented and coordinated. In addition, the representation of this knowledge should be application-independent in order to be usable in various contexts. Therefore, we devised a symbolic model describing specialization, composition and spatial organization of cortical anatomical structures. We also collected numeric knowledge such as 3D models of shape and shape variation about cortical anatomical structures. For each numeric piece of knowledge, a companion file describes the concept it refers to and the nature of the relationship. Demonstration software performs a mapping between the numeric and the symbolic aspects for browsing the knowledge base.

Numerical research of the optimal control problem in the semi-Markov inventory model

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

Gorshenin, Andrey K.; Belousov, Vasily V.; Shnourkoff, Peter V.

2015-03-10

This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented.

Design, Generation and Tooth Contact Analysis (TCA) of Asymmetric Face Gear Drive With Modified Geometry

NASA Technical Reports Server (NTRS)

Litvin, Faydor L.; Fuentes, Alfonso; Hawkins, J. M.; Handschuh, Robert F.

2001-01-01

A new type of face gear drive for application in transmissions, particularly in helicopters, has been developed. The new geometry differs from the existing geometry by application of asymmetric profiles and double-crowned pinion of the face gear mesh. The paper describes the computerized design, simulation of meshing and contact, and stress analysis by finite element method. Special purpose computer codes have been developed to conduct the analysis. The analysis of this new type of face gear is illustrated with a numerical example.

A limiting analysis for edge effects in angle-ply laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.

A study of optical scattering methods in laboratory plasma diagnosis

NASA Technical Reports Server (NTRS)

Phipps, C. R., Jr.

1972-01-01

Electron velocity distributions are deduced along axes parallel and perpendicular to the magnetic field in a pulsed, linear Penning discharge in hydrogen by means of a laser Thomson scattering experiment. Results obtained are numerical averages of many individual measurements made at specific space-time points in the plasma evolution. Because of the high resolution in k-space and the relatively low maximum electron density 2 x 10 to the 13th power/cu cm, special techniques were required to obtain measurable scattering signals. These techniques are discussed and experimental results are presented.

The average motion of a charged particle in a dipole field

NASA Technical Reports Server (NTRS)

Chen, A. J.; Stern, D. P.

1974-01-01

The numerical representation of the average motion of a charged particle trapped in a geomagnetic field is developed. An assumption is made of the conservation of the first two adiabatic invariants where integration is along a field line between mirror points. The averaged motion also involved the parameters defining the magnetic field line to which the particle is attached. Methods involved in obtaining the motion in the equatorial plane of model magnetospheres are based on Hamiltonian functions. The restrictions imposed by the special nature of the dipole field are defined.

Gold nanostars as thermoplasmonic nanoparticles for optical heating.

PubMed

Rodríguez-Oliveros, R; Sánchez-Gil, José A

2012-01-02

Gold nanostars are theoretically studied as efficient thermal heaters at their corresponding localized surface-plasmon resonances (LSPRs). Numerical calculations are performed through the 3D Green's Theorem method to obtain the absorption and scattering cross sections for Au nanoparticles with star-like shape of varying symmetry and tip number. Their unique thermoplasmonic properties, with regard to their (red-shifted) LSPR wavelentgh, (∼ 30-fold increase) steady-state temperature, and scattering/absorption cross section ratios, make them specially suitable for optical heating and in turn for cancer thermal therapy.

KEWPIE: A dynamical cascade code for decaying exited compound nuclei

NASA Astrophysics Data System (ADS)

Bouriquet, Bertrand; Abe, Yasuhisa; Boilley, David

2004-05-01

A new dynamical cascade code for decaying hot nuclei is proposed and specially adapted to the synthesis of super-heavy nuclei. For such a case, the interesting channel is of the tiny fraction that will decay through particles emission, thus the code avoids classical Monte-Carlo methods and proposes a new numerical scheme. The time dependence is explicitely taken into account in order to cope with the fact that fission decay rate might not be constant. The code allows to evaluate both statistical and dynamical observables. Results are successfully compared to experimental data.

Secure Multiparty Quantum Computation for Summation and Multiplication.

PubMed

Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2016-01-21

As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics.

Secure Multiparty Quantum Computation for Summation and Multiplication

PubMed Central

Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2016-01-01

As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics. PMID:26792197

Pseudo-random properties of a linear congruential generator investigated by b-adic diaphony

NASA Astrophysics Data System (ADS)

Stoev, Peter; Stoilova, Stanislava

2017-12-01

In the proposed paper we continue the study of the diaphony, defined in b-adic number system, and we extend it in different directions. We investigate this diaphony as a tool for estimation of the pseudorandom properties of some of the most used random number generators. This is done by evaluating the distribution of specially constructed two-dimensional nets on the base of the obtained random numbers. The aim is to see how the generated numbers are suitable for calculations in some numerical methods (Monte Carlo etc.).

Field Museum of Natural History Library.

ERIC Educational Resources Information Center

Williams, Benjamin W.; Fawcett, W. Peyton

1986-01-01

Founded in 1894 to support museum research, the Field Museum of Natural History Library specializes in fields of anthropology, archaeology, botany, geology, palaeontology, and zoology. A rich serials collection and numerous special collections serve both the scientific community and wider public as noncirculating reference collection and through…

Integration Of Heat Transfer Coefficient In Glass Forming Modeling With Special Interface Element

NASA Astrophysics Data System (ADS)

Moreau, P.; César de Sá, J.; Grégoire, S.; Lochegnies, D.

2007-05-01

Numerical modeling of the glass forming processes requires the accurate knowledge of the heat exchange between the glass and the forming tools. A laboratory testing is developed to determine the evolution of the heat transfer coefficient in different glass/mould contact conditions (contact pressure, temperature, lubrication…). In this paper, trials are performed to determine heat transfer coefficient evolutions in experimental conditions close to the industrial blow-and-blow process conditions. In parallel of this work, a special interface element is implemented in a commercial Finite Element code in order to deal with heat transfer between glass and mould for non-meshing meshes and evolutive contact. This special interface element, implemented by using user subroutines, permits to introduce the previous heat transfer coefficient evolutions in the numerical modelings at the glass/mould interface in function of the local temperatures, contact pressures, contact time and kind of lubrication. The blow-and-blow forming simulation of a perfume bottle is finally performed to assess the special interface element performance.

A hybrid model for traffic flow and crowd dynamics with random individual properties.

PubMed

Schleper, Veronika

2015-04-01

Based on an established mathematical model for the behavior of large crowds, a new model is derived that is able to take into account the statistical variation of individual maximum walking speeds. The same model is shown to be valid also in traffic flow situations, where for instance the statistical variation of preferred maximum speeds can be considered. The model involves explicit bounds on the state variables, such that a special Riemann solver is derived that is proved to respect the state constraints. Some care is devoted to a valid construction of random initial data, necessary for the use of the new model. The article also includes a numerical method that is shown to respect the bounds on the state variables and illustrative numerical examples, explaining the properties of the new model in comparison with established models.

A computing method for sound propagation through a nonuniform jet stream

NASA Technical Reports Server (NTRS)

Padula, S. L.; Liu, C. H.

1974-01-01

The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.

Damped gyroscopic effects and axial-flexural-torsional coupling using spinning finite elements for wind-turbine blades characterization

NASA Astrophysics Data System (ADS)

Velazquez, Antonio; Swartz, R. Andrew

2013-04-01

Renewable energy sources like wind are important technologies, useful to alleviate for the current fossil-fuel crisis. Capturing wind energy in a more efficient way has resulted in the emergence of more sophisticated designs of wind turbines, particularly Horizontal-Axis Wind Turbines (HAWTs). To promote efficiency, traditional finite element methods have been widely used to characterize the aerodynamics of these types of multi-body systems and improve their design. Given their aeroelastic behavior, tapered-swept blades offer the potential to optimize energy capture and decrease fatigue loads. Nevertheless, modeling special complex geometries requires huge computational efforts necessitating tradeoffs between faster computation times at lower cost, and reliability and numerical accuracy. Indeed, the computational cost and the numerical effort invested, using traditional FE methods, to reproduce dependable aerodynamics of these complex-shape beams are sometimes prohibitive. A condensed Spinning Finite Element (SFE) method scheme is presented in this study aimed to alleviate this issue by means of modeling wind-turbine rotor blades properly with tapered-swept cross-section variations of arbitrary order via Lagrangian equations. Axial-flexural-torsional coupling is carried out on axial deformation, torsion, in-plane bending and out-of-plane bending using super-convergent elements. In this study, special attention is paid for the case of damped yaw effects, expressed within the described skew-symmetric damped gyroscopic matrix. Dynamics of the model are analyzed by achieving modal analysis with complex-number eigen-frequencies. By means of mass, damped gyroscopic, and stiffness (axial-flexural-torsional coupling) matrix condensation (order reduction), numerical analysis is carried out for several prototypes with different tapered, swept, and curved variation intensities, and for a practical range of spinning velocities at different rotation angles. A convergence study for the resulting natural frequencies is performed to evaluate the dynamic collateral effects of tapered-swept blade profiles in spinning motion using this new model. Stability analysis in boundary conditions of the postulated model is achieved to test the convergence and integrity of the mathematical model. The proposed framework presumes to be particularly suitable to characterize models with complex-shape cross-sections at low computation cost.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Scaling characteristics of one-dimensional fractional diffusion processes in the presence of power-law distributed random noise.

PubMed

Nezhadhaghighi, Mohsen Ghasemi

2017-08-01

Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.

Automated optimization techniques for aircraft synthesis

NASA Technical Reports Server (NTRS)

Vanderplaats, G. N.

1976-01-01

Application of numerical optimization techniques to automated conceptual aircraft design is examined. These methods are shown to be a general and efficient way to obtain quantitative information for evaluating alternative new vehicle projects. Fully automated design is compared with traditional point design methods and time and resource requirements for automated design are given. The NASA Ames Research Center aircraft synthesis program (ACSYNT) is described with special attention to calculation of the weight of a vehicle to fly a specified mission. The ACSYNT procedures for automatically obtaining sensitivity of the design (aircraft weight, performance and cost) to various vehicle, mission, and material technology parameters are presented. Examples are used to demonstrate the efficient application of these techniques.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics.

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

Light and Life in Baltimore—and Beyond

PubMed Central

Edidin, Michael

2015-01-01

Baltimore has been the home of numerous biophysical studies using light to probe cells. One such study, quantitative measurement of lateral diffusion of rhodopsin, set the standard for experiments in which recovery after photobleaching is used to measure lateral diffusion. Development of this method from specialized microscopes to commercial scanning confocal microscopes has led to widespread use of the technique to measure lateral diffusion of membrane proteins and lipids, and as well diffusion and binding interactions in cell organelles and cytoplasm. Perturbation of equilibrium distributions by photobleaching has also been developed into a robust method to image molecular proximity in terms of fluorescence resonance energy transfer between donor and acceptor fluorophores. PMID:25650914

High-order cyclo-difference techniques: An alternative to finite differences

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Otto, John C.

1993-01-01

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.

New algorithms for solving high even-order differential equations using third and fourth Chebyshev-Galerkin methods

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.; Bassuony, M. A.

2013-03-01

This paper is concerned with spectral Galerkin algorithms for solving high even-order two point boundary value problems in one dimension subject to homogeneous and nonhomogeneous boundary conditions. The proposed algorithms are extended to solve two-dimensional high even-order differential equations. The key to the efficiency of these algorithms is to construct compact combinations of Chebyshev polynomials of the third and fourth kinds as basis functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithms, and some comparisons with some other methods are made.

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1997-07-05

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution.

Hydraulic fracturing - an attempt of DEM simulation

NASA Astrophysics Data System (ADS)

Kosmala, Alicja; Foltyn, Natalia; Klejment, Piotr; Dębski, Wojciech

2017-04-01

Hydraulic fracturing is a technique widely used in oil, gas and unconventional reservoirs exploitation in order to enable the oil/gas to flow more easily and enhance the production. It relays on pumping into a rock a special fluid under a high pressure which creates a set of microcracks which enhance porosity of the reservoir rock. In this research, attempt of simulation of such hydrofracturing process using the Discrete Element Method approach is presented. The basic assumption of this approach is that the rock can be represented as an assembly of discrete particles cemented into a rigid sample (Potyondy 2004). An existence of voids among particles simulates then a pore system which can be filled out by fracturing fluid, numerically represented by much smaller particles. Following this microscopic point of view and its numerical representation by DEM method we present primary results of numerical analysis of hydrofracturing phenomena, using the ESyS-Particle Software. In particular, we consider what is happening in distinct vicinity of the border between rock sample and fracking particles, how cracks are creating and evolving by breaking bonds between particles, how acoustic/seismic energy is releasing and so on. D.O. Potyondy, P.A. Cundall. A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 41 (2004), pp. 1329-1364.

Relationships between magnitude representation, counting and memory in 4- to 7-year-old children: A developmental study

PubMed Central

2010-01-01

Background The development of an evolutionarily grounded analogue magnitude representation linked to the parietal lobes is frequently thought to be a major factor in the arithmetic development of humans. We investigated the relationship between counting and the development of magnitude representation in children, assessing also children's knowledge of number symbols, their arithmetic fact retrieval, their verbal skills, and their numerical and verbal short-term memory. Methods The magnitude representation was tested by a non-symbolic magnitude comparison task. We have perfected previous experimental designs measuring magnitude discrimination skills in 65 children kindergarten (4-7-year-olds) by controlling for several variables which were not controlled for in previous similar research. We also used a large number of trials which allowed for running a full factorial ANOVA including all relevant factors. Tests of verbal counting, of short term memory, of number knowledge, of problem solving abilities and of verbal fluency were administered and correlated with performance in the magnitude comparison task. Results and discussion Verbal counting knowledge and performance on simple arithmetic tests did not correlate with non-symbolic magnitude comparison at any age. Older children performed successfully on the number comparison task, showing behavioural patterns consistent with an analogue magnitude representation. In contrast, 4-year-olds were unable to discriminate number independently of task-irrelevant perceptual variables. Sensitivity to irrelevant perceptual features of the magnitude discrimination task was also affected by age, and correlated with memory, suggesting that more general cognitive abilities may play a role in performance in magnitude comparison tasks. Conclusion We conclude that young children are not able to discriminate numerical magnitudes when co-varying physical magnitudes are methodically pitted against number. We propose, along with others, that a rather domain general magnitude representation provides the later basis for a specialized representation of numerical magnitudes. For this representational specialization, the acquisition of the concept of abstract numbers, together with the development of other cognitive abilities, is indispensable. PMID:20167066

FLUX-CORRECTED TRANSPORT TECHNIQUE FOR OPEN CHANNEL FLOW. (R825200)

EPA Science Inventory

In modeling flow in open channels, the traditional finite difference/finite volume schemes become inefficient and warrant special numerical treatment in the presence of shocks and discontinuities. The numerical oscillations that arise by making use of a second- and higher-order s...

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

Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel W.

Coupled-cluster methods provide highly accurate models of molecular structure by explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix-matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts tomore » extend the Libtensor framework to work in the distributed memory environment in a scalable and energy efficient manner. We achieve up to 240 speedup compared with the best optimized shared memory implementation. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures, (Cray XC30&XC40, BlueGene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance. Nevertheless, we preserve a uni ed interface to both programming models to maintain the productivity of computational quantum chemists.« less

A parallel finite element procedure for contact-impact problems using edge-based smooth triangular element and GPU

NASA Astrophysics Data System (ADS)

Cai, Yong; Cui, Xiangyang; Li, Guangyao; Liu, Wenyang

2018-04-01

The edge-smooth finite element method (ES-FEM) can improve the computational accuracy of triangular shell elements and the mesh partition efficiency of complex models. In this paper, an approach is developed to perform explicit finite element simulations of contact-impact problems with a graphical processing unit (GPU) using a special edge-smooth triangular shell element based on ES-FEM. Of critical importance for this problem is achieving finer-grained parallelism to enable efficient data loading and to minimize communication between the device and host. Four kinds of parallel strategies are then developed to efficiently solve these ES-FEM based shell element formulas, and various optimization methods are adopted to ensure aligned memory access. Special focus is dedicated to developing an approach for the parallel construction of edge systems. A parallel hierarchy-territory contact-searching algorithm (HITA) and a parallel penalty function calculation method are embedded in this parallel explicit algorithm. Finally, the program flow is well designed, and a GPU-based simulation system is developed, using Nvidia's CUDA. Several numerical examples are presented to illustrate the high quality of the results obtained with the proposed methods. In addition, the GPU-based parallel computation is shown to significantly reduce the computing time.

Physical retrieval of precipitation water contents from Special Sensor Microwave/Imager (SSM/I) data. Part 2: Retrieval method and applications (report version)

NASA Technical Reports Server (NTRS)

Olson, William S.

1990-01-01

A physical retrieval method for estimating precipitating water distributions and other geophysical parameters based upon measurements from the DMSP-F8 SSM/I is developed. Three unique features of the retrieval method are (1) sensor antenna patterns are explicitly included to accommodate varying channel resolution; (2) precipitation-brightness temperature relationships are quantified using the cloud ensemble/radiative parameterization; and (3) spatial constraints are imposed for certain background parameters, such as humidity, which vary more slowly in the horizontal than the cloud and precipitation water contents. The general framework of the method will facilitate the incorporation of measurements from the SSMJT, SSM/T-2 and geostationary infrared measurements, as well as information from conventional sources (e.g., radiosondes) or numerical forecast model fields.

Recommendations for numerical solution of reinforced-panel and fuselage-ring problems

NASA Technical Reports Server (NTRS)

Hoff, N J; Libby, Paul A

1949-01-01

Procedures are recommended for solving the equations of equilibrium of reinforced panels and isolated fuselage rings as represented by the external loads and the operations table established according to Southwell's method. From the solution of these equations the stress distribution can be easily determined. The method of systematic relaxations, the matrix-calculus method, and several other methods applicable in special cases are discussed. Definite recommendations are made for obtaining the solution of reinforced-panel problems which are generally designated as shear lag problems. The procedures recommended are demonstrated in the analysis of a number of panels. In the case of fuselage rings it is not possible to make definite recommendations for the solution of the equilibrium equations for all rings and loadings. However, suggestions based on the latest experience are made and demonstrated on several rings.

Linear sampling method applied to non destructive testing of an elastic waveguide: theory, numerics and experiments

NASA Astrophysics Data System (ADS)

Baronian, Vahan; Bourgeois, Laurent; Chapuis, Bastien; Recoquillay, Arnaud

2018-07-01

This paper presents an application of the linear sampling method to ultrasonic non destructive testing of an elastic waveguide. In particular, the NDT context implies that both the solicitations and the measurements are located on the surface of the waveguide and are given in the time domain. Our strategy consists in using a modal formulation of the linear sampling method at multiple frequencies, such modal formulation being justified theoretically in Bourgeois et al (2011 Inverse Problems 27 055001) for rigid obstacles and in Bourgeois and Lunéville (2013 Inverse Problems 29 025017) for cracks. Our strategy requires the inversion of some emission and reception matrices which deserve some special attention due to potential ill-conditioning. The feasibility of our method is proved with the help of artificial data as well as real data.

Superhydrophobic Natural and Artificial Surfaces—A Structural Approach

PubMed Central

Avrămescu, Roxana-Elena; Ghica, Mihaela Violeta; Dinu-Pîrvu, Cristina; Prisada, Răzvan; Popa, Lăcrămioara

2018-01-01

Since ancient times humans observed animal and plants features and tried to adapt them according to their own needs. Biomimetics represents the foundation of many inventions from various fields: From transportation devices (helicopter, airplane, submarine) and flying techniques, to sports’ wear industry (swimming suits, scuba diving gear, Velcro closure system), bullet proof vests made from Kevlar etc. It is true that nature provides numerous noteworthy models (shark skin, spider web, lotus leaves), referring both to the plant and animal kingdom. This review paper summarizes a few of “nature’s interventions” in human evolution, regarding understanding of surface wettability and development of innovative special surfaces. Empirical models are described in order to reveal the science behind special wettable surfaces (superhydrophobic /superhydrophilic). Materials and methods used in order to artificially obtain special wettable surfaces are described in correlation with plants’ and animals’ unique features. Emphasis is placed on joining superhydrophobic and superhydrophilic surfaces, with important applications in cell culturing, microorganism isolation/separation and molecule screening techniques. Bio-inspired wettability is presented as a constitutive part of traditional devices/systems, intended to improve their characteristics and extend performances. PMID:29789488

Superhydrophobic Natural and Artificial Surfaces-A Structural Approach.

PubMed

Avrămescu, Roxana-Elena; Ghica, Mihaela Violeta; Dinu-Pîrvu, Cristina; Prisada, Răzvan; Popa, Lăcrămioara

2018-05-22

Since ancient times humans observed animal and plants features and tried to adapt them according to their own needs. Biomimetics represents the foundation of many inventions from various fields: From transportation devices (helicopter, airplane, submarine) and flying techniques, to sports' wear industry (swimming suits, scuba diving gear, Velcro closure system), bullet proof vests made from Kevlar etc. It is true that nature provides numerous noteworthy models (shark skin, spider web, lotus leaves), referring both to the plant and animal kingdom. This review paper summarizes a few of "nature's interventions" in human evolution, regarding understanding of surface wettability and development of innovative special surfaces. Empirical models are described in order to reveal the science behind special wettable surfaces (superhydrophobic /superhydrophilic). Materials and methods used in order to artificially obtain special wettable surfaces are described in correlation with plants' and animals' unique features. Emphasis is placed on joining superhydrophobic and superhydrophilic surfaces, with important applications in cell culturing, microorganism isolation/separation and molecule screening techniques. Bio-inspired wettability is presented as a constitutive part of traditional devices/systems, intended to improve their characteristics and extend performances.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

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

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Fast online generalized multiscale finite element method using constraint energy minimization

NASA Astrophysics Data System (ADS)

Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat

2018-02-01

Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online stage with a specific input parameter to solve the global problem at a reduced computational cost. Recently, online approaches have been introduced, where multiscale basis functions are adaptively constructed in some regions to reduce the error significantly. In multiscale methods, it is desired to have only 1-2 iterations to reduce the error to a desired threshold. Using Generalized Multiscale Finite Element Framework [10], it was shown that by choosing sufficient number of offline basis functions, the error reduction can be made independent of physical parameters, such as scales and contrast. In this paper, our goal is to improve this. Using our recently proposed approach [4] and special online basis construction in oversampled regions, we show that the error reduction can be made sufficiently large by appropriately selecting oversampling regions. Our numerical results show that one can achieve a three order of magnitude error reduction, which is better than our previous methods. We also develop an adaptive algorithm and enrich in selected regions with large residuals. In our adaptive method, we show that the convergence rate can be determined by a user-defined parameter and we confirm this by numerical simulations. The analysis of the method is presented.

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

PubMed Central

Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

2015-01-01

The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

Making the Road While Walking It: A Conversation with Richard Simpson

ERIC Educational Resources Information Center

Zabel, Robert H.; Kaff, Marilyn; Teagarden, James

2016-01-01

Richard Simpson is professor of special education at the University of Kansas (KU). Dr. Simpson's duties at KU have included roles of staff psychologist, teaching associate, assistant professor, project director, associate professor, professor, and chairperson for the Department of Special Education. He has directed numerous University of Kansas…

Precision Machining. FasTrak Specialization Integrated Technical and Academic Competency (ITAC). 2002 Revision.

ERIC Educational Resources Information Center

Ohio State Dept. of Education, Columbus. Div. of Career-Technical and Adult Education.

This publication provided the competencies and key indicators for a program that enables students to prepare for a number of occupations within the broader metalworking industry. Specializations include machinist, computer numerical control programmers, and maintenance and machine builders. Competencies and the related key indicators are presented…

A direct method for unfolding the resolution function from measurements of neutron induced reactions

NASA Astrophysics Data System (ADS)

Žugec, P.; Colonna, N.; Sabate-Gilarte, M.; Vlachoudis, V.; Massimi, C.; Lerendegui-Marco, J.; Stamatopoulos, A.; Bacak, M.; Warren, S. G.; n TOF Collaboration

2017-12-01

The paper explores the numerical stability and the computational efficiency of a direct method for unfolding the resolution function from the measurements of the neutron induced reactions. A detailed resolution function formalism is laid out, followed by an overview of challenges present in a practical implementation of the method. A special matrix storage scheme is developed in order to facilitate both the memory management of the resolution function matrix, and to increase the computational efficiency of the matrix multiplication and decomposition procedures. Due to its admirable computational properties, a Cholesky decomposition is at the heart of the unfolding procedure. With the smallest but necessary modification of the matrix to be decomposed, the method is successfully applied to system of 105 × 105. However, the amplification of the uncertainties during the direct inversion procedures limits the applicability of the method to high-precision measurements of neutron induced reactions.

Finite difference methods for transient signal propagation in stratified dispersive media

NASA Technical Reports Server (NTRS)

Lam, D. H.

1975-01-01

Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.

A semi-analytical method for near-trapped mode and fictitious frequencies of multiple scattering by an array of elliptical cylinders in water waves

NASA Astrophysics Data System (ADS)

Chen, Jeng-Tzong; Lee, Jia-Wei

2013-09-01

In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.

New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, W. M.

2014-01-01

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

Periodic Inclusion—Matrix Microstructures with Constant Field Inclusions

NASA Astrophysics Data System (ADS)

Liu, Liping; James, Richard D.; Leo, Perry H.

2007-04-01

We find a class of special microstructures consisting of a periodic array of inclusions, with the special property that constant magnetization (or eigenstrain) of the inclusion implies constant magnetic field (or strain) in the inclusion. The resulting inclusions, which we term E-inclusions, have the same property in a finite periodic domain as ellipsoids have in infinite space. The E-inclusions are found by mapping the magnetostatic or elasticity equations to a constrained minimization problem known as a free-boundary obstacle problem. By solving this minimization problem, we can construct families of E-inclusions with any prescribed volume fraction between zero and one. In two dimensions, our results coincide with the microstructures first introduced by Vigdergauz,[1,2] while in three dimensions, we introduce a numerical method to calculate E-inclusions. E-inclusions extend the important role of ellipsoids in calculations concerning phase transformations and composite materials.

Kinematics of velocity and vorticity correlations in turbulent flow

NASA Technical Reports Server (NTRS)

Bernard, P. S.

1983-01-01

The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.

A hybrid hydrostatic and non-hydrostatic numerical model for shallow flow simulations

NASA Astrophysics Data System (ADS)

Zhang, Jingxin; Liang, Dongfang; Liu, Hua

2018-05-01

Hydrodynamics of geophysical flows in oceanic shelves, estuaries, and rivers, are often studied by solving shallow water model equations. Although hydrostatic models are accurate and cost efficient for many natural flows, there are situations where the hydrostatic assumption is invalid, whereby a fully hydrodynamic model is necessary to increase simulation accuracy. There is a growing concern about the decrease of the computational cost of non-hydrostatic pressure models to improve the range of their applications in large-scale flows with complex geometries. This study describes a hybrid hydrostatic and non-hydrostatic model to increase the efficiency of simulating shallow water flows. The basic numerical model is a three-dimensional hydrostatic model solved by the finite volume method (FVM) applied to unstructured grids. Herein, a second-order total variation diminishing (TVD) scheme is adopted. Using a predictor-corrector method to calculate the non-hydrostatic pressure, we extended the hydrostatic model to a fully hydrodynamic model. By localising the computational domain in the corrector step for non-hydrostatic pressure calculations, a hybrid model was developed. There was no prior special treatment on mode switching, and the developed numerical codes were highly efficient and robust. The hybrid model is applicable to the simulation of shallow flows when non-hydrostatic pressure is predominant only in the local domain. Beyond the non-hydrostatic domain, the hydrostatic model is still accurate. The applicability of the hybrid method was validated using several study cases.

A new numerically stable implementation of the T-matrix method for electromagnetic scattering by spheroidal particles

NASA Astrophysics Data System (ADS)

Somerville, W. R. C.; Auguié, B.; Le Ru, E. C.

2013-07-01

We propose, describe, and demonstrate a new numerically stable implementation of the extended boundary-condition method (EBCM) to compute the T-matrix for electromagnetic scattering by spheroidal particles. Our approach relies on the fact that for many of the EBCM integrals in the special case of spheroids, a leading part of the integrand integrates exactly to zero, which causes catastrophic loss of precision in numerical computations. This feature was in fact first pointed out by Waterman in the context of acoustic scattering and electromagnetic scattering by infinite cylinders. We have recently studied it in detail in the case of electromagnetic scattering by particles. Based on this study, the principle of our new implementation is therefore to compute all the integrands without the problematic part to avoid the primary cause of loss of precision. Particular attention is also given to choosing the algorithms that minimise loss of precision in every step of the method, without compromising on speed. We show that the resulting implementation can efficiently compute in double precision arithmetic the T-matrix and therefore optical properties of spheroidal particles to a high precision, often down to a remarkable accuracy (10-10 relative error), over a wide range of parameters that are typically considered problematic. We discuss examples such as high-aspect ratio metallic nanorods and large size parameter (≈35) dielectric particles, which had been previously modelled only using quadruple-precision arithmetic codes.

Functional vs. Structural Modularity: do they imply each other?

NASA Astrophysics Data System (ADS)

Toroczkai, Zoltan

2009-03-01

While many deterministic and stochastic processes have been proposed to produce heterogeneous graphs mimicking real-world networks, only a handful of studies attempt to connect structure and dynamics with the function(s) performed by the network. In this talk I will present an approach built on the premise that structure, dynamics, and their observed heterogeneity, are implementations of various functions and their compositions. After a brief review of real-world networks where this connection can explicitly be made, I will focus on biological networks. Biological networks are known to possess functionally specialized modules, which perform tasks almost independently of each other. While proposals have been made for the evolutionary emergence of modularity, it is far from clear that adaptation on evolutionary timescales is the sole mechanism leading to functional specialization. We show that non-evolutionary learning can also lead to the formation of functionally specialized modules in a system exposed to multiple environmental constraints. A natural example suggesting that this is possible is the cerebral cortex, where there are clearly delineated functional areas in spite of the largely uniform anatomical construction of the cortical tissue. However, as numerous experiments show, when damaged, regions specialized for a certain function can be retrained to perform functions normally attributed to other regions. We use the paradigm of neural networks to represent a multitasking system, and use several non-evolutionary learning algorithms as mechanisms for phenotypic adaptation. We show that for a network learning to perform multiple tasks, the degree of independence between the tasks dictates the degree of functional specialization emerging in the network. To uncover the functional modules, we introduce a method of node knockouts that explicitly rates the contribution of each node to different tasks (differential robustness). Through a concrete example we also demonstrate the potential inability of purely topology-based clustering methods to detect functional modules. The robustness of these results suggests that similar mechanisms might be responsible for the emergence of functional specialization in other multitasking networks, as well, including social networks.

Suzuki-Trotter Formula for Real-Time Dependent LDA I: Electron Dynamics

NASA Astrophysics Data System (ADS)

Sugino, Osamu; Miyamoto, Yoshiyuki

1998-03-01

To investigate various physical and chemical processes where electron dynamics play a role (e.g. collisions or photochemical reactions), solving the real-time Schrödinger equation is essentially important. ihbar fracpartialφpartial t=H φ Trial of solving eqn. (1) from first principles has begun very recently(K. Yabana and G. F. Bertch, Phys. Rev. B54) 4484 (1996)., and it is now in the stage of establishing efficient, stable, and accurate method for numerical calculation. In this talk, we present several improvements in the method of solving eqn. (1) within the density functional theory: (A) higher order Suzuki-Trotter formula(M. Suzuki, Phys. Lett. A146) 319 (1990). to integrate eqn. (1) keeping the orthonormality of the wavefunctions, (B) special interpolation scheme for the self-consistent potential to reduce the drift in the total-energy, and (C) the preconditioning techniques to increase the time step for the simulation. We will demonstrate numerical stability and efficiency using several cluster calculations, and will address the accuracy by comparing the computed cross sections for atom-electron collisions with experiment.

A Computing Method for Sound Propagation Through a Nonuniform Jet Stream

NASA Technical Reports Server (NTRS)

Padula, S. L.; Liu, C. H.

1974-01-01

Understanding the principles of jet noise propagation is an essential ingredient of systematic noise reduction research. High speed computer methods offer a unique potential for dealing with complex real life physical systems whereas analytical solutions are restricted to sophisticated idealized models. The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions and a more suitable approach was needed. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.

Three-dimensional formulation of dislocation climb

NASA Astrophysics Data System (ADS)

Gu, Yejun; Xiang, Yang; Quek, Siu Sin; Srolovitz, David J.

2015-10-01

We derive a Green's function formulation for the climb of curved dislocations and multiple dislocations in three-dimensions. In this new dislocation climb formulation, the dislocation climb velocity is determined from the Peach-Koehler force on dislocations through vacancy diffusion in a non-local manner. The long-range contribution to the dislocation climb velocity is associated with vacancy diffusion rather than from the climb component of the well-known, long-range elastic effects captured in the Peach-Koehler force. Both long-range effects are important in determining the climb velocity of dislocations. Analytical and numerical examples show that the widely used local climb formula, based on straight infinite dislocations, is not generally applicable, except for a small set of special cases. We also present a numerical discretization method of this Green's function formulation appropriate for implementation in discrete dislocation dynamics (DDD) simulations. In DDD implementations, the long-range Peach-Koehler force is calculated as is commonly done, then a linear system is solved for the climb velocity using these forces. This is also done within the same order of computational cost as existing discrete dislocation dynamics methods.

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

NASA Astrophysics Data System (ADS)

Beckstein, Pascal; Galindo, Vladimir; Vukčević, Vuko

2017-09-01

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

Detection of symmetric homoclinic orbits to saddle-centres in reversible systems

NASA Astrophysics Data System (ADS)

Yagasaki, Kazuyuki; Wagenknecht, Thomas

2006-02-01

We present a perturbation technique for the detection of symmetric homoclinic orbits to saddle-centre equilibria in reversible systems of ordinary differential equations. We assume that the unperturbed system has primary, symmetric homoclinic orbits, which may be either isolated or appear in a family, and use an idea similar to that of Melnikov’s method to detect homoclinic orbits in their neighbourhood. This technique also allows us to identify bifurcations of unperturbed or perturbed, symmetric homoclinic orbits. Our technique is of importance in applications such as nonlinear optics and water waves since homoclinic orbits to saddle-centre equilibria describe embedded solitons (ESs) in systems of partial differential equations representing physical models, and except for special cases their existence has been previously studied only numerically using shooting methods and continuation techniques. We apply the general theory to two examples, a four-dimensional system describing ESs in nonlinear optical media and a six-dimensional system which can possess a one-parameter family of symmetric homoclinic orbits in the unperturbed case. For these examples, the analysis is compared with numerical computations and an excellent agreement between both results is found.

The special case of the 2 × 2 table: asymptotic unconditional McNemar test can be used to estimate sample size even for analysis based on GEE.

PubMed

Borkhoff, Cornelia M; Johnston, Patrick R; Stephens, Derek; Atenafu, Eshetu

2015-07-01

Aligning the method used to estimate sample size with the planned analytic method ensures the sample size needed to achieve the planned power. When using generalized estimating equations (GEE) to analyze a paired binary primary outcome with no covariates, many use an exact McNemar test to calculate sample size. We reviewed the approaches to sample size estimation for paired binary data and compared the sample size estimates on the same numerical examples. We used the hypothesized sample proportions for the 2 × 2 table to calculate the correlation between the marginal proportions to estimate sample size based on GEE. We solved the inside proportions based on the correlation and the marginal proportions to estimate sample size based on exact McNemar, asymptotic unconditional McNemar, and asymptotic conditional McNemar. The asymptotic unconditional McNemar test is a good approximation of GEE method by Pan. The exact McNemar is too conservative and yields unnecessarily large sample size estimates than all other methods. In the special case of a 2 × 2 table, even when a GEE approach to binary logistic regression is the planned analytic method, the asymptotic unconditional McNemar test can be used to estimate sample size. We do not recommend using an exact McNemar test. Copyright © 2015 Elsevier Inc. All rights reserved.

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration.

PubMed

Bearup, Daniel; Petrovskaya, Natalia; Petrovskii, Sergei

2015-05-01

Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. First, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called "activity-density" problem). Second, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a mean-field mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a well-studied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth. Copyright © 2015 Elsevier Inc. All rights reserved.

Computation of resistive instabilities by matched asymptotic expansions

DOE PAGES

Glasser, A. H.; Wang, Z. R.; Park, J. -K.

2016-11-17

Here, we present a method for determining the linear resistive magnetohydrodynamic (MHD) stability of an axisymmetric toroidal plasma, based on the method of matched asymptotic expansions. The plasma is partitioned into a set of ideal MHD outer regions, connected through resistive MHD inner regions about singular layers where q = m/n, with m and n toroidal mode numbers, respectively, and q the safety factor. The outer regions satisfy the ideal MHD equations with zero-frequency, which are identical to the Euler-Lagrange equations for minimizing the potential energy delta W. The solutions to these equations go to infinity at the singular surfaces.more » The inner regions satisfy the equations of motion of resistive MHD with a finite eigenvalue, resolving the singularity. Both outer and inner regions are solved numerically by newly developed singular Galerkin methods, using specialized basis functions. These solutions are matched asymptotically, providing a complex dispersion relation which is solved for global eigenvalues and eigenfunctions in full toroidal geometry. The dispersion relation may have multiple complex unstable roots, which are found by advanced root-finding methods. These methods are much faster and more robust than the previous numerical methods. The new methods are applicable to more challenging high-pressure and strongly shaped plasma equilibria and generalizable to more realistic inner region dynamics. In the thermonuclear regime, where the outer and inner regions overlap, they are also much faster and more accurate than the straight-through methods, which treat the resistive MHD equations in the whole plasma volume.« less

A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: Towards minimalism

NASA Astrophysics Data System (ADS)

Ohwada, Taku; Shibata, Yuki; Kato, Takuma; Nakamura, Taichi

2018-06-01

Developed is a high-order accurate shock-capturing scheme for the compressible Euler/Navier-Stokes equations; the formal accuracy is 5th order in space and 4th order in time. The performance and efficiency of the scheme are validated in various numerical tests. The main ingredients of the scheme are nothing special; they are variants of the standard numerical flux, MUSCL, the usual Lagrange's polynomial and the conventional Runge-Kutta method. The scheme can compute a boundary layer accurately with a rational resolution and capture a stationary contact discontinuity sharply without inner points. And yet it is endowed with high resistance against shock anomalies (carbuncle phenomenon, post-shock oscillations, etc.). A good balance between high robustness and low dissipation is achieved by blending three types of numerical fluxes according to physical situation in an intuitively easy-to-understand way. The performance of the scheme is largely comparable to that of WENO5-Rusanov, while its computational cost is 30-40% less than of that of the advanced scheme.

Synthesis and Analysis of Custom Bi-directional Reflectivity Distribution Functions in DIRSIG

NASA Astrophysics Data System (ADS)

Dank, J.; Allen, D.

2016-09-01

The bi-directional reflectivity distribution (BRDF) function is a fundamental optical property of materials, characterizing important properties of light scattered by a surface. For accurate radiance calculations using synthetic targets and numerical simulations such as the Digital Imaging and Remote Sensing Image Generation (DIRSIG) model, fidelity of the target BRDFs is critical. While fits to measured BRDF data can be used in DIRSIG, obtaining high-quality data over a large spectral continuum can be time-consuming and expensive, requiring significant investment in illumination sources, sensors, and other specialized hardware. As a consequence, numerous parametric BRDF models are available to approximate actual behavior; but these all have shortcomings. Further, DIRSIG doesn't allow direct visualization of BRDFs, making it difficult for the user to understand the numerical impact of various models. Here, we discuss the innovative use of "mixture maps" to synthesize custom BRDFs as linear combinations of parametric models and measured data. We also show how DIRSIG's interactive mode can be used to visualize and analyze both available parametric models currently used in DIRSIG and custom BRDFs developed using our methods.

Phospholipid dynamics in graphene of different topologies: predictive modeling

NASA Astrophysics Data System (ADS)

Glukhova, O. E.; Slepchenkov, M. M.

2017-02-01

The subject of our scientific interest is the dynamics of the phospholipid molecules into a corrugated graphene sheet. According to our assumption by changing the topology of graphene properly it is possible to find the ways for management of the selective localization of phospholipid molecules to form the desired configuration of these structures. We considered DPPC (dipalmitoylphosphatidylcholine) phospholipids, which are the part of cell membranes and lipoproteins. We investigated the behavior of the phospholipids on the graphene sheet consisting of 1710 atoms with the size of 6.9 nm along the zigzag edge and 6.25 nm along the armchair edge. The numerical experiment was carried out using the original AMBER/AIREBO hybrid method with Lennard-Jones potential to describe the interaction between unbound atoms of different structures. The temperature was maintained at 300 K during the numerical experiment. All numerical experiments were performed using KVAZAR software system. We considered several cases of corrugated graphene with different width and dept of the corrugation. Special attention in our work was paid to the orientation of the phospholipids in the plane of graphene sheet.

Specialization in the Human Brain: The Case of Numbers

PubMed Central

Kadosh, Roi Cohen; Bahrami, Bahador; Walsh, Vincent; Butterworth, Brian; Popescu, Tudor; Price, Cathy J.

2011-01-01

How numerical representation is encoded in the adult human brain is important for a basic understanding of human brain organization, its typical and atypical development, its evolutionary precursors, cognitive architectures, education, and rehabilitation. Previous studies have shown that numerical processing activates the same intraparietal regions irrespective of the presentation format (e.g., symbolic digits or non-symbolic dot arrays). This has led to claims that there is a single format-independent, numerical representation. In the current study we used a functional magnetic resonance adaptation paradigm, and effective connectivity analysis to re-examine whether numerical processing in the intraparietal sulci is dependent or independent on the format of the stimuli. We obtained two novel results. First, the whole brain analysis revealed that format change (e.g., from dots to digits), in the absence of a change in magnitude, activated the same intraparietal regions as magnitude change, but to a greater degree. Second, using dynamic causal modeling as a tool to disentangle neuronal specialization across regions that are commonly activated, we found that the connectivity between the left and right intraparietal sulci is format-dependent. Together, this line of results supports the idea that numerical representation is subserved by multiple mechanisms within the same parietal regions. PMID:21808615

Varieties of numerical abilities.

PubMed

Dehaene, S

1992-08-01

This paper provides a tutorial introduction to numerical cognition, with a review of essential findings and current points of debate. A tacit hypothesis in cognitive arithmetic is that numerical abilities derive from human linguistic competence. One aim of this special issue is to confront this hypothesis with current knowledge of number representations in animals, infants, normal and gifted adults, and brain-lesioned patients. First, the historical evolution of number notations is presented, together with the mental processes for calculating and transcoding from one notation to another. While these domains are well described by formal symbol-processing models, this paper argues that such is not the case for two other domains of numerical competence: quantification and approximation. The evidence for counting, subitizing and numerosity estimation in infants, children, adults and animals is critically examined. Data are also presented which suggest a specialization for processing approximate numerical quantities in animals and humans. A synthesis of these findings is proposed in the form of a triple-code model, which assumes that numbers are mentally manipulated in an arabic, verbal or analogical magnitude code depending on the requested mental operation. Only the analogical magnitude representation seems available to animals and preverbal infants.

The Evolution and Discharge of Electric Fields within a Thunderstorm

NASA Astrophysics Data System (ADS)

Hager, William W.; Nisbet, John S.; Kasha, John R.

1989-05-01

A 3-dimensional electrical model for a thunderstorm is developed and finite difference approximations to the model are analyzed. If the spatial derivatives are approximated by a method akin to the ☐ scheme and if the temporal derivative is approximated by either a backward difference or the Crank-Nicholson scheme, we show that the resulting discretization is unconditionally stable. The forward difference approximation to the time derivative is stable when the time step is sufficiently small relative to the ratio between the permittivity and the conductivity. Max-norm error estimates for the discrete approximations are established. To handle the propagation of lightning, special numerical techniques are devised based on the Inverse Matrix Modification Formula and Cholesky updates. Numerical comparisons between the model and theoretical results of Wilson and Holzer-Saxon are presented. We also apply our model to a storm observed at the Kennedy Space Center on July 11, 1978.

Relative motion of orbiting satellites

NASA Technical Reports Server (NTRS)

Eades, J. B., Jr.

1972-01-01

The relative motion problem is analyzed, as a linearized case, and as a numerically determined solution to provide a time history of the geometries representing the motion state. The displacement history and the hodographs for families of solutions are provided, analytically and graphically, to serve as an aid to understanding this problem area. Linearized solutions to relative motion problems of orbiting particles are presented for the impulsive and fixed thrust cases. Second order solutions are described to enhance the accuracy of prediction. A method was developed to obtain accurate, numerical solutions to the intercept and rendezvous problem; and, special situations are examined. A particular problem related to relative motions, where the motion traces develop a cusp, is examined in detail. This phenomenon is found to be dependent on a particular relationship between orbital eccentricity and the inclination between orbital planes. These conditions are determined, and, example situations are presented and discussed.

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Initiation Capacity of a Specially Shaped Booster Pellet and Numerical Simulation of Its Initiation Process

NASA Astrophysics Data System (ADS)

Hu, Li-Shuang; Hu, Shuang-Qi; Cao, Xiong; Zhang, Jian-Ren

2014-01-01

The insensitive main charge explosive is creating new requirements for the booster pellet of detonation trains. The traditional cylindrical booster pellet has insufficient energy output to reliably initiate the insensitive main charge explosive. In this research, a concave spherical booster pellet was designed. The initiation capacity of the concave spherical booster pellet was studied using varied composition and axial steel dent methods. The initiation process of the concave spherical booster pellet was also simulated by ANSYS/LS-DYNA. The results showed that using a concave spherical booster allows a 42% reduction in the amount of explosive needed to match the initiation capacity of a conventional cylindrical booster of the same dimensions. With the other parameters kept constant, the initiation capacity of the concave spherical booster pellet increases with decreased cone angle and concave radius. The numerical simulation results are in good agreement with the experimental data.

Computational Aeroacoustics: An Overview

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.

2003-01-01

An overview of recent advances in computational aeroacoustics (CAA) is presented. CAA algorithms must not be dispersive and dissipative. It should propagate waves supported by the Euler equations with the correct group velocities. Computation domains are inevitably finite in size. To avoid the reflection of acoustic and other outgoing waves at the boundaries of the computation domain, it is required that special boundary conditions be imposed at the boundary region. These boundary conditions either absorb all the outgoing waves without reflection or allow the waves to exit smoothly. High-order schemes, invariably, supports spurious short waves. These spurious waves tend to pollute the numerical solution. They must be selectively damped or filtered out. All these issues and relevant computation methods are briefly reviewed. Jet screech tones are known to have caused structural fatigue in military combat aircrafts. Numerical simulation of the jet screech phenomenon is presented as an example of a successful application of CAA.

Diffraction of a shock wave by a compression corner; regular and single Mach reflection

NASA Technical Reports Server (NTRS)

Vijayashankar, V. S.; Kutler, P.; Anderson, D.

1976-01-01

The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.

Generating random numbers by means of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-07-01

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the angular displacements of chaotic motion, random binary numerical arrays can be generated. To check the randomness of generated numerical arrays, the NIST Special Publication 800-20 method was adopted. As a result, it was found that all the random arrays which were generated by the chaotic motion could pass the validity criteria and some of them were even better than the quality of pseudo-random numbers generated by a computer. Through the experiments, it is demonstrated that chaotic pendulum can be used as an efficient mechanical facility in generating random numbers, and can be applied in teaching random motion to the students.

Project TANDEM (Tsunamis in the Atlantic and the English ChaNnel: Definition of the Effects through numerical Modeling) (2014-2018): a French initiative to draw lessons from the Tohoku-oki tsunami on French coastal nuclear facilities

NASA Astrophysics Data System (ADS)

Hébert, Hélène; Abadie, Stéphane; Benoit, Michel; Créach, Ronan; Frère, Antoine; Gailler, Audrey; Garzaglia, Sébastien; Hayashi, Yutaka; Loevenbruck, Anne; Macary, Olivier; Marcer, Richard; Morichon, Denis; Pedreros, Rodrigo; Rebour, Vincent; Ricchiuto, Mario; Silva Jacinto, Ricardo; Terrier, Monique; Toucanne, Samuel; Traversa, Paola; Violeau, Damien

2014-05-01

TANDEM (Tsunamis in the Atlantic and the English ChaNnel: Definition of the Effects through numerical Modeling) is a French research project dedicated to the appraisal of coastal effects due to tsunami waves on the French coastlines, with a special focus on the Atlantic and Channel coastlines, where French civil nuclear facilities have been operating since about 30 years. This project aims at drawing conclusions from the 2011 catastrophic tsunami, and will allow, together with a Japanese research partner, to design, adapt and validate numerical methods of tsunami hazard assessment, using the outstanding database of the 2011 tsunami. Then the validated methods will be applied to estimate, as accurately as possible, the tsunami hazard for the French Atlantic and Channel coastlines, in order to provide guidance for risk assessment on the nuclear facilities. The project TANDEM follows the recommendations of International Atomic Energy Agency (IAEA) to analyse the tsunami exposure of the nuclear facilities, as well as the recommendations of the French Nuclear Safety Authority (Autorité de Sûreté Nucléaire, ASN) in the aftermath of the 2011 catastrophe, which required the licensee of nuclear facilities to conduct complementary safety assessments (CSA), also including "the robustness beyond their design basis". The tsunami hazard deserves an appraisal in the light of the 2011 catastrophe, to check whether any unforeseen tsunami impact can be expected for these facilities. TANDEM aims at defining the tsunami effects expected for the French Atlantic and Channel coastlines, basically from numerical modeling methods, through adaptation and improvement of numerical methods, in order to study tsunami impacts down to the interaction with coastal structures (thus sometimes using 3D approaches) (WP1). Then the methods will be tested to better characterize and quantify the associated uncertainties (in the source, the propagation, and the coastal impact) (WP2). The project will benefit from a Japanese cooperation (Meteorological Research Institute, MRI) to study in detail the coastal impact of the 2011 Tohoku tsunami (WP3). In this framework TANDEM will apply the models to the French study area, which includes investigating historical documents, defining the possible tsunamigenic sources able to strike the regions of interest (earthquakes and/or landslides), and modeling the coastal effects at a regional scale and for selected sites. Using high resolution bathymetric and topographic data in the frame of Litto3D (a French project whose main objective is to build a seamless integrated topographic and bathymetric coastal Digital Terrain Model), TANDEM will thoroughly investigate possible sources, through a detailed characterization of the slope stability off the coastlines (for the Celtic and Armorican margins, Bay of Biscay), and estimate the coastal impacts. It will also consider events (Canaries) whose assumed catastrophic impact has been widely discussed these recent years, needing a reappraisal regarding French coastlines. A special attention will also be paid to the estimation of the return periods expected for the tsunami scenarios.

Practicing Collaboration: What We Learn from a Cohort that Functions Well

ERIC Educational Resources Information Center

Ross, Dorene D.; Stafford, Lynn; Church-Pupke, Penny; Bondy, Elizabeth

2006-01-01

Students in the Unified Elementary/Special Education Program at the University of Florida are organized into cohort groups, a common recommendation within the special education teacher education literature. Although highly effective in some instances, the literature also documents numerous problems in the use of cohorts. The current study was…

Collection-Level Surveys for Special Collections: Coalescing Descriptors across Standards

ERIC Educational Resources Information Center

Ascher, James P.; Ferris, Anna M.

2012-01-01

Developing collection-level surveys to expose hidden collections in special collections and archives departments within ARL libraries has received a great deal of scholarly attention in the recent years. Numerous standards have been explored, and each has its strengths and weaknesses. This paper summarizes some of the major initiatives in…

Busting the Limits of Science Laboratory Economics

ERIC Educational Resources Information Center

Bush, Robert C.

2008-01-01

This article discusses the trend facing today's scientific laboratories: that the more specialized the lab, the more expensive it is, and the less accessible it becomes. Or conversely, the more accessible a lab needs to be, the fewer resources can be dedicated per capita, and the less specialized it becomes. From a numerical standpoint, "real"…

Risk in Schooling: The Contribution of Qualitative Research to Our Understanding of the Overrepresentation of Minorities in Special Education

ERIC Educational Resources Information Center

Harry, Beth; Fenton, Patrice

2016-01-01

This article reviews 15 qualitative studies examining factors contributing to the overrepresentation of minorities in special education. Eleven studies constituted numerical surveys of practitioner perspectives, with additional questions that were analyzed qualitatively. Four studies relied on face-to-face interviews or qualitative surveys,…

Integration Of Heat Transfer Coefficient In Glass Forming Modeling With Special Interface Element

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

Moreau, P.; Gregoire, S.; Lochegnies, D.

2007-05-17

Numerical modeling of the glass forming processes requires the accurate knowledge of the heat exchange between the glass and the forming tools. A laboratory testing is developed to determine the evolution of the heat transfer coefficient in different glass/mould contact conditions (contact pressure, temperature, lubrication...). In this paper, trials are performed to determine heat transfer coefficient evolutions in experimental conditions close to the industrial blow-and-blow process conditions. In parallel of this work, a special interface element is implemented in a commercial Finite Element code in order to deal with heat transfer between glass and mould for non-meshing meshes and evolutivemore » contact. This special interface element, implemented by using user subroutines, permits to introduce the previous heat transfer coefficient evolutions in the numerical modelings at the glass/mould interface in function of the local temperatures, contact pressures, contact time and kind of lubrication. The blow-and-blow forming simulation of a perfume bottle is finally performed to assess the special interface element performance.« less

A special case of the Poisson PDE formulated for Earth's surface and its capability to approximate the terrain mass density employing land-based gravity data, a case study in the south of Iran

NASA Astrophysics Data System (ADS)

AllahTavakoli, Yahya; Safari, Abdolreza; Vaníček, Petr

2016-12-01

This paper resurrects a version of Poisson's Partial Differential Equation (PDE) associated with the gravitational field at the Earth's surface and illustrates how the PDE possesses a capability to extract the mass density of Earth's topography from land-based gravity data. Herein, first we propound a theorem which mathematically introduces this version of Poisson's PDE adapted for the Earth's surface and then we use this PDE to develop a method of approximating the terrain mass density. Also, we carry out a real case study showing how the proposed approach is able to be applied to a set of land-based gravity data. In the case study, the method is summarized by an algorithm and applied to a set of gravity stations located along a part of the north coast of the Persian Gulf in the south of Iran. The results were numerically validated via rock-samplings as well as a geological map. Also, the method was compared with two conventional methods of mass density reduction. The numerical experiments indicate that the Poisson PDE at the Earth's surface has the capability to extract the mass density from land-based gravity data and is able to provide an alternative and somewhat more precise method of estimating the terrain mass density.

A Perturbation Analysis of Harmonics Generation from Saturated Elements in Power Systems

NASA Astrophysics Data System (ADS)

Kumano, Teruhisa

Nonlinear phenomena such as saturation in magnetic flux give considerable effects in power system analysis. It is reported that a failure in a real 500kV system triggered islanding operation, where resultant even harmonics caused malfunctions in protective relays. It is also reported that the major origin of this wave distortion is nothing but unidirectional magnetization of the transformer iron core. Time simulation is widely used today to analyze this type of phenomena, but it has basically two shortcomings. One is that the time simulation takes two much computing time in the vicinity of inflection points in the saturation characteristic curve because certain iterative procedure such as N-R (Newton-Raphson) should be used and such methods tend to be caught in an ill conditioned numerical hunting. The other is that such simulation methods sometimes do not help intuitive understanding of the studied phenomenon because the whole nonlinear equations are treated in a matrix form and not properly divided into understandable parts as done in linear systems. This paper proposes a new computation scheme which is based on so called perturbation method. Magnetic saturation in iron cores in a generator and a transformer are taken into account. The proposed method has a special feature against the first shortcoming of the N-R based time simulation method stated above. In the proposed method no iterative process is used to reduce the equation residue but uses perturbation series, which means free from the ill condition problem. Users have only to calculate each perturbation terms one by one until he reaches necessary accuracy. In a numerical example treated in the present paper the first order perturbation can make reasonably high accuracy, which means very fast computing. In numerical study three nonlinear elements are considered. Calculated results are almost identical to the conventional Newton-Raphson based time simulation, which shows the validity of the method. The proposed method would be effectively used in a screening where many case studies are needed.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

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

Strehl, Robert; Ilie, Silvana, E-mail: silvana@ryerson.ca

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated onmore » three benchmarking systems, with special focus on approximation accuracy and efficiency.« less

Light and life in Baltimore--and beyond.

PubMed

Edidin, Michael

2015-02-03

Baltimore has been the home of numerous biophysical studies using light to probe cells. One such study, quantitative measurement of lateral diffusion of rhodopsin, set the standard for experiments in which recovery after photobleaching is used to measure lateral diffusion. Development of this method from specialized microscopes to commercial scanning confocal microscopes has led to widespread use of the technique to measure lateral diffusion of membrane proteins and lipids, and as well diffusion and binding interactions in cell organelles and cytoplasm. Perturbation of equilibrium distributions by photobleaching has also been developed into a robust method to image molecular proximity in terms of fluorescence resonance energy transfer between donor and acceptor fluorophores. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Research on periodic orbits in the three problem

NASA Astrophysics Data System (ADS)

Fernández, S.; Gámez, J.

In order to investigate the possible existence of small planets in extrasolar systems, a restricted, circular and plane three body problem is used. One of the two primaries has a mass similar to the Sun and the other one has a mass greater than Jupiter. Periodic and quasi-periodic orbits for the third body with different values of the Jacobi constant (C) are found by numerical methods. One of the three cases studied is fictitious, the others resemble two real systems of ext rasolar planets. The Everhart method is used and the results show the existence of periodic and quasi-periodic orbits for the lesser value of C. Irregular orbits appear for the other values of C, specially on the exterior zone of the secondary body.

Logarithm conformal mapping brings the cloaking effect

PubMed Central

Xu, Lin; Chen, Huanyang

2014-01-01

Over the past years, invisibility cloaks have been extensively discussed since transformation optics emerges. Generally, the electromagnetic parameters of invisibility cloaks are complicated tensors, yet difficult to realize. As a special method of transformation optics, conformal mapping helps us design invisibility cloak with isotropic materials of a refractive index distribution. However, for all proposed isotropic cloaks, the refractive index range is at such a breadth that challenges current experimental fabrication. In this work, we propose two new kinds of logarithm conformal mappings for invisible device designs. For one of the mappings, the refractive index distribution of conformal cloak varies from 0 to 9.839, which is more feasible for future implementation. Numerical simulations by using finite element method are performed to confirm the theoretical analysis. PMID:25359138

Numerical treatment of free surface problems in ferrohydrodynamics

NASA Astrophysics Data System (ADS)

Lavrova, O.; Matthies, G.; Mitkova, T.; Polevikov, V.; Tobiska, L.

2006-09-01

The numerical treatment of free surface problems in ferrohydrodynamics is considered. Starting from the general model, special attention is paid to field-surface and flow-surface interactions. Since in some situations these feedback interactions can be partly or even fully neglected, simpler models can be derived. The application of such models to the numerical simulation of dissipative systems, rotary shaft seals, equilibrium shapes of ferrofluid drops, and pattern formation in the normal-field instability of ferrofluid layers is given. Our numerical strategy is able to recover solitary surface patterns which were discovered recently in experiments.

On analytic modeling of lunar perturbations of artificial satellites of the earth

NASA Astrophysics Data System (ADS)

Lane, M. T.

1989-06-01

Two different procedures for analytically modeling the effects of the moon's direct gravitational force on artificial earth satellites are discussed from theoretical and numerical viewpoints. One is developed using classical series expansions of inclination and eccentricity for both the satellite and the moon, and the other employs the method of averaging. Both solutions are seen to have advantages, but it is shown that while the former is more accurate in special situations, the latter is quicker and more practical for the general orbit determination problem where observed data are used to correct the orbit in near real time.

Practical adaptive quantum tomography

NASA Astrophysics Data System (ADS)

Granade, Christopher; Ferrie, Christopher; Flammia, Steven T.

2017-11-01

We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods. Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states. By contrast, our approach combines the efficiency of online optimization with generally applicable and well-motivated data-processing techniques. We numerically demonstrate these advantages in several scenarios including mixed states, higher-dimensional systems, and restricted measurements. http://cgranade.com complete data and source code for this work are available online [1], and can be previewed at https://goo.gl/koiWxR.

Transient Phenomena in Multiphase and Multicomponent Systems: Research Report

NASA Astrophysics Data System (ADS)

Zur Beurteilung von Stoffen in der Landwirtschaft, Senatskommission

2000-09-01

Due to the reinforced risk and safety-analysis of industrial plants in chemical and energy-engineering there has been increased demand in industry for more information on thermo- and fluiddynamic effects of non-equilibria during strong transients. Therefore, the 'Deutsche Forschungsgemeinschaft' initiated a special research program focusing on the study of transient phenomena in multiphase systems with one or several components. This book describes macroscopic as well as microscopic transient situations. A large part of the book deals with numerical methods for describing transients in two-phase mixtures. New developments in measuring techniques are also presented.

Dispersion relation and electron acceleration in the combined circular and elliptical metallic-dielectric waveguide filled by plasma

NASA Astrophysics Data System (ADS)

Abdoli-Arani, A.; Montazeri, M. M.

2018-04-01

Two special types of metallic waveguide having dielectric cladding and plasma core including the combined circular and elliptical structure are studied. Longitudinal and transverse field components in the different regions are obtained. Applying the boundary conditions, dispersion relations of the electromagnetic waves in the structures are obtained and then plotted. The acceleration of an injected external relativistic electron in the considered waveguides is studied. The obtained differential equations related to electron motion are solved by the fourth-order Runge-Kutta method. Numerical computations are made, and the results are graphically presented.

Programming Probabilistic Structural Analysis for Parallel Processing Computer

NASA Technical Reports Server (NTRS)

Sues, Robert H.; Chen, Heh-Chyun; Twisdale, Lawrence A.; Chamis, Christos C.; Murthy, Pappu L. N.

1991-01-01

The ultimate goal of this research program is to make Probabilistic Structural Analysis (PSA) computationally efficient and hence practical for the design environment by achieving large scale parallelism. The paper identifies the multiple levels of parallelism in PSA, identifies methodologies for exploiting this parallelism, describes the development of a parallel stochastic finite element code, and presents results of two example applications. It is demonstrated that speeds within five percent of those theoretically possible can be achieved. A special-purpose numerical technique, the stochastic preconditioned conjugate gradient method, is also presented and demonstrated to be extremely efficient for certain classes of PSA problems.

Generalized self-adjustment method for statistical mechanics of composite materials

NASA Astrophysics Data System (ADS)

Pan'kov, A. A.

1997-03-01

A new method is developed for the statistical mechanics of composite materials — the generalized selfadjustment method — which makes it possible to reduce the problem of predicting effective elastic properties of composites with random structures to the solution of two simpler "averaged" problems of an inclusion with transitional layers in a medium with the desired effective elastic properties. The inhomogeneous elastic properties and dimensions of the transitional layers take into account both the "approximate" order of mutual positioning, and also the variation in the dimensions and elastics properties of inclusions through appropriate special averaged indicator functions of the random structure of the composite. A numerical calculation of averaged indicator functions and effective elastic characteristics is performed by the generalized self-adjustment method for a unidirectional fiberglass on the basis of various models of actual random structures in the plane of isotropy.

Structural optimisation of cage induction motors using finite element analysis

NASA Astrophysics Data System (ADS)

Palko, S.

The current trend in motor design is to have highly efficient, low noise, low cost, and modular motors with a high power factor. High torque motors are useful in applications like servo motors, lifts, cranes, and rolling mills. This report contains a detailed review of different optimization methods applicable in various design problems. Special attention is given to the performance of different methods, when they are used with finite element analysis (FEA) as an objective function, and accuracy problems arising from the numerical simulations. Also an effective method for designing high starting torque and high efficiency motors is presented. The method described in this work utilizes FEA combined with algorithms for the optimization of the slot geometry. The optimization algorithm modifies the position of the nodal points in the element mesh. The number of independent variables ranges from 14 to 140 in this work.

Fast spacecraft adaptive attitude tracking control through immersion and invariance design

NASA Astrophysics Data System (ADS)

Wen, Haowei; Yue, Xiaokui; Li, Peng; Yuan, Jianping

2017-10-01

This paper presents a novel non-certainty-equivalence adaptive control method for the attitude tracking control problem of spacecraft with inertia uncertainties. The proposed immersion and invariance (I&I) based adaptation law provides a more direct and flexible approach to circumvent the limitations of the basic I&I method without employing any filter signal. By virtue of the adaptation high-gain equivalence property derived from the proposed adaptive method, the closed-loop adaptive system with a low adaptation gain could recover the high adaptation gain performance of the filter-based I&I method, and the resulting control torque demands during the initial transient has been significantly reduced. A special feature of this method is that the convergence of the parameter estimation error has been observably improved by utilizing an adaptation gain matrix instead of a single adaptation gain value. Numerical simulations are presented to highlight the various benefits of the proposed method compared with the certainty-equivalence-based control method and filter-based I&I control schemes.

Generation of structural topologies using efficient technique based on sorted compliances

NASA Astrophysics Data System (ADS)

Mazur, Monika; Tajs-Zielińska, Katarzyna; Bochenek, Bogdan

2018-01-01

Topology optimization, although well recognized is still widely developed. It has gained recently more attention since large computational ability become available for designers. This process is stimulated simultaneously by variety of emerging, innovative optimization methods. It is observed that traditional gradient-based mathematical programming algorithms, in many cases, are replaced by novel and e cient heuristic methods inspired by biological, chemical or physical phenomena. These methods become useful tools for structural optimization because of their versatility and easy numerical implementation. In this paper engineering implementation of a novel heuristic algorithm for minimum compliance topology optimization is discussed. The performance of the topology generator is based on implementation of a special function utilizing information of compliance distribution within the design space. With a view to cope with engineering problems the algorithm has been combined with structural analysis system Ansys.

Role to Be Played by Independent Geotechnical Supervision in the Foundation for Bridge Construction

NASA Astrophysics Data System (ADS)

Sobala, Dariusz; Rybak, Jarosław

2017-10-01

Some remarks concerning the necessity of employing an independent and over all ethical geotechnical survey were presented in the paper. Starting from the design phase, through the whole construction process, the importance of geotechnical engineer is stated in legal acts. Numerous testing technologies serve for the calibration of geotechnical technologies and allow for confirming the quality and capacity of piles. Special emphasis was payed to the involvement of scientifical and research institutions which can not only serve services but also can postprocess and methodize collected data. Such databases enable for new codes, methods and recommendations. Selection of deep foundations for bridge-type structures is most often dependent on complex geotechnical conditions, concentrated loads and constraints for pier displacements. Besides the last ones, prior to more common introduction of the design-construct system, could be a convenient justification for design engineer, who imposed deep foundation because he did not want or was not able to estimate the effect of pier settlement on civil engineering structure. The paper provides some notes about the need to engage a geotechnical supervising service of high competency and ethical quality during engineering and construction stages of foundations for bridge-type structures where legal requirements are of special consideration. Successive stages of projects are reviewed and research methods used for current calibration of geotechnical technologies and verification of geotechnical work quality are analysed. Special attention is given to potential involvement of independent R&D institutions which, apart from rendering specific services, also collect and systemize the research results thus enabling, in the long term, to revise engineering standards, instructions and guidelines.

Testing the conditional mass function of dark matter haloes against numerical N-body simulations

NASA Astrophysics Data System (ADS)

Tramonte, D.; Rubiño-Martín, J. A.; Betancort-Rijo, J.; Dalla Vecchia, C.

2017-05-01

We compare the predicted conditional mass function (CMF) of dark matter haloes from two theoretical prescriptions against numerical N-body simulations, both in overdense and underdense regions and at different Eulerian scales ranging from 5 to 30 h-1 Mpc. In particular, we consider in detail a locally implemented rescaling of the unconditional mass function (UMF) already discussed in the literature, and also a generalization of the standard rescaling method described in the extended Press-Schechter formalism. First, we test the consistency of these two rescalings by verifying the normalization of the CMF at different scales, and showing that none of the proposed cases provides a normalized CMF. In order to satisfy the normalization condition, we include a modification in the rescaling procedure. After this modification, the resulting CMF generally provides a better description of numerical results. We finally present an analytical fit to the ratio between the CMF and the UMF (also known as the matter-to-halo bias function) in underdense regions, which could be of special interest to speed up the computation of the halo abundance when studying void statistics. In this case, the CMF prescription based on the locally implemented rescaling provides a slightly better description of the numerical results when compared to the standard rescaling.

Numerical Investigation of Different Radial Inlet Forms for Centrifugal Compressor and Influence of the Deflectors Number by Means of Computational Fluid Dynamics Methods with Computational Model Validation

NASA Astrophysics Data System (ADS)

Kozhukhov, Y. V.; Yun, V. K.; Reshetnikova, L. V.; Prokopovich, M. V.

2015-08-01

The goal of this work is numerical experiments for five different types of the centrifugal compressor's inlet chambers with the help of CFD-methods and comparison of the computational results with the results of the real experiment which was held in the Nevskiy Lenin Plant in Saint-Petersburg. In the context of one of the chambers the influence of deflectors on its characteristics was investigated. The objects of investigation are 5 inlet chambers of different types which differ from each other by deflectors’ existence and by its number. The comparative analyze of the results of numerical and real experiments was held by means of comparison of relative velocity and static pressure coefficient distribution on hub and shroud region, and also by means of loss coefficient values change for all five chambers. As a result of the numerical calculation the quantitative and qualitative departure of CFD- calculations results and real experiment were found out. The investigation of the influence of the number of deflectors on flow parameters was carried out. The results of the study prove that the presence of the deflectors on flow path significantly increases the probability of the flow separations and reversed flows appearance on them. At the same time, the complete absence of the deflectors in the chamber significantly increases circumferential distortion of the flow; however the loss coefficient decreases anyway, the high values of which are caused by the shock flow existence. Thus, the profiling of the deflectors of the inlet chamber should be given a special attention.

A special purpose silicon compiler for designing supercomputing VLSI systems

NASA Technical Reports Server (NTRS)

Venkateswaran, N.; Murugavel, P.; Kamakoti, V.; Shankarraman, M. J.; Rangarajan, S.; Mallikarjun, M.; Karthikeyan, B.; Prabhakar, T. S.; Satish, V.; Venkatasubramaniam, P. R.

1991-01-01

Design of general/special purpose supercomputing VLSI systems for numeric algorithm execution involves tackling two important aspects, namely their computational and communication complexities. Development of software tools for designing such systems itself becomes complex. Hence a novel design methodology has to be developed. For designing such complex systems a special purpose silicon compiler is needed in which: the computational and communicational structures of different numeric algorithms should be taken into account to simplify the silicon compiler design, the approach is macrocell based, and the software tools at different levels (algorithm down to the VLSI circuit layout) should get integrated. In this paper a special purpose silicon (SPS) compiler based on PACUBE macrocell VLSI arrays for designing supercomputing VLSI systems is presented. It is shown that turn-around time and silicon real estate get reduced over the silicon compilers based on PLA's, SLA's, and gate arrays. The first two silicon compiler characteristics mentioned above enable the SPS compiler to perform systolic mapping (at the macrocell level) of algorithms whose computational structures are of GIPOP (generalized inner product outer product) form. Direct systolic mapping on PLA's, SLA's, and gate arrays is very difficult as they are micro-cell based. A novel GIPOP processor is under development using this special purpose silicon compiler.

Reflections on the Conception, Birth, and Childhood of Numerical Weather Prediction

NASA Astrophysics Data System (ADS)

Lorenz, Edward N.

2006-05-01

In recognition of the contributions of Norman Phillips and Joseph Smagorinsky to the field of numerical weather prediction (NWP), a symposium was held in 2003; this account is an amplification of a talk presented there. Ideas anticipating the advent of NWP, the first technically successful numerical weather forcast, and the subsequent progression of NWP to a mature discipline are described, with special emphasis on the work of Phillips and Smagorinsky and their mentor Jule Charney.

Learning about the Numerator and Denominator in Teacher-Designed Lessons

ERIC Educational Resources Information Center

Kullberg, Angelika; Runesson, Ulla

2013-01-01

This study concerns pupils' experience of unit and non-unit fractions of a discrete quantity during specially designed lessons. The aim was to explore pupils' understanding of operations such as "b/c of a" in lessons where the teachers were aware of some pupils' difficulties beforehand and what needed special attention.…

Teachers' Perception of Mobile Edutainment for Special Needs Learners: The Malaysian Case

ERIC Educational Resources Information Center

Mohd Yusof, Anuar; Daniel, Esther Gnanamalar Sarojini; Low, Wah Yun; Ab. Aziz, Kamarulzaman

2014-01-01

Study of Malaysian adoption of mobile learning (m-learning) is still in the early stages. However, there are numerous researchers in the country exploring the potential and application of m-learning in the Malaysian education system, including special education. A key question is whether teachers are prepared to incorporate mobile technology as…

The world wide web: an emerging technology for marketing special forest products (poster abstract)

Treesearch

A.L. Hammett; Shelby Jones; Philip A. Araman

1999-01-01

Interest by forest landowners and agriculturist in Special Forest Products (SFPs) is increasing rapidly. At present there are numerous efforts to increase awareness of these products and the market potential. However, there is a shortage of information available and there are few means effective in disseminating the information necessary for the sustainable management...

DIAGNOSTIC EVALUATION OF NUMBERICAL AIR QUALITY MODELS WITH SPECIALIZED AMBIENT OBSERVATIONS: TESTING THE COMMUNITY MULTISCALE AIR QUALITY MODELING SYSTEM (CMAQ) AT SELECTED SOS 95 GROUND SITES

EPA Science Inventory

Three probes for diagnosing photochemical dynamics are presented and applied to specialized ambient surface-level observations and to a numerical photochemical model to better understand rates of production and other process information in the atmosphere and in the model. Howeve...

For Lesbian Parents: Your Guide to Helping Your Family Grow Up Happy, Healthy, and Proud.

ERIC Educational Resources Information Center

Johnson, Suzanne M.; O'Connor, Elizabeth

In addition to those adjustments that any new parents must make, lesbian mothers face numerous special concerns. This book offers information and support for lesbian parents on relations between lesbian mothers and the outside world, child development and social issues, and special circumstances. Chapter 1 introduces a group of lesbian mothers and…

Air motions inside dome room of Big Telescope Alt-azimuth at Special Astrophysical Observatory RAS. Numerical solutions of Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Nosov, V. V.; Lukin, V. P.; Nosov, E. V.; Torgaev, A. V.

2017-11-01

The structure of air turbulent motion inside the closed dome room of Big Telescope Alt-azimuth at Special Astrophysical Observatory of the Russian Academy of Sciences (RAS) has been experimentally and theoretically studied. Theoretical results have been reached by numerical solving of boundary value problem for Navier-Stokes equations. Solitary large vortices (coherent structures, topological solitons) are observed indoors. Coherent breakdown of these vortices leads to the coherent turbulence. In the case of identical boundary conditions the pattern of air motions as a result of the simulation and the pattern, registered experimentally using the compact portable ultrasonic weather station, are practically the same.

Cross-scale efficient tensor contractions for coupled cluster computations through multiple programming model backends

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

Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel

Coupled-cluster methods provide highly accurate models of molecular structure through explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix–matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts tomore » extend the Libtensor framework to work in the distributed memory environment in a scalable and energy-efficient manner. We achieve up to 240× speedup compared with the optimized shared memory implementation of Libtensor. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures (Cray XC30 and XC40, and IBM Blue Gene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance, tasking and bulk synchronous models. Nevertheless, we preserve a unified interface to both programming models to maintain the productivity of computational quantum chemists.« less

Cross-scale efficient tensor contractions for coupled cluster computations through multiple programming model backends

DOE PAGES

Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel; ...

2017-03-08

Coupled-cluster methods provide highly accurate models of molecular structure through explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix–matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts tomore » extend the Libtensor framework to work in the distributed memory environment in a scalable and energy-efficient manner. We achieve up to 240× speedup compared with the optimized shared memory implementation of Libtensor. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures (Cray XC30 and XC40, and IBM Blue Gene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance, tasking and bulk synchronous models. Nevertheless, we preserve a unified interface to both programming models to maintain the productivity of computational quantum chemists.« less

Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow

NASA Technical Reports Server (NTRS)

Broeze, Jan; Geurts, Bernard; Kuerten, Hans; Streng, Martin

1996-01-01

An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.

An automatic multigrid method for the solution of sparse linear systems

NASA Technical Reports Server (NTRS)

Shapira, Yair; Israeli, Moshe; Sidi, Avram

1993-01-01

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Factors that affect general practice as a choice of medical speciality: implications for policy development.

PubMed

Vohra, Amit; Ladyshewsky, Richard; Trumble, Stephen

2017-11-28

Objective This article critically appraises the range of personal, professional and social factors that affect the choice of speciality across medical students, prevocational doctors, general practice registrars and general practitioners. Methods This qualitative study applied constructs from the fields of decision theory and career theory to better understand the complex nature of choosing a speciality. In all, 47 in-depth interviews were conducted with participants at different stages of their career cycle. The data was codified and analysed using NVivo to identify key factors that influenced speciality choice. Results The research identified 77 individual findings influencing general practice as a choice of medical speciality. These were distilled into a matrix to show that factors such as money, prestige and peer interaction did not have a compelling effect, whereas clinical and academic role models, flexibility, work-life balance, scope of practice, connection with patients, training environment and practical opportunities did. Conclusion The findings indicate that the decision in relation to the choice of medical speciality is a complex cognitive process that is undertaken within a personal, social and professional context particular to each individual. What is known about the topic? Current literature aims to quantify changes in attitudes towards choice of speciality or the effect of particular variables in isolation while ignoring the complexity of this decision process and how the numerous variables compare with each other. What does this paper add? The present study is the first intergenerational research on this topic in the Australian context and the paper dismisses the role of prestige and remuneration as key drivers of choice in picking general practice as a speciality, noting that money is merely a 'hygiene factor'. What are the implications for policy makers? A policy framework outlining 10 key principles is presented to assist policy makers seeking to affect workforce outcomes by applying policy levers to influence doctors' choice of speciality.

Weak-value amplification and optimal parameter estimation in the presence of correlated noise

NASA Astrophysics Data System (ADS)

Sinclair, Josiah; Hallaji, Matin; Steinberg, Aephraim M.; Tollaksen, Jeff; Jordan, Andrew N.

2017-11-01

We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement strategy that involves sorting data into separate subsets based on the outcome of a second "partitioning" measurement. Using a simplified correlated noise model that can be analyzed exactly together with optimal statistical estimators, we compare WVA to a conventional measurement method. We find that WVA indeed yields a much lower variance of the parameter of interest than the conventional technique does, optimized in the absence of any partitioning measurements. In contrast, a statistically optimal analysis that employs partitioning measurements, incorporating all partitioned results and their known correlations, is found to yield an improvement—typically slight—over the noise reduction achieved by WVA. This result occurs because the simple WVA technique is not tailored to any specific noise environment and therefore does not make use of correlations between the different partitions. We also compare WVA to traditional background subtraction, a familiar technique where measurement outcomes are partitioned to eliminate unknown offsets or errors in calibration. Surprisingly, for the cases we consider, background subtraction turns out to be a special case of the optimal partitioning approach, possessing a similar typically slight advantage over WVA. These results give deeper insight into the role of partitioning measurements (with or without postselection) in enhancing measurement precision, which some have found puzzling. They also resolve previously made conflicting claims about the usefulness of weak-value amplification to precision measurement in the presence of correlated noise. We finish by presenting numerical results to model a more realistic laboratory situation of time-decaying correlations, showing that our conclusions hold for a wide range of statistical models.

Numerical Model of Multiple Scattering and Emission from Layering Snowpack for Microwave Remote Sensing

NASA Astrophysics Data System (ADS)

Jin, Y.; Liang, Z.

2002-12-01

The vector radiative transfer (VRT) equation is an integral-deferential equation to describe multiple scattering, absorption and transmission of four Stokes parameters in random scatter media. From the integral formal solution of VRT equation, the lower order solutions, such as the first-order scattering for a layer medium or the second order scattering for a half space, can be obtained. The lower order solutions are usually good at low frequency when high-order scattering is negligible. It won't be feasible to continue iteration for obtaining high order scattering solution because too many folds integration would be involved. In the space-borne microwave remote sensing, for example, the DMSP (Defense Meterological Satellite Program) SSM/I (Special Sensor Microwave/Imager) employed seven channels of 19, 22, 37 and 85GHz. Multiple scattering from the terrain surfaces such as snowpack cannot be neglected at these channels. The discrete ordinate and eigen-analysis method has been studied to take into account for multiple scattering and applied to remote sensing of atmospheric precipitation, snowpack etc. Snowpack was modeled as a layer of dense spherical particles, and the VRT for a layer of uniformly dense spherical particles has been numerically studied by the discrete ordinate method. However, due to surface melting and refrozen crusts, the snowpack undergoes stratifying to form inhomegeneous profiles of the ice grain size, fractional volume and physical temperature etc. It becomes necessary to study multiple scattering and emission from stratified snowpack of dense ice grains. But, the discrete ordinate and eigen-analysis method cannot be simply applied to multi-layers model, because numerically solving a set of multi-equations of VRT is difficult. Stratifying the inhomogeneous media into multi-slabs and employing the first order Mueller matrix of each thin slab, this paper developed an iterative method to derive high orders scattering solutions of whole scatter media. High order scattering and emission from inhomogeneous stratifying media of dense spherical particles are numerically obtained. The brightness temperature at low frequency such as 5.3 GHz without high order scattering and at SSM/I channels with high order scattering are obtained. This approach is also compared with the conventional discrete ordinate method for an uniform layer model. Numerical simulation for inhomogeneous snowpack is also compared with the measurements of microwave remote sensing.

Random learning units using WIRIS quizzes in Moodle

NASA Astrophysics Data System (ADS)

Mora, Ángel; Mérida, Enrique; Eixarch, Ramon

2011-09-01

Moodle is an extended learning management system for developing learning units, including mathematically-based subjects. A wide variety of material can be developed in Moodle which contains facilities for forums, questionnaires, lessons, tasks, wikis, glossaries and chats. Therefore, the Moodle platform provides a meeting point for those working in a mathematics course. Mathematics requires special materials and activities: The material must include mathematical objects and the activities included in the virtual course must be able to do mathematical computations. WIRIS is a powerful software for educational environments. It has libraries for calculus, algebra, geometry and much more. In this article, examples showing the use of WIRIS in numerical methods and examples of using a new tool, WIRIS quizzes, are illustrated. By enhancing Moodle with WIRIS, we can add random learning questions to modules. Moodle has a simpler version of this capability, but WIRIS extends the method in which the random material is presented to the students. Random objects can appear in a question, in a variable of a question, in a plot or in the definition of a mathematical object. This article illustrates material prepared for numerical methods using a WIRIS library integrated in WIRIS quizzes. As a result, WIRIS in Moodle can be considered as a global solution for mathematics education.

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

NASA Astrophysics Data System (ADS)

Forssén, C.; Carlsson, B. D.; Johansson, H. T.; Sääf, D.; Bansal, A.; Hagen, G.; Papenbrock, T.

2018-03-01

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding 1010 on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to Nmax=22 and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.

Brownian dynamics of confined rigid bodies

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

Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar, E-mail: donev@courant.nyu.edu

2015-10-14

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the othermore » based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.« less

An alternative representation of the receptance: The 'elliptical plane' and its modal properties

NASA Astrophysics Data System (ADS)

Montalvão, Diogo; Amafabia, Daerefa-a. Mitsheal

2018-03-01

Modal Identification from Frequency Response Functions (FRFs) has been extensively investigated up to the point its research reached a stagnation state. Yet, a new approach to determine the modal damping factors from FRFs was recently proposed, showing that there still is scope for new findings in the field. Contrary to other modal identification methods which are based on the dynamic motion governing equations, the method used the dissipated energy per cycle of vibration as a starting point. For lightly damped systems with conveniently spaced modes, it produced quite accurate results, especially when compared to the well-known method of the inverse. The method used a plot of the sine of the phase of the receptance against its amplitude, whereby damping was determined from the slope of a linear fit to the resulting plot. In this paper, it is shown that this plot has other (perhaps more important) special properties that were not explored before. Near resonant frequencies, its shape is elliptical, whereby the real and imaginary parts of the modal constants can be determined from numerical curve-fitting. This finding allowed developing a new method which formulation is presented in this paper. The method is discussed through numerical and experimental examples. Although the intention is not to present a new modal identification method that is superior to other existing ones (like the method of the inverse or those based on the Nyquist plot), the authors believe that this new representation of the receptance and its properties may bring valuable insights for other researchers in the field.

Finite basis representations with nondirect product basis functions having structure similar to that of spherical harmonics.

PubMed

Czakó, Gábor; Szalay, Viktor; Császár, Attila G

2006-01-07

The currently most efficient finite basis representation (FBR) method [Corey et al., in Numerical Grid Methods and Their Applications to Schrodinger Equation, NATO ASI Series C, edited by C. Cerjan (Kluwer Academic, New York, 1993), Vol. 412, p. 1; Bramley et al., J. Chem. Phys. 100, 6175 (1994)] designed specifically to deal with nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc., employs very special l-independent grids and results in a symmetric FBR. While highly efficient, this method is not general enough. For instance, it cannot deal with nondirect product bases of the above structure efficiently if the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are discrete variable representation (DVR) functions of the infinite type. The optimal-generalized FBR(DVR) method [V. Szalay, J. Chem. Phys. 105, 6940 (1996)] is designed to deal with general, i.e., direct and/or nondirect product, bases and grids. This robust method, however, is too general, and its direct application can result in inefficient computer codes [Czako et al., J. Chem. Phys. 122, 024101 (2005)]. It is shown here how the optimal-generalized FBR method can be simplified in the case of nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc. As a result the commonly used symmetric FBR is recovered and simplified nonsymmetric FBRs utilizing very special l-dependent grids are obtained. The nonsymmetric FBRs are more general than the symmetric FBR in that they can be employed efficiently even when the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are DVR functions of the infinite type. Arithmetic operation counts and a simple numerical example presented show unambiguously that setting up the Hamiltonian matrix requires significantly less computer time when using one of the proposed nonsymmetric FBRs than that in the symmetric FBR. Therefore, application of this nonsymmetric FBR is more efficient than that of the symmetric FBR when one wants to diagonalize the Hamiltonian matrix either by a direct or via a basis-set contraction method. Enormous decrease of computer time can be achieved, with respect to a direct application of the optimal-generalized FBR, by employing one of the simplified nonsymmetric FBRs as is demonstrated in noniterative calculations of the low-lying vibrational energy levels of the H3+ molecular ion. The arithmetic operation counts of the Hamiltonian matrix vector products and the properties of a recently developed diagonalization method [Andreozzi et al., J. Phys. A Math. Gen. 35, L61 (2002)] suggest that the nonsymmetric FBR applied along with this particular diagonalization method is suitable to large scale iterative calculations. Whether or not the nonsymmetric FBR is competitive with the symmetric FBR in large-scale iterative calculations still has to be investigated numerically.

GIS Methodic and New Database for Magmatic Rocks. Application for Atlantic Oceanic Magmatism.

NASA Astrophysics Data System (ADS)

Asavin, A. M.

2001-12-01

There are several geochemical Databases in INTERNET available now. There one of the main peculiarities of stored geochemical information is geographical coordinates of each samples in those Databases. As rule the software of this Database use spatial information only for users interface search procedures. In the other side, GIS-software (Geographical Information System software),for example ARC/INFO software which using for creation and analyzing special geological, geochemical and geophysical e-map, have been deeply involved with geographical coordinates for of samples. We join peculiarities GIS systems and relational geochemical Database from special software. Our geochemical information system created in Vernadsky Geological State Museum and institute of Geochemistry and Analytical Chemistry from Moscow. Now we tested system with data of geochemistry oceanic rock from Atlantic and Pacific oceans, about 10000 chemical analysis. GIS information content consist from e-map covers Wold Globes. Parts of these maps are Atlantic ocean covers gravica map (with grid 2''), oceanic bottom hot stream, altimeteric maps, seismic activity, tectonic map and geological map. Combination of this information content makes possible created new geochemical maps and combination of spatial analysis and numerical geochemical modeling of volcanic process in ocean segment. Now we tested information system on thick client technology. Interface between GIS system Arc/View and Database resides in special multiply SQL-queries sequence. The result of the above gueries were simple DBF-file with geographical coordinates. This file act at the instant of creation geochemical and other special e-map from oceanic region. We used more complex method for geophysical data. From ARC\\View we created grid cover for polygon spatial geophysical information.

Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1990-01-01

In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.

HOPE: Just-in-time Python compiler for astrophysical computations

NASA Astrophysics Data System (ADS)

Akeret, Joel; Gamper, Lukas; Amara, Adam; Refregier, Alexandre

2014-11-01

HOPE is a specialized Python just-in-time (JIT) compiler designed for numerical astrophysical applications. HOPE focuses on a subset of the language and is able to translate Python code into C++ while performing numerical optimization on mathematical expressions at runtime. To enable the JIT compilation, the user only needs to add a decorator to the function definition. By using HOPE, the user benefits from being able to write common numerical code in Python while getting the performance of compiled implementation.

Discontinuous Finite Element Quasidiffusion Methods

DOE PAGES

Anistratov, Dmitriy Yurievich; Warsa, James S.

2018-05-21

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

Discontinuous Finite Element Quasidiffusion Methods

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

Anistratov, Dmitriy Yurievich; Warsa, James S.

Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

Map-invariant spectral analysis for the identification of DNA periodicities

PubMed Central

2012-01-01

Many signal processing based methods for finding hidden periodicities in DNA sequences have primarily focused on assigning numerical values to the symbolic DNA sequence and then applying spectral analysis tools such as the short-time discrete Fourier transform (ST-DFT) to locate these repeats. The key results pertaining to this approach are however obtained using a very specific symbolic to numerical map, namely the so-called Voss representation. An important research problem is to therefore quantify the sensitivity of these results to the choice of the symbolic to numerical map. In this article, a novel algebraic approach to the periodicity detection problem is presented and provides a natural framework for studying the role of the symbolic to numerical map in finding these repeats. More specifically, we derive a new matrix-based expression of the DNA spectrum that comprises most of the widely used mappings in the literature as special cases, shows that the DNA spectrum is in fact invariable under all these mappings, and generates a necessary and sufficient condition for the invariance of the DNA spectrum to the symbolic to numerical map. Furthermore, the new algebraic framework decomposes the periodicity detection problem into several fundamental building blocks that are totally independent of each other. Sophisticated digital filters and/or alternate fast data transforms such as the discrete cosine and sine transforms can therefore be always incorporated in the periodicity detection scheme regardless of the choice of the symbolic to numerical map. Although the newly proposed framework is matrix based, identification of these periodicities can be achieved at a low computational cost. PMID:23067324

Korean Affairs Report.

DTIC Science & Technology

1986-10-24

Meets Japanese Delegation 112 Foreign Visitors 112 CSSR Trade Group Arrives 112 Hungarian Embassy Hosts Film Show ill Chinese Buddhists Delegation...of ground, sea and air forces, special units which use "nuclear backpacks " along with numerous units and personnel specializing in nuclear warfare...considered encouraging to all Asian nations, particularly since the Chinese sports champions and officials are presently participating in the Seoul Asiad in

[Hospital financing in 2015. Relevant changes for rheumatology].

PubMed

Fiori, W; Lakomek, H-J; Buscham, K; Lehmann, H; Fuchs, A-K; Bessler, F; Roeder, N

2015-06-01

The announced major reforms will most probably not have an impact on hospital financing before 2016. Nevertheless, the numerous minor changes in the legislative framework and the new version of the German diagnosis-related groups (G-DRG) system can be important for hospitals specialized in rheumatology. The following article presents the relevant changes and discusses the consequences for hospitals specialized in rheumatology.

Mechanisms of interactive specialization and emergence of functional brain circuits supporting cognitive development in children

NASA Astrophysics Data System (ADS)

Battista, Christian; Evans, Tanya M.; Ngoon, Tricia J.; Chen, Tianwen; Chen, Lang; Kochalka, John; Menon, Vinod

2018-01-01

Cognitive development is thought to depend on the refinement and specialization of functional circuits over time, yet little is known about how this process unfolds over the course of childhood. Here we investigated growth trajectories of functional brain circuits and tested an interactive specialization model of neurocognitive development which posits that the refinement of task-related functional networks is driven by a shared history of co-activation between cortical regions. We tested this model in a longitudinal cohort of 30 children with behavioral and task-related functional brain imaging data at multiple time points spanning childhood and adolescence, focusing on the maturation of parietal circuits associated with numerical problem solving and learning. Hierarchical linear modeling revealed selective strengthening as well as weakening of functional brain circuits. Connectivity between parietal and prefrontal cortex decreased over time, while connectivity within posterior brain regions, including intra-hemispheric and inter-hemispheric parietal connectivity, as well as parietal connectivity with ventral temporal occipital cortex regions implicated in quantity manipulation and numerical symbol recognition, increased over time. Our study provides insights into the longitudinal maturation of functional circuits in the human brain and the mechanisms by which interactive specialization shapes children's cognitive development and learning.

Preface paper to the Semi-Arid Land-Surface-Atmosphere (SALSA) Program special issue

USGS Publications Warehouse

Goodrich, D.C.; Chehbouni, A.; Goff, B.; MacNish, B.; Maddock, T.; Moran, S.; Shuttleworth, W.J.; Williams, D.G.; Watts, C.; Hipps, L.H.; Cooper, D.I.; Schieldge, J.; Kerr, Y.H.; Arias, H.; Kirkland, M.; Carlos, R.; Cayrol, P.; Kepner, W.; Jones, B.; Avissar, R.; Begue, A.; Bonnefond, J.-M.; Boulet, G.; Branan, B.; Brunel, J.P.; Chen, L.C.; Clarke, T.; Davis, M.R.; DeBruin, H.; Dedieu, G.; Elguero, E.; Eichinger, W.E.; Everitt, J.; Garatuza-Payan, J.; Gempko, V.L.; Gupta, H.; Harlow, C.; Hartogensis, O.; Helfert, M.; Holifield, C.; Hymer, D.; Kahle, A.; Keefer, T.; Krishnamoorthy, S.; Lhomme, J.-P.; Lagouarde, J.-P.; Lo, Seen D.; Luquet, D.; Marsett, R.; Monteny, B.; Ni, W.; Nouvellon, Y.; Pinker, R.; Peters, C.; Pool, D.; Qi, J.; Rambal, S.; Rodriguez, J.; Santiago, F.; Sano, E.; Schaeffer, S.M.; Schulte, M.; Scott, R.; Shao, X.; Snyder, K.A.; Sorooshian, S.; Unkrich, C.L.; Whitaker, M.; Yucel, I.

2000-01-01

The Semi-Arid Land-Surface-Atmosphere Program (SALSA) is a multi-agency, multi-national research effort that seeks to evaluate the consequences of natural and human-induced environmental change in semi-arid regions. The ultimate goal of SALSA is to advance scientific understanding of the semi-arid portion of the hydrosphere-biosphere interface in order to provide reliable information for environmental decision making. SALSA approaches this goal through a program of long-term, integrated observations, process research, modeling, assessment, and information management that is sustained by cooperation among scientists and information users. In this preface to the SALSA special issue, general program background information and the critical nature of semi-arid regions is presented. A brief description of the Upper San Pedro River Basin, the initial location for focused SALSA research follows. Several overarching research objectives under which much of the interdisciplinary research contained in the special issue was undertaken are discussed. Principal methods, primary research sites and data collection used by numerous investigators during 1997-1999 are then presented. Scientists from about 20 US, five European (four French and one Dutch), and three Mexican agencies and institutions have collaborated closely to make the research leading to this special issue a reality. The SALSA Program has served as a model of interagency cooperation by breaking new ground in the approach to large scale interdisciplinary science with relatively limited resources.

Numerical analysis of the Anderson localization

NASA Astrophysics Data System (ADS)

Markoš, P.

2006-10-01

The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems. These systems undergo the metal insulator transition when either Fermi energy crosses the mobility edge or the strength of the disorder increases over critical value. We study how disorder affects the energy spectrum and spatial distribution of electronic eigenstates in the diffusive and insulating regime, as well as in the critical region of the metal-insulator transition. Then, we introduce the transfer matrix and conductance, and we discuss how the quantum character of the electron propagation influences the transport properties of disordered samples. In the weakly disordered systems, the weak localization and anti-localization as well as the universal conductance fluctuation are numerically simulated and discussed. The localization in the one dimensional system is described and interpreted as a purely quantum effect. Statistical properties of the conductance in the critical and localized regimes are demonstrated. Special attention is given to the numerical study of the transport properties of the critical regime and to the numerical verification of the single parameter scaling theory of localization. Numerical data for the critical exponent in the orthogonal models in dimension 2 < d, ≤ 5 are compared with theoretical predictions. We argue that the discrepancy between the theory and numerical data is due to the absence of the self-averaging of transmission quantities. This complicates the analytical analysis of the disordered systems. Finally, theoretical methods of description of weakly disordered systems are explained and their possible generalization to the localized regime is discussed. Since we concentrate on the one-electron propagation at zero temperature, no effects of electron-electron interaction and incoherent scattering are discussed in the paper.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.

PubMed

Mohan, B M; Sinha, Arpita

2008-07-01

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

Use of statistical study methods for the analysis of the results of the imitation modeling of radiation transfer

NASA Astrophysics Data System (ADS)

Alekseenko, M. A.; Gendrina, I. Yu.

2017-11-01

Recently, due to the abundance of various types of observational data in the systems of vision through the atmosphere and the need for their processing, the use of various methods of statistical research in the study of such systems as correlation-regression analysis, dynamic series, variance analysis, etc. is actual. We have attempted to apply elements of correlation-regression analysis for the study and subsequent prediction of the patterns of radiation transfer in these systems same as in the construction of radiation models of the atmosphere. In this paper, we present some results of statistical processing of the results of numerical simulation of the characteristics of vision systems through the atmosphere obtained with the help of a special software package.1

Critical Analyses of Data Differences Between FNMOC and AFGWC Spawned SSM/I Datasets

NASA Technical Reports Server (NTRS)

Ritchie, Adrian A., Jr.; Smith, Matthew R.; Goodman, H. Michael; Schudalla, Ronald L.; Conway, Dawn K.; LaFontaine, Frank J.; Moss, Don; Motta, Brian

1998-01-01

Antenna temperatures and the corresponding geolocation data from the five sources of the Special Sensor Microwave/Imager data from the Defense Meteorological Satellite Program F11 satellite have been characterized. Data from the Fleet Numerical Meteorology and Oceanography Center (FNMOC) have been compared with data from other sources to define and document the differences resulting from different processing systems. While all sources used similar methods to calculate antenna temperatures, different calibration averaging techniques and other processing methods yielded temperature differences. Analyses of the geolocation data identified perturbations in the FNMOC and National Environmental Satellite, Data and Information Service data. The effects of the temperature differences were examined by generating rain rates using the Goddard Scattering Algorithm. Differences in the geophysical precipitation products are directly attributable to antenna temperature differences.

New Developments in Magnetostatic Cleanliness Modeling

NASA Astrophysics Data System (ADS)

Mehlem, K.; Wiegand, A.; Weickert, S.

2012-05-01

The paper describes improvements and extensions of the multiple magnetic dipole modeling method (MDM) for cleanliness verification which had been introduced by the author1 in 1977 and then applied during 3 decades to numerous international projects. The solutions of specific modeling problems which had been left unsolved so far, are described in the present paper. Special attention is given to the ambiguities of MDM solutions caused by the limited data coverage available. Constraint handling by the constraint-free NLP solver, optimal MDM sizing and multiple-point far-field compensation techniques are presented. The recent extension of the MDM method to field gradient data is formulated and demonstrated by an example. Finally, a complex MDM application (Ulysses) is presented. Finally, a short description of the MDM software GAMAG, recently introduced by the author1, is given.

Satellite observed thermodynamics during FGGE

NASA Technical Reports Server (NTRS)

Smith, W. L.

1985-01-01

During the First Global Atmospheric Research Program (GARP) Global Experiment (FGGE), determinations of temperature and moisture were made from TIROS-N and NOAA-6 satellite infrared and microwave sounding radiance measurements. The data were processed by two methods differing principally in their horizontal resolution. At the National Earth Satellite Service (NESS) in Washington, D.C., the data were produced operationally with a horizontal resolution of 250 km for inclusion in the FGGE Level IIb data sets for application to large-scale numerical analysis and prediction models. High horizontal resolution (75 km) sounding data sets were produced using man-machine interactive methods for the special observing periods of FGGE at the NASA/Goddard Space Flight Center and archived as supplementary Level IIb. The procedures used for sounding retrieval and the characteristics and quality of these thermodynamic observations are given.

Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity

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

Fraysse, F., E-mail: francois.fraysse@rs2n.eu; E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid; Redondo, C.

This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is appliedmore » to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.« less

The fast algorithm of spark in compressive sensing

NASA Astrophysics Data System (ADS)

Xie, Meihua; Yan, Fengxia

2017-01-01

Compressed Sensing (CS) is an advanced theory on signal sampling and reconstruction. In CS theory, the reconstruction condition of signal is an important theory problem, and spark is a good index to study this problem. But the computation of spark is NP hard. In this paper, we study the problem of computing spark. For some special matrixes, for example, the Gaussian random matrix and 0-1 random matrix, we obtain some conclusions. Furthermore, for Gaussian random matrix with fewer rows than columns, we prove that its spark equals to the number of its rows plus one with probability 1. For general matrix, two methods are given to compute its spark. One is the method of directly searching and the other is the method of dual-tree searching. By simulating 24 Gaussian random matrixes and 18 0-1 random matrixes, we tested the computation time of these two methods. Numerical results showed that the dual-tree searching method had higher efficiency than directly searching, especially for those matrixes which has as much as rows and columns.

The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y

Computational Modeling to Predict Fatigue Behavior of NiTi Stents: What Do We Need?

PubMed Central

Dordoni, Elena; Petrini, Lorenza; Wu, Wei; Migliavacca, Francesco; Dubini, Gabriele; Pennati, Giancarlo

2015-01-01

NiTi (nickel-titanium) stents are nowadays commonly used for the percutaneous treatment of peripheral arterial disease. However, their effectiveness is still debated in the clinical field. In fact a peculiar cyclic biomechanical environment is created before and after stent implantation, with the risk of device fatigue failure. An accurate study of the device fatigue behavior is of primary importance to ensure a successful stenting procedure. Regulatory authorities recognize the possibility of performing computational analyses instead of experimental tests for the assessment of medical devices. However, confidence in numerical methods is only possible after verification and validation of the models used. For the case of NiTi stents, mechanical properties are strongly dependent on the device dimensions and the whole treatments undergone during manufacturing process. Hence, special attention should be paid to the accuracy of the description of the device geometry and the material properties implementation into the numerical code, as well as to the definition of the fatigue limit. In this paper, a path for setting up an effective numerical model for NiTi stent fatigue assessment is proposed and the results of its application in a specific case study are illustrated. PMID:26011245

Modeling of single film bubble and numerical study of the plateau structure in foam system

NASA Astrophysics Data System (ADS)

Sun, Zhong-guo; Ni, Ni; Sun, Yi-jie; Xi, Guang

2018-02-01

The single-film bubble has a special geometry with a certain amount of gas shrouded by a thin layer of liquid film under the surface tension force both on the inside and outside surfaces of the bubble. Based on the mesh-less moving particle semi-implicit (MPS) method, a single-film double-gas-liquid-interface surface tension (SDST) model is established for the single-film bubble, which characteristically has totally two gas-liquid interfaces on both sides of the film. Within this framework, the conventional surface free energy surface tension model is improved by using a higher order potential energy equation between particles, and the modification results in higher accuracy and better symmetry properties. The complex interface movement in the oscillation process of the single-film bubble is numerically captured, as well as typical flow phenomena and deformation characteristics of the liquid film. In addition, the basic behaviors of the coalescence and connection process between two and even three single-film bubbles are studied, and the cases with bubbles of different sizes are also included. Furthermore, the classic plateau structure in the foam system is reproduced and numerically proved to be in the steady state for multi-bubble connections.

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

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

Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to themore » proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.« less

Worldline approach for numerical computation of electromagnetic Casimir energies: Scalar field coupled to magnetodielectric media

DOE PAGES

Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.

2016-10-12

Here, we present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to themore » proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. Lastly, while these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.« less

Numerical modeling of the transitional boundary layer over a flat plate

NASA Astrophysics Data System (ADS)

Ivanov, Dimitry; Chorny, Andrei

2015-11-01

Our example is connected with fundamental research on understanding how an initially laminar boundary layer becomes turbulent. We have chosen the flow over a flat plate as a prototype for boundary-layer flows around bodies. Special attention was paid to the near-wall region in order to capture all levels of the boundary layer. In this study, the numerical software package OpenFOAM has been used in order to solve the flow field. The results were used in a comparative study with data obtained from Large Eddy Simulation (LES). The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. Presently this model is extended to the LES of the zero-pressure gradient, flat-plate turbulent boundary layer. In current study the time discretization is based on a second order Crank-Nicolson/Adams-Bashforth method. LES solver using Smagorinsky and the one-equation LES turbulence models. The transition models significantly improve the prediction of the onset location compared to the fully turbulent models.LES methods appear to be the most promising new tool for the design and analysis of flow devices including transition regions of the turbulent flow.

Effective Thermal Property Estimation of Unitary Pebble Beds Based on a CFD-DEM Coupled Method for a Fusion Blanket

NASA Astrophysics Data System (ADS)

Chen, Lei; Chen, Youhua; Huang, Kai; Liu, Songlin

2015-12-01

Lithium ceramic pebble beds have been considered in the solid blanket design for fusion reactors. To characterize the fusion solid blanket thermal performance, studies of the effective thermal properties, i.e. the effective thermal conductivity and heat transfer coefficient, of the pebble beds are necessary. In this paper, a 3D computational fluid dynamics discrete element method (CFD-DEM) coupled numerical model was proposed to simulate heat transfer and thereby estimate the effective thermal properties. The DEM was applied to produce a geometric topology of a prototypical blanket pebble bed by directly simulating the contact state of each individual particle using basic interaction laws. Based on this geometric topology, a CFD model was built to analyze the temperature distribution and obtain the effective thermal properties. The current numerical model was shown to be in good agreement with the existing experimental data for effective thermal conductivity available in the literature. supported by National Special Project for Magnetic Confined Nuclear Fusion Energy of China (Nos. 2013GB108004, 2015GB108002, 2014GB122000 and 2014GB119000), and National Natural Science Foundation of China (No. 11175207)

On the application of hybrid meshes in hydraulic machinery CFD simulations

NASA Astrophysics Data System (ADS)

Schlipf, M.; Tismer, A.; Riedelbauch, S.

2016-11-01

The application of two different hybrid mesh types for the simulation of a Francis runner for automated optimization processes without user input is investigated. Those mesh types are applied to simplified test cases such as flow around NACA airfoils to identify the special mesh resolution effects with reduced complexity, like rotating cascade flows, as they occur in a turbomachine runner channel. The analysis includes the application of those different meshes on the geometries by keeping defined quality criteria and exploring the influences on the simulation results. All results are compared with reference values gained by simulations with blockstructured hexahedron meshes and the same numerical scheme. This avoids additional inaccuracies caused by further numerical and experimental measurement methods. The results show that a simulation with hybrid meshes built up by a blockstructured domain with hexahedrons around the blade in combination with a tetrahedral far field in the channel is sufficient to get results which are almost as accurate as the results gained by the reference simulation. Furthermore this method is robust enough for automated processes without user input and enables comparable meshes in size, distribution and quality for different similar geometries as occurring in optimization processes.

Eigensolutions of nonviscously damped systems based on the fixed-point iteration

NASA Astrophysics Data System (ADS)

Lázaro, Mario

2018-03-01

In this paper, nonviscous, nonproportional, symmetric vibrating structures are considered. Nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions. Solutions of the free motion equation leads to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices, this latter as dependent on frequency. Viscous damping can be considered as a particular case, involving damping forces as function of the instantaneous velocity of the degrees of freedom. In this work, a new numerical procedure to compute eigensolutions is proposed. The method is based on the construction of certain recursive functions which, under a iterative scheme, allow to reach eigenvalues and eigenvectors simultaneously and avoiding computation of eigensensitivities. Eigenvalues can be read then as fixed-points of those functions. A deep analysis of the convergence is carried out, focusing specially on relating the convergence conditions and error-decay rate to the damping model features, such as the nonproportionality and the viscoelasticity. The method is validated using two 6 degrees of freedom numerical examples involving both nonviscous and viscous damping and a continuous system with a local nonviscous damper. The convergence and the sequences behavior are in agreement with the results foreseen by the theory.

Optimization-based mesh correction with volume and convexity constraints

DOE PAGES

D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; ...

2016-02-24

In this study, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimizationmore » problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.« less

A Decentralized Eigenvalue Computation Method for Spectrum Sensing Based on Average Consensus

NASA Astrophysics Data System (ADS)

Mohammadi, Jafar; Limmer, Steffen; Stańczak, Sławomir

2016-07-01

This paper considers eigenvalue estimation for the decentralized inference problem for spectrum sensing. We propose a decentralized eigenvalue computation algorithm based on the power method, which is referred to as generalized power method GPM; it is capable of estimating the eigenvalues of a given covariance matrix under certain conditions. Furthermore, we have developed a decentralized implementation of GPM by splitting the iterative operations into local and global computation tasks. The global tasks require data exchange to be performed among the nodes. For this task, we apply an average consensus algorithm to efficiently perform the global computations. As a special case, we consider a structured graph that is a tree with clusters of nodes at its leaves. For an accelerated distributed implementation, we propose to use computation over multiple access channel (CoMAC) as a building block of the algorithm. Numerical simulations are provided to illustrate the performance of the two algorithms.

A Least-Squares Finite Element Method for Electromagnetic Scattering Problems

NASA Technical Reports Server (NTRS)

Wu, Jie; Jiang, Bo-nan

1996-01-01

The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems.

Tacky COC: a solvent bonding technique for fabrication of microfluidic systems

NASA Astrophysics Data System (ADS)

Keller, Nico; Nargang, Tobias M.; Helmer, Dorothea; Rapp, Bastian E.

2016-03-01

The academic community knows cyclic olefin copolymer (COC) as a well suited material for microfluidic applications because COC has numerous interesting properties such as high transmittance, good chemical resistance and good biocompatibility. Here we present a fast and cost-effective method for bonding of two COC substrates: exposure to appropriate solvents gives a tacky COC surface which when brought in contact with untreated COC forms a strong and optical clear bond. The bonding process is carried out at room temperature and takes less than three minutes which makes it significantly faster than currently described methods: This method does not require special lab equipment such as hot plates or hydraulic presses. The mild conditions of the bond process also allow for such "tacky COC" lids to be used for sealing of microfluidic chips containing immobilized protein patterns which is of high interest for immunodiagnostic testing inside microfluidic chips.

Simulations of Scatterometry Down to 22 nm Structure Sizes and Beyond with Special Emphasis on LER

NASA Astrophysics Data System (ADS)

Osten, W.; Ferreras Paz, V.; Frenner, K.; Schuster, T.; Bloess, H.

2009-09-01

In recent years, scatterometry has become one of the most commonly used methods for CD metrology. With decreasing structure size for future technology nodes, the search for optimized scatterometry measurement configurations gets more important to exploit maximum sensitivity. As widespread industrial scatterometry tools mainly still use a pre-set measurement configuration, there are still free parameters to improve sensitivity. Our current work uses a simulation based approach to predict and optimize sensitivity of future technology nodes. Since line edge roughness is getting important for such small structures, these imperfections of the periodic continuation cannot be neglected. Using fourier methods like e.g. rigorous coupled wave approach (RCWA) for diffraction calculus, nonperiodic features are hard to reach. We show that in this field certain types of fieldstitching methods show nice numerical behaviour and lead to useful results.

ULTRA-SHARP solution of the Smith-Hutton problem

NASA Technical Reports Server (NTRS)

Leonard, B. P.; Mokhtari, Simin

1992-01-01

Highly convective scalar transport involving near-discontinuities and strong streamline curvature was addressed in a paper by Smith and Hutton in 1982, comparing several different convection schemes applied to a specially devised test problem. First order methods showed significant artificial diffusion, whereas higher order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low order artificially diffusive schemes, especially in the numerical heat transfer industry. The present paper describes an alternate strategy of using non-artificially diffusive high order methods, while maintaining strictly monotonic transitions through the use of simple flux limited constraints. Limited third order upwinding is usually found to be the most cost effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

Unsteady two dimensional airloads acting on oscillating thin airfoils in subsonic ventilated wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J.; Golberg, M.

1978-01-01

The numerical calculation of unsteady two dimensional airloads which act upon thin airfoils in subsonic ventilated wind tunnels was studied. Neglecting certain quadrature errors, Bland's collocation method is rigorously proved to converge to the mathematically exact solution of Bland's integral equation, and a three way equivalence was established between collocation, Galerkin's method and least squares whenever the collocation points are chosen to be the nodes of the quadrature rule used for Galerkin's method. A computer program displayed convergence with respect to the number of pressure basis functions employed, and agreement with known special cases was demonstrated. Results are obtained for the combined effects of wind tunnel wall ventilation and wind tunnel depth to airfoil chord ratio, and for acoustic resonance between the airfoil and wind tunnel walls. A boundary condition is proposed for permeable walls through which mass flow rate is proportional to pressure jump.

Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian-Eulerian hydrodynamics in 2D rz - Cylindrical coordinates

NASA Astrophysics Data System (ADS)

Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail

2014-07-01

We present a new discretization for 2D arbitrary Lagrangian-Eulerian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic Lagrangian hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the Lagrangian equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for Lagrangian equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary Lagrangian-Eulerian algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a local constrained-optimization-based approach for each zone to find the subzonal mass fluxes. In this paper we give a systematic and complete description of the algorithm for the axisymmetric case and provide justification for our approach. The ALE algorithm conserves total energy on arbitrary meshes and preserves symmetry when remapping from one equiangular polar mesh to another. The principal contributions of this part of the paper are the extension of this algorithm to general polygonal meshes and 2D rz geometry with requirement of symmetry preservation on special meshes. We present numerical examples that demonstrate the robustness of the new ALE method on a variety of grids and test problems including polygonal meshes and some realistic experiments. We confirm the importance of conservation of total energy for correctly modeling shock waves.

Uniqueness of the Isotropic Frame and Usefulness of the Lorentz Transformation

NASA Astrophysics Data System (ADS)

Choi, Yang-Ho

2018-05-01

According to the postulates of the special theory of relativity (STR), physical quantities such as proper times and Doppler shifts can be obtained from any inertial frame by regarding it as isotropic. Nonetheless many inconsistencies arise from the postulates, as shown in this paper. However, there are numerous experimental results that agree with the predictions of STR. It is explained why they are accurate despite the inconsistencies. The Lorentz transformation (LT), unless subject to the postulates of STR, may be a useful method to approach physics problems. As an example to show the usefulness of LT, the problem of the generalized Sagnac effect is solved by utilizing it.

Overview of the CHarring Ablator Response (CHAR) Code

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Oliver, A. Brandon; Kirk, Benjamin S.; Salazar, Giovanni; Droba, Justin

2016-01-01

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation and contact interfaces, and example simulations are included. Finally, a discussion of ongoing development efforts is presented.

Overview of the CHarring Ablator Response (CHAR) Code

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Oliver, A. Brandon; Kirk, Benjamin S.; Salazar, Giovanni; Droba, Justin

2016-01-01

An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation, surface-to-surface radiation exchange, and flowfield coupling. Finally, a discussion of ongoing development efforts is presented.

A new scheme of general hybrid projective complete dislocated synchronization

NASA Astrophysics Data System (ADS)

Chu, Yan-dong; Chang, Ying-Xiang; An, Xin-lei; Yu, Jian-Ning; Zhang, Jian-Gang

2011-03-01

Based on the Lyapunov stability theorem, a new type of chaos synchronization, general hybrid projective complete dislocated synchronization (GHPCDS), is proposed under the framework of drive-response systems. The difference between the GHPCDS and complete synchronization is that every state variable of drive system does not equal the corresponding state variable, but equal other ones of response system while evolving in time. The GHPCDS includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. As examples, the Lorenz chaotic system, Rössler chaotic system, hyperchaotic Chen system and hyperchaotic Lü system are discussed. Numerical simulations are given to show the effectiveness of these methods.

The museum maze in oral pathology demystifed: part II.

PubMed

Patil, Shankargouda; Rao, Roopa S; Ganavi, Bs

2013-09-01

Museum technology is perpetually changing due to current requirements and added inventions for our comfort and furbished display of specimens. Hence numerous methods of specimen preservation have been put on trial by diverse people in the medical feld as are the inventions. But only few have caught people's interest and are popularized today. This part provides unique insights into specialized custom-made techniques, evolution of recent advances like plastination and virtual museum that have popularized as visual delights. Plastination gives handy, perennial life-like acrylic specimens, whereas virtual museum takes museum feld to the electronic era making use of computers and virtual environment.

A review of carrier thermoelectric-transport theory in organic semiconductors.

PubMed

Lu, Nianduan; Li, Ling; Liu, Ming

2016-07-20

Carrier thermoelectric-transport theory has recently become of growing interest and numerous thermoelectric-transport models have been proposed for organic semiconductors, due to pressing current issues involving energy production and the environment. The purpose of this review is to provide a theoretical description of the thermoelectric Seebeck effect in organic semiconductors. Special attention is devoted to the carrier concentration, temperature, polaron effect and dipole effect dependence of the Seebeck effect and its relationship to hopping transport theory. Furthermore, various theoretical methods are used to discuss carrier thermoelectric transport. Finally, an outlook of the remaining challenges ahead for future theoretical research is provided.

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

Hewett, D.W.; Yu-Jiuan Chen

The authors describe how they hold onto orthogonal mesh discretization when dealing with curved boundaries. Special difference operators were constructed to approximate numerical zones split by the domain boundary; the operators are particularly simple for this rectangular mesh. The authors demonstrated that this simple numerical approach, termed Dynamic Alternating Direction Implicit, turned out to be considerably more efficient than more complex grid-adaptive algorithms that were tried previously.

Developmental Specialization in the Right Intraparietal Sulcus for the Abstract Representation of Numerical Magnitude

ERIC Educational Resources Information Center

Holloway, Ian D.; Ansari, Daniel

2010-01-01

Because number is an abstract quality of a set, the way in which a number is externally represented does not change its quantitative meaning. In this study, we examined the development of the brain regions that support format-independent representation of numerical magnitude. We asked children and adults to perform both symbolic (Hindu-Arabic…

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

Bailey, David

In the January 2002 edition of SIAM News, Nick Trefethen announced the '$100, 100-Digit Challenge'. In this note he presented ten easy-to-state but hard-to-solve problems of numerical analysis, and challenged readers to find each answer to ten-digit accuracy. Trefethen closed with the enticing comment: 'Hint: They're hard! If anyone gets 50 digits in total, I will be impressed.' This challenge obviously struck a chord in hundreds of numerical mathematicians worldwide, as 94 teams from 25 nations later submitted entries. Many of these submissions exceeded the target of 50 correct digits; in fact, 20 teams achieved a perfect score of 100more » correct digits. Trefethen had offered $100 for the best submission. Given the overwhelming response, a generous donor (William Browning, founder of Applied Mathematics, Inc.) provided additional funds to provide a $100 award to each of the 20 winning teams. Soon after the results were out, four participants, each from a winning team, got together and agreed to write a book about the problems and their solutions. The team is truly international: Bornemann is from Germany, Laurie is from South Africa, Wagon is from the USA, and Waldvogel is from Switzerland. This book provides some mathematical background for each problem, and then shows in detail how each of them can be solved. In fact, multiple solution techniques are mentioned in each case. The book describes how to extend these solutions to much larger problems and much higher numeric precision (hundreds or thousands of digit accuracy). The authors also show how to compute error bounds for the results, so that one can say with confidence that one's results are accurate to the level stated. Numerous numerical software tools are demonstrated in the process, including the commercial products Mathematica, Maple and Matlab. Computer programs that perform many of the algorithms mentioned in the book are provided, both in an appendix to the book and on a website. In the process, the authors take the reader on a wide-ranging tour of modern numerical mathematics, with enough background material so that even readers with little or no training in numerical analysis can follow. Here is a list of just a few of the topics visited: numerical quadrature (i.e., numerical integration), series summation, sequence extrapolation, contour integration, Fourier integrals, high-precision arithmetic, interval arithmetic, symbolic computing, numerical linear algebra, perturbation theory, Euler-Maclaurin summation, global minimization, eigenvalue methods, evolutionary algorithms, matrix preconditioning, random walks, special functions, elliptic functions, Monte-Carlo methods, and numerical differentiation.« less

Synchronization of coupled stochastic complex-valued dynamical networks with time-varying delays via aperiodically intermittent adaptive control

NASA Astrophysics Data System (ADS)

Wang, Pengfei; Jin, Wei; Su, Huan

2018-04-01

This paper deals with the synchronization problem of a class of coupled stochastic complex-valued drive-response networks with time-varying delays via aperiodically intermittent adaptive control. Different from the previous works, the intermittent control is aperiodic and adaptive, and the restrictions on the control width and time delay are removed, which lead to a larger application scope for this control strategy. Then, based on the Lyapunov method and Kirchhoff's Matrix Tree Theorem as well as differential inequality techniques, several novel synchronization conditions are derived for the considered model. Specially, impulsive control is also considered, which can be seen as a special case of the aperiodically intermittent control when the control width tends to zero. And the corresponding synchronization criteria are given as well. As an application of the theoretical results, a class of stochastic complex-valued coupled oscillators with time-varying delays is studied, and the numerical simulations are also given to demonstrate the effectiveness of the control strategies.

Interaction of transient radiation in nongray gaseous systems

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Singh, D. J.

1987-01-01

A general formulation is presented to investigate the transient radiative interaction in nongray absorbing-emitting species between two parallel plates. Depending on the desired sophistication and accuracy, any nongray absorption model from line-by-line models to the wide band model correlations can be employed in the formulation to investigate the radiative interaction. Special attention is directed to investigate the radiative interaction in a system initially at a uniform reference temperature and suddenly the temperature of the bottom plate is reduced to a lower but constant temperature. The interaction is considered for the case of radiative equilibrium as well as for combined radiation and conduction. General as well as limiting forms of the governing equations are presented and solutions are obtained numerically by employing the method of variation of parameters. Specific results are obtained for CO, CO2, H2O, and OH. The information on species H2O and OH is of special interest for the proposed scramjet engine application. The results demonstrate the relative ability of different species for radiative interactions.

Developmental specialization in the right intraparietal sulcus for the abstract representation of numerical magnitude.

PubMed

Holloway, Ian D; Ansari, Daniel

2010-11-01

Because number is an abstract quality of a set, the way in which a number is externally represented does not change its quantitative meaning. In this study, we examined the development of the brain regions that support format-independent representation of numerical magnitude. We asked children and adults to perform both symbolic (Hindu-Arabic numerals) and nonsymbolic (arrays of squares) numerical comparison tasks as well as two control tasks while their brains were scanned using fMRI. In a preliminary analysis, we calculated the conjunction between symbolic and nonsymbolic numerical comparison. We then examined in which brain regions this conjunction differed between children and adults. This analysis revealed a large network of visual and parietal regions that showed greater activation in adults relative to children. In our primary analysis, we examined age-related differences in the conjunction of symbolic and nonsymbolic comparison after subtracting the control tasks. This analysis revealed a much more limited set of regions including the right inferior parietal lobe near the intraparietal sulcus. In addition to showing increased activation to both symbolic and nonsymbolic magnitudes over and above activation related to response selection, this region showed age-related differences in the distance effect. Our findings demonstrate that the format-independent representation of numerical magnitude in the right inferior parietal lobe is the product of developmental processes of cortical specialization and highlight the importance of using appropriate control tasks when conducting developmental neuroimaging studies.

Special Issue: NextGen Materials for 3D Printing.

PubMed

Chua, Chee Kai; Yeong, Wai Yee; An, Jia

2018-04-04

Only a handful of materials are well-established in three-dimensional (3D) printing and well-accepted in industrial manufacturing applications. However, recent advances in 3D printable materials have shown potential for enabling numerous novel applications in the future. This special issue, consisting of 2 reviews and 10 research articles, intends to explore the possible materials that could define next-generation 3D printing.

Building fast well-balanced two-stage numerical schemes for a model of two-phase flows

NASA Astrophysics Data System (ADS)

Thanh, Mai Duc

2014-06-01

We present a set of well-balanced two-stage schemes for an isentropic model of two-phase flows arisen from the modeling of deflagration-to-detonation transition in granular materials. The first stage is to absorb the source term in nonconservative form into equilibria. Then in the second stage, these equilibria will be composed into a numerical flux formed by using a convex combination of the numerical flux of a stable Lax-Friedrichs-type scheme and the one of a higher-order Richtmyer-type scheme. Numerical schemes constructed in such a way are expected to get the interesting property: they are fast and stable. Tests show that the method works out until the parameter takes on the value CFL, and so any value of the parameter between zero and this value is expected to work as well. All the schemes in this family are shown to capture stationary waves and preserves the positivity of the volume fractions. The special values of the parameter 0,1/2,1/(1+CFL), and CFL in this family define the Lax-Friedrichs-type, FAST1, FAST2, and FAST3 schemes, respectively. These schemes are shown to give a desirable accuracy. The errors and the CPU time of these schemes and the Roe-type scheme are calculated and compared. The constructed schemes are shown to be well-balanced and faster than the Roe-type scheme.

Motives of former interns in general practice for speciality-choice − Results of a cross-sectional study among graduates 2007 to 2012

PubMed Central

Abendroth, Jens; Schnell, Ute; Lichte, Thomas; Oemler, Matthias; Klement, Andreas

2014-01-01

Background: The influence of a final-year elective internship in general practice (IGP) on motives affecting graduates’ choice of specialty is the object of great public interest, yet still insufficiently evaluated. Longitudinal studies show the influence of numerous motives (e.g. work-life balance), but not following the IGP experience itself. Thus, we performed a cross-sectional questionnaire study of all graduates who completed the IGP in Saxony-Anhalt during 2007-2012 regarding their motives for choosing a speciality. Method: A standardized questionnaire was sent to 109 former interns in general practice. The questionnaire contained 29 items addressing three topics (personal attitudes, concept of personal and professional life, motives for speciality choice) and used single-choice and multiple-choice answers, as well as Likert scales. Correlation analysis was carried out by means of Kendall's tau. Results: The questionnaire reached 97 former interns, of which 45 (46%) responded. In the overall ranking of motives for speciality choice, family (71%), leisure time (66%) and job opportunities (48%) rated as more important than income (36%), mentoring (20%), status or scientific work (20%). Only 29% of the respondents stated that their speciality choice was changed by the IGP. If the speciality choice was already established before the IGP, the influence of the IGP on speciality choice was significantly low (r=-.5; p<.01). However, if the IGP had an influence on speciality choice, it was correlated with a new perception of general practice (r=.36; p<.01). This new perception was associated with a positive influence of the medical teacher during the IGP. Conclusion: The final-year IGP is an opportunity to change the perception of general practice in students who are still undecided. This can lead to different speciality choices in a subgroup. Personal attitudes and concepts of personal life and career were also important factors affecting speciality choice. The aspects of the positive influence exerted by medical teachers on those students who are still undecided during the IGP should be carefully evaluated. PMID:24575153

MHD effects and heat transfer for the UCM fluid along with Joule heating and thermal radiation using Cattaneo-Christov heat flux model

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

Shah, S., E-mail: sajidshah313@yahoo.com; Hussain, S.; Sagheer, M.

2016-08-15

Present study examines the numerical analysis of MHD flow of Maxwell fluid with thermal radiation and Joule heating by considering the recently developed Cattaneo-Christov heat flux model which explains the time relaxation characteristics for the heat flux. The objective is to analyze the governing parameters such as viscoelastic fluid parameter, Magnetic parameter, Eckert and Prandtl number’s impact on the velocity and temperature profiles through graphs and tables. Suitable similarity transformations have been used to reduce the formulated PDEs into a system of coupled non-linear ODEs. Shooting technique has been invoked for finding the numerical solutions of the dimensionless velocity andmore » temperature profiles. Additionally, the MATLAB built-in routine bvp4c has also been used to verify and strengthen the results obtained by shooting method. From some special cases of the present work, a comparison with the previously published results has been presented.« less

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

Khan, Masood; Malik, Rabia, E-mail: rabiamalik.qau@gmail.com; Munir, Asif

In this article, the mixed convective heat transfer to Sisko fluid over a radially stretching surface in the presence of convective boundary conditions is investigated. The viscous dissipation and thermal radiation effects are also taken into account. The suitable transformations are applied to convert the governing partial differential equations into a set of nonlinear coupled ordinary differential equations. The analytical solution of the governing problem is obtained by using the homotopy analysis method (HAM). Additionally, these analytical results are compared with the numerical results obtained by the shooting technique. The obtained results for the velocity and temperature are analyzed graphicallymore » for several physical parameters for the assisting and opposing flows. It is found that the effect of buoyancy parameter is more prominent in case of the assisting flow as compared to the opposing flow. Further, in tabular form the numerical values are given for the local skin friction coefficient and local Nusselt number. A remarkable agreement is noticed by comparing the present results with the results reported in the literature as a special case.« less

Linear theory of boundary effects in open wind tunnels with finite jet lengths

NASA Technical Reports Server (NTRS)

Katzoff, S; Gardner, Clifford S; Diesendruck, Leo; Eisenstadt, Bertram J

1950-01-01

In the first part, the boundary conditions for an open wind tunnel (incompressible flow) are examined with special reference to the effects of the closed entrance and exit sections. Basic conditions are that the velocity must be continuous at the entrance lip and that the velocities in the upstream and downstream closed portions must be equal. In the second part, solutions are derived for four types of two-dimensional open tunnels, including one in which the pressures on the two free surfaces are not equal. Numerical results are given for every case. In general, if the lifting element is more than half the tunnel height from the inlet, the boundary effect at the lifting element is the same as for an infinitely long open tunnel. In the third part, a general method is given for calculating the boundary effect in an open circular wind tunnel of finite jet length. Numerical results are given for a lifting element concentrate at a point on the axis.

BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework

DOE PAGES

Wang, Qi; Sprague, Michael A.; Jonkman, Jason; ...

2017-03-14

Here, this paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre-spectral-finite-element (LSFE) method. The displacement-based geometrically exact beam theory is presented, and the special treatment of three-dimensional rotation parameters is reviewed. An LSFE is a high-order finite element with nodes located at the Gauss-Legendre-Lobatto points. These elements can be an order of magnitude more computationally efficient than low-order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades within the FAST aeroelastic engineering model. The frameworkmore » allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand-alone high-fidelity beam tool.« less

FE-simulation of hot forging with an integrated heat treatment with the objective of residual stress prediction

NASA Astrophysics Data System (ADS)

Behrens, Bernd-Arno; Chugreeva, Anna; Chugreev, Alexander

2018-05-01

Hot forming as a coupled thermo-mechanical process comprises numerous material phenomena with a corresponding impact on the material behavior during and after the forming process as well as on the final component performance. In this context, a realistic FE-simulation requires reliable mathematical models as well as detailed thermo-mechanical material data. This paper presents experimental and numerical results focused on the FE-based simulation of a hot forging process with a subsequent heat treatment step aiming at the prediction of the final mechanical properties and residual stress state in the forged component made of low alloy CrMo-steel DIN 42CrMo4. For this purpose, hot forging experiments of connecting rod geometry with a corresponding metallographic analysis and x-ray residual stress measurements have been carried out. For the coupled thermo-mechanical-metallurgical FE-simulations, a special user-defined material model based on the additive strain decomposition method and implemented in Simufact Forming via MSC.Marc solver features has been used.

Study on the extrusion of nickel-based spark plug electrodes by numerical simulation

NASA Astrophysics Data System (ADS)

Saby, Q.; Courbon, C.; Salvatore, F.; Fabre, D.; Romeyer, F.

2018-05-01

Interest in metal forming simulation has grown rapidly during the last decades and is now well established even in industry. It provides a flexible and relatively cheap method to perform sensitivity analyses, getting a better insight into the forming process and use it as an optimisation tool. As far as wear is concerned, numerical simulation can be seen as a relevant approach to assess the thermomechanical loadings applied to the active die surface and therefore predict their wear behaviour. In this study, a Finite-Element (FE) based model has been developed in order to investigate the cold forming process of a nickel-based sparkplug electrode. A fully thermo-mechanically coupled implicit formulation has been used in order to model the forward extrusion step with a special emphasis on the contact conditions at the workpiece-die interface. Contact pressure, relative sliding velocity and temperature profiles have been extracted versus time and qualitatively compared to the wear phenomena observed on the worn production dies.

BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework

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

Wang, Qi; Sprague, Michael A.; Jonkman, Jason

Here, this paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre-spectral-finite-element (LSFE) method. The displacement-based geometrically exact beam theory is presented, and the special treatment of three-dimensional rotation parameters is reviewed. An LSFE is a high-order finite element with nodes located at the Gauss-Legendre-Lobatto points. These elements can be an order of magnitude more computationally efficient than low-order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades within the FAST aeroelastic engineering model. The frameworkmore » allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand-alone high-fidelity beam tool.« less

Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

NASA Astrophysics Data System (ADS)

Vogman, Genia

Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space coordinates present a new development in the field of computational plasma physics. A fourth-order finite-volume method for solving the Vlasov-Maxwell equation system is presented first for Cartesian and then for cylindrical phase space coordinates. Special attention is given to the treatment of the discrete primary variables and to the quadrature rule for evaluating the surface and line integrals that appear in the governing equations. The finite-volume treatment of conducting wall and axis boundaries is particularly nuanced when it comes to phase space coordinates, and is described in detail. In addition to the mechanics of each part of the finite-volume discretization in the two different coordinate systems, the complete algorithm is also presented. The Cartesian coordinate discretization is applied to several well-known test problems. Since even linear analysis of kinetic theory governing equations is complicated on account of velocity being an independent coordinate, few analytic or semi-analytic predictions exist. Benchmarks are particularly scarce for configurations that have magnetic fields and involve more than two phase space dimensions. Ensuring that simulations are true to the physics thus presents a difficulty in the development of robust numerical methods. The research described in this dissertation addresses this challenge through the development of more complete physics-based benchmarks based on the Dory-Guest-Harris instability. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. Furthermore, a specialized form of perturbation is shown to strongly excite the fastest growing mode. The fourth-order finite-volume algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. The Dory-Guest-Harris instability benchmark extends the scope of standard test problems by providing a substantive means of validating continuum kinetic simulations of warm magnetized plasmas in higher-dimensional 3D ( x,vx,vy) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented. The cylindrical coordinate finite-volume discretization is applied to model axisymmetric systems. Since mitigating the prohibitive computational cost of simulating six dimensions is another challenge in phase space simulations, the development of a robust means of exploiting symmetry is a major advance when it comes to numerically solving the Vlasov-Maxwell equation system. The discretization is applied to a uniform distribution function to assess the nature of the singularity at the axis, and is demonstrated to converge at fourth-order accuracy. The numerical method is then applied to simulate electrostatic ion confinement in an axisymmetric Z-pinch configuration. To the author's knowledge this presents the first instance of a conservative finite-volume discretization of the cylindrical coordinate Vlasov equation. The computational framework for the Vlasov-Maxwell solver is described, and an outlook for future research is presented.

Novel residual-based large eddy simulation turbulence models for incompressible magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Sondak, David

The goal of this work was to develop, introduce, and test a promising computational paradigm for the development of turbulence models for incompressible magnetohydrodynamics (MHD). MHD governs the behavior of an electrically conducting fluid in the presence of an external electromagnetic (EM) field. The incompressible MHD model is used in many engineering and scientific disciplines from the development of nuclear fusion as a sustainable energy source to the study of space weather and solar physics. Many interesting MHD systems exhibit the phenomenon of turbulence which remains an elusive problem from all scientific perspectives. This work focuses on the computational perspective and proposes techniques that enable the study of systems involving MHD turbulence. Direct numerical simulation (DNS) is not a feasible approach for studying MHD turbulence. In this work, turbulence models for incompressible MHD were developed from the variational multiscale (VMS) formulation wherein the solution fields were decomposed into resolved and unresolved components. The unresolved components were modeled with a term that is proportional to the residual of the resolved scales. Two additional MHD models were developed based off of the VMS formulation: a residual-based eddy viscosity (RBEV) model and a mixed model that partners the VMS formulation with the RBEV model. These models are endowed with several special numerical and physics features. Included in the numerical features is the internal numerical consistency of each of the models. Physically, the new models are able to capture desirable MHD physics such as the inverse cascade of magnetic energy and the subgrid dynamo effect. The models were tested with a Fourier-spectral numerical method and the finite element method (FEM). The primary test problem was the Taylor-Green vortex. Results comparing the performance of the new models to DNS were obtained. The performance of the new models was compared to classic and cutting-edge dynamic Smagorinsky eddy viscosity (DSEV) models. The new models typically outperform the classical models.

Quantifying Variations In Multi-parameter Models With The Photon Clean Method (PCM) And Bootstrap Methods

NASA Astrophysics Data System (ADS)

Carpenter, Matthew H.; Jernigan, J. G.

2007-05-01

We present examples of an analysis progression consisting of a synthesis of the Photon Clean Method (Carpenter, Jernigan, Brown, Beiersdorfer 2007) and bootstrap methods to quantify errors and variations in many-parameter models. The Photon Clean Method (PCM) works well for model spaces with large numbers of parameters proportional to the number of photons, therefore a Monte Carlo paradigm is a natural numerical approach. Consequently, PCM, an "inverse Monte-Carlo" method, requires a new approach for quantifying errors as compared to common analysis methods for fitting models of low dimensionality. This presentation will explore the methodology and presentation of analysis results derived from a variety of public data sets, including observations with XMM-Newton, Chandra, and other NASA missions. Special attention is given to the visualization of both data and models including dynamic interactive presentations. This work was performed under the auspices of the Department of Energy under contract No. W-7405-Eng-48. We thank Peter Beiersdorfer and Greg Brown for their support of this technical portion of a larger program related to science with the LLNL EBIT program.

Development of Pelton turbine using numerical simulation

NASA Astrophysics Data System (ADS)

Patel, K.; Patel, B.; Yadav, M.; Foggia, T.

2010-08-01

This paper describes recent research and development activities in the field of Pelton turbine design. Flow inside Pelton turbine is most complex due to multiphase (mixture of air and water) and free surface in nature. Numerical calculation is useful to understand flow physics as well as effect of geometry on flow. The optimized design is obtained using in-house special optimization loop. Either single phase or two phase unsteady numerical calculation could be performed. Numerical results are used to visualize the flow pattern in the water passage and to predict performance of Pelton turbine at full load as well as at part load. Model tests are conducted to determine performance of turbine and it shows good agreement with numerically predicted performance.

Preface to advances in numerical simulation of plasmas

NASA Astrophysics Data System (ADS)

Parker, Scott E.; Chacon, Luis

2016-10-01

This Journal of Computational Physics Special Issue, titled ;Advances in Numerical Simulation of Plasmas,; presents a snapshot of the international state of the art in the field of computational plasma physics. The articles herein are a subset of the topics presented as invited talks at the 24th International Conference on the Numerical Simulation of Plasmas (ICNSP), August 12-14, 2015 in Golden, Colorado. The choice of papers was highly selective. The ICNSP is held every other year and is the premier scientific meeting in the field of computational plasma physics.

Nondestructive Inspection System for Special Nuclear Material Using Inertial Electrostatic Confinement Fusion Neutrons and Laser Compton Scattering Gamma-Rays

NASA Astrophysics Data System (ADS)

Ohgaki, H.; Daito, I.; Zen, H.; Kii, T.; Masuda, K.; Misawa, T.; Hajima, R.; Hayakawa, T.; Shizuma, T.; Kando, M.; Fujimoto, S.

2017-07-01

A Neutron/Gamma-ray combined inspection system for hidden special nuclear materials (SNMs) in cargo containers has been developed under a program of Japan Science and Technology Agency in Japan. This inspection system consists of an active neutron-detection system for fast screening and a laser Compton backscattering gamma-ray source in coupling with nuclear resonance fluorescence (NRF) method for precise inspection. The inertial electrostatic confinement fusion device has been adopted as a neutron source and two neutron-detection methods, delayed neutron noise analysis method and high-energy neutron-detection method, have been developed to realize the fast screening system. The prototype system has been constructed and tested in the Reactor Research Institute, Kyoto University. For the generation of the laser Compton backscattering gamma-ray beam, a race track microtron accelerator has been used to reduce the size of the system. For the NRF measurement, an array of LaBr3(Ce) scintillation detectors has been adopted to realize a low-cost detection system. The prototype of the gamma-ray system has been demonstrated in the Kansai Photon Science Institute, National Institutes for Quantum and Radiological Science and Technology. By using numerical simulations based on the data taken from these prototype systems and the inspection-flow, the system designed by this program can detect 1 kg of highly enriched 235U (HEU) hidden in an empty 20-ft container within several minutes.

A generalized vortex lattice method for subsonic and supersonic flow applications

NASA Technical Reports Server (NTRS)

Miranda, L. R.; Elliot, R. D.; Baker, W. M.

1977-01-01

If the discrete vortex lattice is considered as an approximation to the surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vorticity-induced velocity field. The proper incorporation of this term to the velocity field generated by the discrete vortex lines renders the present vortex lattice method valid for supersonic flow. Special techniques for simulating nonzero thickness lifting surfaces and fusiform bodies with vortex lattice elements are included. Thickness effects of wing-like components are simulated by a double (biplanar) vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentrical cylindrical surfaces. The analysis of sideslip effects by the subject method is described. Numerical considerations peculiar to the application of these techniques are also discussed. The method has been implemented in a digital computer code. A users manual is included along with a complete FORTRAN compilation, an executed case, and conversion programs for transforming input for the NASA wave drag program.

BOOK REVIEW: Vortex Methods: Theory and Practice

NASA Astrophysics Data System (ADS)

Cottet, G.-H.; Koumoutsakos, P. D.

2001-03-01

The book Vortex Methods: Theory and Practice presents a comprehensive account of the numerical technique for solving fluid flow problems. It provides a very nice balance between the theoretical development and analysis of the various techniques and their practical implementation. In fact, the presentation of the rigorous mathematical analysis of these methods instills confidence in their implementation. The book goes into some detail on the more recent developments that attempt to account for viscous effects, in particular the presence of viscous boundary layers in some flows of interest. The presentation is very readable, with most points illustrated with well-chosen examples, some quite sophisticated. It is a very worthy reference book that should appeal to a large body of readers, from those interested in the mathematical analysis of the methods to practitioners of computational fluid dynamics. The use of the book as a text is compromised by its lack of exercises for students, but it could form the basis of a graduate special topics course. Juan Lopez

Review of Batteryless Wireless Sensors Using Additively Manufactured Microwave Resonators.

PubMed

Memon, Muhammad Usman; Lim, Sungjoon

2017-09-09

The significant improvements observed in the field of bulk-production of printed microchip technologies in the past decade have allowed the fabrication of microchip printing on numerous materials including organic and flexible substrates. Printed sensors and electronics are of significant interest owing to the fast and low-cost fabrication techniques used in their fabrication. The increasing amount of research and deployment of specially printed electronic sensors in a number of applications demonstrates the immense attention paid by researchers to this topic in the pursuit of achieving wider-scale electronics on different dielectric materials. Although there are many traditional methods for fabricating radio frequency (RF) components, they are time-consuming, expensive, complicated, and require more power for operation than additive fabrication methods. This paper serves as a summary/review of improvements made to the additive printing technologies. The article focuses on three recently developed printing methods for the fabrication of wireless sensors operating at microwave frequencies. The fabrication methods discussed include inkjet printing, three-dimensional (3D) printing, and screen printing.

Neural image analysis in the process of quality assessment: domestic pig oocytes

NASA Astrophysics Data System (ADS)

Boniecki, P.; Przybył, J.; Kuzimska, T.; Mueller, W.; Raba, B.; Lewicki, A.; Przybył, K.; Zaborowicz, M.; Koszela, K.

2014-04-01

The questions related to quality classification of animal oocytes are explored by numerous scientific and research centres. This research is important, particularly in the context of improving the breeding value of farm animals. The methods leading to the stimulation of normal development of a larger number of fertilised animal oocytes in extracorporeal conditions are of special importance. Growing interest in the techniques of supported reproduction resulted in searching for new, increasingly effective methods for quality assessment of mammalian gametes and embryos. Progress in the production of in vitro animal embryos in fact depends on proper classification of obtained oocytes. The aim of this paper was the development of an original method for quality assessment of oocytes, performed on the basis of their graphical presentation in the form of microscopic digital images. The classification process was implemented on the basis of the information coded in the form of microphotographic pictures of the oocytes of domestic pig, using the modern methods of neural image analysis.

Review of Batteryless Wireless Sensors Using Additively Manufactured Microwave Resonators

PubMed Central

2017-01-01

The significant improvements observed in the field of bulk-production of printed microchip technologies in the past decade have allowed the fabrication of microchip printing on numerous materials including organic and flexible substrates. Printed sensors and electronics are of significant interest owing to the fast and low-cost fabrication techniques used in their fabrication. The increasing amount of research and deployment of specially printed electronic sensors in a number of applications demonstrates the immense attention paid by researchers to this topic in the pursuit of achieving wider-scale electronics on different dielectric materials. Although there are many traditional methods for fabricating radio frequency (RF) components, they are time-consuming, expensive, complicated, and require more power for operation than additive fabrication methods. This paper serves as a summary/review of improvements made to the additive printing technologies. The article focuses on three recently developed printing methods for the fabrication of wireless sensors operating at microwave frequencies. The fabrication methods discussed include inkjet printing, three-dimensional (3D) printing, and screen printing. PMID:28891947

An implicit spatial and high-order temporal finite difference scheme for 2D acoustic modelling

NASA Astrophysics Data System (ADS)

Wang, Enjiang; Liu, Yang

2018-01-01

The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-Wendroff FD scheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields.

Least squares polynomial chaos expansion: A review of sampling strategies

NASA Astrophysics Data System (ADS)

Hadigol, Mohammad; Doostan, Alireza

2018-04-01

As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments (ODE), Gaussian quadratures, as well as more recent techniques, such as coherence-optimal and randomized quadratures are discussed. We also propose a hybrid sampling method, dubbed alphabetic-coherence-optimal, that employs the so-called alphabetic optimality criteria used in the context of ODE in conjunction with coherence-optimal samples. A comparison between the empirical performance of the selected sampling methods applied to three numerical examples, including high-order PCE's, high-dimensional problems, and low oversampling ratios, is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand. We observed that the alphabetic-coherence-optimal technique outperforms other sampling methods, specially when high-order ODE are employed and/or the oversampling ratio is low.

Viscous wing theory development. Volume 1: Analysis, method and results

NASA Technical Reports Server (NTRS)

Chow, R. R.; Melnik, R. E.; Marconi, F.; Steinhoff, J.

1986-01-01

Viscous transonic flows at large Reynolds numbers over 3-D wings were analyzed using a zonal viscid-inviscid interaction approach. A new numerical AFZ scheme was developed in conjunction with the finite volume formulation for the solution of the inviscid full-potential equation. A special far-field asymptotic boundary condition was developed and a second-order artificial viscosity included for an improved inviscid solution methodology. The integral method was used for the laminar/turbulent boundary layer and 3-D viscous wake calculation. The interaction calculation included the coupling conditions of the source flux due to the wing surface boundary layer, the flux jump due to the viscous wake, and the wake curvature effect. A method was also devised incorporating the 2-D trailing edge strong interaction solution for the normal pressure correction near the trailing edge region. A fully automated computer program was developed to perform the proposed method with one scalar version to be used on an IBM-3081 and two vectorized versions on Cray-1 and Cyber-205 computers.

F--Ray: A new algorithm for efficient transport of ionizing radiation

NASA Astrophysics Data System (ADS)

Mao, Yi; Zhang, J.; Wandelt, B. D.; Shapiro, P. R.; Iliev, I. T.

2014-04-01

We present a new algorithm for the 3D transport of ionizing radiation, called F2-Ray (Fast Fourier Ray-tracing method). The transfer of ionizing radiation with long mean free path in diffuse intergalactic gas poses a special challenge to standard numerical methods which transport the radiation in position space. Standard methods usually trace each individual ray until it is fully absorbed by the intervening gas. If the mean free path is long, the computational cost and memory load are likely to be prohibitive. We have developed an algorithm that overcomes these limitations and is, therefore, significantly more efficient. The method calculates the transfer of radiation collectively, using the Fast Fourier Transform to convert radiation between position and Fourier spaces, so the computational cost will not increase with the number of ionizing sources. The method also automatically combines parallel rays with the same frequency at the same grid cell, thereby minimizing the memory requirement. The method is explicitly photon-conserving, i.e. the depletion of ionizing photons is guaranteed to equal the photoionizations they caused, and explicitly obeys the periodic boundary condition, i.e. the escape of ionizing photons from one side of a simulation volume is guaranteed to be compensated by emitting the same amount of photons into the volume through the opposite side. Together, these features make it possible to numerically simulate the transfer of ionizing photons more efficiently than previous methods. Since ionizing radiation such as the X-ray is responsible for heating the intergalactic gas when first stars and quasars form at high redshifts, our method can be applied to simulate thermal distribution, in addition to cosmic reionization, in three-dimensional inhomogeneous cosmological density field.

A hybrid perturbation-Galerkin method for differential equations containing a parameter

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1989-01-01

A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

Symmetries and Boundary Conditions with a Twist

NASA Astrophysics Data System (ADS)

Zawadzki, Krissia; D'Amico, Irene; Oliveira, Luiz N.

2017-10-01

Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices. Independently of the envisioned application, special attention must be given to boundary condition, which may or may not preserve the symmetry of the infinite lattice. Here, we present a detailed study of the compatibility between boundary conditions and conservation laws. The conflict between open boundary conditions and momentum conservation is well understood, but we examine other symmetries, as well: we discuss gauge invariance, inversion, spin, and particle-hole symmetry and their compatibility with open, periodic, and twisted boundary conditions. In the interest of clarity, we develop the reasoning in the framework of the one-dimensional half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries. Our discussion includes analytical and numerical results. Our analytical survey shows that, as a rule, boundary conditions break one or more symmetries of the infinite-lattice Hamiltonian. The exception is twisted boundary condition with the special torsion Θ = πL/2, where L is the lattice size. Our numerical results for the ground-state energy at half-filling and the energy gap for L = 2-7 show how the breaking of symmetry affects the convergence to the L → ∞ limit. We compare the computed energies and gaps with the exact results for the infinite lattice drawn from the Bethe-Ansatz solution. The deviations are boundary-condition dependent. The special torsion yields more rapid convergence than open or periodic boundary conditions. For sizes as small as L = 7, the numerical results for twisted condition are very close to the L → ∞ limit. We also discuss the ground-state electronic density and magnetization at half filling under the three boundary conditions.

Special Issue: NextGen Materials for 3D Printing

PubMed Central

Yeong, Wai Yee

2018-01-01

Only a handful of materials are well-established in three-dimensional (3D) printing and well-accepted in industrial manufacturing applications. However, recent advances in 3D printable materials have shown potential for enabling numerous novel applications in the future. This special issue, consisting of 2 reviews and 10 research articles, intends to explore the possible materials that could define next-generation 3D printing. PMID:29617311

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

PubMed

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Mathematical modeling of the stress-strain state of the outlet guide vane made of various materials

NASA Astrophysics Data System (ADS)

Grinev, M. A.; Anoshkin, A. N.; Pisarev, P. V.; Zuiko, V. Yu.; Shipunov, G. S.

2016-11-01

The present work is devoted to the detailed stress-strain analysis of the composite outlet guide vane (OGV) for aircraft engines with a special focus on areas with twisted layers where the initiation of high interlaminar stresses is most expected. Various polymer composite materials and reinforcing schemes are researched. The technological scheme of laying-out of anisotropic plies and the fastening method are taken into account in the model. The numerical simulation is carried out by the finite element method (FEM) with the ANSYS Workbench software. It is shown that interlaminar shear stresses are most dangerous. It is found that balanced carbon fiber reinforced plastic (CFRP) with the [0°/±45°] reinforcing scheme allows us to provide the double strength margin under working loads for the developed OGV.

Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

NASA Astrophysics Data System (ADS)

Klimczak, Marek; Cecot, Witold

2018-01-01

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

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

Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.

2014-02-15

Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to variousmore » forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.« less

Randomized Controlled Trial of a Special Acupuncture Technique for Pain after Thoracotomy

PubMed Central

Deng, Gary; Rusch, Valerie; Vickers, Andrew; Malhortra, Vivek; Ginex, Pamela; Downey, Robert; Bains, Manjit; Park, Bernard; Rizk, Nabil; Flores, Raja; Yeung, Simon; Cassileth, Barrie

2009-01-01

Objective To determine whether an acupuncture technique specially developed for a surgical oncology population (intervention) reduces pain or analgesic use after thoracotomy compared to a sham acupuncture technique (control). Methods One hundred and sixty two cancer patients undergoing thoracotomy were randomized to group A) preoperative implantation of small intradermal needles which were retained for 4 weeks or B) preoperative placement of sham needles at the same schedule. Numerical Rating Scale (NRS) of pain and total opioid use we evaluated during the in-patient stay; Brief Pain Inventory (BPI) and Medication Quantification Scale (MQS) were evaluated after discharge up to 3 months after the surgery. Results The principal analysis, a comparison of BPI pain intensity scores at the 30 day follow-up, showed no significant difference between the intervention and control group. Pain scores were marginally higher in the intervention group 0.05 (95% C.I.: 0.74, -0.64; p=0.9). There were also no statistically significant differences between groups for secondary endpoints, including chronic pain assessments at 60 and 90 days, in-patient pain, and medication use in hospital and after discharge. Conclusion A special acupuncture technique as provided in this study did not reduce pain or use of pain medication after thoracotomy more than a sham technique. PMID:19114190

Thermal equilibrium and statistical thermometers in special relativity.

PubMed

Cubero, David; Casado-Pascual, Jesús; Dunkel, Jörn; Talkner, Peter; Hänggi, Peter

2007-10-26

There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Jüttner function as well as modifications thereof. Here we report results from fully relativistic one-dimensional molecular dynamics simulations that resolve the ambiguity. The numerical evidence unequivocally favors the Jüttner distribution. Moreover, our simulations illustrate that the concept of "thermal equilibrium" extends naturally to special relativity only if a many-particle system is spatially confined. They make evident that "temperature" can be statistically defined and measured in an observer frame independent way.

Long-range correlations in time series generated by time-fractional diffusion: A numerical study

NASA Astrophysics Data System (ADS)

Barbieri, Davide; Vivoli, Alessandro

2005-09-01

Time series models showing power law tails in autocorrelation functions are common in econometrics. A special non-Markovian model for such kind of time series is provided by the random walk introduced by Gorenflo et al. as a discretization of time fractional diffusion. The time series so obtained are analyzed here from a numerical point of view in terms of autocorrelations and covariance matrices.

The NASTRAN theoretical manual

NASA Technical Reports Server (NTRS)

1981-01-01

Designed to accommodate additions and modifications, this commentary on NASTRAN describes the problem solving capabilities of the program in a narrative fashion and presents developments of the analytical and numerical procedures that underlie the program. Seventeen major sections and numerous subsections cover; the organizational aspects of the program, utility matrix routines, static structural analysis, heat transfer, dynamic structural analysis, computer graphics, special structural modeling techniques, error analysis, interaction between structures and fluids, and aeroelastic analysis.

A strategy to couple the material point method (MPM) and smoothed particle hydrodynamics (SPH) computational techniques

NASA Astrophysics Data System (ADS)

Raymond, Samuel J.; Jones, Bruce; Williams, John R.

2018-01-01

A strategy is introduced to allow coupling of the material point method (MPM) and smoothed particle hydrodynamics (SPH) for numerical simulations. This new strategy partitions the domain into SPH and MPM regions, particles carry all state variables and as such no special treatment is required for the transition between regions. The aim of this work is to derive and validate the coupling methodology between MPM and SPH. Such coupling allows for general boundary conditions to be used in an SPH simulation without further augmentation. Additionally, as SPH is a purely particle method, and MPM is a combination of particles and a mesh. This coupling also permits a smooth transition from particle methods to mesh methods, where further coupling to mesh methods could in future provide an effective farfield boundary treatment for the SPH method. The coupling technique is introduced and described alongside a number of simulations in 1D and 2D to validate and contextualize the potential of using these two methods in a single simulation. The strategy shown here is capable of fully coupling the two methods without any complicated algorithms to transform information from one method to another.

Interactive visualization to advance earthquake simulation

USGS Publications Warehouse

Kellogg, L.H.; Bawden, G.W.; Bernardin, T.; Billen, M.; Cowgill, E.; Hamann, B.; Jadamec, M.; Kreylos, O.; Staadt, O.; Sumner, D.

2008-01-01

The geological sciences are challenged to manage and interpret increasing volumes of data as observations and simulations increase in size and complexity. For example, simulations of earthquake-related processes typically generate complex, time-varying data sets in two or more dimensions. To facilitate interpretation and analysis of these data sets, evaluate the underlying models, and to drive future calculations, we have developed methods of interactive visualization with a special focus on using immersive virtual reality (VR) environments to interact with models of Earth's surface and interior. Virtual mapping tools allow virtual "field studies" in inaccessible regions. Interactive tools allow us to manipulate shapes in order to construct models of geological features for geodynamic models, while feature extraction tools support quantitative measurement of structures that emerge from numerical simulation or field observations, thereby enabling us to improve our interpretation of the dynamical processes that drive earthquakes. VR has traditionally been used primarily as a presentation tool, albeit with active navigation through data. Reaping the full intellectual benefits of immersive VR as a tool for scientific analysis requires building on the method's strengths, that is, using both 3D perception and interaction with observed or simulated data. This approach also takes advantage of the specialized skills of geological scientists who are trained to interpret, the often limited, geological and geophysical data available from field observations. ?? Birkhaueser 2008.

Materials properties numerical database system established and operational at CINDAS/Purdue University

NASA Technical Reports Server (NTRS)

Ho, C. Y.; Li, H. H.

1989-01-01

A computerized comprehensive numerical database system on the mechanical, thermophysical, electronic, electrical, magnetic, optical, and other properties of various types of technologically important materials such as metals, alloys, composites, dielectrics, polymers, and ceramics has been established and operational at the Center for Information and Numerical Data Analysis and Synthesis (CINDAS) of Purdue University. This is an on-line, interactive, menu-driven, user-friendly database system. Users can easily search, retrieve, and manipulate the data from the database system without learning special query language, special commands, standardized names of materials, properties, variables, etc. It enables both the direct mode of search/retrieval of data for specified materials, properties, independent variables, etc., and the inverted mode of search/retrieval of candidate materials that meet a set of specified requirements (which is the computer-aided materials selection). It enables also tabular and graphical displays and on-line data manipulations such as units conversion, variables transformation, statistical analysis, etc., of the retrieved data. The development, content, accessibility, etc., of the database system are presented and discussed.

Analytical study of the effects of clouds on the light produced by lightning

NASA Technical Reports Server (NTRS)

Phanord, Dieudonne D.

1990-01-01

Researchers consider the scattering of visible and infrared light due to lightning by cubic, cylindrical and spherical clouds. The researchers extend to cloud physics the work by Twersky for single and multiple scattering of electromagnetic waves. They solve the interior problem separately to obtain the bulk parameters for the scatterer equivalent to the ensemble of spherical droplets. With the interior solution or the equivalent medium approach, the multiple scattering problem is reduced to that of a single scatterer in isolation. Hence, the computing methods of Wiscombe or Bohren specialized to Mie scattering with the possibility for absorption were used to generate numerical results in short computer time.

Adaptive exponential synchronization of complex-valued Cohen-Grossberg neural networks with known and unknown parameters.

PubMed

Hu, Jin; Zeng, Chunna

2017-02-01

The complex-valued Cohen-Grossberg neural network is a special kind of complex-valued neural network. In this paper, the synchronization problem of a class of complex-valued Cohen-Grossberg neural networks with known and unknown parameters is investigated. By using Lyapunov functionals and the adaptive control method based on parameter identification, some adaptive feedback schemes are proposed to achieve synchronization exponentially between the drive and response systems. The results obtained in this paper have extended and improved some previous works on adaptive synchronization of Cohen-Grossberg neural networks. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics

NASA Astrophysics Data System (ADS)

Guercilena, Federico; Radice, David; Rezzolla, Luciano

2017-07-01

We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J. Comput. Phys. 230(11):4248-4267, 2011, doi: 10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J. Comput. Phys. 136(1):83-99, 1997, doi: 10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to {˜}50% speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.

Phenolic Compounds in Apple (Malus x domestica Borkh.): Compounds Characterization and Stability during Postharvest and after Processing

PubMed Central

Francini, Alessandra; Sebastiani, Luca

2013-01-01

This paper summarizes the information on the occurrence of phenolic compounds in apple (Malus x domestica Borkh.) fruit and juice, with special reference to their health related properties. As phytochemical molecules belonging to polyphenols are numerous, we will focus on the main apples phenolic compounds with special reference to changes induced by apple cultivar, breeding approaches, fruit postharvest and transformation into juice. PMID:26784345

Statistical Methods Applied to Gamma-ray Spectroscopy Algorithms in Nuclear Security Missions

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

Fagan, Deborah K.; Robinson, Sean M.; Runkle, Robert C.

2012-10-01

In a wide range of nuclear security missions, gamma-ray spectroscopy is a critical research and development priority. One particularly relevant challenge is the interdiction of special nuclear material for which gamma-ray spectroscopy supports the goals of detecting and identifying gamma-ray sources. This manuscript examines the existing set of spectroscopy methods, attempts to categorize them by the statistical methods on which they rely, and identifies methods that have yet to be considered. Our examination shows that current methods effectively estimate the effect of counting uncertainty but in many cases do not address larger sources of decision uncertainty—ones that are significantly moremore » complex. We thus explore the premise that significantly improving algorithm performance requires greater coupling between the problem physics that drives data acquisition and statistical methods that analyze such data. Untapped statistical methods, such as Bayes Modeling Averaging and hierarchical and empirical Bayes methods have the potential to reduce decision uncertainty by more rigorously and comprehensively incorporating all sources of uncertainty. We expect that application of such methods will demonstrate progress in meeting the needs of nuclear security missions by improving on the existing numerical infrastructure for which these analyses have not been conducted.« less

A Riemannian geometric mapping technique for identifying incompressible equivalents to subsonic potential flows

NASA Astrophysics Data System (ADS)

German, Brian Joseph

This research develops a technique for the solution of incompressible equivalents to planar steady subsonic potential flows. Riemannian geometric formalism is used to develop a gauge transformation of the length measure followed by a curvilinear coordinate transformation to map the given subsonic flow into a canonical Laplacian flow with the same boundary conditions. The effect of the transformation is to distort both the immersed profile shape and the domain interior nonuniformly as a function of local flow properties. The method represents the full nonlinear generalization of the classical methods of Prandtl-Glauert and Karman-Tsien. Unlike the classical methods which are "corrections," this method gives exact results in the sense that the inverse mapping produces the subsonic full potential solution over the original airfoil, up to numerical accuracy. The motivation for this research was provided by an observed analogy between linear potential flow and the special theory of relativity that emerges from the invariance of the d'Alembert wave equation under Lorentz transformations. This analogy is well known in an operational sense, being leveraged widely in linear unsteady aerodynamics and acoustics, stemming largely from the work of Kussner. Whereas elements of the special theory can be invoked for compressibility effects that are linear and global in nature, the question posed in this work was whether other mathematical techniques from the realm of relativity theory could be used to similar advantage for effects that are nonlinear and local. This line of thought led to a transformation leveraging Riemannian geometric methods common to the general theory of relativity. A gauge transformation is used to geometrize compressibility through the metric tensor of the underlying space to produce an equivalent incompressible flow that lives not on a plane but on a curved surface. In this sense, forces owing to compressibility can be ascribed to the geometry of space in much the same way that general relativity ascribes gravitational forces to the curvature of space-time. Although the analogy with general relativity is fruitful, it is important not to overstate the similarities between compressibility and the physics of gravity, as the interest for this thesis is primarily in the mathematical framework and not physical phenomenology or epistemology. The thesis presents the philosophy and theory for the transformation method followed by a numerical method for practical solutions of equivalent incompressible flows over arbitrary closed profiles. The numerical method employs an iterative approach involving the solution of the equivalent incompressible flow with a panel method, the calculation of the metric tensor for the gauge transformation, and the solution of the curvilinear coordinate mapping to the canonical flow with a finite difference approach for the elliptic boundary value problem. This method is demonstrated for non-circulatory flow over a circular cylinder and both symmetric and lifting flows over a NACA 0012 profile. Results are validated with accepted subcritical full potential test cases available in the literature. For chord-preserving mapping boundary conditions, the results indicate that the equivalent incompressible profiles thicken with Mach number and develop a leading edge droop with increased angle of attack. Two promising areas of potential applicability of the method have been identified. The first is in airfoil inverse design methods leveraging incompressible flow knowledge including heuristics and empirical data for the potential field effects on viscous phenomena such as boundary layer transition and separation. The second is in aerodynamic testing using distorted similarity-scaled models.

Implementing New Methods of Laser Marking of Items in the Nuclear Material Control and Accountability System at SSC RF-IPPE: An Automated Laser Marking System

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

Regoushevsky, V I; Tambovtsev, S D; Dvukhsherstnov, V G

2009-05-18

For over ten years SSC RF-IPPE, together with the US DOE National Laboratories, has been working on implementing automated control and accountability methods for nuclear materials and other items. Initial efforts to use adhesive bar codes or ones printed (painted) onto metal revealed that these methods were inconvenient and lacked durability under operational conditions. For NM disk applications in critical stands, there is the additional requirement that labels not affect the neutron characteristics of the critical assembly. This is particularly true for the many stainless-steel clad disks containing highly enriched uranium (HEU) and plutonium that are used at SSC RF-IPPEmore » for modeling nuclear power reactors. In search of an alternate method for labeling these disks, we tested several technological options, including laser marking and two-dimensional codes. As a result, the method of laser coloring was chosen in combination with Data Matrix ECC200 symbology. To implement laser marking procedures for the HEU disks and meet all the nuclear material (NM) handling standards and rules, IPPE staff, with U.S. technical and financial support, implemented an automated laser marking system; there are also specially developed procedures for NM movements during laser marking. For the laser marking station, a Zenith 10F system by Telesis Technologies (10 watt Ytterbium Fiber Laser and Merlin software) is used. The presentation includes a flowchart for the automated system and a list of specially developed procedures with comments. Among other things, approaches are discussed for human-factor considerations. To date, markings have been applied to numerous steel-clad HEU disks, and the work continues. In the future this method is expected to be applied to other MC&A items.« less

Numerical studies of interacting vortices

NASA Technical Reports Server (NTRS)

Liu, G. C.; Hsu, C. H.

1985-01-01

To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two dimensional vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis.

Relationships between magnitude representation, counting and memory in 4- to 7-year-old children: a developmental study.

PubMed

Soltész, Fruzsina; Szucs, Dénes; Szucs, Lívia

2010-02-18

The development of an evolutionarily grounded analogue magnitude representation linked to the parietal lobes is frequently thought to be a major factor in the arithmetic development of humans. We investigated the relationship between counting and the development of magnitude representation in children, assessing also children's knowledge of number symbols, their arithmetic fact retrieval, their verbal skills, and their numerical and verbal short-term memory. The magnitude representation was tested by a non-symbolic magnitude comparison task. We have perfected previous experimental designs measuring magnitude discrimination skills in 65 children kindergarten (4-7-year-olds) by controlling for several variables which were not controlled for in previous similar research. We also used a large number of trials which allowed for running a full factorial ANOVA including all relevant factors. Tests of verbal counting, of short term memory, of number knowledge, of problem solving abilities and of verbal fluency were administered and correlated with performance in the magnitude comparison task. Verbal counting knowledge and performance on simple arithmetic tests did not correlate with non-symbolic magnitude comparison at any age. Older children performed successfully on the number comparison task, showing behavioural patterns consistent with an analogue magnitude representation. In contrast, 4-year-olds were unable to discriminate number independently of task-irrelevant perceptual variables. Sensitivity to irrelevant perceptual features of the magnitude discrimination task was also affected by age, and correlated with memory, suggesting that more general cognitive abilities may play a role in performance in magnitude comparison tasks. We conclude that young children are not able to discriminate numerical magnitudes when co-varying physical magnitudes are methodically pitted against number. We propose, along with others, that a rather domain general magnitude representation provides the later basis for a specialized representation of numerical magnitudes. For this representational specialization, the acquisition of the concept of abstract numbers, together with the development of other cognitive abilities, is indispensable.

Predictors of health literacy and numeracy concordance among adolescent with special health care needs and their parents

PubMed Central

Chisolm, Deena J; Sarkar, Madhurima; Kelleher, Kelly J.; Sanders, Lee M.

2015-01-01

Background Parent and teen health literacies (HL) are employed as teens with chronic illnesses transition to health self-management and the adult health system. This study explores the relationships between parent and teen HL. Methods Teens ages 12-18 with chronic conditions and their parents, sampled from a pediatric Medicaid ACO, completed an interview assessing HL and self-reported competence with written and numeric health information. Rates of teen and parent HL, degree of concordance, and relationship between concordance and teen-reported competence with health materials were measured. Results Half (52%) of teens had adequate HL. 62% of teens reported competence with written health materials and 69% with numeric information. Correlation between parent and teen HL was modest but significant (phi=0.13; p=0.03). 47% of parent-teen dyads were concordant for adequate HL while 10% were concordant inadequate. Adequate teen HL was associated with parental adequate HL and parental education. Discordance was associated with self-reported competence with written material and numeric material. Conclusion Over half of parent-teen dyads had at least one member with less than adequate health literacy and parent-teen HL concordance were associated with teen perception of health literacy. These findings support the consideration of both independent and dyad HL levels in adolescent care. PMID:26513030

Fish Hearing.

ERIC Educational Resources Information Center

Blaxter, J. H. S.

1980-01-01

Provides related information about hearing in fish, including the sensory stimulus of sound in the underwater environment, mechanoreceptors in fish, pressure perception and the swimbladder, specializations in sound conduction peculiar to certain fish families. Includes numerous figures. (CS)

Silicon Carbide Transistor For Detecting Hydrocarbon Gases

NASA Technical Reports Server (NTRS)

Shields, Virgil B.; Ryan, Margaret A.; Williams, Roger M.

1996-01-01

Proposed silicon carbide variable-potential insulated-gate field-effect transistor specially designed for use in measuring concentrations of hydrocarbon gases. Devices like this prove useful numerous automotive, industrial, aeronautical, and environmental monitoring applications.

Sensational placodes: Neurogenesis in the otic and olfactory systems

PubMed Central

Maier, Esther C.; Saxena, Ankur; Alsina, Berta; Bronner, Marianne E.; Whitfield, Tanya T.

2014-01-01

For both the intricate morphogenetic layout of the sensory cells in the ear and the elegantly radial arrangement of the sensory neurons in the nose, numerous signaling molecules and genetic determinants are required in concert to generate these specialized neuronal populations that help connect us to our environment. In this review, we outline many of the proteins and pathways that play essential roles in the differentiation of otic and olfactory neurons and their integration into their non-neuronal support structures. In both cases, well-known signaling pathways together with region-specific factors transform thickened ectodermal placodes into complex sense organs containing numerous, diverse neuronal subtypes. Olfactory and otic placodes, in combination with migratory neural crest stem cells, generate highly specialized subtypes of neuronal cells that sense sound, position and movement in space, odors and pheromones throughout our lives. PMID:24508480

An Application of the Difference Potentials Method to Solving External Problems in CFD

NASA Technical Reports Server (NTRS)

Ryaben 'Kii, Victor S.; Tsynkov, Semyon V.

1997-01-01

Numerical solution of infinite-domain boundary-value problems requires some special techniques that would make the problem available for treatment on the computer. Indeed, the problem must be discretized in a way that the computer operates with only finite amount of information. Therefore, the original infinite-domain formulation must be altered and/or augmented so that on one hand the solution is not changed (or changed slightly) and on the other hand the finite discrete formulation becomes available. One widely used approach to constructing such discretizations consists of truncating the unbounded original domain and then setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The role of the ABC's is to close the truncated problem and at the same time to ensure that the solution found inside the finite computational domain would be maximally close to (in the ideal case, exactly the same as) the corresponding fragment of the original infinite-domain solution. Let us emphasize that the proper treatment of artificial boundaries may have a profound impact on the overall quality and performance of numerical algorithms. The latter statement is corroborated by the numerous computational experiments and especially concerns the area of CFD, in which external problems present a wide class of practically important formulations. In this paper, we review some work that has been done over the recent years on constructing highly accurate nonlocal ABC's for calculation of compressible external flows. The approach is based on implementation of the generalized potentials and pseudodifferential boundary projection operators analogous to those proposed first by Calderon. The difference potentials method (DPM) by Ryaben'kii is used for the effective computation of the generalized potentials and projections. The resulting ABC's clearly outperform the existing methods from the standpoints of accuracy and robustness, in many cases noticeably speed up the multigrid convergence, and at the same time are quite comparable to other methods from the standpoints of geometric universality and simplicity of implementation.

Reliability enhancement of Navier-Stokes codes through convergence acceleration

NASA Technical Reports Server (NTRS)

Merkle, Charles L.; Dulikravich, George S.

1995-01-01

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Large-eddy simulation of flow past a circular cylinder

NASA Technical Reports Server (NTRS)

Mittal, R.

1995-01-01

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

Simultaneous determination of mean pressure and deviatoric stress based on numerical tensor analysis: a case study for polycrystalline x-ray diffraction of gold enclosed in a methanol-ethanol mixture.

PubMed

Yoneda, A; Kubo, A

2006-06-28

It is known that the {100} and {111} planes of cubic crystals subjected to uniaxial deviatoric stress conditions have strain responses that are free from the effect of lattice preferred orientation. By utilizing this special character, one can unambiguously and simultaneously determine the mean pressure and deviatoric stress from polycrystalline diffraction data of the cubic sample. Here we introduce a numerical tensor calculation method based on the generalized Hooke's law to simultaneously determine the hydrostatic component of the stress (mean pressure) and deviatoric stress in the sample. The feasibility of this method has been tested by examining the experimental data of the Au pressure marker enclosed in a diamond anvil cell using a pressure medium of methanol-ethanol mixture. The results demonstrated that the magnitude of the deviatoric stress is ∼0.07 GPa at the mean pressure of 10.5 GPa, which is consistent with previous results of Au strength under high pressure. Our results also showed that even a small deviatoric stress (∼0.07 GPa) could yield a ∼0.3 GPa mean pressure error at ∼10 GPa.

Comet assay: an essential tool in toxicological research.

PubMed

Glei, M; Schneider, T; Schlörmann, W

2016-10-01

The comet assay is a versatile, reliable, cost-efficient, and fast technique for detecting DNA damage and repair in any tissue. It is useable in almost any cell type and applicable to both eukaryotic and prokaryotic organisms. Instead of highlighting one of the numerous specific aspects of the comet assay, the present review aims at giving an overview about the evolution of this widely applicable method from the first description by Ostling and Johanson to the OECD Guideline 489 for the in vivo mammalian comet assay. In addition, methodical aspects and the influence of critical steps of the assay as well as the evaluation of results and improvements of the method are reviewed. Methodical aspects regarding oxidative DNA damage and repair are also addressed. An overview about the most recent works and relevant cutting-edge reviews based on the comet assay with special regard to, e.g., clinical applications, nanoparticles or environmental risk assessment concludes this review. Taken together, the presented overview raises expectations to further decades of successful applications and enhancements of this excellent method.

Analyzing Association Mapping in Pedigree-Based GWAS Using a Penalized Multitrait Mixed Model

PubMed Central

Liu, Jin; Yang, Can; Shi, Xingjie; Li, Cong; Huang, Jian; Zhao, Hongyu; Ma, Shuangge

2017-01-01

Genome-wide association studies (GWAS) have led to the identification of many genetic variants associated with complex diseases in the past 10 years. Penalization methods, with significant numerical and statistical advantages, have been extensively adopted in analyzing GWAS. This study has been partly motivated by the analysis of Genetic Analysis Workshop (GAW) 18 data, which have two notable characteristics. First, the subjects are from a small number of pedigrees and hence related. Second, for each subject, multiple correlated traits have been measured. Most of the existing penalization methods assume independence between subjects and traits and can be suboptimal. There are a few methods in the literature based on mixed modeling that can accommodate correlations. However, they cannot fully accommodate the two types of correlations while conducting effective marker selection. In this study, we develop a penalized multitrait mixed modeling approach. It accommodates the two different types of correlations and includes several existing methods as special cases. Effective penalization is adopted for marker selection. Simulation demonstrates its satisfactory performance. The GAW 18 data are analyzed using the proposed method. PMID:27247027

A highly accurate boundary integral equation method for surfactant-laden drops in 3D

NASA Astrophysics Data System (ADS)

Sorgentone, Chiara; Tornberg, Anna-Karin

2018-05-01

The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of increased importance. At such small scales, viscous forces dominate and inertial effects are often negligible. Considering Stokes flow, a numerical method based on a boundary integral formulation is presented for simulating 3D drops covered by an insoluble surfactant. The method is able to simulate drops with different viscosities and close interactions, automatically controlling the time step size and maintaining high accuracy also when substantial drop deformation appears. To achieve this, the drop surfaces as well as the surfactant concentration on each surface are represented by spherical harmonics expansions. A novel reparameterization method is introduced to ensure a high-quality representation of the drops also under deformation, specialized quadrature methods for singular and nearly singular integrals that appear in the formulation are evoked and the adaptive time stepping scheme for the coupled drop and surfactant evolution is designed with a preconditioned implicit treatment of the surfactant diffusion.

xLIPA: Promotion of Electrons from the K-shell to 2 GeV using 10 PW Laser Pulses

DTIC Science & Technology

2015-08-19

field [34]. Since then numerous analytical and numerical approaches have been employed with special emphasis on laser photoionization . Besides interest in... photoionization as a fundamental physical process there are many applications for photoelectrons. Knowledge of the electron properties, e.g., energy...Schwinger field. Photoionization of inner-shell electrons in high-Z atoms is another example where relativistic effects are important. Two analytical

NONLINEAR AND FIBER OPTICS: Self-similar solution obtained by self-focusing of annular laser beams

NASA Astrophysics Data System (ADS)

Azimov, B. S.; Platonenko, Viktor T.; Sagatov, M. M.

1991-03-01

A numerical modeling is reported of steady-state self-focusing of an annular beam with thin "walls." An approximate similar solution is found to describe well the relationships observed in the numerical experiment for a special selection of the input parameters of the beam. This solution is used to estimate the focal length. Such self-similar self-focusing is shown to affect the whole power of the beam.

Nonequilibrium flow computations. 1: An analysis of numerical formulations of conservation laws

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

1988-01-01

Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, nonequilibrium flows. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer Flux-vector splittings, and Roe's approximate Riemann solver are presented for 3-D, time-varying grids. The analysis is based on a thermodynamic model that includes the most general thermal and chemical nonequilibrium flow of an arbitrary gas. Various special cases are also discussed.

Validation of numerical simulations for nano-aluminum composite solid propellants

NASA Astrophysics Data System (ADS)

Yan, Allen H.

2011-12-01

Nano-aluminum is of interest as an energetic additive in composite solid propellant formulations for its demonstrated ability to increase combustion efficiency and burning rate. However, due to the current cost of nano-aluminum and the associated safety risks associated with propellant testing, it may not always be practical to spend the time and effort to mix, cast, and thoroughly evaluate the burning rate of a new formulation. To provide an alternative method of determining this parameter, numerical methods have been developed to predict the performance of nano-aluminum composite propellants, but these codes still require thorough validation before application. For this purpose, six propellant compositions were formulated, fully characterized, and burn rates were measured at several pressures between 34.0 and 129.3 atmospheres at room temperature, 20°C, and at an elevated temperature of 71.1°C in order to test the code's ability to predict pressure dependent burn rate and temperature sensitivity. To ensure the most accurate model possible, special emphasis was placed on characterizing the size distribution of the constituent nano-aluminum and ammonium perchlorate powders through optical diffraction or optical imaging techniques. Experimental burn rate is compared to the propellant combustion model and shows excellent agreement within 5% for a range of formulations and pressures, however under other conditions the model deviates by as much as 21%. An analysis of the results suggests that the current framework of the numerical model is unable to accurately simulate all the combustion physics of high aluminum content propellants, and suggestions for improvements are identified.

Shack-Hartmann wavefront sensor with large dynamic range by adaptive spot search method.

PubMed

Shinto, Hironobu; Saita, Yusuke; Nomura, Takanori

2016-07-10

A Shack-Hartmann wavefront sensor (SHWFS) that consists of a microlens array and an image sensor has been used to measure the wavefront aberrations of human eyes. However, a conventional SHWFS has finite dynamic range depending on the diameter of the each microlens. The dynamic range cannot be easily expanded without a decrease of the spatial resolution. In this study, an adaptive spot search method to expand the dynamic range of an SHWFS is proposed. In the proposed method, spots are searched with the help of their approximate displacements measured with low spatial resolution and large dynamic range. By the proposed method, a wavefront can be correctly measured even if the spot is beyond the detection area. The adaptive spot search method is realized by using the special microlens array that generates both spots and discriminable patterns. The proposed method enables expanding the dynamic range of an SHWFS with a single shot and short processing time. The performance of the proposed method is compared with that of a conventional SHWFS by optical experiments. Furthermore, the dynamic range of the proposed method is quantitatively evaluated by numerical simulations.

Numerical Simulation of Two-Fluid Mingling Using the Particle Finite Element Method with Applications to Magmatic and Volcanic Processes

NASA Astrophysics Data System (ADS)

de Mier, M.; Costa, F.; Idelsohn, S.

2008-12-01

Many magmatic and volcanic processes (e.g., magma differentiation, mingling, transport in the volcanic conduit) are controlled by the physical properties and flow styles of high-temperature silicate melts. Such processes can be experimentally investigated using analog systems and scaling methods, but it is difficult to find the suitable material and it is generally not possible to quantitatively extrapolate the results to the natural system. An alternative means of studying fluid dynamics in volcanic systems is with numerical models. We have chosen the Particle Finite Element Method (PFEM), which is based on a Delaunay mesh that moves with the fluid velocity, the Navier-Stokes equations in Lagrangian formulation, and linear elements for velocity, pressure, and temperature. Remeshing is performed when the grid becomes too distorted [E. Oñate et al., 2004. The Particle Finite Element Method: An Overview. Int. J. Comput. Meth. 1, 267-307]. The method is ideal for tracking material interfaces between different fluids or media. Methods based on Eulerian reference frames need special techniques, such as level-set or volume-of-fluid, to capture the interface position, and these techniques add a significant numerical diffusion at the interface. We have performed a series of two-dimensional simulations of a classical problem of fluid dynamics in magmatic and volcanic systems: intrusion of a basaltic melt in a silica-rich magma reservoir. We have used realistic physical properties and equations of state for the silicate melts (e.g., temperature, viscosity, and density) and tracked the changes in the system for geologically relevant time scales (up to 100 years). The problem is modeled by the low-Mach-number equations derived from an asymptotic analysis of the compressible Navier-Stokes equations that removes shock waves from the flow but allows however large variations of density due to temperature variations. Non-constant viscosity and volume changes are taken into account in the momentum conservation equation through the full shear-stress tensor. The implications of different magma intrusion rates, volumes, and times will be discussed in the context of mafic-silicic magma mixing and eruption triggers.

Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous, Anisotropic Media

NASA Astrophysics Data System (ADS)

Zhou, Bing; Greenhalgh, S. A.

2011-10-01

2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity of the seismograms to changes in the model parameters. This paper applies two methods, called `the perturbation method' and `the matrix method', to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green's function vectors and their gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The two Green's function vectors are the responses of the displacement vector to the two directed unit vectors located at the source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green's function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic (TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen parameters) plus one angle defining the symmetry axis.

A numerical study on the influence of slope and curvature on smoke flow in special section tunnel with natural ventilation

NASA Astrophysics Data System (ADS)

Wang, Wenzhou; Zhou, Xianping; Liu, Zhigang; Liu, Ya; Liu, Wanfu; Hong, Li

2017-09-01

In this study, a special section tunnel model was established by using FDS (Fire Dynamics Simulator). The influences of lope and curvature on smoke flow under natural ventilation have been studied. The results showed that under the condition of natural ventilation, the slope has some influences on the smoke flow in special section tunnel. The smoke spreading speed is accelerated along the upstream direction and decrease along the downstream direction due to buoyancy effect of slope. The steeper the tunnel, the more obvious the buoyancy effect. The curvature has little effect on the flow of flue gas.

3-D Lagrangian-based investigations of the time-dependent cloud cavitating flows around a Clark-Y hydrofoil with special emphasis on shedding process analysis

NASA Astrophysics Data System (ADS)

Cheng, Huai-yu; Long, Xin-ping; Ji, Bin; Liu, Qi; Bai, Xiao-rui

2018-02-01

In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model (FBDCM), a turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures (LCSs). Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet, the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage III, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.

PREFACE: Topics in the application of scattering methods to investigate the structure and dynamics of soft condensed matter

NASA Astrophysics Data System (ADS)

Chen, Sow-Hsin; Baglioni, Piero

2006-09-01

This special issue of Journal of Physics: Condensed Matter gathers together a series of contributions presented at the workshop entitled `Topics in the Application of Scattering Methods to Investigate the Structure and Dynamics of Soft Condensed Matter' held at Pensione Bencista, Fiesole, Italy, a wonderful Italian jewel tucked high in the hills above Florence. This immaculate 14th century villa is a feast for the eyes with antiques and original artwork everywhere you turn, and a stunning view of Florence, overlooking numerous villas and groves of olive trees. The meeting consisted of about 40 invited talks delivered by a selected group of prominent physicists and chemists from the USA, Mexico, Europe and Asia working in the fields of complex and glassy liquids. The topics covered by the talks included: simulations on the liquid-liquid transition phenomenon dynamic crossover in deeply supercooled confined water thermodynamics and dynamics of complex fluids dynamics of interfacial water structural arrest transitions in colloidal systems structure and dynamics in complex systems structure of supramolecular assemblies The choice of topics is obviously heavily biased toward the current interests of the two organizers of the workshop, in view of the fact that one of the incentives for organizing the meeting was to celebrate Sow-Hsin Chen’s life-long scientific activities on the occasion of his 70th birthday. The 21 articles presented in this issue are a state-of-the-art description of the different aspects reported at the workshop from all points of view---experimental, theoretical and numerical. The interdisciplinary nature of the talks should make this special issue of interest to a broad community of scientists involved in the study of the properties of complex fluids, soft condensed matter and disordered glassy systems. We are grateful to the Consorzio per lo Sviluppo dei Sistemi a Grande Interfase (CSGI), Florence, Italy and to the Materials Science Program of the US Department of Energy for their support of the workshop.

A fast CT reconstruction scheme for a general multi-core PC.

PubMed

Zeng, Kai; Bai, Erwei; Wang, Ge

2007-01-01

Expensive computational cost is a severe limitation in CT reconstruction for clinical applications that need real-time feedback. A primary example is bolus-chasing computed tomography (CT) angiography (BCA) that we have been developing for the past several years. To accelerate the reconstruction process using the filtered backprojection (FBP) method, specialized hardware or graphics cards can be used. However, specialized hardware is expensive and not flexible. The graphics processing unit (GPU) in a current graphic card can only reconstruct images in a reduced precision and is not easy to program. In this paper, an acceleration scheme is proposed based on a multi-core PC. In the proposed scheme, several techniques are integrated, including utilization of geometric symmetry, optimization of data structures, single-instruction multiple-data (SIMD) processing, multithreaded computation, and an Intel C++ compilier. Our scheme maintains the original precision and involves no data exchange between the GPU and CPU. The merits of our scheme are demonstrated in numerical experiments against the traditional implementation. Our scheme achieves a speedup of about 40, which can be further improved by several folds using the latest quad-core processors.

The search for the number form area: A functional neuroimaging meta-analysis.

PubMed

Yeo, Darren J; Wilkey, Eric D; Price, Gavin R

2017-07-01

Recent studies report a putative "number form area" (NFA) in the inferior temporal gyrus (ITG) suggested to be specialized for Arabic numeral processing. However, a number of earlier studies report no such NFA. The reasons for such discrepancies across studies are unclear. To examine evidence for a convergent NFA across studies, we conducted two activation likelihood estimation meta-analyses on 31 and a subset of 20 neuroimaging studies that have contrasted digits with other meaningful symbols. Results suggest the potential existence of an NFA in the right ITG, in addition to a 'symbolic number processing network' comprising bilateral parietal regions, and right-lateralized superior and inferior frontal regions. Critically, convergent localization for the NFA was only evident when contrasts were appropriately controlled for task demands, and does not appear to depend on employing methods designed to overcome fMRI signal dropout in the ITG. Importantly, only five studies had foci within the identified ITG NFA cluster boundary, indicating that more empirical evidence is necessary to determine the true functional specialization and regional specificity of the putative NFA. Copyright © 2017 Elsevier Ltd. All rights reserved.

Thoughts for food in cognitive neuroscience: An introduction to the special issue.

PubMed

Rumiati, Raffaella I; di Pellegrino, Giuseppe

2016-12-01

Food is essential to our survival. It is also one of the greatest pleasures of life. Over the last decade, our understanding about how the brain responds to food cues and guides food search and intake has greatly increased. This special issue brings together various perspectives and research approaches on food cognitive neuroscience, encompassing a wide variety of techniques and methods. As these studies will add substantially to the ever-growing research on food cognitive neuroscience, we hope that they will also inspire new and useful ideas to fill the gaps that remain in this critical area of inquiry. By providing nutrients to generate energy and sustain life, food is an essential fuel for our survival and a pervasive element of our daily environment. Food also represents one of the greatest pleasures that we experience in life. More recently, numerous cognitive neuroscientific studies about how the brain responds to food cues and guides food search and consumption have been published. Evidence points to several and closely interrelated neural circuits underlying the homeostatic and hedonic mechanisms that regulate food intake. Copyright © 2016. Published by Elsevier Inc.

A Fast CT Reconstruction Scheme for a General Multi-Core PC

PubMed Central

Zeng, Kai; Bai, Erwei; Wang, Ge

2007-01-01

Expensive computational cost is a severe limitation in CT reconstruction for clinical applications that need real-time feedback. A primary example is bolus-chasing computed tomography (CT) angiography (BCA) that we have been developing for the past several years. To accelerate the reconstruction process using the filtered backprojection (FBP) method, specialized hardware or graphics cards can be used. However, specialized hardware is expensive and not flexible. The graphics processing unit (GPU) in a current graphic card can only reconstruct images in a reduced precision and is not easy to program. In this paper, an acceleration scheme is proposed based on a multi-core PC. In the proposed scheme, several techniques are integrated, including utilization of geometric symmetry, optimization of data structures, single-instruction multiple-data (SIMD) processing, multithreaded computation, and an Intel C++ compilier. Our scheme maintains the original precision and involves no data exchange between the GPU and CPU. The merits of our scheme are demonstrated in numerical experiments against the traditional implementation. Our scheme achieves a speedup of about 40, which can be further improved by several folds using the latest quad-core processors. PMID:18256731

A model of freezing foods with liquid nitrogen using special functions

NASA Astrophysics Data System (ADS)

Rodríguez Vega, Martín.

2014-05-01

A food freezing model is analyzed analytically. The model is based on the heat diffusion equation in the case of cylindrical shaped food frozen by liquid nitrogen; and assuming that the thermal conductivity of the cylindrical food is radially modulated. The model is solved using the Laplace transform method, the Bromwich theorem, and the residue theorem. The temperature profile in the cylindrical food is presented as an infinite series of special functions. All the required computations are performed with computer algebra software, specifically Maple. Using the numeric values of the thermal and geometric parameters for the cylindrical food, as well as the thermal parameters of the liquid nitrogen freezing system, the temporal evolution of the temperature in different regions in the interior of the cylindrical food is presented both analytically and graphically. The duration of the liquid nitrogen freezing process to achieve the specified effect on the cylindrical food is computed. The analytical results are expected to be of importance in food engineering and cooking engineering. As a future research line, the formulation and solution of freezing models with thermal memory is proposed.

Matrix eigenvalue method for free-oscillations modelling of spherical elastic bodies

NASA Astrophysics Data System (ADS)

Zábranová, E.; Hanyk, L.; Matyska, C.

2017-11-01

Deformations and changes of the gravitational potential of pre-stressed self-gravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spherically symmetric bodies, the equations and boundary conditions are transformed into ordinary differential equations of the second order by the spherical harmonic decomposition and further discretized by highly accurate pseudospectral difference schemes on Chebyshev grids; we pay special attention to the conditions at the centre of the models. We thus obtain a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Accuracy of the presented numerical approach is tested by means of the Rayleigh quotients calculated for the eigenfrequencies up to 500 mHz. Both the modal frequencies and eigenfunctions are benchmarked against the output from the Mineos software package based on shooting methods. The presented technique is a promising alternative to widely used methods because it is stable and with a good capability up to high frequencies.

Automated Approach to Very High-Order Aeroacoustic Computations. Revision

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.; Goodrich, John W.

2001-01-01

Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials

NASA Astrophysics Data System (ADS)

Zhou, W. J.; Li, X. P.; Wang, Y. S.; Chen, W. Q.; Huang, G. L.

2018-01-01

The objective of this work is to analyze wave packet propagation in weakly nonlinear acoustic metamaterials and reveal the interior nonlinear wave mechanism through spectro-spatial analysis. The spectro-spatial analysis is based on full-scale transient analysis of the finite system, by which dispersion curves are generated from the transmitted waves and also verified by the perturbation method (the L-P method). We found that the spectro-spatial analysis can provide detailed information about the solitary wave in short-wavelength region which cannot be captured by the L-P method. It is also found that the optical wave modes in the nonlinear metamaterial are sensitive to the parameters of the nonlinear constitutive relation. Specifically, a significant frequency shift phenomenon is found in the middle-wavelength region of the optical wave branch, which makes this frequency region behave like a band gap for transient waves. This special frequency shift is then used to design a direction-biased waveguide device, and its efficiency is shown by numerical simulations.

Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method

NASA Astrophysics Data System (ADS)

Shen-Shen, Chen; Juan, Wang; Qing-Hua, Li

2016-04-01

A scaled boundary node method (SBNM) is developed for two-dimensional fracture analysis of piezoelectric material, which allows the stress and electric displacement intensity factors to be calculated directly and accurately. As a boundary-type meshless method, the SBNM employs the moving Kriging (MK) interpolation technique to an approximate unknown field in the circumferential direction and therefore only a set of scattered nodes are required to discretize the boundary. As the shape functions satisfy Kronecker delta property, no special techniques are required to impose the essential boundary conditions. In the radial direction, the SBNM seeks analytical solutions by making use of analytical techniques available to solve ordinary differential equations. Numerical examples are investigated and satisfactory solutions are obtained, which validates the accuracy and simplicity of the proposed approach. Project supported by the National Natural Science Foundation of China (Grant Nos. 11462006 and 21466012), the Foundation of Jiangxi Provincial Educational Committee, China (Grant No. KJLD14041), and the Foundation of East China Jiaotong University, China (Grant No. 09130020).

Discontinuous Galerkin algorithms for fully kinetic plasmas

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

Juno, J.; Hakim, A.; TenBarge, J.

Here, we present a new algorithm for the discretization of the non-relativistic Vlasov–Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge–Kutta method. Since the Vlasov equation in the Vlasov–Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the costmore » while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.« less

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.; Goodrich, John W.

2000-01-01

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Discontinuous Galerkin algorithms for fully kinetic plasmas

DOE PAGES

Juno, J.; Hakim, A.; TenBarge, J.; ...

2017-10-10

Here, we present a new algorithm for the discretization of the non-relativistic Vlasov–Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge–Kutta method. Since the Vlasov equation in the Vlasov–Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the costmore » while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.« less

Identification of Defects in Piles Through Dynamic Testing

NASA Astrophysics Data System (ADS)

Liao, Shutao T.; Roesset, Jose M.

1997-04-01

The objective of this work was to evaluate the theoretical capabilities of the non-destructive impact-response method in detecting the existence of a single defect in a pile, its location and its length. The cross-section of the pile is assumed to be circular and the defects are assumed to be axisymmetric in geometry. As mentioned in the companion paper, special codes utilizing one-dimensional (1-D) and three-dimensional (3-D) axisymmetric finite element models were developed to simulate the responses of defective piles to an impact load. Extensive parametric studies were then performed. In each study, the results from the direct use of time histories of displacements or velocities and the mechanical admittance (or mobility) function were compared in order to assess their capabilities. The effects of the length and the width of a defect were also investigated using these methods. Int. J. Numer. Anal. Meth. Geomech., vol. 21, 277-291 (1997)

Application of program generation technology in solving heat and flow problems

NASA Astrophysics Data System (ADS)

Wan, Shui; Wu, Bangxian; Chen, Ningning

2007-05-01

Based on a new DIY concept for software development, an automatic program-generating technology attached on a software system called as Finite Element Program Generator (FEPG) provides a platform of developing programs, through which a scientific researcher can submit his special physico-mathematical problem to the system in a more direct and convenient way for solution. For solving flow and heat problems by using finite element method, the stabilization technologies and fraction-step methods are adopted to overcome the numerical difficulties caused mainly due to the dominated convection. A couple of benchmark problems are given in this paper as examples to illustrate the usage and the superiority of the automatic program generation technique, including the flow in a lid-driven cavity, the starting flow in a circular pipe, the natural convection in a square cavity, and the flow past a circular cylinder, etc. They are also shown as the verification of the algorithms.