WorldWideScience

Sample records for solving numerous practical

  1. Problem Solving in Practice

    Science.gov (United States)

    Greene, Kim; Heyck-Williams, Jeff; Timpson Gray, Elicia

    2017-01-01

    Problem solving spans all grade levels and content areas, as evidenced by this compilation of projects from schools across the United States. In one project, high school girls built a solar-powered tent to serve their city's homeless population. In another project, 4th graders explored historic Jamestown to learn about the voices lost to history.…

  2. A numerical method for solving singular De`s

    Energy Technology Data Exchange (ETDEWEB)

    Mahaver, W.T.

    1996-12-31

    A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

  3. New numerical method for solving the solute transport equation

    International Nuclear Information System (INIS)

    Ross, B.; Koplik, C.M.

    1978-01-01

    The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

  4. Infinite occupation number basis of bosons: Solving a numerical challenge

    Science.gov (United States)

    Geißler, Andreas; Hofstetter, Walter

    2017-06-01

    In any bosonic lattice system, which is not dominated by local interactions and thus "frozen" in a Mott-type state, numerical methods have to cope with the infinite size of the corresponding Hilbert space even for finite lattice sizes. While it is common practice to restrict the local occupation number basis to Nc lowest occupied states, the presence of a finite condensate fraction requires the complete number basis for an exact representation of the many-body ground state. In this work we present a truncation scheme to account for contributions from higher number states. By simply adding a single coherent-tail state to this common truncation, we demonstrate increased numerical accuracy and the possible increase in numerical efficiency of this method for the Gutzwiller variational wave function and within dynamical mean-field theory.

  5. A New Method to Solve Numeric Solution of Nonlinear Dynamic System

    Directory of Open Access Journals (Sweden)

    Min Hu

    2016-01-01

    Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

  6. Problem solving therapy - use and effectiveness in general practice.

    Science.gov (United States)

    Pierce, David

    2012-09-01

    Problem solving therapy (PST) is one of the focused psychological strategies supported by Medicare for use by appropriately trained general practitioners. This article reviews the evidence base for PST and its use in the general practice setting. Problem solving therapy involves patients learning or reactivating problem solving skills. These skills can then be applied to specific life problems associated with psychological and somatic symptoms. Problem solving therapy is suitable for use in general practice for patients experiencing common mental health conditions and has been shown to be as effective in the treatment of depression as antidepressants. Problem solving therapy involves a series of sequential stages. The clinician assists the patient to develop new empowering skills, and then supports them to work through the stages of therapy to determine and implement the solution selected by the patient. Many experienced GPs will identify their own existing problem solving skills. Learning about PST may involve refining and focusing these skills.

  7. Problem solving teaching practices: Observer and teacher's view

    OpenAIRE

    Felmer , Patricio; Perdomo-Díaz , Josefa; Giaconi , Valentina; Espinoza , Carmen ,

    2015-01-01

    International audience; In this article, we report on an exploratory study on teaching practices related to problem solving of a group of 29 novel secondary mathematics teachers. For this purpose, two independent instruments were designed, the first one is based on lesson observations, and the second one is a questionnaire answered by teachers about their teaching practices while working on non-routine problem solving with their students. For each instrument, we perform a statistical analysis...

  8. New Numerical Treatment for Solving the KDV Equation

    Directory of Open Access Journals (Sweden)

    khalid ali

    2017-01-01

    Full Text Available In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using collocation method with the modified exponential cubic B-spline. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply.

  9. An uncoupling strategy for numerically solving the dynamic thermoelasticity equations

    International Nuclear Information System (INIS)

    Moura, C.A. de; Feijoo, R.A.

    1981-01-01

    The dynamic equations of coupled linear thermoelasticity are presented. A numerical algorithm which combines finite-element space approximation with a two-step time discretization in such a way as to reach significant computational savings is presented: It features a strategy for independently calculating the displacement and temperature fields through equations that nevertheless remain coupled. The scheme convergence was shown to be optimal and its machine performance, as ilustrated by some examples, fairly satisfactory. (Author) [pt

  10. Numerical method for solving integral equations of neutron transport. II

    International Nuclear Information System (INIS)

    Loyalka, S.K.; Tsai, R.W.

    1975-01-01

    In a recent paper it was pointed out that the weakly singular integral equations of neutron transport can be quite conveniently solved by a method based on subtraction of singularity. This previous paper was devoted entirely to the consideration of simple one-dimensional isotropic-scattering and one-group problems. The present paper constitutes interesting extensions of the previous work in that in addition to a typical two-group anisotropic-scattering albedo problem in the slab geometry, the method is also applied to an isotropic-scattering problem in the x-y geometry. These results are compared with discrete S/sub N/ (ANISN or TWOTRAN-II) results, and for the problems considered here, the proposed method is found to be quite effective. Thus, the method appears to hold considerable potential for future applications. (auth)

  11. Applying recursive numerical integration techniques for solving high dimensional integrals

    International Nuclear Information System (INIS)

    Ammon, Andreas; Genz, Alan; Hartung, Tobias; Jansen, Karl; Volmer, Julia; Leoevey, Hernan

    2016-11-01

    The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.

  12. Numerical treatments for solving nonlinear mixed integral equation

    Directory of Open Access Journals (Sweden)

    M.A. Abdou

    2016-12-01

    Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.

  13. Applying recursive numerical integration techniques for solving high dimensional integrals

    Energy Technology Data Exchange (ETDEWEB)

    Ammon, Andreas [IVU Traffic Technologies AG, Berlin (Germany); Genz, Alan [Washington State Univ., Pullman, WA (United States). Dept. of Mathematics; Hartung, Tobias [King' s College, London (United Kingdom). Dept. of Mathematics; Jansen, Karl; Volmer, Julia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leoevey, Hernan [Humboldt Univ. Berlin (Germany). Inst. fuer Mathematik

    2016-11-15

    The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with N samples behaves like 1/√(N). This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. It is therefore highly desirable to have alternative methods at hand which show an improved error scaling. One candidate for such an alternative integration technique is the method of recursive numerical integration (RNI). The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights. We present the application of such an algorithm to the topological rotor and the anharmonic oscillator and compare the error scaling to MCMC results. In particular, we demonstrate that the RNI technique shows an error scaling in the number of integration points m that is at least exponential.

  14. The effects of cumulative practice on mathematics problem solving.

    Science.gov (United States)

    Mayfield, Kristin H; Chase, Philip N

    2002-01-01

    This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.

  15. Two split cell numerical methods for solving 2-D non-equilibrium radiation transport equations

    International Nuclear Information System (INIS)

    Feng Tinggui

    2004-11-01

    Two numerically positive methods, the step characteristic integral method and subcell balance method, for solving radiative transfer equations on quadrilateral grids are presented. Numerical examples shows that the schemes presented are feasible on non-rectangle grid computation, and that the computing results by the schemes presented are comparative to that by the discrete ordinate diamond scheme on rectangle grid. (author)

  16. The Role of Problem Solving in Construction Management Practices

    DEFF Research Database (Denmark)

    Schultz, Casper Siebken

    2012-01-01

    industry. An Industrial PhD carried out at a large Danish contractor examined how failures and defects are produced and handled in the social practices of construction projects. The study addresses quality issues related to project management and examines the role of problem solving practices......Quality issues are a topic of continuous interest in the Danish construction industry. Not only can failures and defects be vital to the success of the single project but also the annual profits of the whole company can be put at risk. Moreover quality issues jeopardize the reputation of the entire......-dispositions regarding quality issues in the decision making and redressing of defects and failures in the processes. The role of problem solving and trouble-shooting is analysed through the well-organized processes of erecting the precast concrete structure and the chaotic processes of constructing the penthouse storey...

  17. Numerical Simulation of Different Models of Heat Pipe Heat Exchanger Using AcuSolve

    Directory of Open Access Journals (Sweden)

    Zainal Nurul Amira

    2017-01-01

    Full Text Available In this paper, a numerical simulation of heat pipe heat exchanger (HPHE is computed by using CFD solver program i.e. AcuSolve. Two idealized model of HPHE are created with different variant of entry’s dimension set to be case 1 and case 2. The geometry of HPHE is designed in SolidWorks and imported to AcuSolve to simulate the fluid flow numerically. The design of HPHE is the key to provide a heat exchanger system to work proficient as expected. Finally, the result is used to optimize and improving heat recovery systems of the increasing demand for energy efficiency in industry.

  18. Numerical method for solving linear Fredholm fuzzy integral equations of the second kind

    Energy Technology Data Exchange (ETDEWEB)

    Abbasbandy, S. [Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Ghazvin 34194 (Iran, Islamic Republic of)]. E-mail: saeid@abbasbandy.com; Babolian, E. [Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, Tehran 15618 (Iran, Islamic Republic of); Alavi, M. [Department of Mathematics, Arak Branch, Islamic Azad University, Arak 38135 (Iran, Islamic Republic of)

    2007-01-15

    In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.

  19. Comparison of numerical approaches to solve a Poincare-covariant Faddeev equation

    International Nuclear Information System (INIS)

    Alkofer, R.; Eichmann, G.; Krassnigg, A.; Schwinzerl, M.

    2006-01-01

    Full text: The quark core of Baryons can be described with the help of the numerical solution of the Poincare-Faddeev equation. Hereby the used elements, as e.g. the quark propagator are taken from non-perturbative studies of Landau gauge QCD. Different numerical approaches to solve in this way the relativistic three quark problem are compared and benchmarked results for the efficiency of different algorithms are presented. (author)

  20. Numerical method for solving the inverse problem of quantum scattering theory

    International Nuclear Information System (INIS)

    Ajrapetyan, R.G.; Puzynin, I.V.; Zhidkov, E.P.

    1996-01-01

    A new numerical method for solving the problem of the reconstruction of interaction potential by a phase shift given on a set of closed intervals in (l,k)-plane, satisfying certain geometrical 'Staircase Condition', is suggested. The method is based on the Variable Phase Approach and on the modification of the Continuous Analogy of the Newton Method. 22 refs., 1 fig

  1. Modifying a numerical algorithm for solving the matrix equation X + AX T B = C

    Science.gov (United States)

    Vorontsov, Yu. O.

    2013-06-01

    Certain modifications are proposed for a numerical algorithm solving the matrix equation X + AX T B = C. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from O( n 4) to O( n 3) arithmetic operations.

  2. An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2014-01-01

    Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

  3. Development of a set of benchmark problems to verify numerical methods for solving burnup equations

    International Nuclear Information System (INIS)

    Lago, Daniel; Rahnema, Farzad

    2017-01-01

    Highlights: • Description transmutation chain benchmark problems. • Problems for validating numerical methods for solving burnup equations. • Analytical solutions for the burnup equations. • Numerical solutions for the burnup equations. - Abstract: A comprehensive set of transmutation chain benchmark problems for numerically validating methods for solving burnup equations was created. These benchmark problems were designed to challenge both traditional and modern numerical methods used to solve the complex set of ordinary differential equations used for tracking the change in nuclide concentrations over time due to nuclear phenomena. Given the development of most burnup solvers is done for the purpose of coupling with an established transport solution method, these problems provide a useful resource in testing and validating the burnup equation solver before coupling for use in a lattice or core depletion code. All the relevant parameters for each benchmark problem are described. Results are also provided in the form of reference solutions generated by the Mathematica tool, as well as additional numerical results from MATLAB.

  4. Arithmetic and algebraic problem solving and resource allocation: the distinct impact of fluid and numerical intelligence.

    Science.gov (United States)

    Dix, Annika; van der Meer, Elke

    2015-04-01

    This study investigates cognitive resource allocation dependent on fluid and numerical intelligence in arithmetic/algebraic tasks varying in difficulty. Sixty-six 11th grade students participated in a mathematical verification paradigm, while pupil dilation as a measure of resource allocation was collected. Students with high fluid intelligence solved the tasks faster and more accurately than those with average fluid intelligence, as did students with high compared to average numerical intelligence. However, fluid intelligence sped up response times only in students with average but not high numerical intelligence. Further, high fluid but not numerical intelligence led to greater task-related pupil dilation. We assume that fluid intelligence serves as a domain-general resource that helps to tackle problems for which domain-specific knowledge (numerical intelligence) is missing. The allocation of this resource can be measured by pupil dilation. Copyright © 2014 Society for Psychophysiological Research.

  5. Numerical methods to solve the two-dimensional heat conduction equation

    International Nuclear Information System (INIS)

    Santos, R.S. dos.

    1981-09-01

    A class of numerical methods, called 'Hopscotch Algorithms', was used to solve the heat conduction equation in cylindrical geometry. Using a time dependent heat source, the temperature versus time behaviour of cylindric rod was analysed. Numerical simulation was used to study the stability and the convergence of each different method. Another test had the temperature specified on the outer surface as boundary condition. The various Hopscotch methods analysed exhibit differing degrees of accuracy, few of them being so accurate as the ADE method, but requiring more computational operations than the later, were observed. Finally, compared with the so called ODD-EVEN method, two other Hopscotch methods, are more time consuming. (Author) [pt

  6. Numerical method for solving the three-dimensional time-dependent neutron diffusion equation

    International Nuclear Information System (INIS)

    Khaled, S.M.; Szatmary, Z.

    2005-01-01

    A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)

  7. A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations

    Directory of Open Access Journals (Sweden)

    F. Ghomanjani

    2016-10-01

    Full Text Available In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.

  8. A difference quotient-numerical integration method for solving radiative transfer problems

    International Nuclear Information System (INIS)

    Ding Peizhu

    1992-01-01

    A difference quotient-numerical integration method is adopted to solve radiative transfer problems in an anisotropic scattering slab medium. By using the method, the radiative transfer problem is separated into a system of linear algebraic equations and the coefficient matrix of the system is a band matrix, so the method is very simple to evaluate on computer and to deduce formulae and easy to master for experimentalists. An example is evaluated and it is shown that the method is precise

  9. Teacher Practices with Toddlers during Social Problem Solving Opportunities

    Science.gov (United States)

    Gloeckler, Lissy; Cassell, Jennifer

    2012-01-01

    This article explores how teachers can foster an environment that facilitates social problem solving when toddlers experience conflict, emotional dysregulation, and aggression. This article examines differences in child development and self-regulation outcomes when teachers engage in problem solving "for" toddlers and problem solving "with"…

  10. Solving point reactor kinetic equations by time step-size adaptable numerical methods

    International Nuclear Information System (INIS)

    Liao Chaqing

    2007-01-01

    Based on the analysis of effects of time step-size on numerical solutions, this paper showed the necessity of step-size adaptation. Based on the relationship between error and step-size, two-step adaptation methods for solving initial value problems (IVPs) were introduced. They are Two-Step Method and Embedded Runge-Kutta Method. PRKEs were solved by implicit Euler method with step-sizes optimized by using Two-Step Method. It was observed that the control error has important influence on the step-size and the accuracy of solutions. With suitable control errors, the solutions of PRKEs computed by the above mentioned method are accurate reasonably. The accuracy and usage of MATLAB built-in ODE solvers ode23 and ode45, both of which adopt Runge-Kutta-Fehlberg method, were also studied and discussed. (authors)

  11. A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations

    KAUST Repository

    Zhang, Tao; Salama, Amgad; Sun, Shuyu; Zhong, Hua

    2015-01-01

    In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.

  12. A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations

    KAUST Repository

    Zhang, Tao

    2015-06-01

    In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.

  13. A method for solving the KDV equation and some numerical experiments

    International Nuclear Information System (INIS)

    Chang Jinjiang.

    1993-01-01

    In this paper, by means of difference method for discretization of space partial derivatives of KDV equation, an initial value problem in ordinary differential equations of large dimensions is produced. By using this ordinary differential equations the existence and the uniqueness of the solution of the KDV equation and the conservation of scheme are proved. This ordinary differential equation can be solved by using implicit Runge-Kutta methods, so a new method for finding the numerical solution of the KDV equation is presented. Numerical experiments not only describe in detail the procedure of two solitons collision, soliton reflex and soliton produce, but also show that this method is very effective. (author). 7 refs, 3 figs

  14. Problem of the Moving Boundary in Continuous Casting Solved by The Analytic-Numerical Method

    Directory of Open Access Journals (Sweden)

    Grzymkowski R.

    2013-03-01

    Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase - liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

  15. Problem of the Moving Boundary in Continuous Casting Solved by the Analytic-Numerical Method

    Directory of Open Access Journals (Sweden)

    R. Grzymkowski

    2013-01-01

    Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.

  16. Finite difference method and algebraic polynomial interpolation for numerically solving Poisson's equation over arbitrary domains

    Directory of Open Access Journals (Sweden)

    Tsugio Fukuchi

    2014-06-01

    Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.

  17. An efficient numerical method for solving the Boltzmann equation in multidimensions

    Science.gov (United States)

    Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas

    2018-01-01

    In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with conservative fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.

  18. NUMERICAL TECHNIQUES TO SOLVE CONDENSATIONAL AND DISSOLUTIONAL GROWTH EQUATIONS WHEN GROWTH IS COUPLED TO REVERSIBLE REACTIONS (R823186)

    Science.gov (United States)

    Noniterative, unconditionally stable numerical techniques for solving condensational anddissolutional growth equations are given. Growth solutions are compared to Gear-code solutions forthree cases when growth is coupled to reversible equilibrium chemistry. In all cases, ...

  19. A numerical spectral approach to solve the dislocation density transport equation

    International Nuclear Information System (INIS)

    Djaka, K S; Taupin, V; Berbenni, S; Fressengeas, C

    2015-01-01

    A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme. (paper)

  20. Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems

    International Nuclear Information System (INIS)

    Hykes, J. M.; Ferrer, R. M.

    2013-01-01

    The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is 98 Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)

  1. New numerical approximation for solving fractional delay differential equations of variable order using artificial neural networks

    Science.gov (United States)

    Zúñiga-Aguilar, C. J.; Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Martínez, V. M.; Romero-Ugalde, H. M.

    2018-02-01

    In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated.

  2. Role of beliefs and emotions in numerical problem solving in university physics education

    Science.gov (United States)

    Bodin, Madelen; Winberg, Mikael

    2012-06-01

    Numerical problem solving in classical mechanics in university physics education offers a learning situation where students have many possibilities of control and creativity. In this study, expertlike beliefs about physics and learning physics together with prior knowledge were the most important predictors of the quality of performance of a task with many degrees of freedom. Feelings corresponding to control and concentration, i.e., emotions that are expected to trigger students’ intrinsic motivation, were also important in predicting performance. Unexpectedly, intrinsic motivation, as indicated by enjoyment and interest, together with students’ personal interest and utility value beliefs did not predict performance. This indicates that although a certain degree of enjoyment is probably necessary, motivated behavior is rather regulated by integration and identification of expertlike beliefs about learning and are more strongly associated with concentration and control during learning and, ultimately, with high performance. The results suggest that the development of students’ epistemological beliefs is important for students’ ability to learn from realistic problem-solving situations with many degrees of freedom in physics education.

  3. Role of beliefs and emotions in numerical problem solving in university physics education

    Directory of Open Access Journals (Sweden)

    Madelen Bodin

    2012-02-01

    Full Text Available Numerical problem solving in classical mechanics in university physics education offers a learning situation where students have many possibilities of control and creativity. In this study, expertlike beliefs about physics and learning physics together with prior knowledge were the most important predictors of the quality of performance of a task with many degrees of freedom. Feelings corresponding to control and concentration, i.e., emotions that are expected to trigger students’ intrinsic motivation, were also important in predicting performance. Unexpectedly, intrinsic motivation, as indicated by enjoyment and interest, together with students’ personal interest and utility value beliefs did not predict performance. This indicates that although a certain degree of enjoyment is probably necessary, motivated behavior is rather regulated by integration and identification of expertlike beliefs about learning and are more strongly associated with concentration and control during learning and, ultimately, with high performance. The results suggest that the development of students’ epistemological beliefs is important for students’ ability to learn from realistic problem-solving situations with many degrees of freedom in physics education.

  4. A Problem-Solving Model for Literacy Coaching Practice

    Science.gov (United States)

    Toll, Cathy A.

    2017-01-01

    Literacy coaches are more effective when they have a clear plan for their collaborations with teachers. This article provides details of such a plan, which involves identifying a problem, understanding the problem, deciding what to do differently, and trying something different. For each phase of the problem-solving model, there are key tasks for…

  5. A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics

    Directory of Open Access Journals (Sweden)

    E. Kaas

    2013-11-01

    Full Text Available A new hybrid Eulerian–Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass-conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place; i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.

  6. Do practice nurse solve future GP capacity problems?

    NARCIS (Netherlands)

    Lamkaddem, M.; Haan, J. de; Bakker, D. de

    2003-01-01

    Background: Task delegation is viewed as an important policy instrument to counter foreseen future shortages in GP capacity in the Netherlands. Therefore, a national programme to introduce practice nurses in general practice was launched in 1998 by the National Association of General Practice. In

  7. Classical and modern numerical analysis theory, methods and practice

    CERN Document Server

    Ackleh, Azmy S; Kearfott, R Baker; Seshaiyer, Padmanabhan

    2009-01-01

    Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-Eigenvector Computation Basic Results from Linear Algebra The Power Method The Inverse Power Method Deflation T...

  8. Numerical solving of equations in the work of José Mariano Vallejo

    Science.gov (United States)

    Pacheco Castelao, José-Miguel; Pérez-Fern; ández, F. Javier; Suárez Alemán, Carlos-Oswaldo

    2007-09-01

    The progress of Mathematics during the nineteenth century was characterised both by an enormous acquisition of new knowledge and by the attempts to introduce rigour in reasoning patterns and mathematical writing. Cauchy's presentation of Mathematical Analysis was not immediately accepted, and many writers, though aware of that new style, did not use it in their own mathematical production. This paper is devoted to an episode of this sort that took place in Spain during the first half of the century: It deals with the presentation of a method for numerically solving algebraic equations by José Mariano Vallejo, a late Spanish follower of the Enlightenment ideas, politician, writer, and mathematician who published it in the fourth (1840) edition of his book Compendio de Mathemáticas Puras y Mistas, claiming to have discovered it on his own. Vallejo's main achievement was to write down the whole procedure in a very careful way taking into account the different types of roots, although he paid little attention to questions such as convergence checks and the fulfilment of the hypotheses of Rolle's Theorem. For sure this lack of mathematical care prevented Vallejo to occupy a place among the forerunners of Computational Algebra.

  9. A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves

    Science.gov (United States)

    Favrie, N.; Gavrilyuk, S.

    2017-07-01

    A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler-Lagrange equations for a ‘master’ lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge in solving the SGN equations is the resolution of an elliptic problem at each time instant. This is the most time-consuming part of the numerical method. The idea is to replace the ‘master’ lagrangian by a one-parameter family of ‘augmented’ lagrangians, depending on a greater number of variables, for which the corresponding Euler-Lagrange equations are hyperbolic. In such an approach, the ‘master’ lagrangian is recovered by the augmented lagrangian in some limit (for example, when the corresponding parameter is large). The choice of such a family of augmented lagrangians is proposed and discussed. The corresponding hyperbolic system is numerically solved by a Godunov type method. Numerical solutions are compared with exact solutions to the SGN equations. It appears that the computational time in solving the hyperbolic system is much lower than in the case where the elliptic operator is inverted. The new method is applied, in particular, to the study of ‘Favre waves’ representing non-stationary undular bores produced after reflection of the fluid flow with a free surface at an immobile wall.

  10. Practical design of magnetostatic structure using numerical simulation

    CERN Document Server

    Wang, Qiuliang

    2013-01-01

    Covers the practical numerical method for the analysis and design of magnets Extensively covers the magnet design and computation aspects from theories to practical applications, emphasizing design methods of practical structures such as superconducting, electromagnetic and permanent magnet for use in various scientific instruments, industrial processing, biomedicine and special electrical equipments. The computations cover a wide range of numerical techniques and analytical derivation to efficiently provide solutions to complicated problems that are often encountered in practice, where simple analytical calculations are no longer adequate. Chapters include: Introduction of Magnet Technology, Magnetostatic Equation for the Magnet Structure, Finite Element Analysis for Magnetostatic Field, Integral Method for Magnetostatic Field, Numerical Method of Solenoid Coils Design, Series Analysis of Axially Symmetric Magnetic Field, Magnets with High Magnetic Field and High Homogeneity, Permanent Magnet and its App...

  11. Incorporating the Common Core's Problem Solving Standard for Mathematical Practice into an Early Elementary Inclusive Classroom

    Science.gov (United States)

    Fletcher, Nicole

    2014-01-01

    Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

  12. An Investigation into Students' Difficulties in Numerical Problem Solving Questions in High School Biology Using a Numeracy Framework

    Science.gov (United States)

    Scott, Fraser J.

    2016-01-01

    The "mathematics problem" is a well-known source of difficulty for students attempting numerical problem solving questions in the context of science education. This paper illuminates this problem from a biology education perspective by invoking Hogan's numeracy framework. In doing so, this study has revealed that the contextualisation of…

  13. Solving the dynamic rupture problem with different numerical approaches and constitutive laws

    Science.gov (United States)

    Bizzarri, A.; Cocco, M.; Andrews, D.J.; Boschi, Enzo

    2001-01-01

    We study the dynamic initiation, propagation and arrest of a 2-D in-plane shear rupture by solving the elastodynamic equation by using both a boundary integral equation method and a finite difference approach. For both methods we adopt different constitutive laws: a slip-weakening (SW) law, with constant weakening rate, and rate- and state-dependent friction laws (Dieterich-Ruina). Our numerical procedures allow the use of heterogeneous distributions of constitutive parameters along the fault for both formulations. We first compare the two solution methods with an SW law, emphasizing the required stability conditions to achieve a good resolution of the cohesive zone and to avoid artificial complexity in the solutions. Our modelling results show that the two methods provide very similar time histories of dynamic source parameters. We point out that, if a careful control of resolution and stability is performed, the two methods yield identical solutions. We have also compared the rupture evolution resulting from an SW and a rate- and state-dependent friction law. This comparison shows that despite the different constitutive formulations, a similar behaviour is simulated during the rupture propagation and arrest. We also observe a crack tip bifurcation and a jump in rupture velocity (approaching the P-wave speed) with the Dieterich-Ruina (DR) law. The rupture arrest at a barrier (high strength zone) and the barrier-healing mechanism are also reproduced by this law. However, this constitutive formulation allows the simulation of a more general and complex variety of rupture behaviours. By assuming different heterogeneous distributions of the initial constitutive parameters, we are able to model a barrier-healing as well as a self-healing process. This result suggests that if the heterogeneity of the constitutive parameters is taken into account, the different healing mechanisms can be simulated. We also study the nucleation phase duration Tn, defined as the time

  14. Patterns of brain and cardiovascular activation while solving rule-discovery and rule-application numeric tasks.

    Science.gov (United States)

    Sosnowski, Tytus; Rynkiewicz, Andrzej; Wordecha, Małgorzata; Kępkowicz, Anna; Majewska, Adrianna; Pstrągowska, Aleksandra; Oleksy, Tomasz; Wypych, Marek; Marchewka, Artur

    2017-07-01

    It is known that solving mental tasks leads to tonic increase in cardiovascular activity. Our previous research showed that tasks involving rule application (RA) caused greater tonic increase in cardiovascular activity than tasks requiring rule discovery (RD). However, it is not clear what brain mechanisms are responsible for this difference. The aim of two experimental studies was to compare the patterns of brain and cardiovascular activity while both RD and the RA numeric tasks were being solved. The fMRI study revealed greater brain activation while solving RD tasks than while solving RA tasks. In particular, RD tasks evoked greater activation of the left inferior frontal gyrus and selected areas in the parietal, and temporal cortices, including the precuneus, supramarginal gyrus, angular gyrus, inferior parietal lobule, and the superior temporal gyrus, and the cingulate cortex. In addition, RA tasks caused larger increases in HR than RD tasks. The second study, carried out in a cardiovascular laboratory, showed greater increases in heart rate (HR), systolic blood pressure (SBP), diastolic blood pressure (DBP), and mean arterial pressure (MAP) while solving RA tasks than while solving RD tasks. The results support the hypothesis that RD and RA tasks involve different modes of information processing, but the neuronal mechanism responsible for the observed greater cardiovascular response to RA tasks than to RD tasks is not completely clear. Copyright © 2017. Published by Elsevier B.V.

  15. An efficient numerical technique for solving navier-stokes equations for rotating flows

    International Nuclear Information System (INIS)

    Haroon, T.; Shah, T.M.

    2000-01-01

    This paper simulates an industrial problem by solving compressible Navier-Stokes equations. The time-consuming tri-angularization process of a large-banded matrix, performed by memory economical Frontal Technique. This scheme successfully reduces the time for I/O operations even for as large as (40, 000 x 40, 000) matrix. Previously, this industrial problem can solved by using modified Newton's method with Gaussian elimination technique for the large matrix. In the present paper, the proposed Frontal Technique is successfully used, together with Newton's method, to solve compressible Navier-Stokes equations for rotating cylinders. By using the Frontal Technique, the method gives the solution within reasonably acceptance computational time. Results are compared with the earlier works done, and found computationally very efficient. Some features of the solution are reported here for the rotating machines. (author)

  16. Theory and algorithms for solving large-scale numerical problems. Application to the management of electricity production

    International Nuclear Information System (INIS)

    Chiche, A.

    2012-01-01

    This manuscript deals with large-scale optimization problems, and more specifically with solving the electricity unit commitment problem arising at EDF. First, we focused on the augmented Lagrangian algorithm. The behavior of that algorithm on an infeasible convex quadratic optimization problem is analyzed. It is shown that the algorithm finds a point that satisfies the shifted constraints with the smallest possible shift in the sense of the Euclidean norm and that it minimizes the objective on the corresponding shifted constrained set. The convergence to such a point is realized at a global linear rate, which depends explicitly on the augmentation parameter. This suggests us a rule for determining the augmentation parameter to control the speed of convergence of the shifted constraint norm to zero. This rule has the advantage of generating bounded augmentation parameters even when the problem is infeasible. As a by-product, the algorithm computes the smallest translation in the Euclidean norm that makes the constraints feasible. Furthermore, this work provides solution methods for stochastic optimization industrial problems decomposed on a scenario tree, based on the progressive hedging algorithm introduced by [Rockafellar et Wets, 1991]. We also focus on the convergence of that algorithm. On the one hand, we offer a counter-example showing that the algorithm could diverge if its augmentation parameter is iteratively updated. On the other hand, we show how to recover the multipliers associated with the non-dualized constraints defined on the scenario tree from those associated with the corresponding constraints of the scenario subproblems. Their convergence is also analyzed for convex problems. The practical interest of theses solutions techniques is corroborated by numerical experiments performed on the electric production management problem. We apply the progressive hedging algorithm to a realistic industrial problem. More precisely, we solve the French medium

  17. A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Mountassir Hamdi Cherif

    2017-11-01

    Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

  18. A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

    Energy Technology Data Exchange (ETDEWEB)

    Ohsuga, Ken; Takahashi, Hiroyuki R. [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)

    2016-02-20

    We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.

  19. Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel.

    Science.gov (United States)

    Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E

    2016-06-01

    The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.

  20. Excel 2016 for biological and life sciences statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J; Horton, Howard F

    2016-01-01

    This book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical biological and life science problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel is an effective learning tool for quantitative analyses in biological and life sciences courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Biological and Life Sciences Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel 2016 to statistical techniques necessary in their courses and work. Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand biological and life science problems. Practice problems are provided...

  1. Excel 2016 for physical sciences statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J; Horton, Howard F

    2016-01-01

    This book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical physical science problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel is an effective learning tool for quantitative analyses in environmental science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Physical Sciences Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel 2016 to statistical techniques necessary in their courses and work. Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand physical science problems. Practice problems are provided at the end of each chapter with their s...

  2. Excel 2016 for environmental sciences statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J; Horton, Howard F

    2016-01-01

    This book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical environmental science problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel is an effective learning tool for quantitative analyses in environmental science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Environmental Science Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel 2016 to statistical techniques necessary in their courses and work. Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand environmental science problems. Practice problems are provided at the end of each chapte...

  3. Excel 2016 for social work statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2017-01-01

    This text is a step-by-step guide for students taking a first course in statistics for social work and for social work managers and practitioners who want to learn how to use Excel to solve practical statistics problems in in the workplace, whether or not they have taken a course in statistics. There is no other text for a first course in social work statistics that teaches students, step-by-step, how to use Excel to solve interesting social work statistics problems. Excel 2016 for Social Work Statistics explains statistical formulas and offers practical examples for how students can solve real-world social work statistics problems. This book leaves detailed explanations of statistical theory to other statistics textbooks and focuses entirely on practical, real-world problem solving. Each chapter briefly explains a topic and then demonstrates how to use Excel commands and formulas to solve specific social work statistics problems.  This book gives practice in using Excel in two different ways:  (1) writing ...

  4. A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg-Marquardt Algorithm

    Directory of Open Access Journals (Sweden)

    Tao Min

    2014-01-01

    Full Text Available This paper is intended to provide a numerical algorithm involving the combined use of the Levenberg-Marquardt algorithm and the Galerkin finite element method for estimating the diffusion coefficient in an inverse heat conduction problem (IHCP. In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. Numerical experiments are presented to show the efficiency of the proposed method.

  5. From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

    2016-02-15

    We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

  6. Numerical methods for solving the governing equations for a seriated continuum

    International Nuclear Information System (INIS)

    Narum, R.E.; Noble, C.; Mortensen, G.A.; McFadden, J.H.

    1976-09-01

    A desire to more accurately predict the behavior of transient two-phase flows has resulted in an investigation of the feasibility of computing unequal phase velocities and unequal phase temperatures. The finite difference forms of a set of equations governing a seriated continuum are presented along with two methods developed for solving the resulting systems of simultaneous nonlinear equations. Results from a one-dimensional computer code are presented to illustrate the capabilities of one of the solution methods

  7. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

    Science.gov (United States)

    Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

    2013-03-01

    In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

  8. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

    OpenAIRE

    Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

    2013-01-01

    In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...

  9. A practical approximation algorithm for solving massive instances of hybridization number

    NARCIS (Netherlands)

    Iersel, van L.J.J.; Kelk, S.M.; Lekic, N.; Scornavacca, C.; Raphael, B.; Tang, J.

    2012-01-01

    Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. In practice, exact solvers struggle to solve instances with

  10. Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics.

    Science.gov (United States)

    Artzt, Alice F.; Armour-Thomas, Eleanor

    1998-01-01

    Uses a "teaching as problem solving" perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning secondary-school mathematics teachers. Data analysis of observations, lesson plans, videotapes, and audiotapes of structured interviews suggests that the metacognition of…

  11. Enhancing Arithmetic and Word-Problem Solving Skills Efficiently by Individualized Computer-Assisted Practice

    Science.gov (United States)

    Schoppek, Wolfgang; Tulis, Maria

    2010-01-01

    The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a…

  12. Excel 2016 for advertising statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2017-01-01

    This text is a step-by-step guide for students taking a first course in statistics for advertising and for advertising managers and practitioners who want to learn how to use Excel to solve practical statistics problems in in the workplace, whether or not they have taken a course in statistics. Excel 2016 for Advertising Statistics explains statistical formulas and offers practical examples for how students can solve real-world advertising statistics problems. This book leaves detailed explanations of statistical theory to other statistics textbooks and focuses entirely on practical, real-world problem solving. Each chapter briefly explains a topic and then demonstrates how to use Excel commands and formulas to solve specific advertising statistics problems.  This book gives practice in using Excel in two different ways:  (1) writing formulas (e.g., confidence interval about the mean, one-group t-test, two-group t-test, correlation) and (2) using Excel’s drop-down formula menus (e.g., simple linear regres...

  13. On some examples of pollutant transport problems solved numerically using the boundary element method

    Science.gov (United States)

    Azis, Moh. Ivan; Kasbawati; Haddade, Amiruddin; Astuti Thamrin, Sri

    2018-03-01

    A boundary element method (BEM) is obtained for solving a boundary value problem of homogeneous anisotropic media governed by diffusion-convection equation. The application of the BEM is shown for two particular pollutant transport problems of Tello river and Unhas lake in Makassar Indonesia. For the two particular problems a variety of the coefficients of diffusion and the velocity components are taken. The results show that the solutions vary as the parameters change. And this suggests that one has to be careful in measuring or determining the values of the parameters.

  14. A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

    Directory of Open Access Journals (Sweden)

    Muhammed I. Syam

    2017-11-01

    Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.

  15. Numerical Platon: A unified linear equation solver interface by CEA for solving open foe scientific applications

    International Nuclear Information System (INIS)

    Secher, Bernard; Belliard, Michel; Calvin, Christophe

    2009-01-01

    This paper describes a tool called 'Numerical Platon' developed by the French Atomic Energy Commission (CEA). It provides a freely available (GNU LGPL license) interface for coupling scientific computing applications to various freeware linear solver libraries (essentially PETSc, SuperLU and HyPre), together with some proprietary CEA solvers, for high-performance computers that may be used in industrial software written in various programming languages. This tool was developed as part of considerable efforts by the CEA Nuclear Energy Division in the past years to promote massively parallel software and on-shelf parallel tools to help develop new generation simulation codes. After the presentation of the package architecture and the available algorithms, we show examples of how Numerical Platon is used in sequential and parallel CEA codes. Comparing with in-house solvers, the gain in terms of increases in computation capacities or in terms of parallel performances is notable, without considerable extra development cost

  16. Numerical Platon: A unified linear equation solver interface by CEA for solving open foe scientific applications

    Energy Technology Data Exchange (ETDEWEB)

    Secher, Bernard [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Saclay DM2S/SFME/LGLS, Bat. 454, F-91191 Gif-sur-Yvette Cedex (France)], E-mail: bsecher@cea.fr; Belliard, Michel [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Cadarache DER/SSTH/LMDL, Bat. 238, F-13108 Saint-Paul-lez-Durance Cedex (France); Calvin, Christophe [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Saclay DM2S/SERMA/LLPR, Bat. 470, F-91191 Gif-sur-Yvette Cedex (France)

    2009-01-15

    This paper describes a tool called 'Numerical Platon' developed by the French Atomic Energy Commission (CEA). It provides a freely available (GNU LGPL license) interface for coupling scientific computing applications to various freeware linear solver libraries (essentially PETSc, SuperLU and HyPre), together with some proprietary CEA solvers, for high-performance computers that may be used in industrial software written in various programming languages. This tool was developed as part of considerable efforts by the CEA Nuclear Energy Division in the past years to promote massively parallel software and on-shelf parallel tools to help develop new generation simulation codes. After the presentation of the package architecture and the available algorithms, we show examples of how Numerical Platon is used in sequential and parallel CEA codes. Comparing with in-house solvers, the gain in terms of increases in computation capacities or in terms of parallel performances is notable, without considerable extra development cost.

  17. Numerical simulation of the two-phase flows in a hydraulic coupling by solving VOF model

    International Nuclear Information System (INIS)

    Luo, Y; Zuo, Z G; Liu, S H; Fan, H G; Zhuge, W L

    2013-01-01

    The flow in a partially filled hydraulic coupling is essentially a gas-liquid two-phase flow, in which the distribution of two phases has significant influence on its characteristics. The interfaces between the air and the liquid, and the circulating flows inside the hydraulic coupling can be simulated by solving the VOF two-phase model. In this paper, PISO algorithm and RNG k–ε turbulence model were employed to simulate the phase distribution and the flow field in a hydraulic coupling with 80% liquid fill. The results indicate that the flow forms a circulating movement on the torus section with decreasing speed ratio. In the pump impeller, the air phase mostly accumulates on the suction side of the blades, while liquid on the pressure side; in turbine runner, air locates in the middle of the flow passage. Flow separations appear near the blades and the enclosing boundaries of the hydraulic coupling

  18. Results of numerically solving an integral equation for a two-fermion system

    International Nuclear Information System (INIS)

    Skachkov, N.B.; Solov'eva, T.M.

    2003-01-01

    A two-particle system is described by integral equations whose kernels are dependent on the total energy of the system. Such equations can be reduced to an eigenvalue problem featuring an eigenvalue-dependent operator. This nonlinear eigenvalue problem is solved by means of an iterative procedure developed by the present authors. The energy spectra of a two-fermion system formed by particles of identical masses are obtained for two cases, that where the total spin of the system is equal to zero and that where the total spin of the system is equal to unity. The splitting of the ground-state levels of positronium and dimuonium, the frequency of the transition from the ground state of orthopositronium to its first excited state, and the probabilities of parapositronium and paradimuonium decays are computed. The results obtained in this way are found to be in good agreement with experimental data

  19. Attitude and practice of physical activity and social problem-solving ability among university students.

    Science.gov (United States)

    Sone, Toshimasa; Kawachi, Yousuke; Abe, Chihiro; Otomo, Yuki; Sung, Yul-Wan; Ogawa, Seiji

    2017-04-04

    Effective social problem-solving abilities can contribute to decreased risk of poor mental health. In addition, physical activity has a favorable effect on mental health. These previous studies suggest that physical activity and social problem-solving ability can interact by helping to sustain mental health. The present study aimed to determine the association between attitude and practice of physical activity and social problem-solving ability among university students. Information on physical activity and social problem-solving was collected using a self-administered questionnaire. We analyzed data from 185 students who participated in the questionnaire surveys and psychological tests. Social problem-solving as measured by the Social Problem-Solving Inventory-Revised (SPSI-R) (median score 10.85) was the dependent variable. Multiple logistic regression analysis was employed to calculate the odds ratios (ORs) and 95% confidence intervals (CIs) for higher SPSI-R according to physical activity categories. The multiple logistic regression analysis indicated that the ORs (95% CI) in reference to participants who said they never considered exercising were 2.08 (0.69-6.93), 1.62 (0.55-5.26), 2.78 (0.86-9.77), and 6.23 (1.81-23.97) for participants who did not exercise but intended to start, tried to exercise but did not, exercised but not regularly, and exercised regularly, respectively. This finding suggested that positive linear association between physical activity and social problem-solving ability (p value for linear trend social problem-solving ability.

  20. Community problem-solving framed as a distributed information use environment: bridging research and practice

    Directory of Open Access Journals (Sweden)

    Joan C. Durrance

    2006-01-01

    Full Text Available Introduction. This article results from a qualitative study of 1 information behavior in community problem-solving framed as a distributed information use environment and 2 approaches used by a best-practice library to anticipate information needs associated with community problem solving. Method. Several approaches to data collection were used - focus groups, interviews, observation of community and library meetings, and analysis of supporting documents. We focused first on the information behaviour of community groups. Finding that the library supported these activities we sought to understand its approach. Analysis. Data were coded thematically for both information behaviour concepts and themes germane to problem-solving activity. A grounded theory approach was taken to capture aspects of the library staff's practice. Themes evolved from the data; supporting documentation - reports, articles and library communication - was also coded. Results. The study showed 1 how information use environment components (people, setting, problems, problem resolutions combine in this distributed information use environment to determine specific information needs and uses; and 2 how the library contributed to the viability of this distributed information use environment. Conclusion. Community problem solving, here explicated as a distributed IUE, is likely to be seen in multiple communities. The library model presented demonstrates that by reshaping its information practice within the framework of an information use environment, a library can anticipate community information needs as they are generated and where they are most relevant.

  1. Peaks, plateaus, numerical instabilities, and achievable accuracy in Galerkin and norm minimizing procedures for solving Ax=b

    Energy Technology Data Exchange (ETDEWEB)

    Cullum, J. [IBM T.J. Watson Research Center, Yorktown Heights, NY (United States)

    1994-12-31

    Plots of the residual norms generated by Galerkin procedures for solving Ax = b often exhibit strings of irregular peaks. At seemingly erratic stages in the iterations, peaks appear in the residual norm plot, intervals of iterations over which the norms initially increase and then decrease. Plots of the residual norms generated by related norm minimizing procedures often exhibit long plateaus, sequences of iterations over which reductions in the size of the residual norm are unacceptably small. In an earlier paper the author discussed and derived relationships between such peaks and plateaus within corresponding Galerkin/Norm Minimizing pairs of such methods. In this paper, through a set of numerical experiments, the author examines connections between peaks, plateaus, numerical instabilities, and the achievable accuracy for such pairs of iterative methods. Three pairs of methods, GMRES/Arnoldi, QMR/BCG, and two bidiagonalization methods are studied.

  2. A new numerical method to solve the dispersion relation in multispecies plasma

    International Nuclear Information System (INIS)

    Cereceda, C.; Puerta, J.

    2000-01-01

    In this paper a new accurate and fast method for solving the linear dispersion relation for multispecies plasma is introduced. The method uses a four poles fractional approximation for the Z dispersion function, transforming the dispersion relation into a polynomial form. Time and space growth rates are then calculated. Calculations for a single beam - plasma are carried out being in good agreement with several authors. This method is very effective to simplify the calculation of growth rates in multi-ion plasmas. For multispecies plasmas several new modes of propagation arise. For two ion beam - plasma system, two slow modes can propagate, both which are unstable. Two maxima in the growth rates corresponding to each of these modes can be excited. The instability of one of the slow modes is fed by the energy of the light ion beam and the other one is fed by heavy beam ions. Each one of these two maxima is increased when the concentration of the corresponding species increases. But even for a small concentration of the light beam, the growth rate of the mode fed by it is the largest one, because in the single ion beam-plasma system the lighter ion yields the largest growth rate. (orig.)

  3. On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

    Science.gov (United States)

    Kudryavtsev, O.; Rodochenko, V.

    2018-03-01

    We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

  4. Solved problems in classical mechanics analytical and numerical solutions with comments

    CERN Document Server

    de Lange, O L

    2010-01-01

    Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...

  5. Finite element circuit theory of the numerical code EDDYMULT for solving eddy current problems in a multi-torus system

    International Nuclear Information System (INIS)

    Nakamura, Yukiharu; Ozeki, Takahisa

    1986-07-01

    The finite element circuit theory is extended to the general eddy current problem in a multi-torus system, which consists of various torus conductors and axisymmetric coil systems. The numerical procedures are devised to avoid practical restrictions of computer storage and computing time, that is, the reduction technique of eddy current eigen modes to save storage and the introduction of shape function into the double area integral of mode coupling to save time. The numerical code EDDYMULT based on the theory is developed to use in designing tokamak device from the viewpoints of the evaluation of electromagnetic loading on the device components and the control analysis of tokamak equilibrium. (author)

  6. Fast numerical method for solving the three-dimensional Stokes' equations in the presence of suspended particles

    International Nuclear Information System (INIS)

    Fogelson, A.L.; Peskin, C.S.

    1988-01-01

    A new fast numerical method for solving the three-dimensional Stokes' equations in the presence of suspended particles is presented. The fluid dynamics equations are solved on a lattice. A particle is represented by a set of points each of which moves at the local fluid velocity and is not constrained to lie on the lattice. These points are coupled by forces which resist deformation of the particle. These forces contribute to the force density in the Stokes' equations. As a result, a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries. Particles size, shape, and deformability may be prescribed. Computational work increases only linearly with the number of particles, so large numbers (500--1000) of particles may be studied efficiently. The numerical method involves implicit calculation of the particle forces by minimizing an energy function and solution of a finite-difference approximation to the Stokes' equations using the Fourier--Toeplitz method. The numerical method has been implemented to run on all CRAY computers: the implementation exploits the CRAY's vectorized arithmetic, and on machines with insufficient central memory, it performs efficient disk I/O while storing most of the data on disk. Applications of the method to sedimentation of one-, two-, and many-particle systems are described. Trajectories and settling speeds for two-particle sedimentation, and settling speed for multiparticle sedimentation from initial distributions on a cubic lattice or at random give good quantitative agreement with existing theories. copyright 1988 Academic Press, Inc

  7. Excel 2016 for educational and psychological statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2016-01-01

    This book shows the capabilities of Microsoft Excel in teaching educational and psychological statistics effectively. Similar to the previously published Excel 2013 for Educational and Psychological Statistics, this book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical education and psychology problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in education and psychology courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Educational and Psychological Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and man...

  8. Excel 2013 for physical sciences statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J; Horton, Howard F

    2016-01-01

    This book shows the capabilities of Microsoft Excel in teaching physical sciences statistics effectively. Similar to the previously published Excel 2010 for Physical Sciences Statistics, this book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical science problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2013 for Physical Sciences Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their ...

  9. Excel 2016 for engineering statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2016-01-01

    This book shows the capabilities of Microsoft Excel in teaching engineering statistics effectively. Similar to the previously published Excel 2013 for Engineering Statistics, this book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical engineering problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in engineering courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However,Excel 2016 for Engineering Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and...

  10. Excel 2010 for health services management statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2014-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach health services management statistics effectively. It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical health services management problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you.   Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in health services management courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2010 for Health Services Management Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work....

  11. Excel 2013 for human resource management statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2016-01-01

    This book shows how Microsoft Excel is able to teach human resource management statistics effectively. Similar to the previously published Excel 2010 for Human Resource Management Statistics, it is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical human resource management problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in human resource management courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2013 for Human Resource Management Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to ...

  12. Excel 2016 for business statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2016-01-01

    This book shows the capabilities of Microsoft Excel in teaching business statistics effectively. Similar to the previously published Excel 2010 for Business Statistics, this book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical business problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in business courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Business Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work. Each ch...

  13. Excel 2016 for human resource management statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2016-01-01

    This book shows the capabilities of Microsoft Excel in teaching human resource management statistics effectively. Similar to the previously published Excel 2013 for Human Resource Management Statistics, this book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical human resource management problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in human resource management courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Human Resource Management Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how ...

  14. Excel 2013 for health services management statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2016-01-01

    This book shows the capabilities of Microsoft Excel to teach health services management statistics effectively. Similar to the previously published Excel 2010 for Health Services Management Statistics, this book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical health services management problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in health services management courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2013 for Health Services Management Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers ho...

  15. Excel 2016 for marketing statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2016-01-01

    This is the first book to show the capabilities of Microsoft Excel in teaching marketing statistics effectively. It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical marketing problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in marketing courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Marketing Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work. Each chapter explains statistical formulas and directs the reader t...

  16. Excel 2013 for educational and psychological statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2015-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach educational and psychological statistics effectively. It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical problems in education and psychology. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and practitioners, is also an effective teaching and learning tool for quantitative analyses in statistics courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2013 for Educational and Psychological Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and practitioners how to apply Excel to statistical techniques necessary in their courses and work. E...

  17. Excel 2016 for social science statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2016-01-01

    This book shows the capabilities of Microsoft Excel in teaching social science statistics effectively. Similar to the previously published Excel 2013 for Social Sciences Statistics, this book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical social science problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in social science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Social Science Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in ...

  18. 1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method

    Directory of Open Access Journals (Sweden)

    Szu-Hsien Peng

    2012-01-01

    Full Text Available The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative finite volume method, splitting is applied to manage the combination of hyperbolic term and source term of the shallow water equation and then to promote 1D to 2D. The simulations are validated by the comparison with flume experiments. Unsteady dam-break flow movement is found to be reasonably well captured by the model. The proposed concept could be further developed to the numerical calculation of non-Newtonian fluid or multilayers fluid flow.

  19. Creative Problem Solving and Social Cooperation of Effective Physical Therapy Practice: A Pioneer Study and Overview

    Directory of Open Access Journals (Sweden)

    Eli Carmeli

    2003-01-01

    Full Text Available Action research (AR has an important role to play in educating physical therapists. Increasing efforts should be encouraged to instigate AR programs in physical therapy practice and clinical education. Such programs commonly require considerable effort and understanding by clinical instructors, and require adoption of new educational methods. AR programs can lead physical therapists and clinicians to be more questioning and reflective in evaluating practical questions regarding patient therapy and education. The purpose of this article is to educate the readers on the importance of AR and to provide a few relevant references on that topic. A specific study is described in this paper in which physical therapy clinical instructors participated in a structured workshop designed to demonstrate the values of AR and how such values can be incorporated in teaching their students. AR can lead to improved therapist-patient interaction and help solve specific practical problems arising during therapy sessions.

  20. Curriculum providing cognitive knowledge and problem-solving skills for anesthesia systems-based practice.

    Science.gov (United States)

    Wachtel, Ruth E; Dexter, Franklin

    2010-12-01

    Residency programs accredited by the ACGME are required to teach core competencies, including systems-based practice (SBP). Projects are important for satisfying this competency, but the level of knowledge and problem-solving skills required presupposes a basic understanding of the field. The responsibilities of anesthesiologists include the coordination of patient flow in the surgical suite. Familiarity with this topic is crucial for many improvement projects. A course in operations research for surgical services was originally developed for hospital administration students. It satisfies 2 of the Institute of Medicine's core competencies for health professionals: evidence-based practice and work in interdisciplinary teams. The course lasts 3.5 days (eg, 2 weekends) and consists of 45 cognitive objectives taught using 7 published articles, 10 lectures, and 156 computer-assisted problem-solving exercises based on 17 case studies. We tested the hypothesis that the cognitive objectives of the curriculum provide the knowledge and problem-solving skills necessary to perform projects that satisfy the SBP competency. Standardized terminology was used to define each component of the SBP competency for the minimum level of knowledge needed. The 8 components of the competency were examined independently. Most cognitive objectives contributed to at least 4 of the 8 core components of the SBP competency. Each component of SBP is addressed at the minimum requirement level of exemplify by at least 6 objectives. There is at least 1 cognitive objective at the level of summarize for each SBP component. A curriculum in operating room management can provide the knowledge and problem-solving skills anesthesiologists need for participation in projects that satisfy the SBP competency.

  1. Topological insulators and C*-algebras: Theory and numerical practice

    International Nuclear Information System (INIS)

    Hastings, Matthew B.; Loring, Terry A.

    2011-01-01

    Research highlights: → We classify topological insulators using C* algebras. → We present new K-theory invariants. → We develop efficient numerical algorithms based on this technique. → We observe unexpected quantum phase transitions using our algorithm. - Abstract: We apply ideas from C*-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological obstructions to approximating these matrices by exactly commuting matrices, we are able to compute invariants quantifying different topological phases. We generalize previous two dimensional results to higher dimensions; we give a general expression for the topological invariants for arbitrary dimension and several symmetry classes, including chiral symmetry classes, and we present a detailed K-theory treatment of this expression for time reversal invariant three dimensional systems. We can use these results to show non-existence of localized Wannier functions for these systems. We use this approach to calculate the index for time-reversal invariant systems with spin-orbit scattering in three dimensions, on sizes up to 12 3 , averaging over a large number of samples. The results show an interesting separation between the localization transition and the point at which the average index (which can be viewed as an 'order parameter' for the topological insulator) begins to fluctuate from sample to sample, implying the existence of an unsuspected quantum phase transition separating two different delocalized phases in this system. One of the particular advantages of the C*-algebraic technique that we present is that it is significantly faster in practice than other methods of computing the index, allowing the study of larger systems. In this paper, we present a detailed discussion of numerical implementation of our method.

  2. A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

    Science.gov (United States)

    Ge, Liang; Sotiropoulos, Fotis

    2007-08-01

    A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow

  3. Numerical study of a stochastic particle algorithm solving a multidimensional population balance model for high shear granulation

    International Nuclear Information System (INIS)

    Braumann, Andreas; Kraft, Markus; Wagner, Wolfgang

    2010-01-01

    This paper is concerned with computational aspects of a multidimensional population balance model of a wet granulation process. Wet granulation is a manufacturing method to form composite particles, granules, from small particles and binders. A detailed numerical study of a stochastic particle algorithm for the solution of a five-dimensional population balance model for wet granulation is presented. Each particle consists of two types of solids (containing pores) and of external and internal liquid (located in the pores). Several transformations of particles are considered, including coalescence, compaction and breakage. A convergence study is performed with respect to the parameter that determines the number of numerical particles. Averaged properties of the system are computed. In addition, the ensemble is subdivided into practically relevant size classes and analysed with respect to the amount of mass and the particle porosity in each class. These results illustrate the importance of the multidimensional approach. Finally, the kinetic equation corresponding to the stochastic model is discussed.

  4. Excel 2013 for biological and life sciences statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J; Horton, Howard F

    2015-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach biological and life sciences statistics effectively.  It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical science problems.  If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you.  Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand science problems.  Practice problems are provided at the end of each chapter with their solutions in an appendix.  Separately, there is a full Practice Test (with answers in an Appendix) that allows readers to test what they have learned.  Includes 164 illustrations in color Suitable for undergraduates or graduate student Prof. Tom Quirk is currently a Professor of Marketing at The Walker School of Business and Technology at Webster University in St....

  5. Excel 2007 for Business Statistics A Guide to Solving Practical Business Problems

    CERN Document Server

    Quirk, Thomas J

    2012-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach business statistics effectively. It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical business problems. If understanding statistics isn't your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in business courses. Its powerful computat

  6. Socio-Demographic and Practice-Oriented Factors Related to Proficiency in Problem Solving: A Lifelong Learning Perspective

    Science.gov (United States)

    Desjardins, Richard; Ederer, Peer

    2015-01-01

    This article explores the relative importance of different socio-demographic and practice-oriented factors that are related to proficiency in problem solving in technology-rich environments (PSTREs) and by extension may be related to complex problem solving (CPS). The empirical analysis focuses on the proficiency measurements of PSTRE made…

  7. Frequent attenders in general practice: problem solving treatment provided by nurses [ISRCTN51021015

    Directory of Open Access Journals (Sweden)

    van Oppen P

    2005-10-01

    Full Text Available Abstract Background There is a need for assistance from primary care mental health workers in general practice in the Netherlands. General practitioners (GPs experience an overload of frequent attenders suffering from psychological problems. Problem Solving Treatment (PST is a brief psychological treatment tailored for use in a primary care setting. PST is provided by nurses, and earlier research has shown that it is a treatment at least as effective as usual care. However, research outcomes are not totally satisfying. This protocol describes a randomized clinical trial on the effectiveness of PST provided by nurses for patients in general practice. The results of this study, which currently being carried out, will be presented as soon as they are available. Methods/design This study protocol describes the design of a randomized controlled trial to investigate the effectiveness and cost-effectiveness of PST and usual care compared to usual care only. Patients, 18 years and older, who present psychological problems and are frequent attenders in general practice are recruited by the research assistant. The participants receive questionnaires at baseline, after the intervention, and again after 3 months and 9 months. Primary outcome is the reduction of symptoms, and other outcomes measured are improvement in problem solving skills, psychological and physical well being, daily functioning, social support, coping styles, problem evaluation and health care utilization. Discussion Our results may either confirm that PST in primary care is an effective way of dealing with emotional disorders and a promising addition to the primary care in the UK and USA, or may question this assumption. This trial will allow an evaluation of the effects of PST in practical circumstances and in a rather heterogeneous group of primary care patients. This study delivers scientific support for this use and therefore indications for optimal treatment and referral.

  8. Republic Scientific-practical Conference 'The Youth Role in solving the most important issues of globalization process' Proceedings

    International Nuclear Information System (INIS)

    2015-01-01

    Present collection comprises of materials of Republic Scientific-practical Conference 'The Youth Role in solving the most important issues of globalization process'. Present collection is intended for scientific and technical staff, postgraduates, and students of institutes of higher education.

  9. Excel 2010 for environmental sciences statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J; Horton, Howard F

    2015-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach environmental sciences statistics effectively.  It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical environmental sciences problems.  If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you.  Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in environmental science courses.  Its powerful computational ability and graphical functions make learning statistics much easier than in years past.  However, Excel 2010 for Environmental Sciences Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work. Eac...

  10. Excel 2016 in applied statistics for high school students a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2018-01-01

    This textbook is a step-by-step guide for high school, community college, or undergraduate students who are taking a course in applied statistics and wish to learn how to use Excel to solve statistical problems. All of the statistics problems in this book will come from the following fields of study: business, education, psychology, marketing, engineering and advertising. Students will learn how to perform key statistical tests in Excel without being overwhelmed by statistical theory. Each chapter briefly explains a topic and then demonstrates how to use Excel commands and formulas to solve specific statistics problems. This book gives practice in using Excel in two different ways: (1) writing formulas (e.g., confidence interval about the mean, one-group t-test, two-group t-test, correlation) and (2) using Excel’s drop-down formula menus (e.g., simple linear regression, multiple correlations and multiple regression, and one-way ANOVA). Three practice problems are provided at the end of each chapter, along w...

  11. Excel 2013 for social sciences statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2015-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach social science statistics effectively.  It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical social science problems.  If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you.  Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in social science courses.  Its powerful computational ability and graphical functions make learning statistics much easier than in years past.  However, Excel 2013 for Social Science Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work. Each chapter explains statistical formul...

  12. Excel 2013 for engineering statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2015-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach engineering statistics effectively.  It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical engineering problems.  If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in engineering courses.  Its powerful computational ability and graphical functions make learning statistics much easier than in years past.  However, Excel 2013 for Engineering Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work. Each chapter explains statistical formulas and directs...

  13. Excel 2013 for environmental sciences statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J; Horton, Howard F

    2015-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach environmentall sciences statistics effectively.  It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical environmental science problems.  If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you.  Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in environmental science courses.  Its powerful computational ability and graphical functions make learning statistics much easier than in years past.  However, Excel 2013 for Environmental Sciences Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work. Each chap...

  14. Excel 2010 for human resource management statistics a guide to solving practical problems

    CERN Document Server

    Quirk, Thomas J

    2014-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach human resource  management statistics effectively.  It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical human resource management problems.  If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you.  Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in human resource management courses.  Its powerful computational ability and graphical functions make learning statistics much easier than in years past.  However, Excel 2010 for Human Resource Management Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and ...

  15. Excel 2013 for business statistics a guide to solving practical business problems

    CERN Document Server

    Quirk, Thomas J

    2015-01-01

    This is the first book to show the capabilities of Microsoft Excel to teach business statistics effectively.  It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical business problems.  If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you.  Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in business courses.  Its powerful computational ability and graphical functions make learning statistics much easier than in years past.  However, Excel 2013 for Business Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work.                                �...

  16. Practical integrated simulation systems for coupled numerical simulations in parallel

    Energy Technology Data Exchange (ETDEWEB)

    Osamu, Hazama; Zhihong, Guo [Japan Atomic Energy Research Inst., Centre for Promotion of Computational Science and Engineering, Tokyo (Japan)

    2003-07-01

    In order for the numerical simulations to reflect 'real-world' phenomena and occurrences, incorporation of multidisciplinary and multi-physics simulations considering various physical models and factors are becoming essential. However, there still exist many obstacles which inhibit such numerical simulations. For example, it is still difficult in many instances to develop satisfactory software packages which allow for such coupled simulations and such simulations will require more computational resources. A precise multi-physics simulation today will require parallel processing which again makes it a complicated process. Under the international cooperative efforts between CCSE/JAERI and Fraunhofer SCAI, a German institute, a library called the MpCCI, or Mesh-based Parallel Code Coupling Interface, has been implemented together with a library called STAMPI to couple two existing codes to develop an 'integrated numerical simulation system' intended for meta-computing environments. (authors)

  17. A set of numerical meteorological models for solving basic and some special problems in the Boris Kidric Institute

    International Nuclear Information System (INIS)

    Grscic, Z.

    1989-01-01

    Models for solving transport and dispersion problems of radioactive pollutants through atmosphere are briefly shown. These models are the base for solving and some special problems such as: estimating effective and physical heights of radioactive sources, computation of radioactive concentration distribution from multiple sources etc (author)

  18. Practical considerations in developing numerical simulators for thermal recovery

    Energy Technology Data Exchange (ETDEWEB)

    Abou-Kassem, J.H. [Chemical and Petroleum Engineering Department, UAE University, Al-Ain (United Arab Emirates)

    1996-08-15

    Numerical simulation of steam injection and in-situ combustion-based oil recovery processes is of great importance in project design. Development of such numerical simulators is an on-going process, with improvements made as the process description becomes more complete, and also as better methods are devised to resolve certain numerical difficulties. This paper addresses some of the latter, and based on the author`s experience gives useful guidelines for developing more efficient numerical simulators of steam injection and in-situ combustion. The paper takes up a series of questions related to simulating thermal processes. Included are: the elimination of constraint equations at the matrix level, phase change, steam injection rate, alternative treatments of heat loss, relative permeabilities and importance of hysteresis effects, improved solutions to the grid orientation problem and other simulation problems such as potential inversion, grid block size, time-step size control and induced fractures. The points discussed in the paper should be of use to both simulator developers and users alike, and will lead to a better understanding of simulation results

  19. Broadening participation in community problem solving: a multidisciplinary model to support collaborative practice and research.

    Science.gov (United States)

    Lasker, Roz D; Weiss, Elisa S

    2003-03-01

    Over the last 40 years, thousands of communities-in the United States and internationally-have been working to broaden the involvement of people and organizations in addressing community-level problems related to health and other areas. Yet, in spite of this experience, many communities are having substantial difficulty achieving their collaborative objective, and many funders of community partnerships and participation initiatives are looking for ways to get more out of their investment. One of the reasons we are in this predicament is that the practitioners and researchers who are interested in community collaboration come from a variety of contexts, initiatives, and academic disciplines, and few of them have integrated their work with experiences or literatures beyond their own domain. In this article, we seek to overcome some of this fragmentation of effort by presenting a multidisciplinary model that lays out the pathways by which broadly participatory processes lead to more effective community problem solving and to improvements in community health. The model, which builds on a broad array of practical experience as well as conceptual and empirical work in multiple fields, is an outgrowth of a joint-learning work group that was organized to support nine communities in the Turning Point initiative. Following a detailed explication of the model, the article focuses on the implications of the model for research, practice, and policy. It describes how the model can help researchers answer the fundamental effectiveness and "how-to" questions related to community collaboration. In addition, the article explores differences between the model and current practice, suggesting strategies that can help the participants in, and funders of, community collaborations strengthen their efforts.

  20. Being relevant: Practical guidance for early career researchers interested in solving conservation problems

    Directory of Open Access Journals (Sweden)

    J.M. Chapman

    2015-07-01

    Full Text Available In a human-altered world where biodiversity is in decline and conservation problems abound, there is a dire need to ensure that the next generation of conservation scientists have the knowledge, skills, and training to address these problems. So called “early career researchers” (ECRs in conservation science have many challenges before them and it is clear that the status quo must change to bridge the knowledge–action divide. Here we identify thirteen practical strategies that ECRs can employ to become more relevant. In this context, “relevance” refers to the ability to contribute to solving conservation problems through engagement with practitioners, policy makers, and stakeholders. Conservation and career strategies outlined in this article include the following: thinking ‘big picture’ during conservation projects; embracing various forms of knowledge; maintaining positive relationships with locals familiar with the conservation issue; accepting failure as a viable (and potentially valuable outcome; daring to be creative; embracing citizen science; incorporating interdisciplinarity; promoting and practicing pro-environmental behaviours; understanding financial aspects of conservation; forming collaboration from the onset of a project; accepting the limits of technology; ongoing and effective networking; and finally, maintaining a positive outlook by focusing on and sharing conservation success stories. These strategies move beyond the generic and highlight the importance of continuing to have an open mind throughout the entire conservation process, from establishing one’s self as an asset to embracing collaboration and interdisciplinary work, and striving to push for professional and personal connections that strengthen personal career objectives.

  1. Analytic-Numerical Approach to Solving Singularly Perturbed Parabolic Equations with the Use of Dynamic Adapted Meshes

    Directory of Open Access Journals (Sweden)

    D. V. Lukyanenko

    2016-01-01

    Full Text Available The main objective of the paper is to present a new analytic-numerical approach to singularly perturbed reaction-diffusion-advection models with solutions containing moving interior layers (fronts. We describe some methods to generate the dynamic adapted meshes for an efficient numerical solution of such problems. It is based on a priori information about the moving front properties provided by the asymptotic analysis. In particular, for the mesh construction we take into account a priori asymptotic evaluation of the location and speed of the moving front, its width and structure. Our algorithms significantly reduce the CPU time and enhance the stability of the numerical process compared with classical approaches.The article is published in the authors’ wording.

  2. Better modelling practice : an ontological perpsective on multidisciplinary, model-based problem solving

    NARCIS (Netherlands)

    Scholten, H.

    2008-01-01

    Mathematical models are more and more used to support to solve multidisciplinary, real world problems of increasing complexity. They are often plagued by obstacles such as miscommunication between modellers with different disciplinary backgrounds leading to a non-transparent modelling process. Other

  3. Restorative Justice Practice: Cooperative Problem-Solving in New Zealand's Schools

    Science.gov (United States)

    Drewery, Wendy

    2013-01-01

    This article links capability for cooperative problem-solving with socially just global development. From the perspective of the United Nations Development Programme, the work of global development, founded on a concept of global justice, is capability-building. Following Kurasawa, the article proposes that this form of global justice is enacted…

  4. Combined analytical-numerical procedure to solve multigroup spherical harmonics equations in two-dimensional r-z geometry

    International Nuclear Information System (INIS)

    Matausek, M.V.; Milosevic, M.

    1986-01-01

    In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)

  5. Numerical

    Directory of Open Access Journals (Sweden)

    M. Boumaza

    2015-07-01

    Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.

  6. Management of the structure of marketing - practical necessity not solved in theory

    OpenAIRE

    Rutkauskas, Aleksandras Vytautas; Stasytytė, Viktorija; Staskevičiūtė, Giedrė

    2007-01-01

    Marketing is constantly concerned with the following problems - what amount of funds reaches maximum marginal effect and what the optimal structure of expenditures on separate marketing means should be. Moreover, nowadays it is increasingly important to reach business sustainability. The paper proposes means of solving the problem integrating these questions - how to achieve the maximum marginal marketing funds efficiency with optimal funds distribution among separate marketing means. Employi...

  7. "We Definitely Wouldn't Be Able to Solve It All by Ourselves, but Together…": Group Synergy in Tertiary Students' Problem-Solving Practices

    Science.gov (United States)

    Clark, Kathleen; James, Alex; Montelle, Clemency

    2014-01-01

    The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students…

  8. Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

    Science.gov (United States)

    Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

    2018-02-01

    Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

  9. From production to performance: solving the positioning dilemma in dental practice.

    Science.gov (United States)

    Armstrong, James; Pitt, Leyland; Berthon, Pierre

    2006-09-01

    Thriving dental practices are excellent at providing a warm personal experience or are efficient, fast and cost-effective. Those that that attempt to do both end up being mediocre at just about everything. Introducing ideas from dramaturgy and service simultaneity in the services marketing literature, the authors provide a model for the conceptualization and redesign of the dental practice. Successful dental practices will be those that concentrate on low customization of activities in the back office or high customization of activities in the front office.

  10. Solving problems in social-ecological systems: definition, practice and barriers of transdisciplinary research.

    Science.gov (United States)

    Angelstam, Per; Andersson, Kjell; Annerstedt, Matilda; Axelsson, Robert; Elbakidze, Marine; Garrido, Pablo; Grahn, Patrik; Jönsson, K Ingemar; Pedersen, Simen; Schlyter, Peter; Skärbäck, Erik; Smith, Mike; Stjernquist, Ingrid

    2013-03-01

    Translating policies about sustainable development as a social process and sustainability outcomes into the real world of social-ecological systems involves several challenges. Hence, research policies advocate improved innovative problem-solving capacity. One approach is transdisciplinary research that integrates research disciplines, as well as researchers and practitioners. Drawing upon 14 experiences of problem-solving, we used group modeling to map perceived barriers and bridges for researchers' and practitioners' joint knowledge production and learning towards transdisciplinary research. The analysis indicated that the transdisciplinary research process is influenced by (1) the amount of traditional disciplinary formal and informal control, (2) adaptation of project applications to fill the transdisciplinary research agenda, (3) stakeholder participation, and (4) functional team building/development based on self-reflection and experienced leadership. Focusing on implementation of green infrastructure policy as a common denominator for the delivery of ecosystem services and human well-being, we discuss how to diagnose social-ecological systems, and use knowledge production and collaborative learning as treatments.

  11. Vital Involvement Practice: strengths as more than tools for solving problems.

    Science.gov (United States)

    Kivnick, Helen Q; Stoffel, Sharon A

    2005-01-01

    This article describes Vital Involvement Practice, a strength-based approach to clinical practice with elders, including those who are extremely frail. Using this approach, practitioners have been able to help elders increase later-life vitality and associated positive quality of life through: (1) systematic identification of individual strengths and assets (found both in the person and in the surrounding environment), and (2) consideration of these strengths alongside the individual and environmental deficits that are the subject of most geriatric practice. The approach utilizes original data-gathering tools (Occupational Profile; Life Strengths Interview Guide) and a stepwise, worksheet- structured consideration of these data in order to formulate action strategies for achieving client goals (Domain Scan; Domain Goals; Life Plan/Strategy). All elements of VIP emerged in pilot work with gerontological practitioners and their elder clients in such settings as: primary health care; government social service; subsidized senior housing; private clinical practice; community recreation. Limitations, implications, and promise are noted, with respect to practice and research.

  12. TRANING BACHELORS OF BUSINESS INFORMATICS TO SOLVE PRACTICAL PROBLEMS OF MARKETING

    Directory of Open Access Journals (Sweden)

    Л В Дегтярева

    2016-12-01

    Full Text Available In article need of an integrated approach is proved when training bachelors of business informatics for the solution of practical problems of marketing and the example of realization of such approach is given. The illustrated example proves need of use of an integrated approach for training of bachelors of business informatics, in particular, on such disciplines as the mathematics, informatics and marketing where theoretical knowledge uniting, give already synergetic effect in practical refraction. Such integration undergoes already biennial testing at our university and yields positive result.

  13. Numerical modelling of mine workings.

    CSIR Research Space (South Africa)

    Lightfoot, N

    1999-03-01

    Full Text Available to cover most of what is required for a practising rock mechanics engineer to be able to use any of these five programs to solve practical mining problems. The chapters on specific programs discuss their individual strengths and weaknesses and highlight... and applications of numerical modelling in the context of the South African gold and platinum mining industries. This includes an example that utilises a number of different numerical 3 modelling programs to solve a single problem. This particular example...

  14. Restorative Practices from Candy and Punishment to Celebrations and Problem-Solving Circles

    Science.gov (United States)

    Goldys, Patrice H.

    2016-01-01

    Norwood Elementary, a Title I science, technology, engineering, and math (STEM) school in Baltimore County, MD, recently realized that traditional behavior management programs and processes were not working with their students. Over time, school administrators discovered more successful approaches, and restorative practices became the way to…

  15. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part II. Practical applications

    International Nuclear Information System (INIS)

    Saetta, Anna V.; Vitaliani, Renato V.

    2005-01-01

    The mathematical-numerical method developed by the authors to predict the corrosion initiation time of reinforced concrete structures due to carbonation process, recalled in Part I of this work, is here applied to some real cases. The final aim is to develop and test a practical method for determining the durability characteristics of existing buildings liable to carbonation, as well as estimating the corrosion initiation time of a building at the design stage. Two industrial sheds with different ages and located in different areas have been analyzed performing both experimental tests and numerical analyses. Finally, a case of carbonation-induced failure in a prestressed r.c. beam is presented

  16. A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees.

    Science.gov (United States)

    van Iersel, Leo; Kelk, Steven; Lekić, Nela; Scornavacca, Celine

    2014-05-05

    Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for binary trees, exact solvers struggle to solve instances with reticulation number larger than 40-50. Here we present CycleKiller and NonbinaryCycleKiller, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Using simulations, we demonstrate that these algorithms run quickly for large and difficult instances, producing solutions that are very close to optimality. As a spin-off from our simulations we also present TerminusEst, which is the fastest exact method currently available that can handle nonbinary trees: this is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All three methods are based on extensions of previous theoretical work (SIDMA 26(4):1635-1656, TCBB 10(1):18-25, SIDMA 28(1):49-66) and are publicly available. We also apply our methods to real data.

  17. Computer-assisted mammography in clinical practice: Another set of problems to solve

    International Nuclear Information System (INIS)

    Gale, A.G.; Roebuck, E.J.; Worthington, B.S.

    1986-01-01

    To be adopted in radiological practice, computer-assisted diagnosis must address a domain of realistic complexity and have a high performance in terms of speed and reliability. Use of a microcomputer-based system of mammographic diagnoses employing discriminant function analysis resulted in significantly fewer false-positive diagnoses while producing a similar level of correct diagnoses of cancer as normal reporting. Although such a system is a valuable teaching aid, its clinical use is constrained by the problems of unambiguously codifying descriptors, data entry time, and the tendency of radiologists to override predicted diagnoses which conflict with their own

  18. Numerical Analysis of Turbulent Flow around Tube Bundle by Applying CAD Best Practice Guideline

    International Nuclear Information System (INIS)

    Lee, Gong Hee; Bang, Young Seok; Woo, Sweng Woong; Cheng, Ae Ju

    2013-01-01

    In this study, the numerical analysis of a turbulent flow around both a staggered and an incline tube bundle was conducted using Annoys Cfx V. 13, a commercial CAD software. The flow was assumed to be steady, incompressible, and isothermal. According to the CAD Best Practice Guideline, the sensitivity study for grid size, accuracy of the discretization scheme for convection term, and turbulence model was conducted, and its result was compared with the experimental data to estimate the applicability of the CAD Best Practice Guideline. It was concluded that the CAD Best Practice Guideline did not always guarantee an improvement in the prediction performance of the commercial CAD software in the field of tube bundle flow

  19. Investigation of the Practical Possibility of Solving Problems on Generalized Cellular Automata Associated with Cryptanalysis by Mean Algebraic Methods

    Directory of Open Access Journals (Sweden)

    P. G. Klyucharev

    2017-01-01

    Full Text Available A number of previous author’s papers proposed methods for constructing various cryptographic algorithms, including block ciphers and cryptographic hash functions, based on generalized cellular automata. This one is aimed at studying a possibility to use the algebraic cryptanalysis methods related to the construction of Gröbner bases for the generalized cellular automata to be applied in cryptography, i.e. this paper studies the possibility for using algebraic cryptanalysis methods to solve the problems of inversion of a generalized cellular automaton and recovering the key of such an automaton.If the cryptographic algorithm is represented as a system of polynomial equations over a certain finite field, then its breach is reduced to solving this system with respect to the key. Although the problem of solving a system of polynomial equations in a finite field is NP-difficult in the general case, the solution of a particular system can have low computational cost.Cryptanalysis based on the construction of a system of polynomial equations that links plain text, cipher-text and key, and its solution by algebraic methods, is usually called algebraic cryptanalysis. Among the main methods to solve systems of polynomial equations are those to construct Gröbner bases.Cryptanalysis of ciphers and hash functions based on generalized cellular automata can be reduced to various problems. We will consider two such problems: the problem of inversion of a generalized cellular automaton, which, in case we know the values of the cells after k iterations, enables us to find the initial values. And the task of recovering the key, which is to find the initial values of the remaining cells, using the cell values after k steps and the initial values of a part of the cells.A computational experiment was carried out to solve the two problems above stated in order to determine the maximum size of a generalized cellular automaton for which the solution of these

  20. A practical approach for solving multi-objective reliability redundancy allocation problems using extended bare-bones particle swarm optimization

    International Nuclear Information System (INIS)

    Zhang, Enze; Wu, Yifei; Chen, Qingwei

    2014-01-01

    This paper proposes a practical approach, combining bare-bones particle swarm optimization and sensitivity-based clustering for solving multi-objective reliability redundancy allocation problems (RAPs). A two-stage process is performed to identify promising solutions. Specifically, a new bare-bones multi-objective particle swarm optimization algorithm (BBMOPSO) is developed and applied in the first stage to identify a Pareto-optimal set. This algorithm mainly differs from other multi-objective particle swarm optimization algorithms in the parameter-free particle updating strategy, which is especially suitable for handling the complexity and nonlinearity of RAPs. Moreover, by utilizing an approach based on the adaptive grid to update the global particle leaders, a mutation operator to improve the exploration ability and an effective constraint handling strategy, the integrated BBMOPSO algorithm can generate excellent approximation of the true Pareto-optimal front for RAPs. This is followed by a data clustering technique based on difference sensitivity in the second stage to prune the obtained Pareto-optimal set and obtain a small, workable sized set of promising solutions for system implementation. Two illustrative examples are presented to show the feasibility and effectiveness of the proposed approach

  1. Robotics and STEM Learning: Students' Achievements in Assignments According to the P3 Task Taxonomy--Practice, Problem Solving, and Projects

    Science.gov (United States)

    Barak, Moshe; Assal, Muhammad

    2018-01-01

    This study presents the case of development and evaluation of a STEM-oriented 30-h robotics course for junior high school students (n = 32). Class activities were designed according to the P3 Task Taxonomy, which included: (1) practice-basic closed-ended tasks and exercises; (2) problem solving--small-scale open-ended assignments in which the…

  2. Examining the Effects of Principals' Transformational Leadership on Teachers' Creative Practices and Students' Performance in Problem-Solving

    Science.gov (United States)

    Owoh, Jeremy Strickland

    2015-01-01

    In today's technology enriched schools and workforces, creative problem-solving is involved in many aspects of a person's life. The educational systems of developed nations are designed to raise students who are creative and skillful in solving complex problems. Technology and the age of information require nations to develop generations of…

  3. A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

    Science.gov (United States)

    Parand, K.; Nikarya, M.

    2017-11-01

    In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

  4. Experimental and numerical studies of burning velocities and kinetic modeling for practical and surrogate fuels

    Science.gov (United States)

    Zhao, Zhenwei

    To help understand the fuel oxidation process in practical combustion environments, laminar flame speeds and high temperature chemical kinetic models were studied for several practical fuels and "surrogate" fuels, such as propane, dimethyl ether (DME), and primary reference fuel (PRF) mixtures, gasoline and n-decane. The PIV system developed for the present work is described. The general principles for PIV measurements are outlined and the specific considerations are also reported. Laminar flame speeds were determined for propane/air over a range of equivalence ratios at initial temperature of 298 K, 500 K and 650 K and atmospheric pressure. Several data sets for propane/air laminar flame speeds with N 2 dilution are also reported. These results are compared to the literature data collected at the same conditions. The propane flame speed is also numerically calculated with a detailed kinetic model and multi component diffusion, including Soret effects. This thesis also presents experimentally determined laminar flame speeds for primary reference fuel (PRF) mixtures of n-heptane/iso-octane and real gasoline fuel at different initial temperature and at atmospheric pressure. Nitrogen dilution effects on the laminar flame speed are also studied for selected equivalence ratios at the same conditions. A minimization of detailed kinetic model for PRF mixtures on laminar flame speed conditions was performed and the measured flame speeds were compared with numerical predictions using this model. The measured laminar flame speeds of n-decane/air mixtures at 500 K and at atmospheric pressure with and without dilution were determined. The measured flame speeds are significantly different that those predicted using existing published kinetic models, including a model validated previously against high temperature data from flow reactor, jet-stirred reactor, shock tube ignition delay, and burner stabilized flame experiments. A significant update of this model is described which

  5. Planning under uncertainty solving large-scale stochastic linear programs

    Energy Technology Data Exchange (ETDEWEB)

    Infanger, G. [Stanford Univ., CA (United States). Dept. of Operations Research]|[Technische Univ., Vienna (Austria). Inst. fuer Energiewirtschaft

    1992-12-01

    For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.

  6. Simultaneous and Comparable Numerical Indicators of International, National and Local Collaboration Practices in English-Medium Astrophysics Research Papers

    Science.gov (United States)

    Méndez, David I.; Alcaraz, M. Ángeles

    2016-01-01

    Introduction: We report an investigation on collaboration practices in research papers published in the most prestigious English-medium astrophysics journals. Method: We propose an evaluation method based on three numerical indicators to study and compare, in absolute terms, three different types of collaboration (international, national and…

  7. Numerical investigation on practicability of reducing MCST by using grid spacer in a tight rod bundle

    International Nuclear Information System (INIS)

    Zhu, Xiaojing; Morooka, Shinichi; Oka, Yoshiaki

    2014-01-01

    Highlights: • Standard grid spacer design causes decreased heat transfer in a tight rod bundle. • Heat transfer is greatly enhanced by flow-enhancing features. • Swirling flow adversely affects the heat transfer downstream of grid spacer. • Enhanced heat transfer by existing grid spacer is limited in a short region. • Improved grid spacer can effectively reduce MCST. - Abstract: The numerical investigation was carried out to reveal the practicability of reducing the maximum cladding surface temperature (MCST) within the inner sub-channel of a tight, hexagon rod bundle using commercial CFD code STAR CCM+ 6.04. The special heat transfer and pressure drop characteristics caused by four existing grid spacer designs were discussed in detail by analyzing the effects of grid strap length, different flow enhancing features and different Reynolds numbers. It was found that the local heat transfer within the grid strap is greatly enhanced due to the raised flow velocity. Both the standard grid spacer and the grid spacer with split-vanes cause decreased heat transfer in the downstream region. The friction drag is very influential in the tight rod bundle and can eliminate the positive effect of flow blockage on the heat transfer performance. The grid spacer with flow blockage discs induces relatively good heat transfer performance and higher pressure drop within sub-channels, indicating a tradeoff between the heat transfer augmentation and the pressure drop. The combination of multiple existing grid spacers can reduce the MCST to a certain level, but the corresponding disadvantages cannot be ignored. The improved grid spacer design was proposed based on the overall considerations of heat transfer and pressure drop characteristics and has been proved more suitable to widely reduce MCST for SCWR than any other grid spacer designs involved in present study

  8. Fostering of ability to solve problems toward consensus-making. From teaching practice on the use of nuclear power as a core of energy issues

    International Nuclear Information System (INIS)

    Harada, Tadanori

    2005-01-01

    In Hiroshima, it is practicing the peace education which aimed to bring up the citizen who practices world peace. In this research, in the nuclear power generation, at the teaching materials, it did the curriculum development to bring up the problem-solving ability to have paid to the consensus building. After practicing a class for the ninth grade life, it got to actually feel ''the problem solving depend on our future''. It understood the following point from this practice. (1) It thinks that the student wants to know the truth. (2) In to devise a way of guiding a teacher, the student becomes able to develop independent learning. (3) If there is not a mistake in the way of taking a problem, it is possible to do a student and a discussion even if it is the problem which touches a sense of values. (4) The understanding of a student is promoted when learning the difference of the mechanism of the atomic bomb and the nuclear power generation. (author)

  9. Cognitive Skills Used to Solve Mathematical Word Problems and Numerical Operations: A Study of 6- to 7-Year-Old Children

    Science.gov (United States)

    Bjork, Isabel Maria; Bowyer-Crane, Claudine

    2013-01-01

    This study investigates the relationship between skills that underpin mathematical word problems and those that underpin numerical operations, such as addition, subtraction, division and multiplication. Sixty children aged 6-7 years were tested on measures of mathematical ability, reading accuracy, reading comprehension, verbal intelligence and…

  10. Numerical relativity

    International Nuclear Information System (INIS)

    Piran, T.

    1982-01-01

    There are many recent developments in numerical relativity, but there remain important unsolved theoretical and practical problems. The author reviews existing numerical approaches to solution of the exact Einstein equations. A framework for classification and comparison of different numerical schemes is presented. Recent numerical codes are compared using this framework. The discussion focuses on new developments and on currently open questions, excluding a review of numerical techniques. (Auth.)

  11. Development of a numerical experiment technique to solve inverse gamma-ray transport problems with application to nondestructive assay of nuclear waste barrels

    International Nuclear Information System (INIS)

    Chang, C.J.; Anghaie, S.

    1998-01-01

    A numerical experimental technique is presented to find an optimum solution to an undetermined inverse gamma-ray transport problem involving the nondestructive assay of radionuclide inventory in a nuclear waste drum. The method introduced is an optimization scheme based on performing a large number of numerical simulations that account for the counting statistics, the nonuniformity of source distribution, and the heterogeneous density of the self-absorbing medium inside the waste drum. The simulation model uses forward projection and backward reconstruction algorithms. The forward projection algorithm uses randomly selected source distribution and a first-flight kernel method to calculate external detector responses. The backward reconstruction algorithm uses the conjugate gradient with nonnegative constraint or the maximum likelihood expectation maximum method to reconstruct the source distribution based on calculated detector responses. Total source activity is determined by summing the reconstructed activity of each computational grid. By conducting 10,000 numerical simulations, the error bound and the associated confidence level for the prediction of total source activity are determined. The accuracy and reliability of the simulation model are verified by performing a series of experiments in a 208-ell waste barrel. Density heterogeneity is simulated by using different materials distributed in 37 egg-crate-type compartments simulating a vertical segment of the barrel. Four orthogonal detector positions are used to measure the emerging radiation field from the distributed source. Results of the performed experiments are in full agreement with the estimated error and the confidence level, which are predicted by the simulation model

  12. Numerical linear algebra with applications using Matlab

    CERN Document Server

    Ford, William

    2014-01-01

    Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for

  13. Teachers' Teaching Practices and Beliefs Regarding Context-Based Tasks and Their Relation with Students' Difficulties in Solving These Tasks

    Science.gov (United States)

    Wijaya, Ariyadi; van den Heuvel-Panhuizen, Marja; Doorman, Michiel

    2015-01-01

    In this study, we investigated teachers' teaching practices and their underlying beliefs regarding context-based tasks to find a possible explanation for students' difficulties with these tasks. The research started by surveying 27 Junior High School teachers from seven schools in Indonesia through a written questionnaire. Then, to further examine…

  14. Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks

    NARCIS (Netherlands)

    Wijaya, Ariyadi; Van den Heuvel-Panhuizen, M.; Doorman, Michiel

    2015-01-01

    In this study, we investigated teachers’ teaching practices and their underlying beliefs regarding context-based tasks to find a possible explanation for students’ difficulties with these tasks. The research started by surveying 27 Junior High School teachers from seven schools in Indonesia through

  15. Riemann solvers and numerical methods for fluid dynamics a practical introduction

    CERN Document Server

    Toro, Eleuterio F

    2009-01-01

    High resolution upwind and centred methods are a mature generation of computational techniques applicable to a range of disciplines, Computational Fluid Dynamics being the most prominent. This book gives a practical presentation of this class of techniques.

  16. Research on the Numerical Simulation of Sleeper in the Pipeline Global Buckling Controlling Practice

    Directory of Open Access Journals (Sweden)

    Liu Wen-Bin

    2017-01-01

    Full Text Available This paper analyzed the lateral buckling of pipelines located in Western Africa with ABAQUS software. The application of sleepers in practice is explored to guide the pipeline buckling controlling design.

  17. Aspects of numerical modelling in expert practice; Aspekte der numerischen Modellierung in der gutachterlichen Praxis

    Energy Technology Data Exchange (ETDEWEB)

    Schaedler, G.

    1998-01-01

    Referring to a relatively restricted field, namely the preparation of expertises in small-scale climatology and air hygiene, the paper wants to give insight into the methods of, and the problems associated with, the numerical modellings used. Frequently occurring tasks are described, the numerical models used are briefly outlined, and some of the problems are discussed which are encountered when using these models. (orig./KW) [Deutsch] Der vorliegende Aufsatz soll am Beispiel eines relativ eng umgrenzten Themenkreises, naemlich der gutachterlichen Taetigkeit im Bereich der kleinraeumigen Klimatologie und Lufthygiene, einen Einblick in die Methoden und Probleme der dabei eingesetzten numerischen Modellierung geben. Zunaechst werden haeufig auftretende Aufgabenstellungen dargestellt, dann die verwendeten numerischen Modelle kurz vorgestellt und schliesslich einige der Probleme angesprochen, die sich beim praktischen Einsatz dieser Modelle stellen. (orig./KW)

  18. Fostering Scientific and Numerate Practices in Journalism to Support Rapid Public Learning

    Directory of Open Access Journals (Sweden)

    Louise Yarnall

    2017-01-01

    Full Text Available Journalism has the potential––and arguably the mandate––to expand public understanding of societally important phenomena. However, some methods for more effectively educating the public have been persistently underutilized: in particular, embedding informative numerical rates and efficient scientific explanations in news reports. In the current era of disrupting and downsizing the news business, the challenges to using such methods have only increased. To address this problem, this article seeks to (a raise awareness about the psychological reasons that help explain why it is crucial to use such elements in news reports, and (b exhibit some methods for doing so that require modest effort. Building on a review of relevant psychological literatures, principles, and existing reporting methods, we describe findings from a series of cognitive-scientific studies that demonstrate how using key––and relatively minimal––scientific and numerical elements can enhance public learning from news reports. We conclude by also describing curricula and resources designed to help journalists and bloggers use these methods.

  19. Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient.

    Science.gov (United States)

    Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I

    2017-01-01

    This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

  20. Numerical analysis

    CERN Document Server

    Rao, G Shanker

    2006-01-01

    About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...

  1. Empirical Mining of Large Data Sets Already Helps to Solve Practical Ecological Problems; A Panoply of Working Examples (Invited)

    Science.gov (United States)

    Hargrove, W. W.; Hoffman, F. M.; Kumar, J.; Spruce, J.; Norman, S. P.

    2013-12-01

    Here we present diverse examples where empirical mining and statistical analysis of large data sets have already been shown to be useful for a wide variety of practical decision-making problems within the realm of large-scale ecology. Because a full understanding and appreciation of particular ecological phenomena are possible only after hypothesis-directed research regarding the existence and nature of that process, some ecologists may feel that purely empirical data harvesting may represent a less-than-satisfactory approach. Restricting ourselves exclusively to process-driven approaches, however, may actually slow progress, particularly for more complex or subtle ecological processes. We may not be able to afford the delays caused by such directed approaches. Rather than attempting to formulate and ask every relevant question correctly, empirical methods allow trends, relationships and associations to emerge freely from the data themselves, unencumbered by a priori theories, ideas and prejudices that have been imposed upon them. Although they cannot directly demonstrate causality, empirical methods can be extremely efficient at uncovering strong correlations with intermediate "linking" variables. In practice, these correlative structures and linking variables, once identified, may provide sufficient predictive power to be useful themselves. Such correlation "shadows" of causation can be harnessed by, e.g., Bayesian Belief Nets, which bias ecological management decisions, made with incomplete information, toward favorable outcomes. Empirical data-harvesting also generates a myriad of testable hypotheses regarding processes, some of which may even be correct. Quantitative statistical regionalizations based on quantitative multivariate similarity have lended insights into carbon eddy-flux direction and magnitude, wildfire biophysical conditions, phenological ecoregions useful for vegetation type mapping and monitoring, forest disease risk maps (e.g., sudden oak

  2. Nonlinear ordinary differential equations analytical approximation and numerical methods

    CERN Document Server

    Hermann, Martin

    2016-01-01

    The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

  3. Numerical Validation of Chemical Compositional Model for Wettability Alteration Processes

    Science.gov (United States)

    Bekbauov, Bakhbergen; Berdyshev, Abdumauvlen; Baishemirov, Zharasbek; Bau, Domenico

    2017-12-01

    Chemical compositional simulation of enhanced oil recovery and surfactant enhanced aquifer remediation processes is a complex task that involves solving dozens of equations for all grid blocks representing a reservoir. In the present work, we perform a numerical validation of the newly developed mathematical formulation which satisfies the conservation laws of mass and energy and allows applying a sequential solution approach to solve the governing equations separately and implicitly. Through its application to the numerical experiment using a wettability alteration model and comparisons with existing chemical compositional model's numerical results, the new model has proven to be practical, reliable and stable.

  4. Series: The research agenda for general practice/family medicine and primary health care in Europe. Part 4. Results: specific problem solving skills.

    Science.gov (United States)

    Hummers-Pradier, Eva; Beyer, Martin; Chevallier, Patrick; Eilat-Tsanani, Sophia; Lionis, Christos; Peremans, Lieve; Petek, Davorina; Rurik, Imre; Soler, Jean Karl; Stoffers, Henri Ejh; Topsever, Pinar; Ungan, Mehmet; van Royen, Paul

    2010-09-01

    The 'Research Agenda for General Practice/Family Medicine and Primary Health Care in Europe' summarizes the evidence relating to the core competencies and characteristics of the Wonca Europe definition of GP/FM, and its implications for general practitioners/family doctors, researchers and policy makers. The European Journal of General Practice publishes a series of articles based on this document. The previous articles presented background, objectives, and methodology, as well results on 'primary care management' and 'community orientation' and the person-related core competencies of GP/FM. This article reflects on the general practitioner's 'specific problem solving skills'. These include decision making on diagnosis and therapy of specific diseases, accounting for the properties of primary care, but also research questions related to quality management and resource use, shared decision making, or professional education and development. Clinical research covers most specific diseases, but often lacks pragmatism and primary care relevance. Quality management is a stronghold of GP/FM research. Educational interventions can be effective when well designed for a specific setting and situation. However, their message that 'usual care' by general practitioners is insufficient may be problematic. GP and their patients need more research into diagnostic reasoning with a step-wise approach to increase predictive values in a setting characterized by uncertainty and low prevalence of specific diseases. Pragmatic comparative effectiveness studies of new and established drugs or non-pharmaceutical therapy are needed. Multi-morbidity and complexity should be addressed. Studies on therapy, communication strategies and educational interventions should consider impact on health and sustainability of effects.

  5. Parallel Algorithm Solves Coupled Differential Equations

    Science.gov (United States)

    Hayashi, A.

    1987-01-01

    Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

  6. Aprendizaje basado en la resolución de problemas: una experiencia práctica Problem-based-solving learning: a practical experience

    Directory of Open Access Journals (Sweden)

    E. González-López

    2010-03-01

    Full Text Available El aprendizaje basado en la resolución de problemas incorpora herramientas metodológicas capaces de facilitar la consecución de los objetivos propuestos para la formación de los futuros médicos dentro del marco de la docencia universitaria en el Espacio Europeo de Educación Superior. Promueve una formación más activa, flexible y práctica, que concede mayor protagonismo al trabajo personal tutorizado (aprendizaje autodirigido, en detrimento de las clásicas clases teóricas, eminentemente expositivas, en las que el papel del estudiante es, en general, más pasivo. La Unidad de Medicina de Familia de la Universidad Autónoma de Madrid incorporó el aprendizaje basado en la resolución de problemas en el desarrollo de la asignatura optativa 'Atención Primaria y Medicina de Familia', ofertada como optativa a los alumnos de segundo ciclo de licenciatura (cursos 4.º a 6.º desde el curso 2005-2006. Intentamos con ella promover la formación de médicos capaces de aprender y mantener su competencia durante toda su vida profesional, no sólo en lo referido a la adquisición/integración de conocimientos científicos suficientes, sino también en cuanto al desarrollo de las habilidades necesarias para su adecuada aplicación práctica considerando a cada paciente de modo integral como realidad biopsicosocial, en un contexto sanitario definido, sin olvidar los aspectos bioéticos implícitos al quehacer del médico (respeto hacia el paciente y compromiso social. Revisamos en este artículo el diseño práctico de la asignatura.Learning based on problem-solving incorporates methodological tools that make it easier to fulfil the aims set for the training of future physicians within the framework of university education in the European Higher Education Area. It encourages a more active, flexible and practical training, which grants a leading role to tutor-guided personal work (self-directed learning rather than the classical theoretical, eminently

  7. A Proposed Method for Solving Fuzzy System of Linear Equations

    Directory of Open Access Journals (Sweden)

    Reza Kargar

    2014-01-01

    Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

  8. Practical investigation of a monopod fabrication method and the numerical investigation of its up-righting process

    Directory of Open Access Journals (Sweden)

    Khaled A. Hafez

    2013-09-01

    Full Text Available The principal purpose of this paper is to present a novel two phases rational scenario applied in constructing an offshore monopod platform; in which the two phases are the all-ground horizontal construction phase and the post-construction phase. Concerning the all-ground construction phase, a brief investigation of its different stages, i.e., pre-fabrication, fabrication, pre-assembling, positioning, assembling, and surface finishing is introduced. The important practical aspects of such construction phase are investigated without going into the nitty-gritty of the details involved therein. Concerning the post-construction phase, a clear investigation of its sequential stages, i.e., lifting, moving and up-righting is introduced. A finite element model (FEM of the monopod platform is created to perform the structural analysis necessary to decide the suspension points/devices and the handling scenario during the various stages of the post-construction phase on a rational wise. Such structural analysis is performed within the framework of the three dimensional quasi-static modeling and analysis aiming at simulating the realistic handling condition, and hence introducing a reliable physical interpretation of the numerical results. For the whole effort to be demonstrated efficiently, the results obtained are analyzed, the conclusions are presented, and few related recommendations are suggested.

  9. Numerical analysis of electromagnetic fields

    CERN Document Server

    Zhou Pei Bai

    1993-01-01

    Numerical methods for solving boundary value problems have developed rapidly. Knowledge of these methods is important both for engineers and scientists. There are many books published that deal with various approximate methods such as the finite element method, the boundary element method and so on. However, there is no textbook that includes all of these methods. This book is intended to fill this gap. The book is designed to be suitable for graduate students in engineering science, for senior undergraduate students as well as for scientists and engineers who are interested in electromagnetic fields. Objective Numerical calculation is the combination of mathematical methods and field theory. A great number of mathematical concepts, principles and techniques are discussed and many computational techniques are considered in dealing with practical problems. The purpose of this book is to provide students with a solid background in numerical analysis of the field problems. The book emphasizes the basic theories ...

  10. Advances in Numerical Methods

    CERN Document Server

    Mastorakis, Nikos E

    2009-01-01

    Features contributions that are focused on significant aspects of current numerical methods and computational mathematics. This book carries chapters that advanced methods and various variations on known techniques that can solve difficult scientific problems efficiently.

  11. Treatment outcomes of a Numeric Rating Scale (NRS)-guided pharmacological pain management strategy in symptomatic knee and hip osteoarthritis in daily clinical practice.

    NARCIS (Netherlands)

    Snijders, G.F.; Ende, C.H.M. van den; Bemt, B.J.F van den; Riel, P.L.C.M. van; Hoogen, F.H.J. van den; Broeder, A. den

    2012-01-01

    OBJECTIVES: To describe the results of a Numeric Rating Scale (NRS)-guided pharmacological pain management strategy in symptomatic knee and hip osteoarthritis (OA) in daily clinical practice. METHODS: In this observational cohort study, standardised conservative treatment was offered to patients

  12. Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

    International Nuclear Information System (INIS)

    Dmitriy Y. Anistratov; Adrian Constantinescu; Loren Roberts; William Wieselquist

    2007-01-01

    This is a project in the field of fundamental research on numerical methods for solving the particle transport equation. Numerous practical problems require to use unstructured meshes, for example, detailed nuclear reactor assembly-level calculations, large-scale reactor core calculations, radiative hydrodynamics problems, where the mesh is determined by hydrodynamic processes, and well-logging problems in which the media structure has very complicated geometry. Currently this is an area of very active research in numerical transport theory. main issues in developing numerical methods for solving the transport equation are the accuracy of the numerical solution and effectiveness of iteration procedure. The problem in case of unstructured grids is that it is very difficult to derive an iteration algorithm that will be unconditionally stable

  13. Teachers' Conceptualization and Actual Practice in the Student Evaluation Process at the Upper Secondary School Level in Japan, Focusing on Problem Solving Skills.

    Science.gov (United States)

    Wai, Nu Nu; Hirakawa, Yukiko

    2001-01-01

    Studied the participation and performance of upper secondary school teachers in Japan through surveys completed by 360 Geography teachers. Findings suggest that the importance of developing problem-solving skills is widely recognized among these teachers. Implementing training in such skills is much more difficult. Developing effective teaching…

  14. "Oh" + Apology + Solution: A Practice for Managing the Concomitant Presence of a Possible Offense and a Problem-to-Be-Solved

    Science.gov (United States)

    Pino, Marco; Pozzuoli, Loredana; Riccioni, Ilaria; Castellarin, Valentine

    2016-01-01

    In this article we examine a turn construction ("oh"+apology+solution) that speakers use to deal with the concomitant presence of a possible offense and a problem-to-be-solved in the immediately preceding interactional environment. We show that speakers collaborate in differentiating the offense aspect and the problem aspect of an…

  15. Numerical methods for scientists and engineers

    CERN Document Server

    Antia, H M

    2012-01-01

    This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.

  16. How to solve applied mathematics problems

    CERN Document Server

    Moiseiwitsch, B L

    2011-01-01

    This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

  17. Physical multiscale modeling and numerical simulation of electrochemical devices for energy conversion and storage from theory to engineering to practice

    CERN Document Server

    Franco, Alejandro A; Bessler, Wolfgang G

    2015-01-01

    This book reviews the use of innovative physical multiscale modeling methods to deeply understand the electrochemical mechanisms and numerically simulate the structure and properties of electrochemical devices for energy storage and conversion.

  18. Solved problems in electrochemistry

    International Nuclear Information System (INIS)

    Piron, D.L.

    2004-01-01

    This book presents calculated solutions to problems in fundamental and applied electrochemistry. It uses industrial data to illustrate scientific concepts and scientific knowledge to solve practical problems. It is subdivided into three parts. The first uses modern basic concepts, the second studies the scientific basis for electrode and electrolyte thermodynamics (including E-pH diagrams and the minimum energy involved in transformations) and the kinetics of rate processes (including the energy lost in heat and in parasite reactions). The third part treats larger problems in electrolysis and power generation, as well as in corrosion and its prevention. Each chapter includes three sections: the presentation of useful principles; some twenty problems with their solutions; and, a set of unsolved problems

  19. Numerical relativity

    CERN Document Server

    Nakamura, T

    1993-01-01

    In GR13 we heard many reports on recent. progress as well as future plans of detection of gravitational waves. According to these reports (see the report of the workshop on the detection of gravitational waves by Paik in this volume), it is highly probable that the sensitivity of detectors such as laser interferometers and ultra low temperature resonant bars will reach the level of h ~ 10—21 by 1998. in this level we may expect the detection of the gravitational waves from astrophysical sources such as coalescing binary neutron stars once a year or so. Therefore the progress in numerical relativity is urgently required to predict the wave pattern and amplitude of the gravitational waves from realistic astrophysical sources. The time left for numerical relativists is only six years or so although there are so many difficulties in principle as well as in practice.

  20. Preparing Teacher-Students for Twenty-First-Century Learning Practices (PREP 21): A Framework for Enhancing Collaborative Problem-Solving and Strategic Learning Skills

    Science.gov (United States)

    Häkkinen, Päivi; Järvelä, Sanna; Mäkitalo-Siegl, Kati; Ahonen, Arto; Näykki, Piia; Valtonen, Teemu

    2017-01-01

    With regard to the growing interest in developing teacher education to match the twenty-first-century skills, while many assumptions have been made, there has been less theoretical elaboration and empirical research on this topic. The aim of this article is to present our pedagogical framework for the twenty-first-century learning practices in…

  1. Mathematical modelling and numerical simulation of oil pollution problems

    CERN Document Server

    2015-01-01

    Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics,  together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems.   The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...

  2. A predictor-corrector scheme for solving the Volterra integral equation

    KAUST Repository

    Al Jarro, Ahmed

    2011-08-01

    The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been developed for removing low and high frequency instabilities. On the other hand, literature on stabilizing explicit schemes, which might be considered more efficient since they do not require a matrix inversion at each time step, is practically non-existent. In this work, a stable but still explicit predictor-corrector scheme is proposed for solving the Volterra integral equation and its efficacy is verified numerically. © 2011 IEEE.

  3. Effective methods of solving of model equations of certain class of thermal systems

    International Nuclear Information System (INIS)

    Lach, J.

    1985-01-01

    A number of topics connected with solving of model equations of certain class of thermal systems by the method of successive approximations is touched. A system of partial differential equations of the first degree, appearing most frequently in practical applications of heat and mass transfer theory is reduced to an equivalent system of Volterra integral equations of the second kind. Among a few sample applications the thermal processes appearing in the fuel channel of nuclear reactor are solved. The theoretical analysis is illustrated by the results of numerical calculations given in tables and diagrams. 111 refs., 17 figs., 16 tabs. (author)

  4. Agricultural Recharge Practices for Managing Nitrate in Regional Groundwater: Time-Resolution Assessment of Numerical Modeling Approach

    Science.gov (United States)

    Bastani, M.; Harter, T.

    2017-12-01

    Intentional recharge practices in irrigated landscapes are promising options to control and remediate groundwater quality degradation with respect to nitrate. To better understand the effect of these practices, a fully 3D transient heterogeneous transport model simulation is developed using MODFLOW and MT3D. The model is developed for a long-term study of nitrate improvements in an alluvial groundwater basin in Eastern San Joaquin Valley, CA. Different scenarios of agricultural recharge strategies including crop type change and winter flood flows are investigated. Transient simulations with high spatio-temporal resolutions are performed. We then consider upscaling strategies that would allow us to simplify the modeling process such that it can be applied at a very large basin-scale (1000s of square kilometers) for scenario analysis. We specifically consider upscaling of time-variant boundary conditions (both internal and external) that have significant influence on calculation cost of the model. We compare monthly transient stresses to upscaled annual and further upscaled average steady-state stresses on nitrate transport in groundwater under recharge scenarios.

  5. Introduction to precise numerical methods

    CERN Document Server

    Aberth, Oliver

    2007-01-01

    Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content for this title is now available on the Web. · Clearer, simpler descriptions and explanations ofthe various numerical methods· Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.

  6. The Automatic Generation of Knowledge Spaces From Problem Solving Strategies

    NARCIS (Netherlands)

    Milovanovic, Ivica; Jeuring, Johan

    2016-01-01

    In this paper, we explore theoretical and practical aspects of the automatic generation of knowledge spaces from problem solving strategies. We show how the generated spaces can be used for adapting strategy-based problem solving learning environments (PSLEs).

  7. Methods of solving nonstandard problems

    CERN Document Server

    Grigorieva, Ellina

    2015-01-01

    This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.   It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad. Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions.  The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem.  Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems.   Over 360 problems are included with hints, ...

  8. Numerical problems in physics

    CERN Document Server

    Singh, Devraj

    2015-01-01

    Numerical Problems in Physics, Volume 1 is intended to serve the need of the students pursuing graduate and post graduate courses in universities with Physics and Materials Science as subject including those appearing in engineering, medical, and civil services entrance examinations. KEY FEATURES: * 29 chapters on Optics, Wave & Oscillations, Electromagnetic Field Theory, Solid State Physics & Modern Physics * 540 solved numerical problems of various universities and ompetitive examinations * 523 multiple choice questions for quick and clear understanding of subject matter * 567 unsolved numerical problems for grasping concepts of the various topic in Physics * 49 Figures for understanding problems and concept

  9. Introduction to numerical electrostatics using MATLAB

    CERN Document Server

    Dworsky, Lawrence N

    2014-01-01

    The first of its kind uniquely devoted to the field of computational electrostatics, this book dives headfirst into the actual problems that engineers are expected to solve using method of moment (MoM), finite difference, and finite element techniques. Readers are guided step by step through specific problems and challenges, covering all aspects of electrostatics with an emphasis on numerical procedures. Focusing on practical examples, mathematical equations, and common issues with algorithms, this is an ideal text for students in engineering, physics, and electrostatics-and working engineers

  10. Numerical treatment of linearized equations describing inhomogeneous collisionless plasmas

    International Nuclear Information System (INIS)

    Lewis, H.R.

    1979-01-01

    The equations governing the small-signal response of spatially inhomogeneous collisionless plasmas have practical significance in physics, for example in controlled thermonuclear fusion research. Although the solutions are very complicated and the equations are different to solve numerically, effective methods for them are being developed which are applicable when the equilibrium involves only one nonignorable coordinate. The general theoretical framework probably will provide a basis for progress when there are two or three nonignorable coordinates

  11. Problem solving skills for schizophrenia.

    Science.gov (United States)

    Xia, J; Li, Chunbo

    2007-04-18

    The severe and long-lasting symptoms of schizophrenia are often the cause of severe disability. Environmental stress such as life events and the practical problems people face in their daily can worsen the symptoms of schizophrenia. Deficits in problem solving skills in people with schizophrenia affect their independent and interpersonal functioning and impair their quality of life. As a result, therapies such as problem solving therapy have been developed to improve problem solving skills for people with schizophrenia. To review the effectiveness of problem solving therapy compared with other comparable therapies or routine care for those with schizophrenia. We searched the Cochrane Schizophrenia Group's Register (September 2006), which is based on regular searches of BIOSIS, CENTRAL, CINAHL, EMBASE, MEDLINE and PsycINFO. We inspected references of all identified studies for further trials. We included all clinical randomised trials comparing problem solving therapy with other comparable therapies or routine care. We extracted data independently. For homogenous dichotomous data we calculated random effects, relative risk (RR), 95% confidence intervals (CI) and, where appropriate, numbers needed to treat (NNT) on an intention-to-treat basis. For continuous data, we calculated weighted mean differences (WMD) using a random effects statistical model. We included only three small trials (n=52) that evaluated problem solving versus routine care, coping skills training or non-specific interaction. Inadequate reporting of data rendered many outcomes unusable. We were unable to undertake meta-analysis. Overall results were limited and inconclusive with no significant differences between treatment groups for hospital admission, mental state, behaviour, social skills or leaving the study early. No data were presented for global state, quality of life or satisfaction. We found insufficient evidence to confirm or refute the benefits of problem solving therapy as an additional

  12. Numerical studies of impurities in fusion plasmas

    International Nuclear Information System (INIS)

    Hulse, R.A.

    1982-09-01

    The coupled partial differential equations used to describe the behavior of impurity ions in magnetically confined controlled fusion plasmas require numerical solution for cases of practical interest. Computer codes developed for impurity modeling at the Princeton Plasma Physics Laboratory are used as examples of the types of codes employed for this purpose. These codes solve for the impurity ionization state densities and associated radiation rates using atomic physics appropriate for these low-density, high-temperature plasmas. The simpler codes solve local equations in zero spatial dimensions while more complex cases require codes which explicitly include transport of the impurity ions simultaneously with the atomic processes of ionization and recombination. Typical applications are discussed and computational results are presented for selected cases of interest

  13. A cone-beam tomography system with a reduced size planar detector: A backprojection-filtration reconstruction algorithm as well as numerical and practical experiments

    International Nuclear Information System (INIS)

    Li Liang; Chen Zhiqiang; Zhang Li; Xing Yuxiang; Kang Kejun

    2007-01-01

    In a traditional cone-beam computed tomography (CT) system, the cost of product and computation is very high. In this paper, we develop a transversely truncated cone-beam X-ray CT system with a reduced-size detector positioned off-center, in which X-ray beams only cover half of the object. The existing filtered backprojection (FBP) or backprojection-filtration (BPF) algorithms are not directly applicable in this new system. Hence, we develop a BPF-type direct backprojection algorithm. Different from the traditional rebinning methods, our algorithm directly backprojects the pretreated projection data without rebinning. This makes the algorithm compact and computationally more efficient. Because of avoiding interpolation errors of rebinning process, higher spatial resolution is obtained. Finally, some numerical simulations and practical experiments are done to validate the proposed algorithm and compare with rebinning algorithm

  14. Rational approximatons for solving cauchy problems

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2016-08-01

    Full Text Available In this letter, numerical solutions of Cauchy problems are considered by multivariate Padé approximations (MPA. Multivariate Padé approximations (MPA were applied to power series solutions of Cauchy problems that solved by using He’s variational iteration method (VIM. Then, numerical results obtained by using multivariate Padé approximations were compared with the exact solutions of Cauchy problems.

  15. Solving Mathematical Problems A Personal Perspective

    CERN Document Server

    Tao, Terence

    2006-01-01

    Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.

  16. Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

    Science.gov (United States)

    Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

    2013-01-01

    We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

  17. Solving Complex Problems: A Convergent Approach to Cognitive Load Measurement

    Science.gov (United States)

    Zheng, Robert; Cook, Anne

    2012-01-01

    The study challenged the current practices in cognitive load measurement involving complex problem solving by manipulating the presence of pictures in multiple rule-based problem-solving situations and examining the cognitive load resulting from both off-line and online measures associated with complex problem solving. Forty-eight participants…

  18. Problem Solving and Learning

    Science.gov (United States)

    Singh, Chandralekha

    2009-07-01

    One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts. The limited capacity of short term memory makes the cognitive load high during problem solving tasks, leaving few cognitive resources available for meta-cognition. The abstract nature of the laws of physics and the chain of reasoning required to draw meaningful inferences makes these issues critical. In order to help students, it is crucial to consider the difficulty of a problem from the perspective of students. We are developing and evaluating interactive problem-solving tutorials to help students in the introductory physics courses learn effective problem-solving strategies while solidifying physics concepts. The self-paced tutorials can provide guidance and support for a variety of problem solving techniques, and opportunity for knowledge and skill acquisition.

  19. Teaching Creative Problem Solving.

    Science.gov (United States)

    Christensen, Kip W.; Martin, Loren

    1992-01-01

    Interpersonal and cognitive skills, adaptability, and critical thinking can be developed through problem solving and cooperative learning in technology education. These skills have been identified as significant needs of the workplace as well as for functioning in society. (SK)

  20. The art and science of problem solving

    DEFF Research Database (Denmark)

    Vidal, Rene Victor Valqui

    2005-01-01

    In this paper we will document that real-life problem solving in complex situations demands both rational (scientific) and intuitive (artistic) thinking. First, the concepts of art and science will be discussed; differences and similarities will be enhanced. Thereafter the concept of group problem...... solving facilitation both as science and art will be presented. A case study related to examination's planning will be discussed to illustrate the main concepts in practice. In addition, other cases studies will also be shortly presented....

  1. Numerical Limit Analysis:

    DEFF Research Database (Denmark)

    Damkilde, Lars

    2007-01-01

    Limit State analysis has a long history and many prominent researchers have contributed. The theoretical foundation is based on the upper- and lower-bound theorems which give a very comprehensive and elegant formulation on complicated physical problems. In the pre-computer age Limit State analysis...... also enabled engineers to solve practical problems within reinforced concrete, steel structures and geotechnics....

  2. Numerical model CCC

    International Nuclear Information System (INIS)

    Bodvarsson, G.S.; Lippmann, M.J.

    1980-01-01

    The computer program CCC (conduction-convection-consolidation), developed at Lawrence Berkeley Laboratory, solves numerically the heat and mass flow equations for a fully saturated medium, and computes one-dimensional consolidation of the simulated systems. The model employs the Integrated Finite Difference Method (IFDM) in discretizing the saturated medium and formulating the governing equations. The sets of equations are solved either by an iterative solution technique (old version) or an efficient sparse solver (new version). The deformation of the medium is calculated using the one-dimensional consolidation theory of Terzaghi. In this paper, the numerical code is described, validation examples given and areas of application discussed. Several example problems involving flow through fractured media are also presented

  3. Numerical Characterization of Piezoceramics Using Resonance Curves

    Science.gov (United States)

    Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

    2016-01-01

    Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods. PMID:28787875

  4. Numerical Characterization of Piezoceramics Using Resonance Curves

    Directory of Open Access Journals (Sweden)

    Nicolás Pérez

    2016-01-01

    Full Text Available Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM, to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods.

  5. Numerical analysis

    CERN Document Server

    Khabaza, I M

    1960-01-01

    Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in comput

  6. Numerical relativity

    CERN Document Server

    Shibata, Masaru

    2016-01-01

    This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.

  7. Distributed Problem-Solving

    DEFF Research Database (Denmark)

    Chemi, Tatiana

    2016-01-01

    This chapter aims to deconstruct some persistent myths about creativity: the myth of individualism and of the genius. By looking at literature that approaches creativity as a participatory and distributed phenomenon and by bringing empirical evidence from artists’ studios, the author presents a p......, what can educators at higher education learn from the ways creative groups solve problems? How can artists contribute to inspiring higher education?......This chapter aims to deconstruct some persistent myths about creativity: the myth of individualism and of the genius. By looking at literature that approaches creativity as a participatory and distributed phenomenon and by bringing empirical evidence from artists’ studios, the author presents...... a perspective that is relevant to higher education. The focus here is on how artists solve problems in distributed paths, and on the elements of creative collaboration. Creative problem-solving will be looked at as an ongoing dialogue that artists engage with themselves, with others, with recipients...

  8. Solving Environmental Problems

    DEFF Research Database (Denmark)

    Ørding Olsen, Anders; Sofka, Wolfgang; Grimpe, Christoph

    2017-01-01

    for Research and Technological Development (FP7), our results indicate that the problem-solving potential of a search strategy increases with the diversity of existing knowledge of the partners in a consortium and with the experience of the partners involved. Moreover, we identify a substantial negative effect...... dispersed. Hence, firms need to collaborate. We shed new light on collaborative search strategies led by firms in general and for solving environmental problems in particular. Both topics are largely absent in the extant open innovation literature. Using data from the European Seventh Framework Program...

  9. A Novel Approach for Solving Semidefinite Programs

    Directory of Open Access Journals (Sweden)

    Hong-Wei Jiao

    2014-01-01

    Full Text Available A novel linearizing alternating direction augmented Lagrangian approach is proposed for effectively solving semidefinite programs (SDP. For every iteration, by fixing the other variables, the proposed approach alternatively optimizes the dual variables and the dual slack variables; then the primal variables, that is, Lagrange multipliers, are updated. In addition, the proposed approach renews all the variables in closed forms without solving any system of linear equations. Global convergence of the proposed approach is proved under mild conditions, and two numerical problems are given to demonstrate the effectiveness of the presented approach.

  10. Stopping test of iterative methods for solving PDE

    International Nuclear Information System (INIS)

    Wang Bangrong

    1991-01-01

    In order to assure the accuracy of the numerical solution of the iterative method for solving PDE (partial differential equation), the stopping test is very important. If the coefficient matrix of the system of linear algebraic equations is strictly diagonal dominant or irreducible weakly diagonal dominant, the stopping test formulas of the iterative method for solving PDE is proposed. Several numerical examples are given to illustrate the applications of the stopping test formulas

  11. Introspection in Problem Solving

    Science.gov (United States)

    Jäkel, Frank; Schreiber, Cornell

    2013-01-01

    Problem solving research has encountered an impasse. Since the seminal work of Newell und Simon (1972) researchers do not seem to have made much theoretical progress (Batchelder and Alexander, 2012; Ohlsson, 2012). In this paper we argue that one factor that is holding back the field is the widespread rejection of introspection among cognitive…

  12. Solving Linear Differential Equations

    NARCIS (Netherlands)

    Nguyen, K.A.; Put, M. van der

    2010-01-01

    The theme of this paper is to 'solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field K. Representations of semi-simple Lie algebras and differential Galo is theory are the main tools. The results extend

  13. Solving a binary puzzle

    NARCIS (Netherlands)

    Utomo, P.H.; Makarim, R.H.

    2017-01-01

    A Binary puzzle is a Sudoku-like puzzle with values in each cell taken from the set {0,1} {0,1}. Let n≥4 be an even integer, a solved binary puzzle is an n×n binary array that satisfies the following conditions: (1) no three consecutive ones and no three consecutive zeros in each row and each

  14. Electric Current Solves Mazes

    Science.gov (United States)

    Ayrinhac, Simon

    2014-01-01

    We present in this work a demonstration of the maze-solving problem with electricity. Electric current flowing in a maze as a printed circuit produces Joule heating and the right way is instantaneously revealed with infrared thermal imaging. The basic properties of electric current can be discussed in this context, with this challenging question:…

  15. Transport equation solving methods

    International Nuclear Information System (INIS)

    Granjean, P.M.

    1984-06-01

    This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

  16. On Solving Linear Recurrences

    Science.gov (United States)

    Dobbs, David E.

    2013-01-01

    A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

  17. Toward Solving the Problem of Problem Solving: An Analysis Framework

    Science.gov (United States)

    Roesler, Rebecca A.

    2016-01-01

    Teaching is replete with problem solving. Problem solving as a skill, however, is seldom addressed directly within music teacher education curricula, and research in music education has not examined problem solving systematically. A framework detailing problem-solving component skills would provide a needed foundation. I observed problem solving…

  18. Practical methods of optimization

    CERN Document Server

    Fletcher, R

    2013-01-01

    Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers rev

  19. Numerical Development

    Science.gov (United States)

    Siegler, Robert S.; Braithwaite, David W.

    2016-01-01

    In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

  20. Hindi Numerals.

    Science.gov (United States)

    Bright, William

    In most languages encountered by linguists, the numerals, considered as a paradigmatic set, constitute a morpho-syntactic problem of only moderate complexity. The Indo-Aryan language family of North India, however, presents a curious contrast. The relatively regular numeral system of Sanskrit, as it has developed historically into the modern…

  1. Solving Wicked Problems through Action Learning

    Science.gov (United States)

    Crul, Liselore

    2014-01-01

    This account of practice outlines the Oxyme Action Learning Program which was conducted as part of the Management Challenge in my final year of the MSc in Coaching and Behavioral Change at Henley Business School. The central research questions were: (1) how action learning can help to solve wicked problems and (2) what the effect of an action…

  2. Using Computer Simulations in Chemistry Problem Solving

    Science.gov (United States)

    Avramiotis, Spyridon; Tsaparlis, Georgios

    2013-01-01

    This study is concerned with the effects of computer simulations of two novel chemistry problems on the problem solving ability of students. A control-experimental group, equalized by pair groups (n[subscript Exp] = n[subscript Ctrl] = 78), research design was used. The students had no previous experience of chemical practical work. Student…

  3. Creativity and Problem Solving

    DEFF Research Database (Denmark)

    Vidal, Rene Victor Valqui

    2004-01-01

    This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving...... approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools....

  4. Creativity and problem Solving

    Directory of Open Access Journals (Sweden)

    René Victor Valqui Vidal

    2004-12-01

    Full Text Available This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools.

  5. Solving hyperbolic heat conduction using electrical simulation

    International Nuclear Information System (INIS)

    Gheitaghy, A. M.; Talaee, M. R.

    2013-01-01

    In the present study, the electrical network simulation method is proposed to solve the hyperbolic and parabolic heat conduction problem considering Cattaneo-Vernoute (C.V) constitutive relation. Using this new proposed numerical model and the electrical circuit simulation program HSPICE, transient temperature and heat flux profiles at slab can be obtained easily and quickly. To verify the proposed method, the obtained numerical results for cases of one dimensional two-layer slab under periodic boundary temperature with perfect and imperfect thermal contact are compared with the published results. Comparisons show the proposed technique might be considered as a useful tool in the analysis of parabolic and hyperbolic thermal problems.

  6. Analytical method for solving radioactive transformations

    International Nuclear Information System (INIS)

    Vudakin, Z.

    1999-01-01

    Analytical method for solving radioactive transformations is presented in this paper. High accuracy series expansion of the depletion function and nonsingular Bateman coefficients are used to overcome numerical difficulties when applying well-known Bateman solution of a simple radioactive decay. Generality and simplicity of the method are found to be useful in evaluating nuclide chains with one hundred or more nuclides in the chain. Method enables evaluation of complete chain, without elimination of short-lives nuclides. It is efficient and accurate

  7. A Comparison of the CHILD and Landlab Computational Landscape Evolution Models and Examples of Best Practices in Numerical Modeling of Surface Processes

    Science.gov (United States)

    Gasparini, N. M.; Hobley, D. E. J.; Tucker, G. E.; Istanbulluoglu, E.; Adams, J. M.; Nudurupati, S. S.; Hutton, E. W. H.

    2014-12-01

    Computational models are important tools that can be used to quantitatively understand the evolution of real landscapes. Commonalities exist among most landscape evolution models, although they are also idiosyncratic, in that they are coded in different languages, require different input values, and are designed to tackle a unique set of questions. These differences can make applying a landscape evolution model challenging, especially for novice programmers. In this study, we compare and contrast two landscape evolution models that are designed to tackle similar questions, but the actual model designs are quite different. The first model, CHILD, is over a decade-old and is relatively well-tested, well-developed and well-used. It is coded in C++, operates on an irregular grid and was designed more with function rather than user-experience in mind. In contrast, the second model, Landlab, is relatively new and was designed to be accessible to a wide range of scientists, including those who have not previously used or developed a numerical model. Landlab is coded in Python, a relatively easy language for the non-proficient programmer, and has the ability to model landscapes described on both regular and irregular grids. We present landscape simulations from both modeling platforms. Our goal is to illustrate best practices for implementing a new process module in a landscape evolution model, and therefore the simulations are applicable regardless of the modeling platform. We contrast differences and highlight similarities between the use of the two models, including setting-up the model and input file for different evolutionary scenarios, computational time, and model output. Whenever possible, we compare model output with analytical solutions and illustrate the effects, or lack thereof, of a uniform vs. non-uniform grid. Our simulations focus on implementing a single process, including detachment-limited or transport-limited fluvial bedrock incision and linear or non

  8. Composite Gauss-Legendre Formulas for Solving Fuzzy Integration

    Directory of Open Access Journals (Sweden)

    Xiaobin Guo

    2014-01-01

    Full Text Available Two numerical integration rules based on composition of Gauss-Legendre formulas for solving integration of fuzzy numbers-valued functions are investigated in this paper. The methods' constructions are presented and the corresponding convergence theorems are shown in detail. Two numerical examples are given to illustrate the proposed algorithms finally.

  9. Numerical analysis

    CERN Document Server

    Scott, L Ridgway

    2011-01-01

    Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that ex...

  10. Appreciative Problem Solving

    DEFF Research Database (Denmark)

    Hansen, David

    2012-01-01

    Many industrial production work systems have increased in complexity, and their new business model scompete on innovation, rather than low cost.At a medical device production facility committed to Lean Production, a research project was carried out to use Appreciative Inquiry to better engage...... employee strengths in continuou simprovements of the work system. The research question was: “How can Lean problem solving and Appreciative Inquiry be combined for optimized work system innovation?” The research project was carried out as a co-creation process with close cooperation between researcher...

  11. Simon on problem solving

    DEFF Research Database (Denmark)

    Foss, Kirsten; Foss, Nicolai Juul

    2006-01-01

    as a general approach to problem solving. We apply these Simonian ideas to organisational issues, specifically new organisational forms. Specifically, Simonian ideas allow us to develop a morphology of new organisational forms and to point to some design problems that characterise these forms.......Two of Herbert Simon's best-known papers are 'The Architecture of Complexity' and 'The Structure of Ill-Structured Problems.' We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...

  12. Planning and Problem Solving

    Science.gov (United States)

    1982-10-01

    Artificial Intelig ~ence (Vol. III, edited by Paul R. Cohen and’ Edward A.. Feigenbaum)’, The chapter was written B’ Paul Cohen, with contributions... Artificial Intelligence (Vol. III, edited by Paul R. Cohen and EdWard A. Feigenbaum). The chapter was written by Paul R. Cohen, with contributions by Stephen...Wheevoats"EntermdI’ Planning and Problem ’Solving by Paul R. Cohen Chaptb-rXV-of Volumec III’of the Handbook of Artificial Intelligence edited by Paul R

  13. Numerical computation of MHD equilibria

    International Nuclear Information System (INIS)

    Atanasiu, C.V.

    1982-10-01

    A numerical code for a two-dimensional MHD equilibrium computation has been carried out. The code solves the Grad-Shafranov equation in its integral form, for both formulations: the free-boundary problem and the fixed boundary one. Examples of the application of the code to tokamak design are given. (author)

  14. Numerical methods in software and analysis

    CERN Document Server

    Rice, John R

    1992-01-01

    Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithm

  15. Vacuum engineering, calculations, formulas, and solved exercises

    CERN Document Server

    Berman, Armand

    1992-01-01

    This book was written with two main objectives in mind-to summarize and organize the vast material of vacuum technology in sets of useful formulas, and to provide a collection of worked out exercises showing how to use these formulas for solving technological problems. It is an ideal reference source for those with little time to devote to a full mathematical treatment of the many problems issued in vacuum practice, but who have a working knowledge of the essentials of vacuum technology, elementary physics, and mathematics. This time saving book employs a problem-solving approach throughout, p

  16. Solving Differential Equations in R: Package deSolve

    Science.gov (United States)

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

  17. Solving Differential Equations in R: Package deSolve

    NARCIS (Netherlands)

    Soetaert, K.E.R.; Petzoldt, T.; Setzer, R.W.

    2010-01-01

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The

  18. Comprehension and computation in Bayesian problem solving

    Directory of Open Access Journals (Sweden)

    Eric D. Johnson

    2015-07-01

    Full Text Available Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages, both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on transparent Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point.

  19. The semantic system is involved in mathematical problem solving.

    Science.gov (United States)

    Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

    2018-02-01

    Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

  20. Community-powered problem solving.

    Science.gov (United States)

    Gouillart, Francis; Billings, Douglas

    2013-04-01

    Traditionally, companies have managed their constituencies with specific processes: marketing to customers, procuring from vendors, developing HR policies for employees, and so on. The problem is, such processes focus on repeatability and compliance, so they can lead to stagnation. Inviting your constituencies to collectively help you solve problems and exploit opportunities--"co-creation"--is a better approach. It allows you to continually tap the skills and insights of huge numbers of stakeholders and develop new ways to produce value for all. The idea is to provide stakeholders with platforms (physical and digital forums) on which they can interact, get them to start exploring new experiences and connections, and let the system grow organically. A co-creation initiative by a unit of Becton, Dickinson and Company demonstrates how this works. A global leader in syringes, BD set out to deepen its ties with hospital customers and help them reduce the incidence of infections from unsafe injection and syringe disposal practices. The effort began with a cross-functional internal team, brought in the hospital procurement and supply managers BD had relationships with, and then reached out to hospitals' infection-prevention and occupational health leaders. Eventually product designers, nurses, sustainability staffers, and even hospital CFOs were using the platform, contributing data that generated new best practices and reduced infections.

  1. Improved Quasi-Newton method via PSB update for solving systems of nonlinear equations

    Science.gov (United States)

    Mamat, Mustafa; Dauda, M. K.; Waziri, M. Y.; Ahmad, Fadhilah; Mohamad, Fatma Susilawati

    2016-10-01

    The Newton method has some shortcomings which includes computation of the Jacobian matrix which may be difficult or even impossible to compute and solving the Newton system in every iteration. Also, the common setback with some quasi-Newton methods is that they need to compute and store an n × n matrix at each iteration, this is computationally costly for large scale problems. To overcome such drawbacks, an improved Method for solving systems of nonlinear equations via PSB (Powell-Symmetric-Broyden) update is proposed. In the proposed method, the approximate Jacobian inverse Hk of PSB is updated and its efficiency has improved thereby require low memory storage, hence the main aim of this paper. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.

  2. SOLVING ENGINEERING OPTIMIZATION PROBLEMS WITH THE SWARM INTELLIGENCE METHODS

    Directory of Open Access Journals (Sweden)

    V. Panteleev Andrei

    2017-01-01

    Full Text Available An important stage in problem solving process for aerospace and aerostructures designing is calculating their main charac- teristics optimization. The results of the four constrained optimization problems related to the design of various technical systems: such as determining the best parameters of welded beams, pressure vessel, gear, spring are presented. The purpose of each task is to minimize the cost and weight of the construction. The object functions in optimization practical problem are nonlinear functions with a lot of variables and a complex layer surface indentations. That is why using classical approach for extremum seeking is not efficient. Here comes the necessity of using such methods of optimization that allow to find a near optimal solution in acceptable amount of time with the minimum waste of computer power. Such methods include the methods of Swarm Intelligence: spiral dy- namics algorithm, stochastic diffusion search, hybrid seeker optimization algorithm. The Swarm Intelligence methods are designed in such a way that a swarm consisting of agents carries out the search for extremum. In search for the point of extremum, the parti- cles exchange information and consider their experience as well as the experience of population leader and the neighbors in some area. To solve the listed problems there has been designed a program complex, which efficiency is illustrated by the solutions of four applied problems. Each of the considered applied optimization problems is solved with all the three chosen methods. The ob- tained numerical results can be compared with the ones found in a swarm with a particle method. The author gives recommenda- tions on how to choose methods parameters and penalty function value, which consider inequality constraints.

  3. Numerical analysis

    CERN Document Server

    Brezinski, C

    2012-01-01

    Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<

  4. Solved problems in electromagnetics

    CERN Document Server

    Salazar Bloise, Félix; Bayón Rojo, Ana; Gascón Latasa, Francisco

    2017-01-01

    This book presents the fundamental concepts of electromagnetism through problems with a brief theoretical introduction at the beginning of each chapter. The present book has a strong  didactic character. It explains all the mathematical steps and the theoretical concepts connected with the development of the problem. It guides the reader to understand the employed procedures to learn to solve the exercises independently. The exercises are structured in a similar way: The chapters begin with easy problems increasing progressively in the level of difficulty. This book is written for students of physics and engineering in the framework of the new European Plans of Study for Bachelor and Master and also for tutors and lecturers. .

  5. Threshold Concepts in the Development of Problem-Solving Skills

    Science.gov (United States)

    Wismath, Shelly; Orr, Doug; MacKay, Bruce

    2015-01-01

    Problem-solving skills are often identified as a key component of 21st century education. This study collected data from students enrolled in a university-level Liberal Education science course called "Problems and Puzzles," which introduced students to the theory and practice of problem solving via puzzles. Based on classroom…

  6. A Rubric for Assessing Students' Experimental Problem-Solving Ability

    Science.gov (United States)

    Shadle, Susan E.; Brown, Eric C.; Towns, Marcy H.; Warner, Don L.

    2012-01-01

    The ability to couple problem solving both to the understanding of chemical concepts and to laboratory practices is an essential skill for undergraduate chemistry programs to foster in our students. Therefore, chemistry programs must offer opportunities to answer real problems that require use of problem-solving processes used by practicing…

  7. Strategies, Not Solutions: Involving Students in Problem Solving.

    Science.gov (United States)

    Von Kuster, Lee N.

    1984-01-01

    Defines problem solving, discusses the use of problems developed by students that are relevant to their own lives, presents examples of practical mathematics problems that deal with local situations, discusses fringe benefits of this type of problem solving, and addresses teachers' concern that this method consumes too much time. (MBR)

  8. Numerical Relativity

    Science.gov (United States)

    Baker, John G.

    2009-01-01

    Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.

  9. The influence of transformational leadership on organizational creative problem solving capacity

    Directory of Open Access Journals (Sweden)

    Stevanović Ana

    2015-01-01

    Full Text Available In order to successfully operate and remain in contemporary turbulent marketplace, organizations need to foster their employees' creativity, because it is a prerequisite of organizational innovation. As creativity is a precursor of innovation, and as innovation is an example of creative solutions implementation, there arenumerous situations which require creative behavior of employees and that can be labeled as 'problems'. Therefore, creative problem solving turns out to be relevant in understanding of creativity. The aim of this paper is to offer an answer to the question - how transformational leadership influences the improvement of the capacity for creative problem solving within the organization. On the basis of the relevant literature, but also numerous practical examples of successful companies, we realized that transformational leaders foster a creative attitude of the employees and help them to build capacity for creative problem solving. Also, we realized that many studies have neglected the psychological conditions under which this exchange takes place. As creative problem solving requires extensive and strenuous cognitive processes, we assumed that the role of psychological safety is necessary because employees need to feel free during proposing new creative solutions.

  10. On method of solving third-order ordinary differential equations directly using Bernstein polynomials

    Science.gov (United States)

    Khataybeh, S. N.; Hashim, I.

    2018-04-01

    In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

  11. Analytical method for solving radioactive transformations

    International Nuclear Information System (INIS)

    Vukadin, Z.

    1999-01-01

    The exact method of solving radioactive transformations is presented. Nonsingular Bateman coefficients, which can be computed using recurrence formulas, greatly reduce computational time and eliminate singularities that often arise in problems involving nuclide transmutations. Depletion function power series expansion enables high accuracy of the performed calculations, specially in a case of a decay constants with closely spaced values. Generality and simplicity of the method make the method useful for many practical applications. (author)

  12. A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

    Directory of Open Access Journals (Sweden)

    Rongwu Lu

    2017-01-01

    Full Text Available Considering the popular use of a certain kind of supervision management problem in many fields, we firstly build an ordinary supervision game model of multiple stakeholders. Secondly, a fractional supervision game model is set up and solved based on the theory of fractional calculus and a predictor-corrector numerical approach. Thirdly, the methods of phase diagram and time series graph were applied to simulate and analyse the dynamic process of the fractional order game model. Results of numerical solutions are given to illustrate our conclusions and referred to the practice.

  13. An outline review of numerical transport methods

    International Nuclear Information System (INIS)

    Budd, C.

    1981-01-01

    A brief review is presented of numerical methods for solving the neutron transport equation in the context of reactor physics. First the various forms of transport equation are given. Second, the various ways of classifying numerical transport methods are discussed. Finally each method (or class of methods) is outlined in turn. (U.K.)

  14. Numerical methods for hydrodynamic stability problems

    International Nuclear Information System (INIS)

    Fujimura, Kaoru

    1985-11-01

    Numerical methods for solving the Orr-Sommerfeld equation, which is the fundamental equation of the hydrodynamic stability theory for various shear flows, are reviewed and typical numerical results are presented. The methods of asymptotic solution, finite difference methods, initial value methods and expansions in orthogonal functions are compared. (author)

  15. Numerical simulation of pulse-tube refrigerators

    NARCIS (Netherlands)

    Lyulina, I.A.; Mattheij, R.M.M.; Tijsseling, A.S.; Waele, de A.T.A.M.

    2004-01-01

    A new numerical model has been introduced to study steady oscillatory heat and mass transfer in the tube section of a pulse-tube refrigerator. Conservation equations describing compressible gas flow in the tube are solved numerically, using high resolution schemes. The equation of conservation of

  16. Numerical Analysis Objects

    Science.gov (United States)

    Henderson, Michael

    1997-08-01

    The Numerical Analysis Objects project (NAO) is a project in the Mathematics Department of IBM's TJ Watson Research Center. While there are plenty of numerical tools available today, it is not an easy task to combine them into a custom application. NAO is directed at the dual problems of building applications from a set of tools, and creating those tools. There are several "reuse" projects, which focus on the problems of identifying and cataloging tools. NAO is directed at the specific context of scientific computing. Because the type of tools is restricted, problems such as tools with incompatible data structures for input and output, and dissimilar interfaces to tools which solve similar problems can be addressed. The approach we've taken is to define interfaces to those objects used in numerical analysis, such as geometries, functions and operators, and to start collecting (and building) a set of tools which use these interfaces. We have written a class library (a set of abstract classes and implementations) in C++ which demonstrates the approach. Besides the classes, the class library includes "stub" routines which allow the library to be used from C or Fortran, and an interface to a Visual Programming Language. The library has been used to build a simulator for petroleum reservoirs, using a set of tools for discretizing nonlinear differential equations that we have written, and includes "wrapped" versions of packages from the Netlib repository. Documentation can be found on the Web at "http://www.research.ibm.com/nao". I will describe the objects and their interfaces, and give examples ranging from mesh generation to solving differential equations.

  17. Numerical solution of Boltzmann's equation

    International Nuclear Information System (INIS)

    Sod, G.A.

    1976-04-01

    The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

  18. An approach to solve replacement problems under intuitionistic fuzzy nature

    Science.gov (United States)

    Balaganesan, M.; Ganesan, K.

    2018-04-01

    Due to impreciseness to solve the day to day problems the researchers use fuzzy sets in their discussions of the replacement problems. The aim of this paper is to solve the replacement theory problems with triangular intuitionistic fuzzy numbers. An effective methodology based on fuzziness index and location index is proposed to determine the optimal solution of the replacement problem. A numerical example is illustrated to validate the proposed method.

  19. On Solving "Problems"

    Science.gov (United States)

    Ghez, Richard

    2006-04-01

    Counting and estimating are no doubt ancient survival skills. And yet, present educational methods tend to downplay these very skills. This breeds senseless innumeracy and social disruption. Jumbling inches with centimeters, for example, can cause a Mars mission to fail. With minor distortion, elementary and high schools (and beyond) teach that all fractions are simple, that all square roots are rational, and that trigonometric functions need be evaluated only for 30, 45, and 60 degrees. We thus inflict threefold damage on our children and students. First, they come to believe that numbers beyond 10 (except for current account deficits) are intuitively inaccessible; second, that answers to all mathematical questions are "formulas"; and third, that the art of estimation merely requires punching keys on a calculator—a dismal sort of black magic. These beliefs I wish to expose in the form of eight short numerical tales.

  20. The numerical simulation of convection delayed dominated diffusion equation

    Directory of Open Access Journals (Sweden)

    Mohan Kumar P. Murali

    2016-01-01

    Full Text Available In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution.

  1. Discrete convolution-operators and radioactive disintegration. [Numerical solution

    Energy Technology Data Exchange (ETDEWEB)

    Kalla, S L; VALENTINUZZI, M E [UNIVERSIDAD NACIONAL DE TUCUMAN (ARGENTINA). FACULTAD DE CIENCIAS EXACTAS Y TECNOLOGIA

    1975-08-01

    The basic concepts of discrete convolution and discrete convolution-operators are briefly described. Then, using the discrete convolution - operators, the differential equations associated with the process of radioactive disintegration are numerically solved. The importance of the method is emphasized to solve numerically, differential and integral equations.

  2. Solving Nonlinear Partial Differential Equations with Maple and Mathematica

    CERN Document Server

    Shingareva, Inna K

    2011-01-01

    The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an

  3. Numerical method for the nonlinear Fokker-Planck equation

    International Nuclear Information System (INIS)

    Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K.

    1997-01-01

    A practical method based on distributed approximating functionals (DAFs) is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokker-Planck equation, and the method is compared with the accurate K-point Stirling interpolation formula finite-difference method. The approach is also used successfully to solve a nonlinear self-consistent dynamic mean-field problem for which both the cumulant expansion and scaling theory have been found by Drozdov and Morillo [Phys. Rev. E 54, 931 (1996)] to be inadequate to describe the occurrence of a long-lived transient bimodality. The standard interpretation of the transient bimodality in terms of the flat region in the kinetic potential fails for the present case. An alternative analysis based on the effective potential of the Schroedinger-like Fokker-Planck equation is suggested. Our analysis of the transient bimodality is strongly supported by two examples that are numerically much more challenging than other examples that have been previously reported for this problem. copyright 1997 The American Physical Society

  4. Handbook of numerical analysis

    CERN Document Server

    Ciarlet, Philippe G

    Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas an

  5. Solving fault diagnosis problems linear synthesis techniques

    CERN Document Server

    Varga, Andreas

    2017-01-01

    This book addresses fault detection and isolation topics from a computational perspective. Unlike most existing literature, it bridges the gap between the existing well-developed theoretical results and the realm of reliable computational synthesis procedures. The model-based approach to fault detection and diagnosis has been the subject of ongoing research for the past few decades. While the theoretical aspects of fault diagnosis on the basis of linear models are well understood, most of the computational methods proposed for the synthesis of fault detection and isolation filters are not satisfactory from a numerical standpoint. Several features make this book unique in the fault detection literature: Solution of standard synthesis problems in the most general setting, for both continuous- and discrete-time systems, regardless of whether they are proper or not; consequently, the proposed synthesis procedures can solve a specific problem whenever a solution exists Emphasis on the best numerical algorithms to ...

  6. Language and mathematical problem solving among bilinguals.

    Science.gov (United States)

    Bernardo, Allan B I

    2002-05-01

    Does using a bilingual's 1st or 2nd language have an effect on problem solving in semantically rich domains like school mathematics? The author conducted a study to determine whether Filipino-English bilingual students' understanding and solving of word problems in arithmetic differed when the problems were in the students' 1st and 2nd languages. Two groups participated-students whose 1st language was Filipino and students whose 1st language was English-and easy and difficult arithmetic problems were used. The author used a recall paradigm to assess how students understood the word problems and coded the solution accuracy to assess problem solving. The results indicated a 1st-language advantage; that is, the students were better able to understand and solve problems in their 1st language, whether the 1st language was English or Filipino. Moreover, the advantage was more marked with the easy problems. The theoretical and practical implications of the results are discussed.

  7. Numerical methods

    CERN Document Server

    Dahlquist, Germund

    1974-01-01

    ""Substantial, detailed and rigorous . . . readers for whom the book is intended are admirably served."" - MathSciNet (Mathematical Reviews on the Web), American Mathematical Society.Practical text strikes fine balance between students' requirements for theoretical treatment and needs of practitioners, with best methods for large- and small-scale computing. Prerequisites are minimal (calculus, linear algebra, and preferably some acquaintance with computer programming). Text includes many worked examples, problems, and an extensive bibliography.

  8. Numerical analysis

    CERN Document Server

    Jacques, Ian

    1987-01-01

    This book is primarily intended for undergraduates in mathematics, the physical sciences and engineering. It introduces students to most of the techniques forming the core component of courses in numerical analysis. The text is divided into eight chapters which are largely self-contained. However, with a subject as intricately woven as mathematics, there is inevitably some interdependence between them. The level of difficulty varies and, although emphasis is firmly placed on the methods themselves rather than their analysis, we have not hesitated to include theoretical material when we consider it to be sufficiently interesting. However, it should be possible to omit those parts that do seem daunting while still being able to follow the worked examples and to tackle the exercises accompanying each section. Familiarity with the basic results of analysis and linear algebra is assumed since these are normally taught in first courses on mathematical methods. For reference purposes a list of theorems used in the t...

  9. Difficulties in Genetics Problem Solving.

    Science.gov (United States)

    Tolman, Richard R.

    1982-01-01

    Examined problem-solving strategies of 30 high school students as they solved genetics problems. Proposes a new sequence of teaching genetics based on results: meiosis, sex chromosomes, sex determination, sex-linked traits, monohybrid and dihybrid crosses (humans), codominance (humans), and Mendel's pea experiments. (JN)

  10. Problem Solving, Scaffolding and Learning

    Science.gov (United States)

    Lin, Shih-Yin

    2012-01-01

    Helping students to construct robust understanding of physics concepts and develop good solving skills is a central goal in many physics classrooms. This thesis examine students' problem solving abilities from different perspectives and explores strategies to scaffold students' learning. In studies involving analogical problem solving…

  11. Problem Solving on a Monorail.

    Science.gov (United States)

    Barrow, Lloyd H.; And Others

    1994-01-01

    This activity was created to address a lack of problem-solving activities for elementary children. A "monorail" activity from the Evening Science Program for K-3 Students and Parents program is presented to illustrate the problem-solving format. Designed for performance at stations by groups of two students. (LZ)

  12. Solving complex fisheries management problems

    DEFF Research Database (Denmark)

    Petter Johnsen, Jahn; Eliasen, Søren Qvist

    2011-01-01

    A crucial issue for the new EU common fisheries policy is how to solve the discard problem. Through a study of the institutional set up and the arrangements for solving the discard problem in Denmark, the Faroe Islands, Iceland and Norway, the article identifies the discard problem as related...

  13. Quadrature theory the theory of numerical integration on a compact interval

    CERN Document Server

    Brass, Helmut

    2011-01-01

    Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word "theory" in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called "co-observations," which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of nume...

  14. NUMERICAL SIMULATION OF POLLUTION DISPERSION IN URBAN STREET

    Directory of Open Access Journals (Sweden)

    M. M. Biliaiev

    2017-08-01

    Full Text Available Purpose. The scientific paper solves the question of 2D numerical model development, which allows quick computation of air pollution in streets from vehicles. The aim of the work is numerical model development that would enable to predict the level of air pollution by using protective barriers along the road. Methodology. The developed model is based on the equation of inviscid flow and equation of pollutant transfer. Potential equation is used to compute velocity field of air flow near road in the case of protection barriers application. To solve equation for potential flow implicit difference scheme of «conditional approximation« is used. The implicit change – triangle difference scheme is used to solve equation of convective – diffusive dispersion. Numerical integration is carried out using the rectangular difference grid. Method of porosity technique («markers method» is used to create the form of comprehensive computational region. Emission of toxic gases from vehicle is modeled using Delta function for point source.Findings. Authors developed 2D numerical model. It takes into account the main physical factors affecting the process of dispersion of pollutants in the atmosphere when emissions of vehicle including protection barriers near the road. On the basis of the developed numerical models a computational experiment was performed to estimate the level of air pollution in the street. Originality. A numerical model has been created. It makes it possible to calculate 2D aerodynamics of the wind flow in the presence of noises and the process of mass transfer of toxic gas emissions from the motorway. The model allows taking into account the presence of the car on the road, the form of a protective barrier, the presence of a curb. Calculations have been performed to determine the contamination zone formed at the protective barrier that is located at the motorway. Practical value. An effective numerical model that can be applied in the

  15. Monte Carlo method for solving a parabolic problem

    Directory of Open Access Journals (Sweden)

    Tian Yi

    2016-01-01

    Full Text Available In this paper, we present a numerical method based on random sampling for a parabolic problem. This method combines use of the Crank-Nicolson method and Monte Carlo method. In the numerical algorithm, we first discretize governing equations by Crank-Nicolson method, and obtain a large sparse system of linear algebraic equations, then use Monte Carlo method to solve the linear algebraic equations. To illustrate the usefulness of this technique, we apply it to some test problems.

  16. Solving the Richardson equations close to the critical points

    Energy Technology Data Exchange (ETDEWEB)

    DomInguez, F [Departamento de Matematicas, Universidad de Alcala, 28871 Alcala de Henares (Spain); Esebbag, C [Departamento de Matematicas, Universidad de Alcala, 28871 Alcala de Henares (Spain); Dukelsky, J [Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid (Spain)

    2006-09-15

    We study the Richardson equations close to the critical values of the pairing strength g{sub c}, where the occurrence of divergences precludes numerical solutions. We derive a set of equations for determining the critical g values and the non-collapsing pair energies. Studying the behaviour of the solutions close to the critical points, we develop a procedure to solve numerically the Richardson equations for arbitrary coupling strength.

  17. Using a general problem-solving strategy to promote transfer.

    Science.gov (United States)

    Youssef-Shalala, Amina; Ayres, Paul; Schubert, Carina; Sweller, John

    2014-09-01

    Cognitive load theory was used to hypothesize that a general problem-solving strategy based on a make-as-many-moves-as-possible heuristic could facilitate problem solutions for transfer problems. In four experiments, school students were required to learn about a topic through practice with a general problem-solving strategy, through a conventional problem solving strategy or by studying worked examples. In Experiments 1 and 2 using junior high school students learning geometry, low knowledge students in the general problem-solving group scored significantly higher on near or far transfer tests than the conventional problem-solving group. In Experiment 3, an advantage for a general problem-solving group over a group presented worked examples was obtained on far transfer tests using the same curriculum materials, again presented to junior high school students. No differences between conditions were found in Experiments 1, 2, or 3 using test problems similar to the acquisition problems. Experiment 4 used senior high school students studying economics and found the general problem-solving group scored significantly higher than the conventional problem-solving group on both similar and transfer tests. It was concluded that the general problem-solving strategy was helpful for novices, but not for students that had access to domain-specific knowledge. PsycINFO Database Record (c) 2014 APA, all rights reserved.

  18. Holistic simulation of geotechnical installation processes numerical and physical modelling

    CERN Document Server

    2015-01-01

    The book provides suitable methods for the simulations of boundary value problems of geotechnical installation processes with reliable prediction for the deformation behavior of structures in static or dynamic interaction with the soil. It summarizes the basic research of a research group from scientists dealing with constitutive relations of soils and their implementations as well as contact element formulations in FE-codes. Numerical and physical experiments are presented providing benchmarks for future developments in this field. Boundary value problems have been formulated and solved with the developed tools in order to show the effectivity of the methods. Parametric studies of geotechnical installation processes in order to identify the governing parameters for the optimization of the process are given in such a way that the findings can be recommended to practice for further use. For many design engineers in practice the assessment of the serviceability of nearby structures due to geotechnical installat...

  19. Multiscale empirical interpolation for solving nonlinear PDEs

    KAUST Repository

    Calo, Victor M.

    2014-12-01

    In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM). To solve nonlinear equations, the GMsFEM is used to represent the solution on a coarse grid with multiscale basis functions computed offline. Computing the GMsFEM solution involves calculating the system residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully-resolved fine scale one. The empirical interpolation method uses basis functions which are built by sampling the nonlinear function we want to approximate a limited number of times. The coefficients needed for this approximation are computed in the offline stage by inverting an inexpensive linear system. The proposed multiscale empirical interpolation techniques: (1) divide computing the nonlinear function into coarse regions; (2) evaluate contributions of nonlinear functions in each coarse region taking advantage of a reduced-order representation of the solution; and (3) introduce multiscale proper-orthogonal-decomposition techniques to find appropriate interpolation vectors. We demonstrate the effectiveness of the proposed methods on several nonlinear multiscale PDEs that are solved with Newton\\'s methods and fully-implicit time marching schemes. Our numerical results show that the proposed methods provide a robust framework for solving nonlinear multiscale PDEs on a coarse grid with bounded error and significant computational cost reduction.

  20. Numerical considerations for Lagrangian stochastic dispersion models: Eliminating rogue trajectories, and the importance of numerical accuracy

    Science.gov (United States)

    When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo...

  1. Convergence of hybrid methods for solving non-linear partial ...

    African Journals Online (AJOL)

    This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...

  2. Direct approach for solving nonlinear evolution and two-point

    Indian Academy of Sciences (India)

    Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples ...

  3. New approach to solve symmetric fully fuzzy linear systems

    Indian Academy of Sciences (India)

    In this paper, we present a method to solve fully fuzzy linear systems with symmetric coefficient matrix. The symmetric coefficient matrix is decomposed into two systems of equations by using Cholesky method and then a solution can be obtained. Numerical examples are given to illustrate our method.

  4. Sinc-collocation method for solving the Blasius equation

    International Nuclear Information System (INIS)

    Parand, K.; Dehghan, Mehdi; Pirkhedri, A.

    2009-01-01

    Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.

  5. Using problem-solving instruction to overcome high school ...

    African Journals Online (AJOL)

    kofi.mereku

    identified difficulties in comparison to the conventional lecture method. ... important for chemistry educators to be aware of the difficulties students encounter as they learn .... these concepts before the can solve quantitative numerical problems. Secondly ... development of stepped supporting tools for stoichiometric problems, ...

  6. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

    Science.gov (United States)

    Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

    2018-04-01

    In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

  7. The Effects of Case Libraries in Supporting Collaborative Problem-Solving in an Online Learning Environment

    Science.gov (United States)

    Tawfik, Andrew A.; Sánchez, Lenny; Saparova, Dinara

    2014-01-01

    Various domains require practitioners to encounter and resolve ill-structured problems using collaborative problem-solving. As such, problem-solving is an essential skill that educators must emphasize to prepare learners for practice. One potential way to support problem-solving is through further investigation of instructional design methods that…

  8. Are Middle School Mathematics Teachers Able to Solve Word Problems without Using Variable?

    Science.gov (United States)

    Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tugba; Soylu, Yasin

    2018-01-01

    Many people consider problem solving as a complex process in which variables such as "x," "y" are used. Problems may not be solved by only using "variable." Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is…

  9. Assessing Student Written Problem Solutions: A Problem-Solving Rubric with Application to Introductory Physics

    Science.gov (United States)

    Docktor, Jennifer L.; Dornfeld, Jay; Frodermann, Evan; Heller, Kenneth; Hsu, Leonardo; Jackson, Koblar Alan; Mason, Andrew; Ryan, Qing X.; Yang, Jie

    2016-01-01

    Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic…

  10. Problem Solving with General Semantics.

    Science.gov (United States)

    Hewson, David

    1996-01-01

    Discusses how to use general semantics formulations to improve problem solving at home or at work--methods come from the areas of artificial intelligence/computer science, engineering, operations research, and psychology. (PA)

  11. How to solve mathematical problems

    CERN Document Server

    Wickelgren, Wayne A

    1995-01-01

    Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.

  12. Interactive Problem-Solving Interventions

    African Journals Online (AJOL)

    Frew Demeke Alemu

    concerted efforts of unofficial actors to establish unofficial communication ... Frew Demeke Alemu (LLB, LLM in International Human Rights Law from Lund ..... 24 Tamra Pearson d'Estrée (2009), “Problem-Solving Approaches”, (in The SAGE ...

  13. solving the cell formation problem in group technology

    Directory of Open Access Journals (Sweden)

    Prafulla Joglekar

    2001-01-01

    Full Text Available Over the last three decades, numerous algorithms have been proposed to solve the work-cell formation problem. For practicing manufacturing managers it would be nice to know as to which algorithm would be most effective and efficient for their specific situation. While several studies have attempted to fulfill this need, most have not resulted in any definitive recommendations and a better methodology of evaluation of cell formation algorithms is urgently needed. Prima facie, the methodology underlying Miltenburg and Zhang's (M&Z (1991 evaluation of nine well-known cell formation algorithms seems very promising. The primary performance measure proposed by M&Z effectively captures the objectives of a good solution to a cell formation problem and is worthy of use in future studies. Unfortunately, a critical review of M&Z's methodology also reveals certain important flaws in M&Z's methodology. For example, M&Z may not have duplicated each algorithm precisely as the developer(s of that algorithm intended. Second, M&Z's misrepresent Chandrasekharan and Rajagopalan's [C&R's] (1986 grouping efficiency measure. Third, M&Z's secondary performance measures lead them to unnecessarily ambivalent results. Fourth, several of M&Z's empirical conclusions can be theoretically deduced. It is hoped that future evaluations of cell formation algorithms will benefit from both the strengths and weaknesses of M&Z's work.

  14. The art and science of participative problem solving

    DEFF Research Database (Denmark)

    Vidal, Rene Victor Valqui

    In this paper we will document that real-life problem solving in complex situations demands both rational (scientific) and intuitive (artistic) thinking. First, the concepts of art and science will be discussed; differences and similarities will be enhanced. Thereafter the concept of group problem...... solving facilitation both as science and art will be presented. A case study related to examinations planning will be discussed to illustrate the main concepts in practice. In addition, other cases studies will also be shortly presented....

  15. DESIGN AND EXAMINATION OF ALGORITHMS FOR SOLVING THE KNAPSACK PROBLEM

    Directory of Open Access Journals (Sweden)

    S. Kantsedal

    2015-07-01

    Full Text Available The use of methods of branches and boundaries as well as the methods of dynamic programming at solving the problem of «knapsack» is grounded. The main concepts are expounded. The methods and algorithms development for solving the above specified problem are described. Recommendations on practical application of constructed algorithms based on their experimental investigation and carrying out charactheristics comparison are presented.

  16. Threshold Concepts in the Development of Problem-solving Skills

    OpenAIRE

    Shelly Wismath; Doug Orr; Bruce MacKay

    2015-01-01

    Problem-solving skills are often identified as a key component of 21st century education. This study collected data from students enrolled in a university-level Liberal Education science course called Problems and Puzzles, which introduced students to the theory and practice of problem solving via puzzles. Based on classroom observation and other qualitative data collected over three semesters, we have identified three significant changes in student behaviour at specific points in the course....

  17. Comparing genetic algorithm and particle swarm optimization for solving capacitated vehicle routing problem

    Science.gov (United States)

    Iswari, T.; Asih, A. M. S.

    2018-04-01

    In the logistics system, transportation plays an important role to connect every element in the supply chain, but it can produces the greatest cost. Therefore, it is important to make the transportation costs as minimum as possible. Reducing the transportation cost can be done in several ways. One of the ways to minimizing the transportation cost is by optimizing the routing of its vehicles. It refers to Vehicle Routing Problem (VRP). The most common type of VRP is Capacitated Vehicle Routing Problem (CVRP). In CVRP, the vehicles have their own capacity and the total demands from the customer should not exceed the capacity of the vehicle. CVRP belongs to the class of NP-hard problems. These NP-hard problems make it more complex to solve such that exact algorithms become highly time-consuming with the increases in problem sizes. Thus, for large-scale problem instances, as typically found in industrial applications, finding an optimal solution is not practicable. Therefore, this paper uses two kinds of metaheuristics approach to solving CVRP. Those are Genetic Algorithm and Particle Swarm Optimization. This paper compares the results of both algorithms and see the performance of each algorithm. The results show that both algorithms perform well in solving CVRP but still needs to be improved. From algorithm testing and numerical example, Genetic Algorithm yields a better solution than Particle Swarm Optimization in total distance travelled.

  18. Nodal spectrum method for solving neutron diffusion equation

    International Nuclear Information System (INIS)

    Sanchez, D.; Garcia, C. R.; Barros, R. C. de; Milian, D.E.

    1999-01-01

    Presented here is a new numerical nodal method for solving static multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X, Y directions and then considering flat approximations for the current. These flat approximations are the only approximations that are considered in this method, as a result the numerical solutions are completely free from truncation errors. We show numerical results to illustrate the methods accuracy for coarse mesh calculations

  19. WE-AB-BRB-01: Development of a Probe-Format Graphite Calorimeter for Practical Clinical Dosimetry: Numerical Design Optimization, Prototyping, and Experimental Proof-Of-Concept

    International Nuclear Information System (INIS)

    Renaud, J; Seuntjens, J; Sarfehnia, A

    2015-01-01

    Purpose: In this work, the feasibility of performing absolute dose to water measurements using a constant temperature graphite probe calorimeter (GPC) in a clinical environment is established. Methods: A numerical design optimization study was conducted by simulating the heat transfer in the GPC resulting from irradiation using a finite element method software package. The choice of device shape, dimensions, and materials was made to minimize the heat loss in the sensitive volume of the GPC. The resulting design, which incorporates a novel aerogel-based thermal insulator, and 15 temperature sensitive resistors capable of both Joule heating and measuring temperature, was constructed in house. A software based process controller was developed to stabilize the temperatures of the GPC’s constituent graphite components to within a few 10’s of µK. This control system enables the GPC to operate in either the quasi-adiabatic or isothermal mode, two well-known, and independent calorimetry techniques. Absorbed dose to water measurements were made using these two methods under standard conditions in a 6 MV 1000 MU/min photon beam and subsequently compared against TG-51 derived values. Results: Compared to an expected dose to water of 76.9 cGy/100 MU, the average GPC-measured doses were 76.5 ± 0.5 and 76.9 ± 0.5 cGy/100 MU for the adiabatic and isothermal modes, respectively. The Monte Carlo calculated graphite to water dose conversion was 1.013, and the adiabatic heat loss correction was 1.003. With an overall uncertainty of about 1%, the most significant contributions were the specific heat capacity (type B, 0.8%) and the repeatability (type A, 0.6%). Conclusion: While the quasi-adiabatic mode of operation had been validated in previous work, this is the first time that the GPC has been successfully used isothermally. This proof-of-concept will serve as the basis for further study into the GPC’s application to small fields and MRI-linac dosimetry. This work has been

  20. Programming languages for business problem solving

    CERN Document Server

    Wang, Shouhong

    2007-01-01

    It has become crucial for managers to be computer literate in today's business environment. It is also important that those entering the field acquire the fundamental theories of information systems, the essential practical skills in computer applications, and the desire for life-long learning in information technology. Programming Languages for Business Problem Solving presents a working knowledge of the major programming languages, including COBOL, C++, Java, HTML, JavaScript, VB.NET, VBA, ASP.NET, Perl, PHP, XML, and SQL, used in the current business computing environment. The book examin

  1. Threshold Concepts in the Development of Problem-solving Skills

    Directory of Open Access Journals (Sweden)

    Shelly Wismath

    2015-03-01

    Full Text Available Problem-solving skills are often identified as a key component of 21st century education. This study collected data from students enrolled in a university-level Liberal Education science course called Problems and Puzzles, which introduced students to the theory and practice of problem solving via puzzles. Based on classroom observation and other qualitative data collected over three semesters, we have identified three significant changes in student behaviour at specific points in the course. These changes can be posited to reveal three underlying threshold concepts in the evolution and establishment of students’ problem-solving skills.

  2. Tangram solved? Prefrontal cortex activation analysis during geometric problem solving.

    Science.gov (United States)

    Ayaz, Hasan; Shewokis, Patricia A; Izzetoğlu, Meltem; Çakır, Murat P; Onaral, Banu

    2012-01-01

    Recent neuroimaging studies have implicated prefrontal and parietal cortices for mathematical problem solving. Mental arithmetic tasks have been used extensively to study neural correlates of mathematical reasoning. In the present study we used geometric problem sets (tangram tasks) that require executive planning and visuospatial reasoning without any linguistic representation interference. We used portable optical brain imaging (functional near infrared spectroscopy--fNIR) to monitor hemodynamic changes within anterior prefrontal cortex during tangram tasks. Twelve healthy subjects were asked to solve a series of computerized tangram puzzles and control tasks that required same geometric shape manipulation without problem solving. Total hemoglobin (HbT) concentration changes indicated a significant increase during tangram problem solving in the right hemisphere. Moreover, HbT changes during failed trials (when no solution found) were significantly higher compared to successful trials. These preliminary results suggest that fNIR can be used to assess cortical activation changes induced by geometric problem solving. Since fNIR is safe, wearable and can be used in ecologically valid environments such as classrooms, this neuroimaging tool may help to improve and optimize learning in educational settings.

  3. Numerical Analysis of Partial Differential Equations

    CERN Document Server

    Lui, S H

    2011-01-01

    A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis

  4. Numerical Hydrodynamics in General Relativity

    Directory of Open Access Journals (Sweden)

    Font José A.

    2003-01-01

    Full Text Available 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.

  5. Processes involved in solving mathematical problems

    Science.gov (United States)

    Shahrill, Masitah; Putri, Ratu Ilma Indra; Zulkardi, Prahmana, Rully Charitas Indra

    2018-04-01

    This study examines one of the instructional practices features utilized within the Year 8 mathematics lessons in Brunei Darussalam. The codes from the TIMSS 1999 Video Study were applied and strictly followed, and from the 183 mathematics problems recorded, there were 95 problems with a solution presented during the public segments of the video-recorded lesson sequences of the four sampled teachers. The analyses involved firstly, identifying the processes related to mathematical problem statements, and secondly, examining the different processes used in solving the mathematical problems for each problem publicly completed during the lessons. The findings revealed that for three of the teachers, their problem statements coded as `using procedures' ranged from 64% to 83%, while the remaining teacher had 40% of his problem statements coded as `making connections.' The processes used when solving the problems were mainly `using procedures', and none of the problems were coded as `giving results only'. Furthermore, all four teachers made use of making the relevant connections in solving the problems given to their respective students.

  6. Learning via problem solving in mathematics education

    Directory of Open Access Journals (Sweden)

    Piet Human

    2009-09-01

    problem-solving movement, over the last twenty years, mathematics educators around the world started increasingly to appreciate the role of social interaction and mathematical discourse in classrooms, and to take into consideration the infl uence of the social, socio-mathematical and mathematical norms established in classrooms. This shift away from an emphasis on individualised instruction towards classroom practices characterised by rich and focused social interaction orchestrated by the teacher, became the second element, next to problem-solving, of what is now known as the “reform agenda”. Learning and teaching by means of problem-solving in a socially-interactive classroom, with a strong demand for conceptual understanding, is radically different from traditional expository teaching. However, contrary to commonly-held misunderstandings, it requires substantial teacher involvement. It also requires teachers to assume a much higher level of responsibility for the extent and quality of learning than that which teachers tended to assume traditionally. Over the last 10 years, teaching for and via problem solving has become entrenched in the national mathematics curriculum statements of many countries, and programs have been launched to induce and support teachers to implement it. Actual implementation of the “reform agenda” in classrooms is, however, still limited. The limited implementation is ascribed to a number of factors, including the failure of assessment practices to accommodate problem solving and higher levels of understanding that may be facilitated by teaching via problem solving, lack of clarity about what teaching for and via problem solving may actually mean in practice, and limited mathematical expertise of teachers. Some leading mathematics educators (for example, Schoenfeld, Stigler and Hiebert believe that the reform agenda specifi es classroom practices that are fundamentally foreign to culturally embedded pedagogical traditions, and hence

  7. Problem-Solving Training: Effects on the Problem-Solving Skills and Self-Efficacy of Nursing Students

    OpenAIRE

    Ancel, Gulsum

    2016-01-01

    Problem Statement: Problem-Solving (PS) skills have been determined to be an internationally useful strategy for better nursing. That is why PS skills underlie all nursing practice, teamwork, and health care management, and are a main topic in undergraduate nursing education. Thus, there is a need to develop effective methods to teach problem-solving skills. The present study, as a first study in Turkey, may provide valuable insight for nurse academicians employed at üniversities. Purpose of ...

  8. A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation

    Directory of Open Access Journals (Sweden)

    Mingzhu Li

    2014-01-01

    Full Text Available The main aim of this work is to consider a meshfree algorithm for solving Burgers’ equation with the quartic B-spline quasi-interpolation. Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the ill-conditioning problem resulting from using the B-spline as a global interpolant. The numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Compared to other numerical methods, the main advantages of our scheme are higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.

  9. Numerical differential protection

    CERN Document Server

    Ziegler, Gerhard

    2012-01-01

    Differential protection is a fast and selective method of protection against short-circuits. It is applied in many variants for electrical machines, trans?formers, busbars, and electric lines.Initially this book covers the theory and fundamentals of analog and numerical differential protection. Current transformers are treated in detail including transient behaviour, impact on protection performance, and practical dimensioning. An extended chapter is dedicated to signal transmission for line protection, in particular, modern digital communication and GPS timing.The emphasis is then pla

  10. Numerical Analysis of Multiscale Computations

    CERN Document Server

    Engquist, Björn; Tsai, Yen-Hsi R

    2012-01-01

    This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.

  11. Acquisition and performance of a problem-solving skill.

    Science.gov (United States)

    Morgan, B. B., Jr.; Alluisi, E. A.

    1971-01-01

    The acquisition of skill in the performance of a three-phase code transformation task (3P-COTRAN) was studied with 20 subjects who solved 27 3P-COTRAN problems during each of 8 successive sessions. The purpose of the study was to determine the changes in the 3P-COTRAN factor structure resulting from practice, the distribution of practice-related gains in performance over the nine measures of the five 3P-COTRAN factors, and the effects of transformation complexities on the 3P-COTRAN performance of subjects. A significant performance gain due to practice was observed, with improvements in speed continuing even when accuracy reached asymptotic levels. Transformation complexity showed no effect on early performances but the 3- and 4-element transformations were solved quicker than the 5-element transformation in the problem-solving Phase III of later skilled performances.

  12. Solving-Problems and Hypermedia Systems

    Directory of Open Access Journals (Sweden)

    Ricardo LÓPEZ FERNÁNDEZ

    2009-06-01

    Full Text Available The solving problems like the transfer constitute two nuclei, related, essential in the cognitive investigation and in the mathematical education. No is in and of itself casual that, from the first moment, in the investigations on the application gives the computer science to the teaching the mathematics, cybernetic models were developed that simulated processes problem solving and transfer cotexts (GPS, 1969 and IDEA (Interactive Decision Envisioning Aid, Pea, BrunerCohen, Webster & Mellen, 1987. The present articulates it analyzes, that can contribute to the development in this respect the new technologies hypermedias, give applications that are good to implement processes of learning the heuristic thought and give the capacity of «transfer». From our perspective and from the experience that we have developed in this field, to carry out a function gives analysis and the theories on the problem solving, it requires that we exercise a previous of interpretation the central aspsects over the theories gives the solving problem and transfer starting from the classic theories on the prosecution of the information. In this sense, so much the theory gives the dual memory as the most recent, J. Anderson (1993 based on the mechanisms activation nodes information they allow to establish an interpretation suggester over the mental mechanism that you/they operate in the heuristic processes. On this analysis, the present articulates it develops a theoritical interpretation over the function gives the supports based on technology hypermedia advancing in the definition of a necessary theoretical body, having in it counts that on the other hand the practical experimentation is permanent concluding in the efficiency and effectiveness gives the support hypermedia like mechanism of comunication in the processes heuristic learning.

  13. NUMERICAL DETERMINATION OF HORIZONTAL SETTLERS PERFORMANCE

    Directory of Open Access Journals (Sweden)

    M. M. Biliaiev

    2015-08-01

    Full Text Available Purpose.Horizontal settlers are one of the most important elements in the technological scheme of water purification. Their use is associated with the possibility to pass a sufficiently large volume of water. The important task at the stage of their designing is evaluating of their effectiveness. Calculation of the efficiency of the settler can be made by mathematical modeling. Empirical, analytical models and techniques that are currently used to solve the problem, do not allow to take into account the shape of the sump and various design features that significantly affects the loyalty to a decision on the choice of the size of the settling tank and its design features. The use of analytical models is limited only to one-dimensional solutions, does not allow accounting for nonuniform velocity field of the flow in the settler. The use of advanced turbulence models for the calculation of the hydrodynamics in the settler complex forms now requires very powerful computers. In addition, the calculation of one variant of the settler may last for dozens of hours. The aim of the paper is to build a numerical model to evaluate the effectiveness of horizontal settling tank modified design. Methodology. Numerical models are based on: 1 equation of potential flow; 2 equation of inviscid fluid vortex flow; 3 equation of viscous fluid dynamics; 4 mass transfer equation. For numerical simulation the finite difference schemes are used. The numerical calculation is carried out on a rectangular grid. For the formation of the computational domain markers are used. Findings.The models allow calculating the clarification process in the settler with different form and different configuration of baffles. Originality. A new approach to investigate the mass transfer process in horizontal settler was proposed. This approach is based on the developed CFD models. Three fluid dynamics models were used for the numerical investigation of flows and waste waters purification

  14. Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

    Science.gov (United States)

    Takahashi, Akihiko

    2016-01-01

    Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

  15. Numerical simulation of single bubble boiling behavior

    Directory of Open Access Journals (Sweden)

    Junjie Liu

    2017-06-01

    Full Text Available The phenomena of a single bubble boiling process are studied with numerical modeling. The mass, momentum, energy and level set equations are solved using COMSOL multi-physics software. The bubble boiling dynamics, the transient pressure field, velocity field and temperature field in time are analyzed, and reasonable results are obtained. The numeral model is validated by the empirical equation of Fritz and could be used for various applications.

  16. Solving a Deconvolution Problem in Photon Spectrometry

    CERN Document Server

    Aleksandrov, D; Hille, P T; Polichtchouk, B; Kharlov, Y; Sukhorukov, M; Wang, D; Shabratova, G; Demanov, V; Wang, Y; Tveter, T; Faltys, M; Mao, Y; Larsen, D T; Zaporozhets, S; Sibiryak, I; Lovhoiden, G; Potcheptsov, T; Kucheryaev, Y; Basmanov, V; Mares, J; Yanovsky, V; Qvigstad, H; Zenin, A; Nikolaev, S; Siemiarczuk, T; Yuan, X; Cai, X; Redlich, K; Pavlinov, A; Roehrich, D; Manko, V; Deloff, A; Ma, K; Maruyama, Y; Dobrowolski, T; Shigaki, K; Nikulin, S; Wan, R; Mizoguchi, K; Petrov, V; Mueller, H; Ippolitov, M; Liu, L; Sadovsky, S; Stolpovsky, P; Kurashvili, P; Nomokonov, P; Xu, C; Torii, H; Il'kaev, R; Zhang, X; Peresunko, D; Soloviev, A; Vodopyanov, A; Sugitate, T; Ullaland, K; Huang, M; Zhou, D; Nystrand, J; Punin, V; Yin, Z; Batyunya, B; Karadzhev, K; Nazarov, G; Fil'chagin, S; Nazarenko, S; Buskenes, J I; Horaguchi, T; Djuvsland, O; Chuman, F; Senko, V; Alme, J; Wilk, G; Fehlker, D; Vinogradov, Y; Budilov, V; Iwasaki, T; Ilkiv, I; Budnikov, D; Vinogradov, A; Kazantsev, A; Bogolyubsky, M; Lindal, S; Polak, K; Skaali, B; Mamonov, A; Kuryakin, A; Wikne, J; Skjerdal, K

    2010-01-01

    We solve numerically a deconvolution problem to extract the undisturbed spectrum from the measured distribution contaminated by the finite resolution of the measuring device. A problem of this kind emerges when one wants to infer the momentum distribution of the neutral pions by detecting the it decay photons using the photon spectrometer of the ALICE LHC experiment at CERN {[}1]. The underlying integral equation connecting the sought for pion spectrum and the measured gamma spectrum has been discretized and subsequently reduced to a system of linear algebraic equations. The latter system, however, is known to be ill-posed and must be regularized to obtain a stable solution. This task has been accomplished here by means of the Tikhonov regularization scheme combined with the L-curve method. The resulting pion spectrum is in an excellent quantitative agreement with the pion spectrum obtained from a Monte Carlo simulation. (C) 2010 Elsevier B.V. All rights reserved.

  17. Modeling and Solving the Train Pathing Problem

    Directory of Open Access Journals (Sweden)

    Chuen-Yih Chen

    2009-04-01

    Full Text Available In a railroad system, train pathing is concerned with the assignment of trains to links and tracks, and train timetabling allocates time slots to trains. In this paper, we present an optimization heuristic to solve the train pathing and timetabling problem. This heuristic allows the dwell time of trains in a station or link to be dependent on the assigned tracks. It also allows the minimum clearance time between the trains to depend on their relative status. The heuristic generates a number of alternative paths for each train service in the initialization phase. Then it uses a neighborhood search approach to find good feasible combinations of these paths. A linear program is developed to evaluate the quality of each combination that is encountered. Numerical examples are provided.

  18. Algorithms for solving common fixed point problems

    CERN Document Server

    Zaslavski, Alexander J

    2018-01-01

    This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems, the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning. Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter ...

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

    International Nuclear Information System (INIS)

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

    2017-01-01

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

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

    Science.gov (United States)

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

    2017-11-01

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

  1. Electromagnetic scattering problems -Numerical issues and new experimental approaches of validation

    Energy Technology Data Exchange (ETDEWEB)

    Geise, Robert; Neubauer, Bjoern; Zimmer, Georg [University of Braunschweig, Institute for Electromagnetic Compatibility, Schleinitzstrasse 23, 38106 Braunschweig (Germany)

    2015-03-10

    Electromagnetic scattering problems, thus the question how radiated energy spreads when impinging on an object, are an essential part of wave propagation. Though the Maxwell’s differential equations as starting point, are actually quite simple,the integral formulation of an object’s boundary conditions, respectively the solution for unknown induced currents can only be solved numerically in most cases.As a timely topic of practical importance the scattering of rotating wind turbines is discussed, the numerical description of which is still based on rigorous approximations with yet unspecified accuracy. In this context the issue of validating numerical solutions is addressed, both with reference simulations but in particular with the experimental approach of scaled measurements. For the latter the idea of an incremental validation is proposed allowing a step by step validation of required new mathematical models in scattering theory.

  2. A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

    KAUST Repository

    Bagci, Hakan

    2015-01-01

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability

  3. A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

    KAUST Repository

    Bagci, Hakan

    2015-01-07

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability

  4. Constrained evolution in numerical relativity

    Science.gov (United States)

    Anderson, Matthew William

    The strongest potential source of gravitational radiation for current and future detectors is the merger of binary black holes. Full numerical simulation of such mergers can provide realistic signal predictions and enhance the probability of detection. Numerical simulation of the Einstein equations, however, is fraught with difficulty. Stability even in static test cases of single black holes has proven elusive. Common to unstable simulations is the growth of constraint violations. This work examines the effect of controlling the growth of constraint violations by solving the constraints periodically during a simulation, an approach called constrained evolution. The effects of constrained evolution are contrasted with the results of unconstrained evolution, evolution where the constraints are not solved during the course of a simulation. Two different formulations of the Einstein equations are examined: the standard ADM formulation and the generalized Frittelli-Reula formulation. In most cases constrained evolution vastly improves the stability of a simulation at minimal computational cost when compared with unconstrained evolution. However, in the more demanding test cases examined, constrained evolution fails to produce simulations with long-term stability in spite of producing improvements in simulation lifetime when compared with unconstrained evolution. Constrained evolution is also examined in conjunction with a wide variety of promising numerical techniques, including mesh refinement and overlapping Cartesian and spherical computational grids. Constrained evolution in boosted black hole spacetimes is investigated using overlapping grids. Constrained evolution proves to be central to the host of innovations required in carrying out such intensive simulations.

  5. Customer-centered problem solving.

    Science.gov (United States)

    Samelson, Q B

    1999-11-01

    If there is no single best way to attract new customers and retain current customers, there is surely an easy way to lose them: fail to solve the problems that arise in nearly every buyer-supplier relationship, or solve them in an unsatisfactory manner. Yet, all too frequently, companies do just that. Either we deny that a problem exists, we exert all our efforts to pin the blame elsewhere, or we "Band-Aid" the problem instead of fixing it, almost guaranteeing that we will face it again and again.

  6. Simon on Problem-Solving

    DEFF Research Database (Denmark)

    Foss, Kirsten; Foss, Nicolai Juul

    as a general approach to problem solving. We apply these Simonian ideas to organizational issues, specifically new organizational forms. Specifically, Simonian ideas allow us to develop a morphology of new organizational forms and to point to some design problems that characterize these forms.Keywords: Herbert...... Simon, problem-solving, new organizational forms. JEL Code: D23, D83......Two of Herbert Simon's best-known papers are "The Architecture of Complexity" and "The Structure of Ill-Structured Problems." We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...

  7. Interactive problem solving using LOGO

    CERN Document Server

    Boecker, Heinz-Dieter; Fischer, Gerhard

    2014-01-01

    This book is unique in that its stress is not on the mastery of a programming language, but on the importance and value of interactive problem solving. The authors focus on several specific interest worlds: mathematics, computer science, artificial intelligence, linguistics, and games; however, their approach can serve as a model that may be applied easily to other fields as well. Those who are interested in symbolic computing will find that Interactive Problem Solving Using LOGO provides a gentle introduction from which one may move on to other, more advanced computational frameworks or more

  8. Inference rule and problem solving

    Energy Technology Data Exchange (ETDEWEB)

    Goto, S

    1982-04-01

    Intelligent information processing signifies an opportunity of having man's intellectual activity executed on the computer, in which inference, in place of ordinary calculation, is used as the basic operational mechanism for such an information processing. Many inference rules are derived from syllogisms in formal logic. The problem of programming this inference function is referred to as a problem solving. Although logically inference and problem-solving are in close relation, the calculation ability of current computers is on a low level for inferring. For clarifying the relation between inference and computers, nonmonotonic logic has been considered. The paper deals with the above topics. 16 references.

  9. Application of Trotter approximation for solving time dependent neutron transport equation

    International Nuclear Information System (INIS)

    Stancic, V.

    1987-01-01

    A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)

  10. Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2014-01-01

    A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST

  11. MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids

    KAUST Repository

    Iliev, Oleg; Kirsch, Ralf; Lakdawala, Zahra; Printsypar, Galina

    2014-01-01

    This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid

  12. Using packaged software for solving two differential equation problems that arise in plasma physics

    International Nuclear Information System (INIS)

    Gaffney, P.W.

    1980-01-01

    Experience in using packaged numerical software for solving two related problems that arise in Plasma physics is described. These problems are (i) the solution of the reduced resistive MHD equations and (ii) the solution of the Grad-Shafranov equation

  13. Numerical simulation of flow-induced vibrations in tube bundles

    International Nuclear Information System (INIS)

    Elisabeth Longatte; Zaky Bendjeddou; Mhamed Souli

    2005-01-01

    Full text of publication follows: In many industrial components mechanical structures like rod cluster control assembly, fuel assembly and heat exchanger tube bundles are submitted to complex flows causing possible vibrations and damage. Fluid forces are usually split into two parts: structure motion independent forces and fluid-elastic forces coupled with tube motion and responsible for possible dynamic instability development leading to possible short term failures through high amplitude vibrations. Most classical fluid force identification methods rely on structure response experimental measurements associated with convenient data processes. Owing to recent improvements in Computational Fluid Dynamics (C.F.D.), numerical fluid force identification is now practicable in the presence of industrial configurations. The present paper is devoted to numerical simulation of flow-induced vibrations of tube bundles submitted to single-phase cross flows by using C.F.D. codes. Direct Numerical Simulation (D.N.S.), Arbitrary Lagrange Euler formulation (A.L.E.) and code coupling process are involved to predict fluid forces responsible for tube bundle vibrations in the presence of fluid structure and fluid-elastic coupling effects. In the presence of strong multi-physics coupling, simulation of flow-induced vibrations requires a fluid structure code coupling process. The methodology consists in solving in the same time thermohydraulics and mechanics problems by using an A.L.E. formulation for the fluid computation. The purpose is to take into account coupling between flow and structure motions in order to be able to capture coupling effects. From a numerical point of view, there are three steps in the computation: the fluid problem is solved on the computational domain; fluid forces acting on the moving tube are estimated; finally they are introduced in the structure solver providing the tube displacement that is used to actualize the fluid computational domain. Specific

  14. Exploring hadronic physics by solving QCD with a teraflops computer

    International Nuclear Information System (INIS)

    Negele, J.

    1993-01-01

    Quantum chromodynamics, the theory believed to govern the nucleons, mesons, and other strongly interacting particles making up most of the known mass of the universe is such a challenging, nonlinear many-body problem that it has never been solved using conventional analytical techniques. This talk will describe how this theory can be solved numerically on a space-time lattice, show what has already been understood about the structure of hadrons and the quark gluon phase transition. and describe an exciting initiative to build a dedicated Teraflops computer capable of performing 10 12 operations per second to make fundamental advances in QCD

  15. Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

    Directory of Open Access Journals (Sweden)

    San-Yang Liu

    2014-01-01

    Full Text Available Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

  16. The Interference of Stereotype Threat with Women's Generation of Mathematical Problem-Solving Strategies.

    Science.gov (United States)

    Quinn, Diane M.; Spencer, Steven J.

    2001-01-01

    Investigated whether stereotype threat would depress college women's math performance. In one test, men outperformed women when solving word problems, though women performed equally when problems were converted into numerical equivalents. In another test, participants solved difficult problems in high or reduced stereotype threat conditions. Women…

  17. Human Problem Solving in 2012

    Science.gov (United States)

    Funke, Joachim

    2013-01-01

    This paper presents a bibliography of 263 references related to human problem solving, arranged by subject matter. The references were taken from PsycInfo and Academic Premier data-base. Journal papers, book chapters, and dissertations are included. The topics include human development, education, neuroscience, and research in applied settings. It…

  18. Solved problems in classical electromagnetism

    CERN Document Server

    Franklin, Jerrold

    2018-01-01

    This original Dover publication is the companion to a new edition of the author's Classical Electromagnetism: Second Edition. The latter volume will feature only basic answers; this book will contain some problems from the reissue as well as many other new ones. All feature complete, worked-out solutions and form a valuable source of problem-solving material for students.

  19. Error Patterns in Problem Solving.

    Science.gov (United States)

    Babbitt, Beatrice C.

    Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…

  20. Quantitative Reasoning in Problem Solving

    Science.gov (United States)

    Ramful, Ajay; Ho, Siew Yin

    2015-01-01

    In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.

  1. Students' Problem Solving and Justification

    Science.gov (United States)

    Glass, Barbara; Maher, Carolyn A.

    2004-01-01

    This paper reports on methods of students' justifications of their solution to a problem in the area of combinatorics. From the analysis of the problem solving of 150 students in a variety of settings from high-school to graduate study, four major forms of reasoning evolved: (1) Justification by Cases, (2) Inductive Argument, (3) Elimination…

  2. Solving Differential Equations in R: Package deSolve

    Directory of Open Access Journals (Sweden)

    Karline Soetaert

    2010-02-01

    Full Text Available In this paper we present the R package deSolve to solve initial value problems (IVP written as ordinary differential equations (ODE, differential algebraic equations (DAE of index 0 or 1 and partial differential equations (PDE, the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR, DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1 to demonstrate the potential of using R for dynamic modeling, (2 to highlight typical uses of the different methods implemented and (3 to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to R’s high-level procedures. deSolve is the successor of package odesolve which will be deprecated in

  3. The Missing Curriculum in Physics Problem-Solving Education

    Science.gov (United States)

    Williams, Mobolaji

    2018-05-01

    Physics is often seen as an excellent introduction to science because it allows students to learn not only the laws governing the world around them, but also, through the problems students solve, a way of thinking which is conducive to solving problems outside of physics and even outside of science. In this article, we contest this latter idea and argue that in physics classes, students do not learn widely applicable problem-solving skills because physics education almost exclusively requires students to solve well-defined problems rather than the less-defined problems which better model problem solving outside of a formal class. Using personal, constructed, and the historical accounts of Schrödinger's development of the wave equation and Feynman's development of path integrals, we argue that what is missing in problem-solving education is practice in identifying gaps in knowledge and in framing these knowledge gaps as questions of the kind answerable using techniques students have learned. We discuss why these elements are typically not taught as part of the problem-solving curriculum and end with suggestions on how to incorporate these missing elements into physics classes.

  4. A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems

    Science.gov (United States)

    Chan, Tony; Szeto, Tedd

    1994-03-01

    We propose a new and more stable variant of the CGS method [27] for solving nonsymmetric linear systems. The method is based on squaring the Composite Step BCG method, introduced recently by Bank and Chan [1,2], which itself is a stabilized variant of BCG in that it skips over steps for which the BCG iterate is not defined and causes one kind of breakdown in BCG. By doing this, we obtain a method (Composite Step CGS or CSCGS) which not only handles the breakdowns described above, but does so with the advantages of CGS, namely, no multiplications by the transpose matrix and a faster convergence rate than BCG. Our strategy for deciding whether to skip a step does not involve any machine dependent parameters and is designed to skip near breakdowns as well as produce smoother iterates. Numerical experiments show that the new method does produce improved performance over CGS on practical problems.

  5. Perfecting Scientists' Collaboration and Problem-Solving Skills in the Virtual Team Environment

    Science.gov (United States)

    Jabro, A.; Jabro, J.

    2012-04-01

    PPerfecting Scientists' Collaboration and Problem-Solving Skills in the Virtual Team Environment Numerous factors have contributed to the proliferation of conducting work in virtual teams at the domestic, national, and global levels: innovations in technology, critical developments in software, co-located research partners and diverse funding sources, dynamic economic and political environments, and a changing workforce. Today's scientists must be prepared to not only perform work in the virtual team environment, but to work effectively and efficiently despite physical and cultural barriers. Research supports that students who have been exposed to virtual team experiences are desirable in the professional and academic arenas. Research supports establishing and maintaining established protocols for communication behavior prior to task discussion provides for successful team outcomes. Research conducted on graduate and undergraduate virtual teams' behaviors led to the development of successful pedagogic practices and assessment strategies.

  6. Study on the groundwater sustainable problem by numerical ...

    Indian Academy of Sciences (India)

    Pengpeng Zhou

    2017-10-07

    Oct 7, 2017 ... system in Zhanjiang, China, this paper presents a numerical modelling study to research groundwater sustainability of ... bility is a feasible method for solving the sus- ...... Singh A 2010 Decision support for on-farm water man-.

  7. Numerical solution of large sparse linear systems

    International Nuclear Information System (INIS)

    Meurant, Gerard; Golub, Gene.

    1982-02-01

    This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

  8. A numerical primer for the chemical engineer

    NARCIS (Netherlands)

    Zondervan, E.

    2015-01-01

    This book provides an introduction to numerical methods for students in chemical engineering. The book starts with a recap on linear algebra. It then presents methods for solving linear and nonlinear equations, with a special focus on Gaussian elimination and Newton’s method. It also discusses

  9. Numerical Limit Analysis of Precast Concrete Structures

    DEFF Research Database (Denmark)

    Herfelt, Morten Andersen; Poulsen, Peter Noe; Hoang, Linh Cao

    2016-01-01

    ; the framework is based on the theory of rigid-plasticity, and the resulting mathematical optimisation problem can be solved efficiently using modern algorithms. This paper gives a brief introduction to convex optimisation and numerical limit analysis. The mathematical formulation of lower bound load...

  10. Feedback options in nonlinear numerical finance

    DEFF Research Database (Denmark)

    Hugger, Jens; Mashayekhi, Sima

    2012-01-01

    on an infinite slab is presented and boundary values on a bounded domain are derived. This bounded, nonlinear, 2 dimensional initial-boundary value problem is solved numerically using a number of standard finite difference schemes and the methods incorporated in the symbolic software Maple™....

  11. Some Numerical Characteristics of Image Texture

    Directory of Open Access Journals (Sweden)

    O. Samarina

    2012-05-01

    Full Text Available Texture classification is one of the basic images processing tasks. In this paper we present some numerical characteristics to the images analysis and processing. It can be used at the solving of images classification problems, their recognition, problems of remote sounding, biomedical images analysis, geological researches.

  12. Numerical CFD Comparison of Lillgrund Employing RANS

    DEFF Research Database (Denmark)

    Simisiroglou, N.; Breton, S.-P.; Crasto, G.

    2014-01-01

    The following article will validate the results obtained using the actuator disc method in the state of the art numerical Computational Fluid Dynamic (CFD) tool WindSim using on-site measurements from the offshore wind farm Lillgrund. WindSim solves the mass, momentum and energy conservation...

  13. On the Hughes model and numerical aspects

    KAUST Repository

    Gomes, Diogo A.; Machado Velho, Roberto

    2017-01-01

    We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori

  14. RECOGNITION AND VERIFICATION OF TOUCHING HANDWRITTEN NUMERALS

    NARCIS (Netherlands)

    Zhou, J.; Kryzak, A.; Suen, C.Y.

    2004-01-01

    In the field of financial document processing, recognition of touching handwritten numerals has been limited by lack of good benchmarking databases and low reliability of algorithms. This paper addresses the efforts toward solving the two problems. Two databases IRIS-Bell\\\\\\'98 and TNIST are

  15. Genetics problem solving and worldview

    Science.gov (United States)

    Dale, Esther

    The research goal was to determine whether worldview relates to traditional and real-world genetics problem solving. Traditionally, scientific literacy emphasized content knowledge alone because it was sufficient to solve traditional problems. The contemporary definition of scientific literacy is, "The knowledge and understanding of scientific concepts and processes required for personal decision-making, participation in civic and cultural affairs and economic productivity" (NRC, 1996). An expanded definition of scientific literacy is needed to solve socioscientific issues (SSI), complex social issues with conceptual, procedural, or technological associations with science. Teaching content knowledge alone assumes that students will find the scientific explanation of a phenomenon to be superior to a non-science explanation. Formal science and everyday ways of thinking about science are two different cultures (Palmer, 1999). Students address this rift with cognitive apartheid, the boxing away of science knowledge from other types of knowledge (Jedege & Aikenhead, 1999). By addressing worldview, cognitive apartheid may decrease and scientific literacy may increase. Introductory biology students at the University of Minnesota during fall semester 2005 completed a written questionnaire-including a genetics content-knowledge test, four genetic dilemmas, the Worldview Assessment Instrument (WAI) and some items about demographics and religiosity. Six students responded to the interview protocol. Based on statistical analysis and interview data, this study concluded the following: (1) Worldview, in the form of metaphysics, relates to solving traditional genetic dilemmas. (2) Worldview, in the form of agency, relates to solving traditional genetics problems. (3) Thus, worldview must be addressed in curriculum, instruction, and assessment.

  16. Application of numerical methods, derivatives theory and Monte Carlo simulation in evaluating BM&F BOVESPA's POP (Protected and Participative Investment

    Directory of Open Access Journals (Sweden)

    Giuliano Carrozza Uzêda Iorio de Souza

    2011-08-01

    Full Text Available This article presents a practical case in which two of the most efficient numerical procedures developed for derivative analysis are applied to evaluate the POP (Investment Protection with Participation, a structured operation created by São Paulo Stock Exchange - BM&FBOVESPA. The first procedure solves the differential equation through the use of implicit finite differences method. Due to its characteristics, the approach makes it possible to run sensitivity analysis as well as price estimation. In the second, the problem is solved by Monte Carlo simulation, which facilitates the identification of the probability related to the exercise of the embedded options.

  17. PEMBELAJARAN KONTEKSTUAL OPEN ENDED PROBLEM SOLVING DENGAN KOMIK MATEMATIKA UNTUK MENINGKATKAN KETERAMPILAN PEMECAHAN MASALAH

    Directory of Open Access Journals (Sweden)

    Lenny Kurniati

    2017-01-01

    ABSTRACT The aim of this research to develop a mathematics learning instrument using contextual open ended problem solving with mathematic comic to increase the problem solving skill which valid, practical and effective. The type of research used in this study is development research using modification of Plomp model. Learning instrumen that have been develop are: syllabus, Lesson plan, worksheet, mathematics comic, and problem solving ability test. The results showed: (1 device developed valid; (2 practical learning is characterized by the positive response of students and good teachers ability, (3 Effectiveness characterized by (a problem solving ability score of the experimental class higher than minimum completeness criterion, (b learn interest and problem solving skill, both affected the problem solving ability positively,  (c problem solving ability of the experimental class score is higher than the control class, (d problem solving skill of the experimental class is increasing by 31%, the problem solving ability of the experimental class higher than the control class.. Because of the learning instrument develope are valid, practice and effective, it is shows that the research has ben reach out. Keywords: contextual teaching and learning, open ended problem solving, mathematics comic, problem solving.

  18. Review on solving the forward problem in EEG source analysis

    Directory of Open Access Journals (Sweden)

    Vergult Anneleen

    2007-11-01

    Full Text Available Abstract Background The aim of electroencephalogram (EEG source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes. Methods While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field. Results It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter. In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM, the finite element method (FEM and the finite difference method (FDM. In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative

  19. The Effects of Physical Manipulatives on Children's Numerical Strategies

    Science.gov (United States)

    Manches, Andrew; O'Malley, Claire

    2016-01-01

    This article focuses on how the representational properties of manipulatives affect the strategies children employ in problem solving. Two studies examined the effect of physical materials on 4-7-year-old children's problem solving strategies in a numerical (i.e., additive composition) task. The first study showed how children not only identified…

  20. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods

    International Nuclear Information System (INIS)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-01-01

    In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs

  1. Numerical Limit Analysis of Precast Concrete Structures

    DEFF Research Database (Denmark)

    Herfelt, Morten Andersen

    Precast concrete elements are widely used in the construction industry as they provide a number of advantages over the conventional in-situ cast concrete structures. Joints cast on the construction site are needed to connect the precast elements, which poses several challenges. Moreover, the curr...... problems are solved efficiently using state-of-the-art solvers. It is concluded that the framework and developed joint models have the potential to enable efficient design of precast concrete structures in the near future......., the current practice is to design the joints as the weakest part of the structure, which makes analysis of the ultimate limit state behaviour by general purpose software difficult and inaccurate. Manual methods of analysis based on limit analysis have been used for several decades. The methods provide...... of the ultimate limit state behaviour. This thesis introduces a framework based on finite element limit analysis, a numerical method based on the same extremum principles as the manual limit analysis. The framework allows for efficient analysis and design in a rigorous manner by use of mathematical optimisation...

  2. NUMERICAL SIMULATION OF AIR POLLUTION IN CASE OF UNPLANNED AMMONIA RELEASE

    Directory of Open Access Journals (Sweden)

    L. V. Amelina

    2017-06-01

    Full Text Available Purpose. Development fast calculating model which takes into account the meteorological parameters and buildings which are situated near the source of toxic chemical emission. Methodology. The developed model is based on the equation for potential flow and equation of pollutant dispersion. Equation of potential flow is used to compute wind pattern among buildings. To solve equation for potential flow Samarskii implicit difference scheme is used. The implicit change – triangle difference scheme is used to solve equation of mass transfer. Numerical integration is carried out using the rectangular difference grid. Method of porosity technique («markers method» is used to create the form of comprehensive computational region. Emission of ammonia is modeled using Delta function for point source. Findings. Developed 2D numerical model belongs to the class of «diagnostic models». This model takes into account the main physical factors affecting the process of dispersion of pollutants in the atmosphere. The model takes into account the influence of buildings on pollutant dispersion. On the basis of the developed numerical models a computational experiment was carried out to estimate the level of toxic chemical pollution in the case of unplanned ammonia release at ammonia pump station. Originality. Developed numerical model allows to calculate the 2D wind pattern among buildings and pollutant dispersion in the case unplanned ammonia release. Model allows to perform fast calculations of the atmosphere pollution. Practical value. The model can be used when developing the PLAS (Emergency Response Plan.

  3. A first course in ordinary differential equations analytical and numerical methods

    CERN Document Server

    Hermann, Martin

    2014-01-01

    This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed t...

  4. Numerical Modelling of Electrical Discharges

    International Nuclear Information System (INIS)

    Durán-Olivencia, F J; Pontiga, F; Castellanos, A

    2014-01-01

    The problem of the propagation of an electrical discharge between a spherical electrode and a plane has been solved by means of finite element methods (FEM) using a fluid approximation and assuming weak ionization and local equilibrium with the electric field. The numerical simulation of this type of problems presents the usual difficulties of convection-diffusion-reaction problems, in addition to those associated with the nonlinearities of the charged species velocities, the formation of steep gradients of the electric field and particle densities, and the coexistence of very different temporal scales. The effect of using different temporal discretizations for the numerical integration of the corresponding system of partial differential equations will be here investigated. In particular, the so-called θ-methods will be used, which allows to implement implicit, semi-explicit and fully explicit schemes in a simple way

  5. Numerical simulation of fire vortex

    Science.gov (United States)

    Barannikova, D. D.; Borzykh, V. E.; Obukhov, A. G.

    2018-05-01

    The article considers the numerical simulation of the swirling flow of air around the smoothly heated vertical cylindrical domain in the conditions of gravity and Coriolis forces action. The solutions of the complete system of Navie-Stocks equations are numerically solved at constant viscosity and heat conductivity factors. Along with the proposed initial and boundary conditions, these solutions describe the complex non-stationary 3D flows of viscous compressible heat conducting gas. For various instants of time of the initial flow formation stage using the explicit finite-difference scheme the calculations of all gas dynamics parameters, that is density, temperature, pressure and three velocity components of gas particles, have been run. The current instant lines corresponding to the trajectories of the particles movement in the emerging flow have been constructed. A negative direction of the air flow swirling occurred in the vertical cylindrical domain heating has been defined.

  6. Numerical and Evolutionary Optimization Workshop

    CERN Document Server

    Trujillo, Leonardo; Legrand, Pierrick; Maldonado, Yazmin

    2017-01-01

    This volume comprises a selection of works presented at the Numerical and Evolutionary Optimization (NEO) workshop held in September 2015 in Tijuana, Mexico. The development of powerful search and optimization techniques is of great importance in today’s world that requires researchers and practitioners to tackle a growing number of challenging real-world problems. In particular, there are two well-established and widely known fields that are commonly applied in this area: (i) traditional numerical optimization techniques and (ii) comparatively recent bio-inspired heuristics. Both paradigms have their unique strengths and weaknesses, allowing them to solve some challenging problems while still failing in others. The goal of the NEO workshop series is to bring together people from these and related fields to discuss, compare and merge their complimentary perspectives in order to develop fast and reliable hybrid methods that maximize the strengths and minimize the weaknesses of the underlying paradigms. Throu...

  7. Efficient numerical method for district heating system hydraulics

    International Nuclear Information System (INIS)

    Stevanovic, Vladimir D.; Prica, Sanja; Maslovaric, Blazenka; Zivkovic, Branislav; Nikodijevic, Srdjan

    2007-01-01

    An efficient method for numerical simulation and analyses of the steady state hydraulics of complex pipeline networks is presented. It is based on the loop model of the network and the method of square roots for solving the system of linear equations. The procedure is presented in the comprehensive mathematical form that could be straightforwardly programmed into a computer code. An application of the method to energy efficiency analyses of a real complex district heating system is demonstrated. The obtained results show a potential for electricity savings in pumps operation. It is shown that the method is considerably more effective than the standard Hardy Cross method still widely used in engineering practice. Because of the ease of implementation and high efficiency, the method presented in this paper is recommended for hydraulic steady state calculations of complex networks

  8. Numerical Prediction of Hydromechanical Behaviour of Controllable Pitch Propeller

    Directory of Open Access Journals (Sweden)

    Saman Tarbiat

    2014-01-01

    Full Text Available The research described in this paper was carried out to predict hydrodynamic and frictional forces of controllable pitch propeller (CPP that bring about fretting problems in a blade bearing. The governing equations are Reynolds-averaged Navier-Stokes (RANS and are solved by OpenFOAM solver for hydrodynamic forces behind the ship’s wake. Frictional forces are calculated by practical mechanical formulae. Different advance velocities with constant rotational speed for blades are used to achieve hydrodynamic coefficients in open water and the wake behind the propeller. Results are compared at four different pitches. Detailed numerical results of 3D modelling of the propeller, hydrodynamic characteristics, and probability of the fretting motion in the propeller are presented. Results show that the probability of the fretting movement is related to the pitch.

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

    Science.gov (United States)

    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.

  10. SHA-1, SAT-solving, and CNF

    CSIR Research Space (South Africa)

    Motara, YM

    2017-09-01

    Full Text Available the intersection between the SHA-1 preimage problem, the encoding of that problem for SAT-solving, and SAT-solving. The results demonstrate that SAT-solving is not yet a viable approach to take to solve the preimage problem, and also indicate that some...

  11. Assessing Algebraic Solving Ability: A Theoretical Framework

    Science.gov (United States)

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  12. Guiding brine shrimp through mazes by solving reaction diffusion equations

    Science.gov (United States)

    Singal, Krishma; Fenton, Flavio

    Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.

  13. (CBTP) on knowledge, problem-solving and learning approach

    African Journals Online (AJOL)

    In the first instance attention is paid to the effect of a computer-based teaching programme (CBTP) on the knowledge, problem-solving skills and learning approach of student ... In the practice group (oncology wards) no statistically significant change in the learning approach of respondents was found after using the CBTP.

  14. An ontological framework for model-based problem-solving

    NARCIS (Netherlands)

    Scholten, H.; Beulens, A.J.M.

    2012-01-01

    Multidisciplinary projects to solve real world problems of increasing complexity are more and more plagued by obstacles such as miscommunication between modellers with different disciplinary backgrounds and bad modelling practices. To tackle these difficulties, a body of knowledge on problems, on

  15. Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

    Science.gov (United States)

    Kakhktsyan, V. M.; Khachatryan, A. Kh.

    2013-07-01

    A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

  16. Numerical solution of integral equations, describing mass spectrum of vector mesons

    International Nuclear Information System (INIS)

    Zhidkov, E.P.; Nikonov, E.G.; Sidorov, A.V.; Skachkov, N.B.; Khoromskij, B.N.

    1988-01-01

    The description of the numerical algorithm for solving quasipotential integral equation in impulse space is presented. The results of numerical computations of the vector meson mass spectrum and the leptonic decay width are given in comparison with the experimental data

  17. Confluent-Functional solving systems

    Directory of Open Access Journals (Sweden)

    V.N. Koval

    2001-08-01

    Full Text Available The paper proposes a statistical knowledge-acquision approach. The solving systems are considered, which are able to find unknown structural dependences between situational and transforming variables on the basis of statistically analyzed input information. Situational variables describe features, states and relations between environment objects. Transforming variables describe transforming influences, exerted by a goal-oriented system onto an environment. Unknown environment rules are simulated by a structural equations system, associating situational and transforming variables.

  18. A rational function based scheme for solving advection equation

    International Nuclear Information System (INIS)

    Xiao, Feng; Yabe, Takashi.

    1995-07-01

    A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in surpressinging overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily swicthed as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme. (author)

  19. Gabor Wave Packet Method to Solve Plasma Wave Equations

    International Nuclear Information System (INIS)

    Pletzer, A.; Phillips, C.K.; Smithe, D.N.

    2003-01-01

    A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach

  20. NUMERICAL SIMULATION OF TOXIC CHEMICAL DISPERSION AFTER ACCIDENT AT RAILWAY

    Directory of Open Access Journals (Sweden)

    M. M. Biliaiev

    2016-04-01

    Full Text Available Purpose. This research focuses on the development of an applied numerical model to calculate the dynamics of atmospheric pollution in the emission of dangerous chemical substances in the event of transportation by railway. Methodology. For the numerical simulation of transport process of the dangerous chemical substance in the atmosphere the equation of convection-diffusion pollutant transport is used. This equation takes into account the effect of wind, atmospheric diffusion, the power of emission source, as well as the movement of the source of emission (depressurized tank on the process of pollutant dispersion. When carrying out computing experiment one also takes into account the profile of the speed of the wind flow. For the numerical integration of pollutant transport in the atmosphere implicit finite-difference splitting scheme is used. The numerical calculation is divided into four steps of splitting and at each step of splitting the unknown value of the concentration of hazardous substance is determined by the explicit running account scheme. On the basis of the numerical model it was created the code using the algorithmic language FORTRAN. One conducted the computational experiments to assess the level of air pollution near the railway station «Illarionovo» in the event of a possible accident during transportation of ammonia. Findings. The proposed model allows you to quickly calculate the air pollution after the emission of chemically hazardous substance, taking into account the motion of the emission source. The model makes it possible to determine the size of the land surface pollution zones and the amount of pollutants deposited on a specific area. Using the developed numerical model it was estimated the environmental damage near the railway station «Illarionovo». Originality. One can use the numerical model to calculate the size and intensity of the chemical contamination zones after accidents on transport. Practical value

  1. Numerical methods and modelling for engineering

    CERN Document Server

    Khoury, Richard

    2016-01-01

    This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems. Uses a “building-block” approach, starting with simpler mathemati...

  2. Solving the Stokes problem on a massively parallel computer

    DEFF Research Database (Denmark)

    Axelsson, Owe; Barker, Vincent A.; Neytcheva, Maya

    2001-01-01

    boundary value problem for each velocity component, are solved by the conjugate gradient method with a preconditioning based on the algebraic multi‐level iteration (AMLI) technique. The velocity is found from the computed pressure. The method is optimal in the sense that the computational work...... is proportional to the number of unknowns. Further, it is designed to exploit a massively parallel computer with distributed memory architecture. Numerical experiments on a Cray T3E computer illustrate the parallel performance of the method....

  3. Comments on new iterative methods for solving linear systems

    Directory of Open Access Journals (Sweden)

    Wang Ke

    2017-06-01

    Full Text Available Some new iterative methods were presented by Du, Zheng and Wang for solving linear systems in [3], where it is shown that the new methods, comparing to the classical Jacobi or Gauss-Seidel method, can be applied to more systems and have faster convergence. This note shows that their methods are suitable for more matrices than positive matrices which the authors suggested through further analysis and numerical examples.

  4. Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    S. Narayanamoorthy

    2015-01-01

    Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

  5. Solving fully fuzzy transportation problem using pentagonal fuzzy numbers

    Science.gov (United States)

    Maheswari, P. Uma; Ganesan, K.

    2018-04-01

    In this paper, we propose a simple approach for the solution of fuzzy transportation problem under fuzzy environment in which the transportation costs, supplies at sources and demands at destinations are represented by pentagonal fuzzy numbers. The fuzzy transportation problem is solved without converting to its equivalent crisp form using a robust ranking technique and a new fuzzy arithmetic on pentagonal fuzzy numbers. To illustrate the proposed approach a numerical example is provided.

  6. CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

    Directory of Open Access Journals (Sweden)

    S.H. Nasseri

    2011-07-01

    Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.

  7. CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

    Directory of Open Access Journals (Sweden)

    S.H. Nasseri

    2009-10-01

    Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.

  8. On Solving the Lorenz System by Differential Transformation Method

    International Nuclear Information System (INIS)

    Al-Sawalha, M. Mossa; Noorani, M. S. M.

    2008-01-01

    The differential transformation method (DTM) is employed to solve a nonlinear differential equation, namely the Lorenz system. Numerical results are compared to those obtained by the Runge–Kutta method to illustrate the preciseness and effectiveness of the proposed method. In particular, we examine the accuracy of the (DTM) as the Lorenz system changes from a non-chaotic system to a chaotic one. It is shown that the (DTM) is robust, accurate and easy to apply

  9. A numerical method for transient gas-liquid two-phase flow using a general curvilinear coordinate system. 1. Governing equations and numerical method

    International Nuclear Information System (INIS)

    Tomiyama, Akio; Matsuoka, Toshiyuki.

    1995-01-01

    A simple numerical method for solving a transient incompressible two-fluid model was proposed in the present study. A general curvilinear coordinate system was adopted in this method for predicting transient flows in practical engineering devices. The simplicity of the present method is due to the fact that the field equations and constitutive equations were expressed in a tensor form in the general curvilinear coordinate system. When a conventional rectangular mesh is adopted in a calculation, the method reduces to a numerical method for a Cartesian coordinate system. As an example, the present method was applied to transient air-water bubbly flow in a vertical U-tube. It was confirmed that the effects of centrifugal and gravitational forces on the phase distribution in the U-tube were reasonably predicted. (author)

  10. Problem-Solving Training: Effects on the Problem-Solving Skills and Self-Efficacy of Nursing Students

    Science.gov (United States)

    Ancel, Gulsum

    2016-01-01

    Problem Statement: Problem-Solving (PS) skills have been determined to be an internationally useful strategy for better nursing. That is why PS skills underlie all nursing practice, teamwork, and health care management, and are a main topic in undergraduate nursing education. Thus, there is a need to develop effective methods to teach…

  11. Exploiting Quantum Resonance to Solve Combinatorial Problems

    Science.gov (United States)

    Zak, Michail; Fijany, Amir

    2006-01-01

    Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

  12. Improve Problem Solving Skills through Adapting Programming Tools

    Science.gov (United States)

    Shaykhian, Linda H.; Shaykhian, Gholam Ali

    2007-01-01

    There are numerous ways for engineers and students to become better problem-solvers. The use of command line and visual programming tools can help to model a problem and formulate a solution through visualization. The analysis of problem attributes and constraints provide insight into the scope and complexity of the problem. The visualization aspect of the problem-solving approach tends to make students and engineers more systematic in their thought process and help them catch errors before proceeding too far in the wrong direction. The problem-solver identifies and defines important terms, variables, rules, and procedures required for solving a problem. Every step required to construct the problem solution can be defined in program commands that produce intermediate output. This paper advocates improved problem solving skills through using a programming tool. MatLab created by MathWorks, is an interactive numerical computing environment and programming language. It is a matrix-based system that easily lends itself to matrix manipulation, and plotting of functions and data. MatLab can be used as an interactive command line or a sequence of commands that can be saved in a file as a script or named functions. Prior programming experience is not required to use MatLab commands. The GNU Octave, part of the GNU project, a free computer program for performing numerical computations, is comparable to MatLab. MatLab visual and command programming are presented here.

  13. Asymptotic behavior of a diffusive scheme solving the inviscid one-dimensional pressureless gases system

    OpenAIRE

    Boudin , Laurent; Mathiaud , Julien

    2012-01-01

    In this work, we discuss some numerical properties of the viscous numerical scheme introduced in [Boudin, Mathiaud, NMPDE 2012] to solve the one-dimensional pressureless gases system, and study in particular, from a computational viewpoint, its asymptotic behavior when the viscosity parameter used in the scheme becomes smaller.

  14. A Problem Solving Intervention for hospice caregivers: a pilot study.

    Science.gov (United States)

    Demiris, George; Oliver, Debra Parker; Washington, Karla; Fruehling, Lynne Thomas; Haggarty-Robbins, Donna; Doorenbos, Ardith; Wechkin, Hope; Berry, Donna

    2010-08-01

    The Problem Solving Intervention (PSI) is a structured, cognitive-behavioral intervention that provides people with problem-solving coping skills to help them face major negative life events and daily challenges. PSI has been applied to numerous settings but remains largely unexplored in the hospice setting. The aim of this pilot study was to demonstrate the feasibility of PSI targeting informal caregivers of hospice patients. We enrolled hospice caregivers who were receiving outpatient services from two hospice agencies. The intervention included three visits by a research team member. The agenda for each visit was informed by the problem-solving theoretical framework and was customized based on the most pressing problems identified by the caregivers. We enrolled 29 caregivers. Patient's pain was the most frequently identified problem. On average, caregivers reported a higher quality of life and lower level of anxiety postintervention than at baseline. An examination of the caregiver reaction assessment showed an increase of positive esteem average and a decrease of the average value of lack of family support, impact on finances, impact on schedules, and on health. After completing the intervention, caregivers reported lower levels of anxiety, improved problem solving skills, and a reduced negative impact of caregiving. Furthermore, caregivers reported high levels of satisfaction with the intervention, perceiving it as a platform to articulate their challenges and develop a plan to address them. Findings demonstrate the value of problem solving as a psycho-educational intervention in the hospice setting and call for further research in this area.

  15. A convex optimization approach for solving large scale linear systems

    Directory of Open Access Journals (Sweden)

    Debora Cores

    2017-01-01

    Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.

  16. Matlab programming for numerical analysis

    CERN Document Server

    Lopez, Cesar

    2014-01-01

    MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. Programming MATLAB for Numerical Analysis introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. You will first become

  17. Problem solving strategies integrated into nursing process to promote clinical problem solving abilities of RN-BSN students.

    Science.gov (United States)

    Wang, Jing-Jy; Lo, Chi-Hui Kao; Ku, Ya-Lie

    2004-11-01

    A set of problem solving strategies integrated into nursing process in nursing core courses (PSNP) was developed for students enrolled in a post-RN baccalaureate nursing program (RN-BSN) in a university in Taiwan. The purpose of this study, therefore, was to evaluate the effectiveness of PSNP on students' clinical problem solving abilities. The one-group post-test design with repeated measures was used. In total 114 nursing students with 47 full-time students and 67 part-time students participated in this study. The nursing core courses were undertaken separately in three semesters. After each semester's learning, students would start their clinical practice, and were asked to submit three written nursing process recordings during each clinic. Assignments from the three practices were named post-test I, II, and III sequentially, and provided the data for this study. The overall score of problem solving indicated that score on the post-test III was significantly better than that on post-test I and II, meaning both full-time and part-time students' clinical problem solving abilities improved at the last semester. In conclusion, problem-solving strategies integrated into nursing process designed for future RN-BSN students are recommendable.

  18. Problem solving through recreational mathematics

    CERN Document Server

    Averbach, Bonnie

    1999-01-01

    Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics - problems, puzzles and games - to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire ga

  19. Problem solving and inference mechanisms

    Energy Technology Data Exchange (ETDEWEB)

    Furukawa, K; Nakajima, R; Yonezawa, A; Goto, S; Aoyama, A

    1982-01-01

    The heart of the fifth generation computer will be powerful mechanisms for problem solving and inference. A deduction-oriented language is to be designed, which will form the core of the whole computing system. The language is based on predicate logic with the extended features of structuring facilities, meta structures and relational data base interfaces. Parallel computation mechanisms and specialized hardware architectures are being investigated to make possible efficient realization of the language features. The project includes research into an intelligent programming system, a knowledge representation language and system, and a meta inference system to be built on the core. 30 references.

  20. Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

    Science.gov (United States)

    Agarwal, P.; El-Sayed, A. A.

    2018-06-01

    In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

  1. Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria

    International Nuclear Information System (INIS)

    Johnson, J.L.; Dalhed, H.E.; Greene, J.M.

    1978-07-01

    Numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given. Iterative schemes are used to solve the elliptic nonlinear partial differential equation for the poloidal flux function psi. The principal emphasis is on solving the free boundary (plasma-vacuum interface) equilibrium problem where external current-carrying toroidal coils support the plasma column, but fixed boundary (e.g., conducting shell) cases are also included. The toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi. Examples of the application of the codes to tokamak design at PPPL are given

  2. Numerical methods for differential equations and applications

    International Nuclear Information System (INIS)

    Ixaru, L.G.

    1984-01-01

    This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)

  3. Analysis of numerical solutions for Bateman equations

    International Nuclear Information System (INIS)

    Loch, Guilherme G.; Bevilacqua, Joyce S.

    2013-01-01

    The implementation of stable and efficient numerical methods for solving problems involving nuclear transmutation and radioactive decay chains is the main scope of this work. The physical processes associated with irradiations of samples in particle accelerators, or the burning spent nuclear fuel in reactors, or simply the natural decay chains, can be represented by a set of first order ordinary differential equations with constant coefficients, for instance, the decay radioactive constants of each nuclide in the chain. Bateman proposed an analytical solution for a particular case of a linear chain with n nuclides decaying in series and with different decay constants. For more complex and realistic applications, the construction of analytical solutions is not viable and the introduction of numerical techniques is imperative. However, depending on the magnitudes of the decay radioactive constants, the matrix of coefficients could be almost singular, generating unstable and non convergent numerical solutions. In this work, different numerical strategies for solving systems of differential equations were implemented, the Runge-Kutta 4-4, Adams Predictor-Corrector (PC2) and the Rosenbrock algorithm, this last one more specific for stiff equations. Consistency, convergence and stability of the numerical solutions are studied and the performance of the methods is analyzed for the case of the natural decay chain of Uranium-235 comparing numerical with analytical solutions. (author)

  4. Developmental and Individual Differences in Pure Numerical Estimation

    Science.gov (United States)

    Booth, Julie L.; Siegler, Robert S.

    2006-01-01

    The authors examined developmental and individual differences in pure numerical estimation, the type of estimation that depends solely on knowledge of numbers. Children between kindergarten and 4th grade were asked to solve 4 types of numerical estimation problems: computational, numerosity, measurement, and number line. In Experiment 1,…

  5. Numerical methods for incompressible viscous flows with engineering applications

    Science.gov (United States)

    Rose, M. E.; Ash, R. L.

    1988-01-01

    A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

  6. 2-dimensional numerical modeling of active magnetic regeneration

    DEFF Research Database (Denmark)

    Nielsen, Kaspar Kirstein; Pryds, Nini; Smith, Anders

    2009-01-01

    Various aspects of numerical modeling of Active Magnetic Regeneration (AMR) are presented. Using a 2-dimensional numerical model for solving the unsteady heat transfer equations for the AMR system, a range of physical effects on both idealized and non-idealized AMR are investigated. The modeled...

  7. NUMERICAL PREDICTION MODELS FOR AIR POLLUTION BY MOTOR VEHICLE EMISSIONS

    Directory of Open Access Journals (Sweden)

    M. M. Biliaiev

    2016-12-01

    Full Text Available Purpose. Scientific work involves: 1 development of 3D numerical models that allow calculating the process of air pollution by motor vehicles emissions; 2 creation of models which would allow predicting the air pollution level in urban areas. Methodology. To solve the problem upon assessing the level of air pollution by motor vehicles emissions fundamental equations of aerodynamics and mass transfer are used. For the solution of differential equations of aerodynamics and mass transfer finite-difference methods are used. For the numerical integration of the equation for the velocity potential the method of conditional approximations is applied. The equation for the velocity potential written in differential form, splits into two equations, where at each step of splitting an unknown value of the velocity potential is determined by an explicit scheme of running computation, while the difference scheme is implicit one. For the numerical integration of the emissions dispersion equation in the atmosphere applies the implicit alternating-triangular difference scheme of splitting. Emissions from the road are modeled by a series of point sources of given intensity. Developed numerical models form is the basis of the created software package. Findings. 3D numerical models were developed; they belong to the class of «diagnostic models». These models take into account main physical factors that influence the process of dispersion of harmful substances in the atmosphere when emissions from vehicles in the city occur. Based on the constructed numerical models the computational experiment was conducted to assess the level of air pollution in the street. Originality. Authors have developed numerical models that allow to calculate the 3D aerodynamics of the wind flow in urban areas and the process of mass transfer emissions from the highway. Calculations to determine the area of contamination, which is formed near the buildings, located along the highway were

  8. Probabilistic numerics and uncertainty in computations.

    Science.gov (United States)

    Hennig, Philipp; Osborne, Michael A; Girolami, Mark

    2015-07-08

    We deliver a call to arms for probabilistic numerical methods : algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

  9. Numerical Optimization in Microfluidics

    DEFF Research Database (Denmark)

    Jensen, Kristian Ejlebjærg

    2017-01-01

    Numerical modelling can illuminate the working mechanism and limitations of microfluidic devices. Such insights are useful in their own right, but one can take advantage of numerical modelling in a systematic way using numerical optimization. In this chapter we will discuss when and how numerical...... optimization is best used....

  10. Methods of numerical relativity

    International Nuclear Information System (INIS)

    Piran, T.

    1983-01-01

    Numerical Relativity is an alternative to analytical methods for obtaining solutions for Einstein equations. Numerical methods are particularly useful for studying generation of gravitational radiation by potential strong sources. The author reviews the analytical background, the numerical analysis aspects and techniques and some of the difficulties involved in numerical relativity. (Auth.)

  11. An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

    Science.gov (United States)

    Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

    2016-02-01

    Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

  12. Theory and applications of numerical analysis

    CERN Document Server

    Phillips, G M

    1996-01-01

    This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.* a unique blend of theory and applications* two brand new chapters on eigenvalues and splines* inclusion of formal algorithms* numerous fully worked examples* a large number of problems, many with solutions

  13. An introduction to numerical methods and analysis

    CERN Document Server

    Epperson, James F

    2013-01-01

    Praise for the First Edition "". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.""-Zentralblatt MATH "". . . carefully structured with many detailed worked examples.""-The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to

  14. Parallelization of elliptic solver for solving 1D Boussinesq model

    Science.gov (United States)

    Tarwidi, D.; Adytia, D.

    2018-03-01

    In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.

  15. Assessing student written problem solutions: A problem-solving rubric with application to introductory physics

    OpenAIRE

    Jennifer L. Docktor; Jay Dornfeld; Evan Frodermann; Kenneth Heller; Leonardo Hsu; Koblar Alan Jackson; Andrew Mason; Qing X. Ryan; Jie Yang

    2016-01-01

    Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic classroom work. It is also useful if such tools can be employed by instructors to guide their pedagogy. We describe the design, development, and testing of...

  16. Numerical solution of distributed order fractional differential equations

    Science.gov (United States)

    Katsikadelis, John T.

    2014-02-01

    In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

  17. Solving Large Scale Crew Scheduling Problems in Practice

    NARCIS (Netherlands)

    E.J.W. Abbink (Erwin); L. Albino; T.A.B. Dollevoet (Twan); D. Huisman (Dennis); J. Roussado; R.L. Saldanha

    2010-01-01

    textabstractThis paper deals with large-scale crew scheduling problems arising at the Dutch railway operator, Netherlands Railways (NS). NS operates about 30,000 trains a week. All these trains need a driver and a certain number of guards. Some labor rules restrict the duties of a certain crew base

  18. Solving computationally expensive engineering problems

    CERN Document Server

    Leifsson, Leifur; Yang, Xin-She

    2014-01-01

    Computational complexity is a serious bottleneck for the design process in virtually any engineering area. While migration from prototyping and experimental-based design validation to verification using computer simulation models is inevitable and has a number of advantages, high computational costs of accurate, high-fidelity simulations can be a major issue that slows down the development of computer-aided design methodologies, particularly those exploiting automated design improvement procedures, e.g., numerical optimization. The continuous increase of available computational resources does not always translate into shortening of the design cycle because of the growing demand for higher accuracy and necessity to simulate larger and more complex systems. Accurate simulation of a single design of a given system may be as long as several hours, days or even weeks, which often makes design automation using conventional methods impractical or even prohibitive. Additional problems include numerical noise often pr...

  19. Solving rational expectations models using Excel

    DEFF Research Database (Denmark)

    Strulik, Holger

    2004-01-01

    Problems of discrete time optimal control can be solved using backward iteration and Microsoft Excel. The author explains the method in general and shows how the basic models of neoclassical growth and real business cycles are solved......Problems of discrete time optimal control can be solved using backward iteration and Microsoft Excel. The author explains the method in general and shows how the basic models of neoclassical growth and real business cycles are solved...

  20. Numerical solutions of the N-body problem

    International Nuclear Information System (INIS)

    Marciniak, A.

    1985-01-01

    Devoted to the study of numerical methods for solving the general N-body problem and related problems, this volume starts with an overview of the conventional numerical methods for solving the initial value problem. The major part of the book contains original work and features a presentation of special numerical methods conserving the constants of motion in the general N-body problem and methods conserving the Jacobi constant in the problem of motion of N bodies in a rotating frame, as well as an analysis of the applications of both (conventional and special) kinds of methods for solving these problems. For all the methods considered, the author presents algorithms which are easily programmable in any computer language. Moreover, the author compares various methods and presents adequate numerical results. The appendix contains PL/I procedures for all the special methods conserving the constants of motion. 91 refs.; 35 figs.; 41 tabs

  1. Spectral finite element methods for solving fractional differential equations with applications in anomalous transport

    Energy Technology Data Exchange (ETDEWEB)

    Carella, Alfredo Raul

    2012-09-15

    Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)

  2. LEGO Robotics: An Authentic Problem Solving Tool?

    Science.gov (United States)

    Castledine, Alanah-Rei; Chalmers, Chris

    2011-01-01

    With the current curriculum focus on correlating classroom problem solving lessons to real-world contexts, are LEGO robotics an effective problem solving tool? This present study was designed to investigate this question and to ascertain what problem solving strategies primary students engaged with when working with LEGO robotics and whether the…

  3. Perspectives on Problem Solving and Instruction

    Science.gov (United States)

    van Merrienboer, Jeroen J. G.

    2013-01-01

    Most educators claim that problem solving is important, but they take very different perspective on it and there is little agreement on how it should be taught. This article aims to sort out the different perspectives and discusses problem solving as a goal, a method, and a skill. As a goal, problem solving should not be limited to well-structured…

  4. Introduction to numerical methods for time dependent differential equations

    CERN Document Server

    Kreiss, Heinz-Otto

    2014-01-01

    Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t

  5. Numerical simulation of overflow at vertical weirs using a hybrid level set/VOF method

    Science.gov (United States)

    Lv, Xin; Zou, Qingping; Reeve, Dominic

    2011-10-01

    This paper presents the applications of a newly developed free surface flow model to the practical, while challenging overflow problems for weirs. Since the model takes advantage of the strengths of both the level set and volume of fluid methods and solves the Navier-Stokes equations on an unstructured mesh, it is capable of resolving the time evolution of very complex vortical motions, air entrainment and pressure variations due to violent deformations following overflow of the weir crest. In the present study, two different types of vertical weir, namely broad-crested and sharp-crested, are considered for validation purposes. The calculated overflow parameters such as pressure head distributions, velocity distributions, and water surface profiles are compared against experimental data as well as numerical results available in literature. A very good quantitative agreement has been obtained. The numerical model, thus, offers a good alternative to traditional experimental methods in the study of weir problems.

  6. Analysis of stresses on buried pipeline subjected to landslide based on numerical simulation and regression analysis

    Energy Technology Data Exchange (ETDEWEB)

    Han, Bing; Jing, Hongyuan; Liu, Jianping; Wu, Zhangzhong [PetroChina Pipeline RandD Center, Langfang, Hebei (China); Hao, Jianbin [School of Petroleum Engineering, Southwest Petroleum University, Chengdu, Sichuan (China)

    2010-07-01

    Landslides have a serious impact on the integrity of oil and gas pipelines in the tough terrain of Western China. This paper introduces a solving method of axial stress, which uses numerical simulation and regression analysis for the pipelines subjected to landslides. Numerical simulation is performed to analyze the change regularity of pipe stresses for the five vulnerability assessment indexes, which are: the distance between pipeline and landslide tail; the thickness of landslide; the inclination angle of landslide; the pipeline length passing through landslide; and the buried depth of pipeline. A pipeline passing through a certain landslide in southwest China was selected as an example to verify the feasibility and effectiveness of this method. This method has practical applicability, but it would need large numbers of examples to better verify its reliability and should be modified accordingly. Also, it only considers the case where the direction of the pipeline is perpendicular to the primary slip direction of the landslide.

  7. Numerical Investigation of Flow Control Feasibility with a Trailing Edge Flap

    International Nuclear Information System (INIS)

    Zhu, W J; Shen, W Z; Sørensen, J N

    2014-01-01

    This paper concerns a numerical study of employing an adaptive trailing edge flap to control the lift of an airfoil subject to unsteady inflow conditions. The periodically varying inflow is generated by two oscillating airfoils, which are located upstream of the controlled airfoil. To establish the control system, a standard PID controller is implemented in a finite volume based incompressible flow solver. An immersed boundary method is applied to treat the problem of simulating a deformable airfoil trailing edge. The flow field is solved using a 2D Reynolds averaged Navier-Stokes finite volume solver. In order to more accurately simulate wall bounded flows around the immersed boundary, a modified boundary condition is introduced in the k- ω turbulence model. As an example, turbulent flow over a NACA 64418 airfoil with a deformable trailing edge is investigated. Results from numerical simulations are convincing and may give some highlights for practical implementations of trailing edge flap to a wind turbine rotor blade

  8. Knowledge-Based Instruction: Teaching Problem Solving in a Logo Learning Environment.

    Science.gov (United States)

    Swan, Karen; Black, John B.

    1993-01-01

    Discussion of computer programming and knowledge-based instruction focuses on three studies of elementary and secondary school students which show that five particular problem-solving strategies can be developed in students explicitly taught the strategies and given practice applying them to solve LOGO programming problems. (Contains 53…

  9. The Architecture of Children's Use of Language and Tools When Problem Solving Collaboratively with Robotics

    Science.gov (United States)

    Mills, Kathy A.; Chandra, Vinesh; Park, Ji Yong

    2013-01-01

    This paper demonstrates, following Vygotsky, that language and tool use has a critical role in the collaborative problem-solving behaviour of school-age children. It reports original ethnographic classroom research examining the convergence of speech and practical activity in children's collaborative problem solving with robotics programming…

  10. Developing Physics Concepts through Hands-On Problem Solving: A Perspective on a Technological Project Design

    Science.gov (United States)

    Hong, Jon-Chao; Chen, Mei-Yung; Wong, Ashley; Hsu, Tsui-Fang; Peng, Chih-Chi

    2012-01-01

    In a contest featuring hands-on projects, college students were required to design a simple crawling worm using planning, self-monitoring and self-evaluation processes to solve contradictive problems. To enhance the efficiency of problem solving, one needs to practice meta-cognition based on an application of related scientific concepts. The…

  11. An Intervention Framework Designed to Develop the Collaborative Problem-Solving Skills of Primary School Students

    Science.gov (United States)

    Gu, Xiaoqing; Chen, Shan; Zhu, Wenbo; Lin, Lin

    2015-01-01

    Considerable effort has been invested in innovative learning practices such as collaborative inquiry. Collaborative problem solving is becoming popular in school settings, but there is limited knowledge on how to develop skills crucial in collaborative problem solving in students. Based on the intervention design in social interaction of…

  12. Information Seeking When Problem Solving: Perspectives of Public Health Professionals.

    Science.gov (United States)

    Newman, Kristine; Dobbins, Maureen; Yost, Jennifer; Ciliska, Donna

    2017-04-01

    Given the many different types of professionals working in public health and their diverse roles, it is likely that their information needs, information-seeking behaviors, and problem-solving abilities differ. Although public health professionals often work in interdisciplinary teams, few studies have explored their information needs and behaviors within the context of teamwork. This study explored the relationship between Canadian public health professionals' perceptions of their problem-solving abilities and their information-seeking behaviors with a specific focus on the use of evidence in practice settings. It also explored their perceptions of collaborative information seeking and the work contexts in which they sought information. Key Canadian contacts at public health organizations helped recruit study participants through their list-servs. An electronic survey was used to gather data about (a) individual information-seeking behaviors, (b) collaborative information-seeking behaviors, (c) use of evidence in practice environments, (d) perceived problem-solving abilities, and (e) demographic characteristics. Fifty-eight public health professionals were recruited, with different roles and representing most Canadian provinces and one territory. A significant relationship was found between perceived problem-solving abilities and collaborative information-seeking behavior (r = -.44, p public health professionals take a shared, active approach to problem solving, maintain personal control, and have confidence, they are more likely collaborate with others in seeking information to complete a work task. Administrators of public health organizations should promote collaboration by implementing effective communication and information-seeking strategies, and by providing information resources and retrieval tools. Public health professionals' perceived problem-solving abilities can influence how they collaborate in seeking information. Educators in public health

  13. Practical calculations of quantum breakup cross sections

    International Nuclear Information System (INIS)

    McCurdy, C. W.; Rescigno, T. N.

    2000-01-01

    The Schroedinger equation is solved numerically using the method of exterior complex scaling for several models of the breakup of an atom by electron impact. Using the accurate wave functions thereby obtained for these model problems, several well-known integral expressions for quantum-mechanical breakup amplitudes are tested. It is shown that some formally correct integral expressions for the breakup amplitudes can yield numerically unstable or poorly convergent results. Calculations are presented for a case with simple exponential potentials and a case in which a metastable state of the target, analogous to an autoionizing state, can decay into the breakup channel. For cases involving only short-range (non-Coulomb) interactions, alternative expressions can be found that are stable in calculations of practical scale. (c) 2000 The American Physical Society

  14. Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

    Science.gov (United States)

    Predoi, Mihai Valentin

    2014-09-01

    The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

  15. Problem solving: How can we help students overcome cognitive difficulties

    Directory of Open Access Journals (Sweden)

    Liberato Cardellini

    2014-12-01

    Full Text Available The traditional approach to teach problem solving usually consists in showing students the solutions of some example-problems and then in asking students to practice individually on solving a certain number of related problems. This approach does not ensure that students learn to solve problems and above all to think about the solution process in a consistent manner. Topics such as atoms, molecules, and the mole concept are fundamental in chemistry and instructors may think that, for our students, should be easy to learn these concepts and to use them in solving problems, but it is not always so. If teachers do not put emphasis on the logical process during solving problems, students are at risk to become more proficient at applying the formulas rather than to reason. This disappointing result is clear from the outcomes of questionnaires meant to measure the ability to calculate the mass of a sample from the number of atoms and vice versa. A suggestion from the cognitive load theory has proved a useful way to improve students’ skills for this type of problems: the use of worked out examples. The repetition after two weeks of the Friedel-Maloney test after the use of worked examples shows that students' skills significantly improve. Successful students in all questions jumped from 2 to 64%.

  16. Education for complex problem solving

    DEFF Research Database (Denmark)

    Kjær-Rasmussen, Lone Krogh

    The Problem-Based Learning model as it is practiced at Aalborg University grew out of expectations for future graduates in the 1970s. Many changes and developments have taken place since then in the ways the principles and methodologies are practiced, due to changes in society and governmental...... regulations. However, the basic educational principles and methodologies are still the same and seem to meet expectations from society and academic work places today. This is what surveys and research, done regularly, document. (see for instance Krogh, 2013)....

  17. Numerical Modelling of Flow and Settling in Secondary Settling Tanks

    DEFF Research Database (Denmark)

    Dahl, Claus Poulsen

    This thesis discusses the development of a numerical model for the simulation of secondary settling tanks. In the first part, the status on the development of numerical models for settling tanks and a discussion of the current design practice are presented. A study of the existing numerical models...... and design practice proved a demand for further development to include numerical models in the design of settling tanks, thus improving the future settling tanks....

  18. LEMBAR KERJA PESERTA DIDIK (LKPD BERBASIS PROBLEM SOLVING POLYA

    Directory of Open Access Journals (Sweden)

    Lilis Nurliawaty

    2017-03-01

    Full Text Available Lack of exact use of teaching materials and does not correspond to the needs of student leads to lack of analytical ability of students to the process of problem solving. Research development worksheets based on Polya problem solving on the heat material aims to develop valid LKPD, practical, and effective. Stages of development using the 4D model was modified into 3D, namely define (definition, Design (planning, and Development (development The results of the validity of the learning device in the category valid, obtained from the calculation of CVI are in the range 0-1 and said in category reliably with r11 value greater than rtabel (rcount > rtabel. The results of the analysis of questionnaire responses of students obtained an average percentage of 87.9% on the analysis. The analysis result of sheets assessment of learning physics used LKPD-based Polya problem solving obtained average percentage analysis results in the first meeting is 77.33% with good category, the average percentage of the results of the analysis at the second meeting is 81.11% with a very good category and average of results percentage analysis at the third meeting is 78.89% with good category. So it can say that LKPD-based Polya problem solving developed valid, practical and effective to use.

  19. Design of heat exchangers by numerical methods

    International Nuclear Information System (INIS)

    Konuk, A.A.

    1981-01-01

    Differential equations describing the heat tranfer in shell - and tube heat exchangers are derived and solved numerically. The method of ΔT sub(lm) is compared with the proposed method in cases where the specific heat at constant pressure, Cp and the overall heat transfer coefficient, U, vary with temperature. The error of the method of ΔT sub (lm) for the computation of the exchanger lenght is less than + 10%. However, the numerical method, being more accurate and at the same time easy to use and economical, is recommended for the design of shell-and-tube heat exchangers. (Author) [pt

  20. Numerical computation of linear instability of detonations

    Science.gov (United States)

    Kabanov, Dmitry; Kasimov, Aslan

    2017-11-01

    We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

  1. Theoretical and numerical method in aeroacoustics

    Directory of Open Access Journals (Sweden)

    Nicuşor ALEXANDRESCU

    2010-06-01

    Full Text Available The paper deals with the mathematical and numerical modeling of the aerodynamic noisegenerated by the fluid flow interaction with the solid structure of a rotor blade.Our analysis use Lighthill’s acoustic analogy. Lighthill idea was to express the fundamental equationsof motion into a wave equation for acoustic fluctuation with a source term on the right-hand side. Theobtained wave equation is solved numerically by the spatial discretization. The method is applied inthe case of monopole source placed in different points of blade surfaces to find this effect of noisepropagation.

  2. Masonry constructions mechanical models and numerical applications

    CERN Document Server

    Lucchesi, Massimiliano; Padovani, Cristina

    2008-01-01

    Numerical methods for the structural analysis of masonry constructions can be of great value in assessing the safety of artistically important masonry buildings and optimizing potential operations of maintenance and strengthening in terms of their cost-effectiveness, architectural impact and static effectiveness. This monograph firstly provides a detailed description of the constitutive equation of masonry-like materials, clearly setting out its most important features. It then goes on to provide a numerical procedure to solve the equilibrium problem of masonry solids. A large portion of the w

  3. On the Hughes model and numerical aspects

    KAUST Repository

    Gomes, Diogo A.

    2017-01-05

    We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.

  4. Numerical simulation of real-world flows

    Energy Technology Data Exchange (ETDEWEB)

    Hayase, Toshiyuki, E-mail: hayase@ifs.tohoku.ac.jp [Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 (Japan)

    2015-10-15

    Obtaining real flow information is important in various fields, but is a difficult issue because measurement data are usually limited in time and space, and computational results usually do not represent the exact state of real flows. Problems inherent in the realization of numerical simulation of real-world flows include the difficulty in representing exact initial and boundary conditions and the difficulty in representing unstable flow characteristics. This article reviews studies dealing with these problems. First, an overview of basic flow measurement methodologies and measurement data interpolation/approximation techniques is presented. Then, studies on methods of integrating numerical simulation and measurement, namely, four-dimensional variational data assimilation (4D-Var), Kalman filters (KFs), state observers, etc are discussed. The first problem is properly solved by these integration methodologies. The second problem can be partially solved with 4D-Var in which only initial and boundary conditions are control parameters. If an appropriate control parameter capable of modifying the dynamical structure of the model is included in the formulation of 4D-Var, unstable modes are properly suppressed and the second problem is solved. The state observer and KFs also solve the second problem by modifying mathematical models to stabilize the unstable modes of the original dynamical system by applying feedback signals. These integration methodologies are now applied in simulation of real-world flows in a wide variety of research fields. Examples are presented for basic fluid dynamics and applications in meteorology, aerospace, medicine, etc. (topical review)

  5. Numerical simulation of edge plasma in tokamak

    International Nuclear Information System (INIS)

    Chen Yiping; Qiu Lijian

    1996-02-01

    The transport process and transport property of plasma in edge layer of Tokamak are simulated by solving numerically two-dimensional and multi-fluid plasma transport equations using suitable simulation code. The simulation results can show plasma parameter distribution characteristics in the area of edge layer, especially the characteristics near the first wall and divertor target plate. The simulation results play an important role in the design of divertor and first wall of Tokamak. (2 figs)

  6. A hybrid numerical method for orbit correction

    International Nuclear Information System (INIS)

    White, G.; Himel, T.; Shoaee, H.

    1997-09-01

    The authors describe a simple hybrid numerical method for beam orbit correction in particle accelerators. The method overcomes both degeneracy in the linear system being solved and respects boundaries on the solution. It uses the Singular Value Decomposition (SVD) to find and remove the null-space in the system, followed by a bounded Linear Least Squares analysis of the remaining recast problem. It was developed for correcting orbit and dispersion in the B-factory rings

  7. Exploring New Physics Frontiers Through Numerical Relativity.

    Science.gov (United States)

    Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Sperhake, Ulrich

    2015-01-01

    The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.

  8. Advanced numerical methods for three dimensional two-phase flow calculations

    Energy Technology Data Exchange (ETDEWEB)

    Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)

    1997-07-01

    This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.

  9. Advanced numerical methods for three dimensional two-phase flow calculations

    International Nuclear Information System (INIS)

    Toumi, I.; Caruge, D.

    1997-01-01

    This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe's method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations

  10. Numerical studies on divertor experiments

    International Nuclear Information System (INIS)

    Ueda, N.; Itoh, K.; Itoh, S.-I.; Tanaka, M.; Hasegawa, M.; Shoji, T.; Sugihara, M.

    1988-04-01

    Numerical analysis on the divertor experiments such as JFT-2M tokamak is made by use of the two-dimensional time-dependent simulation code. The plasma in the scrape-off layer (SOL) and divertor region is solved for the given particle and heat sources from the main plasma, Γ p and Q T . Effect of the direction of the toroidal magnetic field is studied. It is found that the heat flux which is proportional to b vector x ∇T i has influences on the divertor plasmas, but has a small effect on the parameters on the midplane in the framework of the fluid model. Parameter survey on Γ p and Q T is made. The transient response of the SOL/divertor plasma to the sudden change of Γ p and Q T is studied. Time delay in the SOL and divertor region is calculated. (author)

  11. Numerical evidence for 'multiscalar stars'

    International Nuclear Information System (INIS)

    Hawley, Scott H.; Choptuik, Matthew W.

    2003-01-01

    We present a class of general relativistic solitonlike solutions composed of multiple minimally coupled, massive, real scalar fields which interact only through the gravitational field. We describe a two-parameter family of solutions we call ''phase-shifted boson stars'' (parametrized by central density ρ 0 and phase δ), which are obtained by solving the ordinary differential equations associated with boson stars and then altering the phase between the real and imaginary parts of the field. These solutions are similar to boson stars as well as the oscillating soliton stars found by Seidel and Suen [E. Seidel and W. M. Suen, Phys. Rev. Lett. 66, 1659 (1991)]; in particular, long-time numerical evolutions suggest that phase-shifted boson stars are stable. Our results indicate that scalar solitonlike solutions are perhaps more generic than has been previously thought

  12. Numerical approach to one-loop integrals

    International Nuclear Information System (INIS)

    Fujimoto, Junpei; Shimizu, Yoshimitsu; Kato, Kiyoshi; Oyanagi, Yoshio.

    1992-01-01

    Two numerical methods are proposed for the calculation of one-loop scalar integrals. In the first method, the singularity is cancelled by the symmetrization of the integrand and the integration is done by a Monte-Carlo method. In the second one, after the transform of the integrand into a standard form, the integral is reduced into a regular numerical integral. These methods provide us practical tools to evaluate one-loop Feynman diagrams with desired numerical accuracy. They are extended to the integral with numerator and the treatment of the one-loop virtual correction to the cross section is also presented. (author)

  13. Modified Projection Algorithms for Solving the Split Equality Problems

    Directory of Open Access Journals (Sweden)

    Qiao-Li Dong

    2014-01-01

    proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.

  14. The Future of Design: Unframed Problem Solving in Design Education

    DEFF Research Database (Denmark)

    Friis, Silje Alberthe Kamille; Gelting, Anne Katrine Gøtzsche

    2016-01-01

    The present paper sets out to investigate the impact and significance of a 3rd semester course in design methods, complex problem solving, and cross-disciplinary collaboration to the students within six design disciplines as experienced by the students three years later. The course reflects a shi......, society, and technology influencing the future disciplines and practices of design and thus the professional roles that they themselves might take....

  15. Students’ difficulties in probabilistic problem-solving

    Science.gov (United States)

    Arum, D. P.; Kusmayadi, T. A.; Pramudya, I.

    2018-03-01

    There are many errors can be identified when students solving mathematics problems, particularly in solving the probabilistic problem. This present study aims to investigate students’ difficulties in solving the probabilistic problem. It focuses on analyzing and describing students errors during solving the problem. This research used the qualitative method with case study strategy. The subjects in this research involve ten students of 9th grade that were selected by purposive sampling. Data in this research involve students’ probabilistic problem-solving result and recorded interview regarding students’ difficulties in solving the problem. Those data were analyzed descriptively using Miles and Huberman steps. The results show that students have difficulties in solving the probabilistic problem and can be divided into three categories. First difficulties relate to students’ difficulties in understanding the probabilistic problem. Second, students’ difficulties in choosing and using appropriate strategies for solving the problem. Third, students’ difficulties with the computational process in solving the problem. Based on the result seems that students still have difficulties in solving the probabilistic problem. It means that students have not able to use their knowledge and ability for responding probabilistic problem yet. Therefore, it is important for mathematics teachers to plan probabilistic learning which could optimize students probabilistic thinking ability.

  16. IDEAL Problem Solving dalam Pembelajaran Matematika

    Directory of Open Access Journals (Sweden)

    Eny Susiana

    2012-01-01

    Full Text Available Most educators agree that problem solving is among the most meaningful and importantkinds of learning and thingking. That is, the central focus of learning and instructionshould be learning to solve problems. There are several warrants supporting that claims.They are authenticity, relevance, problem solving engages deeper learning angtherefore enhances meaning making, and constructed to represent problems (problemsolving is more meaningful. It is the reason why we must provide teaching and learningto make student’s problem solving skill in progress. There are many informationprocessingmodels of problem solving, such as simplified model of the problem-solvingprocess by Gicks, Polya’s problem solving process etc. One of them is IDEAL problemsolving. Each letter of IDEAL is stand for an aspect of thinking that is important forproblem solving. IDEAL is identify problem, Define Goal, Explore possible strategies,Anticipate outcme and Act, and Look back and learn. Using peer interaction andquestion prompt in small group in IDEAL problem solving teaching and Learning canimprove problem solving skill.Kata kunci: IDEAL Problem Solving, Interaksi Sebaya, Pertanyaan Penuntun, KelompokKecil.

  17. On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

    Science.gov (United States)

    Voytishek, Anton V.; Shipilov, Nikolay M.

    2017-11-01

    In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

  18. Shielding practice

    International Nuclear Information System (INIS)

    Sauermann, P.F.

    1985-08-01

    The basis of shielding practice against external irradiation is shown in a simple way. For most sources of radiation (point sources) occurring in shielding practice, the basic data are given, mainly in the form of tables, which are required to solve the shielding problems. The application of these data is explained and discussed using practical examples. Thickness of shielding panes of glove boxes for α and β radiation; shielding of sealed γ-radiography sources; shielding of a Co-60 radiation source, and of the manipulator panels for hot cells; damping factors for γ radiation and neutrons; shielding of fast and thermal neutrons, and of bremsstrahlung (X-ray tubes, Kr-85 pressure gas cylinders, 42 MeV betatrons, 20 MeV linacs); two-fold shielding (lead glass windows for hot cells, 14 MeV neutron generators); shielding against scattered radiation. (orig./HP) [de

  19. Solving inverse problems for biological models using the collage method for differential equations.

    Science.gov (United States)

    Capasso, V; Kunze, H E; La Torre, D; Vrscay, E R

    2013-07-01

    In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.

  20. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  1. Solving Linear Equations by Classical Jacobi-SR Based Hybrid Evolutionary Algorithm with Uniform Adaptation Technique

    OpenAIRE

    Jamali, R. M. Jalal Uddin; Hashem, M. M. A.; Hasan, M. Mahfuz; Rahman, Md. Bazlar

    2013-01-01

    Solving a set of simultaneous linear equations is probably the most important topic in numerical methods. For solving linear equations, iterative methods are preferred over the direct methods especially when the coefficient matrix is sparse. The rate of convergence of iteration method is increased by using Successive Relaxation (SR) technique. But SR technique is very much sensitive to relaxation factor, {\\omega}. Recently, hybridization of classical Gauss-Seidel based successive relaxation t...

  2. Canonical Primal-Dual Method for Solving Non-convex Minimization Problems

    OpenAIRE

    Wu, Changzhi; Li, Chaojie; Gao, David Yang

    2012-01-01

    A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimization problem, which is then solved by a quadratically perturbed primal-dual method. %It is proved that the popular SDP method is indeed a special case of the canonical duality theory. Numerical examples are illustrated. Comparing...

  3. Simultaneous and semi-alternating projection algorithms for solving split equality problems.

    Science.gov (United States)

    Dong, Qiao-Li; Jiang, Dan

    2018-01-01

    In this article, we first introduce two simultaneous projection algorithms for solving the split equality problem by using a new choice of the stepsize, and then propose two semi-alternating projection algorithms. The weak convergence of the proposed algorithms is analyzed under standard conditions. As applications, we extend the results to solve the split feasibility problem. Finally, a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms.

  4. Solving stochastic programs with integer recourse by enumeration : a framework using Gröbner basis reductions

    NARCIS (Netherlands)

    Schultz, R.; Stougie, L.; Vlerk, van der M.H.

    1998-01-01

    In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the

  5. Teaching effective problem solving skills to radiation protection students

    International Nuclear Information System (INIS)

    Waller, Edward

    2008-01-01

    Full text: Problem solving skills are essential for all radiation protection personnel. Although some students have more natural problem solving skills than others, all students require practice to become comfortable using these skills. At the University of Ontario Institute of Technology (UOIT), a unique one-semester course was developed as part of the core curriculum to teach students problem solving skills and elements of modelling and simulation. The underlying emphasis of the course was to allow students to develop their own problem solving strategies, both individually and in groups. Direction was provided on how to examine problems from different perspectives, and how to determine the proper root problem statement. A five-point problem solving strategy was presented as: 1) Problem definition; 2) Solution generation; 3) Decision; 4) Implementation; 5) Evaluation. Within the strategy, problem solving techniques were integrated from diverse areas such as: De Bono 's six thinking hats, Kepner-Tregoe decision analysis, Covey's seven habits of highly effective people, Reason's swiss cheese theory of complex failure, and Howlett's common failure modes. As part of the evaluation step, students critically explore areas such as ethics and environmental responsibility. In addition to exploring problem solving methods, students learn the usefulness of simulation methods, and how to model and simulate complex phenomena of relevance to radiation protection. Computational aspects of problem solving are explored using the commercially available MATLAB computer code. A number of case studies are presented as both examples and problems to the students. Emphasis was placed on solutions to problems of interest to radiation protection, health physics and nuclear engineering. A group project, pertaining to an accident or event related to the nuclear industry is a course requirement. Students learn to utilize common time and project management tools such as flowcharting, Pareto

  6. Numerical model SMODERP

    Science.gov (United States)

    Kavka, P.; Jeřábek, J.; Strouhal, L.

    2016-12-01

    The contribution presents a numerical model SMODERP that is used for calculation and prediction of surface runoff and soil erosion from agricultural land. The physically based model includes the processes of infiltration (Phillips equation), surface runoff routing (kinematic wave based equation), surface retention, surface roughness and vegetation impact on runoff. The model is being developed at the Department of Irrigation, Drainage and Landscape Engineering, Civil Engineering Faculty, CTU in Prague. 2D version of the model was introduced in last years. The script uses ArcGIS system tools for data preparation. The physical relations are implemented through Python scripts. The main computing part is stand alone in numpy arrays. Flow direction is calculated by Steepest Descent algorithm and in multiple flow algorithm. Sheet flow is described by modified kinematic wave equation. Parameters for five different soil textures were calibrated on the set of hundred measurements performed on the laboratory and filed rainfall simulators. Spatially distributed models enable to estimate not only surface runoff but also flow in the rills. Development of the rills is based on critical shear stress and critical velocity. For modelling of the rills a specific sub model was created. This sub model uses Manning formula for flow estimation. Flow in the ditches and streams are also computed. Numerical stability of the model is controled by Courant criterion. Spatial scale is fixed. Time step is dynamic and depends on the actual discharge. The model is used in the framework of the project "Variability of Short-term Precipitation and Runoff in Small Czech Drainage Basins and its Influence on Water Resources Management". Main goal of the project is to elaborate a methodology and online utility for deriving short-term design precipitation series, which could be utilized by a broad community of scientists, state administration as well as design planners. The methodology will account for

  7. Conceptual problem solving in high school physics

    OpenAIRE

    Jennifer L. Docktor; Natalie E. Strand; José P. Mestre; Brian H. Ross

    2015-01-01

    Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in w...

  8. Solving global optimization problems on GPU cluster

    Energy Technology Data Exchange (ETDEWEB)

    Barkalov, Konstantin; Gergel, Victor; Lebedev, Ilya [Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod (Russian Federation)

    2016-06-08

    The paper contains the results of investigation of a parallel global optimization algorithm combined with a dimension reduction scheme. This allows solving multidimensional problems by means of reducing to data-independent subproblems with smaller dimension solved in parallel. The new element implemented in the research consists in using several graphic accelerators at different computing nodes. The paper also includes results of solving problems of well-known multiextremal test class GKLS on Lobachevsky supercomputer using tens of thousands of GPU cores.

  9. Neural network error correction for solving coupled ordinary differential equations

    Science.gov (United States)

    Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.

    1992-01-01

    A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.

  10. Application of ANNs approach for solving fully fuzzy polynomials system

    Directory of Open Access Journals (Sweden)

    R. Novin

    2017-11-01

    Full Text Available In processing indecisive or unclear information, the advantages of fuzzy logic and neurocomputing disciplines should be taken into account and combined by fuzzy neural networks. The current research intends to present a fuzzy modeling method using multi-layer fuzzy neural networks for solving a fully fuzzy polynomials system. To clarify the point, it is necessary to inform that a supervised gradient descent-based learning law is employed. The feasibility of the method is examined using computer simulations on a numerical example. The experimental results obtained from the investigation of the proposed method are valid and delivers very good approximation results.

  11. A recurrent neural network for solving bilevel linear programming problem.

    Science.gov (United States)

    He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie; Huang, Junjian

    2014-04-01

    In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

  12. Solving the generalized Langevin equation with the algebraically correlated noise

    International Nuclear Information System (INIS)

    Srokowski, T.; Ploszajczak, M.

    1997-01-01

    The Langevin equation with the memory kernel is solved. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated at the assumption that the system is in the thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Levy walks with divergent moments of the velocity distribution. The motion of a Brownian particle is considered both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle. (author)

  13. Krylov subspace methods for solving large unsymmetric linear systems

    International Nuclear Information System (INIS)

    Saad, Y.

    1981-01-01

    Some algorithms based upon a projection process onto the Krylov subspace K/sub m/ = Span(r 0 , Ar 0 ,...,A/sup m/-1r 0 ) are developed, generalizing the method of conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldi's algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace K/sub m/ and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed

  14. Various Newton-type iterative methods for solving nonlinear equations

    Directory of Open Access Journals (Sweden)

    Manoj Kumar

    2013-10-01

    Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.

  15. An Unconditionally Stable Method for Solving the Acoustic Wave Equation

    Directory of Open Access Journals (Sweden)

    Zhi-Kai Fu

    2015-01-01

    Full Text Available An unconditionally stable method for solving the time-domain acoustic wave equation using Associated Hermit orthogonal functions is proposed. The second-order time derivatives in acoustic wave equation are expanded by these orthogonal basis functions. By applying Galerkin temporal testing procedure, the time variable can be eliminated from the calculations. The restriction of Courant-Friedrichs-Levy (CFL condition in selecting time step for analyzing thin layer can be avoided. Numerical results show the accuracy and the efficiency of the proposed method.

  16. Modified Chebyshev Collocation Method for Solving Differential Equations

    Directory of Open Access Journals (Sweden)

    M Ziaul Arif

    2015-05-01

    Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.

  17. Numerical kinematic transformation calculations for a parallel link manipulator

    International Nuclear Information System (INIS)

    Killough, S.M.

    1993-01-01

    Parallel link manipulators are often considered for particular robotic applications because of the unique advantages they provide. Unfortunately, they have significant disadvantages with respect to calculating the kinematic transformations because of the high-order equations that must be solved. Presented is a manipulator design that exploits the mechanical advantages of parallel links yet also has a corresponding numerical kinematic solution that can be solved in real time on common microcomputers

  18. Applying Cooperative Techniques in Teaching Problem Solving

    Directory of Open Access Journals (Sweden)

    Krisztina Barczi

    2013-12-01

    Full Text Available Teaching how to solve problems – from solving simple equations to solving difficult competition tasks – has been one of the greatest challenges for mathematics education for many years. Trying to find an effective method is an important educational task. Among others, the question arises as to whether a method in which students help each other might be useful. The present article describes part of an experiment that was designed to determine the effects of cooperative teaching techniques on the development of problem-solving skills.

  19. Assertiveness and problem solving in midwives.

    Science.gov (United States)

    Yurtsal, Zeliha Burcu; Özdemir, Levent

    2015-01-01

    Midwifery profession is required to bring solutions to problems and a midwife is expected to be an assertive person and to develop midwifery care. This study was planned to examine the relationship between assertiveness and problem-solving skills of midwives. This cross-sectional study was conducted with 201 midwives between July 2008 and February 2009 in the city center of Sivas. The Rathus Assertiveness Schedule (RAS) and Problem Solving Inventory (PSI) were used to determine the level of assertiveness and problem-solving skills of midwives. Statistical methods were used as mean, standard deviation, percentage, Student's T, ANOVA and Tukey HSD, Kruskal Wallis, Fisher Exact, Pearson Correlation and Chi-square tests and P problem-solving skills training. A statistically significant negative correlation was found between the RAS and PSI scores. The RAS scores decreased while the problem-solving scores increased (r: -0451, P problem solving skills of midwives, and midwives who were assertive solved their problems better than did others. Assertiveness and problem-solving skills training will contribute to the success of the midwifery profession. Midwives able to solve problems, and display assertive behaviors will contribute to the development of midwifery profession.

  20. An Integrated Architecture for Engineering Problem Solving

    National Research Council Canada - National Science Library

    Pisan, Yusuf

    1998-01-01

    .... This thesis describes the Integrated Problem Solving Architecture (IPSA) that combines qualitative, quantitative and diagrammatic reasoning skills to produce annotated solutions to engineering problems...

  1. Numerical methods and optimization a consumer guide

    CERN Document Server

    Walter, Éric

    2014-01-01

    Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods and Optimization – A Consumer Guide presents methods for dealing with them. Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to ·         discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems; ·         understand the principles behind recognized algorithms used in state-of-the-art numerical software; ·         learn the advantag...

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

    Science.gov (United States)

    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.

  3. Solving the Schroedinger equation using the finite difference time domain method

    International Nuclear Information System (INIS)

    Sudiarta, I Wayan; Geldart, D J Wallace

    2007-01-01

    In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems

  4. Efficient Method to Approximately Solve Retrial Systems with Impatience

    Directory of Open Access Journals (Sweden)

    Jose Manuel Gimenez-Guzman

    2012-01-01

    Full Text Available We present a novel technique to solve multiserver retrial systems with impatience. Unfortunately these systems do not present an exact analytic solution, so it is mandatory to resort to approximate techniques. This novel technique does not rely on the numerical solution of the steady-state Kolmogorov equations of the Continuous Time Markov Chain as it is common for this kind of systems but it considers the system in its Markov Decision Process setting. This technique, known as value extrapolation, truncates the infinite state space using a polynomial extrapolation method to approach the states outside the truncated state space. A numerical evaluation is carried out to evaluate this technique and to compare its performance with previous techniques. The obtained results show that value extrapolation greatly outperforms the previous approaches appeared in the literature not only in terms of accuracy but also in terms of computational cost.

  5. Distance Measurement Solves Astrophysical Mysteries

    Science.gov (United States)

    2003-08-01

    Location, location, and location. The old real-estate adage about what's really important proved applicable to astrophysics as astronomers used the sharp radio "vision" of the National Science Foundation's Very Long Baseline Array (VLBA) to pinpoint the distance to a pulsar. Their accurate distance measurement then resolved a dispute over the pulsar's birthplace, allowed the astronomers to determine the size of its neutron star and possibly solve a mystery about cosmic rays. "Getting an accurate distance to this pulsar gave us a real bonanza," said Walter Brisken, of the National Radio Astronomy Observatory (NRAO) in Socorro, NM. Monogem Ring The Monogem Ring, in X-Ray Image by ROSAT satellite CREDIT: Max-Planck Institute, American Astronomical Society (Click on Image for Larger Version) The pulsar, called PSR B0656+14, is in the constellation Gemini, and appears to be near the center of a circular supernova remnant that straddles Gemini and its neighboring constellation, Monoceros, and is thus called the Monogem Ring. Since pulsars are superdense, spinning neutron stars left over when a massive star explodes as a supernova, it was logical to assume that the Monogem Ring, the shell of debris from a supernova explosion, was the remnant of the blast that created the pulsar. However, astronomers using indirect methods of determining the distance to the pulsar had concluded that it was nearly 2500 light-years from Earth. On the other hand, the supernova remnant was determined to be only about 1000 light-years from Earth. It seemed unlikely that the two were related, but instead appeared nearby in the sky purely by a chance juxtaposition. Brisken and his colleagues used the VLBA to make precise measurements of the sky position of PSR B0656+14 from 2000 to 2002. They were able to detect the slight offset in the object's apparent position when viewed from opposite sides of Earth's orbit around the Sun. This effect, called parallax, provides a direct measurement of

  6. An Evaluation of Java for Numerical Computing

    Directory of Open Access Journals (Sweden)

    Brian Blount

    1999-01-01

    Full Text Available This paper describes the design and implementation of high performance numerical software in Java. Our primary goals are to characterize the performance of object‐oriented numerical software written in Java and to investigate whether Java is a suitable language for such endeavors. We have implemented JLAPACK, a subset of the LAPACK library in Java. LAPACK is a high‐performance Fortran 77 library used to solve common linear algebra problems. JLAPACK is an object‐oriented library, using encapsulation, inheritance, and exception handling. It performs within a factor of four of the optimized Fortran version for certain platforms and test cases. When used with the native BLAS library, JLAPACK performs comparably with the Fortran version using the native BLAS library. We conclude that high‐performance numerical software could be written in Java if a handful of concerns about language features and compilation strategies are adequately addressed.

  7. Numerical Modeling of Ablation Heat Transfer

    Science.gov (United States)

    Ewing, Mark E.; Laker, Travis S.; Walker, David T.

    2013-01-01

    A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

  8. Analytic and numerical studies of Scyllac equilibrium

    International Nuclear Information System (INIS)

    Barnes, D.C.; Brackbill, J.U.; Dagazian, R.Y.; Freidberg, J.P.; Schneider, W.; Betancourt, O.; Garabedian, P.

    1976-01-01

    The results of both numerical and analytic studies of the Scyllac equilibria are presented. Analytic expansions are used to derive equilibrium equations appropriate to noncircular cross sections, and compute the stellarator fields which produce toroidal force balance. Numerical algorithms are used to solve both the equilibrium equations and the full system of dynamical equations in three dimensions. Numerical equilibria are found for both l = 1,0 and l= 1,2 systems. It is found that the stellarator fields which produce equilibria in the l = 1.0 system are larger for diffuse than for sharp boundary plasma profiles, and that the stability of the equilibria depends strongly on the harmonic content of the stellarator fields

  9. Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

    Energy Technology Data Exchange (ETDEWEB)

    Klein, R I; Stone, J M

    2007-11-20

    We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.

  10. Numerical stability in problems of linear algebra.

    Science.gov (United States)

    Babuska, I.

    1972-01-01

    Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

  11. Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

    International Nuclear Information System (INIS)

    Klein, R I; Stone, J M

    2007-01-01

    We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments

  12. Numerical methods using Matlab

    CERN Document Server

    Lindfield, George

    2012-01-01

    Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board. Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of use

  13. Dynamical Systems Method and Applications Theoretical Developments and Numerical Examples

    CERN Document Server

    Ramm, Alexander G

    2012-01-01

    Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and

  14. Numerical discrepancy between serial and MPI parallel computations

    Directory of Open Access Journals (Sweden)

    Sang Bong Lee

    2016-09-01

    Full Text Available Numerical simulations of 1D Burgers equation and 2D sloshing problem were carried out to study numerical discrepancy between serial and parallel computations. The numerical domain was decomposed into 2 and 4 subdomains for parallel computations with message passing interface. The numerical solution of Burgers equation disclosed that fully explicit boundary conditions used on subdomains of parallel computation was responsible for the numerical discrepancy of transient solution between serial and parallel computations. Two dimensional sloshing problems in a rectangular domain were solved using OpenFOAM. After a lapse of initial transient time sloshing patterns of water were significantly different in serial and parallel computations although the same numerical conditions were given. Based on the histograms of pressure measured at two points near the wall the statistical characteristics of numerical solution was not affected by the number of subdomains as much as the transient solution was dependent on the number of subdomains.

  15. A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

    KAUST Repository

    Wu, Zedong

    2018-04-05

    Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.

  16. Practical scientific computing

    CERN Document Server

    Muhammad, A

    2011-01-01

    Scientific computing is about developing mathematical models, numerical methods and computer implementations to study and solve real problems in science, engineering, business and even social sciences. Mathematical modelling requires deep understanding of classical numerical methods. This essential guide provides the reader with sufficient foundations in these areas to venture into more advanced texts. The first section of the book presents numEclipse, an open source tool for numerical computing based on the notion of MATLAB®. numEclipse is implemented as a plug-in for Eclipse, a leading integ

  17. Towards practical multiscale approach for analysis of reinforced concrete structures

    Science.gov (United States)

    Moyeda, Arturo; Fish, Jacob

    2017-12-01

    We present a novel multiscale approach for analysis of reinforced concrete structural elements that overcomes two major hurdles in utilization of multiscale technologies in practice: (1) coupling between material and structural scales due to consideration of large representative volume elements (RVE), and (2) computational complexity of solving complex nonlinear multiscale problems. The former is accomplished using a variant of computational continua framework that accounts for sizeable reinforced concrete RVEs by adjusting the location of quadrature points. The latter is accomplished by means of reduced order homogenization customized for structural elements. The proposed multiscale approach has been verified against direct numerical simulations and validated against experimental results.

  18. Creativity and Insight in Problem Solving

    Science.gov (United States)

    Golnabi, Laura

    2016-01-01

    This paper analyzes the thought process involved in problem solving and its categorization as creative thinking as defined by psychologist R. Weisberg (2006). Additionally, the notion of insight, sometimes present in unconscious creative thinking and often leading to creative ideas, is discussed in the context of geometry problem solving. In…

  19. Metacognition: Student Reflections on Problem Solving

    Science.gov (United States)

    Wismath, Shelly; Orr, Doug; Good, Brandon

    2014-01-01

    Twenty-first century teaching and learning focus on the fundamental skills of critical thinking and problem solving, creativity and innovation, and collaboration and communication. Metacognition is a crucial aspect of both problem solving and critical thinking, but it is often difficult to get students to engage in authentic metacognitive…

  20. Measuring Problem Solving Skills in "Portal 2"

    Science.gov (United States)

    Shute, Valerie J.; Wang, Lubin

    2013-01-01

    This paper examines possible improvement to problem solving skills as a function of playing the video game "Portal 2." Stealth assessment is used in the game to evaluate students' problem solving abilities--specifically basic and flexible rule application. The stealth assessment measures will be validated against commonly accepted…