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.

Automatic numerical integration methods for Feynman integrals through 3-loop

International Nuclear Information System (INIS)

De Doncker, E; Olagbemi, O; Yuasa, F; Ishikawa, T; Kato, K

2015-01-01

We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities. (paper)

Numerical simulations of time-resolved quantum electronics

International Nuclear Information System (INIS)

Gaury, Benoit; Weston, Joseph; Santin, Matthieu; Houzet, Manuel; Groth, Christoph; Waintal, Xavier

2014-01-01

Numerical simulation has become a major tool in quantum electronics both for fundamental and applied purposes. While for a long time those simulations focused on stationary properties (e.g. DC currents), the recent experimental trend toward GHz frequencies and beyond has triggered a new interest for handling time-dependent perturbations. As the experimental frequencies get higher, it becomes possible to conceive experiments which are both time-resolved and fast enough to probe the internal quantum dynamics of the system. This paper discusses the technical aspects–mathematical and numerical–associated with the numerical simulations of such a setup in the time domain (i.e. beyond the single-frequency AC limit). After a short review of the state of the art, we develop a theoretical framework for the calculation of time-resolved observables in a general multiterminal system subject to an arbitrary time-dependent perturbation (oscillating electrostatic gates, voltage pulses, time-varying magnetic fields, etc.) The approach is mathematically equivalent to (i) the time-dependent scattering formalism, (ii) the time-resolved non-equilibrium Green’s function (NEGF) formalism and (iii) the partition-free approach. The central object of our theory is a wave function that obeys a simple Schrödinger equation with an additional source term that accounts for the electrons injected from the electrodes. The time-resolved observables (current, density, etc.) and the (inelastic) scattering matrix are simply expressed in terms of this wave function. We use our approach to develop a numerical technique for simulating time-resolved quantum transport. We find that the use of this wave function is advantageous for numerical simulations resulting in a speed up of many orders of magnitude with respect to the direct integration of NEGF equations. Our technique allows one to simulate realistic situations beyond simple models, a subject that was until now beyond the simulation

Numerical integration of asymptotic solutions of ordinary differential equations

Science.gov (United States)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

A numerical method for resonance integral calculations

International Nuclear Information System (INIS)

Tanbay, Tayfun; Ozgener, Bilge

2013-01-01

A numerical method has been proposed for resonance integral calculations and a cubic fit based on least squares approximation to compute the optimum Bell factor is given. The numerical method is based on the discretization of the neutron slowing down equation. The scattering integral is approximated by taking into account the location of the upper limit in energy domain. The accuracy of the method has been tested by performing computations of resonance integrals for uranium dioxide isolated rods and comparing the results with empirical values. (orig.)

An accurate real-time model of maglev planar motor based on compound Simpson numerical integration

Directory of Open Access Journals (Sweden)

Baoquan Kou

2017-05-01

Full Text Available To realize the high-speed and precise control of the maglev planar motor, a more accurate real-time electromagnetic model, which considers the influence of the coil corners, is proposed in this paper. Three coordinate systems for the stator, mover and corner coil are established. The coil is divided into two segments, the straight coil segment and the corner coil segment, in order to obtain a complete electromagnetic model. When only take the first harmonic of the flux density distribution of a Halbach magnet array into account, the integration method can be carried out towards the two segments according to Lorenz force law. The force and torque analysis formula of the straight coil segment can be derived directly from Newton-Leibniz formula, however, this is not applicable to the corner coil segment. Therefore, Compound Simpson numerical integration method is proposed in this paper to solve the corner segment. With the validation of simulation and experiment, the proposed model has high accuracy and can realize practical application easily.

Numerical method of singular problems on singular integrals

International Nuclear Information System (INIS)

Zhao Huaiguo; Mou Zongze

1992-02-01

As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily

Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

International Nuclear Information System (INIS)

Chernyshenko, Dmitri; Fangohr, Hans

2015-01-01

In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges

Interconnect rise time in superconducting integrating circuits

International Nuclear Information System (INIS)

Preis, D.; Shlager, K.

1988-01-01

The influence of resistive losses on the voltage rise time of an integrated-circuit interconnection is reported. A distribution-circuit model is used to present the interconnect. Numerous parametric curves are presented based on numerical evaluation of the exact analytical expression for the model's transient response. For the superconducting case in which the series resistance of the interconnect approaches zero, the step-response rise time is longer but signal strength increases significantly

Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes

International Nuclear Information System (INIS)

Wehner, M.F.

1983-01-01

A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs

An Integrative Theory of Numerical Development

Science.gov (United States)

Siegler, Robert; Lortie-Forgues, Hugues

2014-01-01

Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme is present, however--progressive broadening of the set of numbers whose magnitudes can be accurately…

Symplectic integrators with adaptive time steps

Science.gov (United States)

Richardson, A. S.; Finn, J. M.

2012-01-01

In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper, we identify the causes for this lack of performance, and find that they fall into two categories. In the first, the time step is considered a function of time alone, Δ = Δ(t). In this case, backward error analysis shows that while the algorithms remain symplectic, parametric instabilities may arise because of resonance between oscillations of Δ(t) and the orbital motion. In the second category the time step is a function of phase space variables Δ = Δ(q, p). In this case, the system of equations to be solved is analyzed by introducing a new time variable τ with dt = Δ(q, p) dτ. The transformed equations are no longer in Hamiltonian form, and thus do not benefit from integration methods which would be symplectic for Hamiltonian systems. We analyze two methods for integrating the transformed equations which do, however, preserve the structure of the original equations. The first is an extended phase space method, which has been successfully used in previous studies of adaptive time step symplectic integrators. The second, novel, method is based on a non-canonical mixed-variable generating function. Numerical trials for both of these methods show good results, without parametric instabilities or spurious growth or damping. It is then shown how to adapt the time step to an error estimate found by backward error analysis, in order to optimize the time-stepping scheme. Numerical results are obtained using this formulation and compared with other time-stepping schemes for the extended phase space symplectic method.

Numerical methods for engine-airframe integration

International Nuclear Information System (INIS)

Murthy, S.N.B.; Paynter, G.C.

1986-01-01

Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment

Cuba: Multidimensional numerical integration library

Science.gov (United States)

Hahn, Thomas

2016-08-01

The Cuba library offers four independent routines for multidimensional numerical integration: Vegas, Suave, Divonne, and Cuhre. The four algorithms work by very different methods, and can integrate vector integrands and have very similar Fortran, C/C++, and Mathematica interfaces. Their invocation is very similar, making it easy to cross-check by substituting one method by another. For further safeguarding, the output is supplemented by a chi-square probability which quantifies the reliability of the error estimate.

Loop integration results using numerical extrapolation for a non-scalar integral

International Nuclear Information System (INIS)

Doncker, E. de; Shimizu, Y.; Fujimoto, J.; Yuasa, F.; Kaugars, K.; Cucos, L.; Van Voorst, J.

2004-01-01

Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar four-point diagram. Extensions to accommodate loop integration by existing integration packages are also discussed. These include: using previously generated partitions of the domain and roundoff error guards

Exponential integrators in time-dependent density-functional calculations

Science.gov (United States)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

Energy Technology Data Exchange (ETDEWEB)

Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2010-10-15

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)

On the initial condition problem of the time domain PMCHWT surface integral equation

KAUST Repository

Uysal, Ismail Enes

2017-05-13

Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced properly. This problem can be remedied by solving the time integral of the surface integral for auxiliary currents that are defined to be the time derivatives of the equivalent currents. Then the equivalent currents are obtained by numerically differentiating the auxiliary ones. In this work, this approach is applied to the marching on-in-time solution of the time domain Poggio-Miller-Chan-Harrington-Wu-Tsai surface integral equation enforced on dispersive/plasmonic scatterers. Accuracy of the proposed method is demonstrated by a numerical example.

Free and constrained symplectic integrators for numerical general relativity

International Nuclear Information System (INIS)

Richter, Ronny; Lubich, Christian

2008-01-01

We consider symplectic time integrators in numerical general relativity and discuss both free and constrained evolution schemes. For free evolution of ADM-like equations we propose the use of the Stoermer-Verlet method, a standard symplectic integrator which here is explicit in the computationally expensive curvature terms. For the constrained evolution we give a formulation of the evolution equations that enforces the momentum constraints in a holonomically constrained Hamiltonian system and turns the Hamilton constraint function from a weak to a strong invariant of the system. This formulation permits the use of the constraint-preserving symplectic RATTLE integrator, a constrained version of the Stoermer-Verlet method. The behavior of the methods is illustrated on two effectively (1+1)-dimensional versions of Einstein's equations, which allow us to investigate a perturbed Minkowski problem and the Schwarzschild spacetime. We compare symplectic and non-symplectic integrators for free evolution, showing very different numerical behavior for nearly-conserved quantities in the perturbed Minkowski problem. Further we compare free and constrained evolution, demonstrating in our examples that enforcing the momentum constraints can turn an unstable free evolution into a stable constrained evolution. This is demonstrated in the stabilization of a perturbed Minkowski problem with Dirac gauge, and in the suppression of the propagation of boundary instabilities into the interior of the domain in Schwarzschild spacetime

Real-time hybrid simulation using the convolution integral method

International Nuclear Information System (INIS)

Kim, Sung Jig; Christenson, Richard E; Wojtkiewicz, Steven F; Johnson, Erik A

2011-01-01

This paper proposes a real-time hybrid simulation method that will allow complex systems to be tested within the hybrid test framework by employing the convolution integral (CI) method. The proposed CI method is potentially transformative for real-time hybrid simulation. The CI method can allow real-time hybrid simulation to be conducted regardless of the size and complexity of the numerical model and for numerical stability to be ensured in the presence of high frequency responses in the simulation. This paper presents the general theory behind the proposed CI method and provides experimental verification of the proposed method by comparing the CI method to the current integration time-stepping (ITS) method. Real-time hybrid simulation is conducted in the Advanced Hazard Mitigation Laboratory at the University of Connecticut. A seismically excited two-story shear frame building with a magneto-rheological (MR) fluid damper is selected as the test structure to experimentally validate the proposed method. The building structure is numerically modeled and simulated, while the MR damper is physically tested. Real-time hybrid simulation using the proposed CI method is shown to provide accurate results

An integral equation-based numerical solver for Taylor states in toroidal geometries

Science.gov (United States)

O'Neil, Michael; Cerfon, Antoine J.

2018-04-01

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

Efficient Simulation of Compressible, Viscous Fluids using Multi-rate Time Integration

Science.gov (United States)

Mikida, Cory; Kloeckner, Andreas; Bodony, Daniel

2017-11-01

In the numerical simulation of problems of compressible, viscous fluids with single-rate time integrators, the global timestep used is limited to that of the finest mesh point or fastest physical process. This talk discusses the application of multi-rate Adams-Bashforth (MRAB) integrators to an overset mesh framework to solve compressible viscous fluid problems of varying scale with improved efficiency, with emphasis on the strategy of timescale separation and the application of the resulting numerical method to two sample problems: subsonic viscous flow over a cylinder and a viscous jet in crossflow. The results presented indicate the numerical efficacy of MRAB integrators, outline a number of outstanding code challenges, demonstrate the expected reduction in time enabled by MRAB, and emphasize the need for proper load balancing through spatial decomposition in order for parallel runs to achieve the predicted time-saving benefit. This material is based in part upon work supported by the Department of Energy, National Nuclear Security Administration, under Award Number DE-NA0002374.

A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations

KAUST Repository

Liu, Meilin

2011-07-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.

Numerical integration subprogrammes in Fortran II-D

Energy Technology Data Exchange (ETDEWEB)

Fry, C. R.

1966-12-15

This note briefly describes some integration subprogrammes written in FORTRAN II-D for the IBM 1620-II at CARDE. These presented are two Newton-Cotes, Chebyshev polynomial summation, Filon's, Nordsieck's and optimum Runge-Kutta and predictor-corrector methods. A few miscellaneous numerical integration procedures are also mentioned covering statistical functions, oscillating integrands and functions occurring in electrical engineering.

Numerical simulation of a cabin ventilation subsystem in a space station oriented real-time system

Directory of Open Access Journals (Sweden)

Zezheng QIU

2017-12-01

Full Text Available An environment control and life support system (ECLSS is an important system in a space station. The ECLSS is a typical complex system, and the real-time simulation technology can help to accelerate its research process by using distributed hardware in a loop simulation system. An implicit fixed time step numerical integration method is recommended for a real-time simulation system with time-varying parameters. However, its computational efficiency is too low to satisfy the real-time data interaction, especially for the complex ECLSS system running on a PC cluster. The instability problem of an explicit method strongly limits its application in the ECLSS real-time simulation although it has a high computational efficiency. This paper proposes an improved numerical simulation method to overcome the instability problem based on the explicit Euler method. A temperature and humidity control subsystem (THCS is firstly established, and its numerical stability is analyzed by using the eigenvalue estimation theory. Furthermore, an adaptive operator is proposed to avoid the potential instability problem. The stability and accuracy of the proposed method are investigated carefully. Simulation results show that this proposed method can provide a good way for some complex time-variant systems to run their real-time simulation on a PC cluster. Keywords: Numerical integration method, Real-time simulation, Stability, THCS, Time-variant system

Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation

OpenAIRE

GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD

2016-01-01

This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...

A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations

KAUST Repository

Liu, Meilin; Bagci, Hakan

2011-01-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results

Numerical integration of some new unified plasticity-creep formulations

International Nuclear Information System (INIS)

Krieg, R.D.

1977-01-01

The unified formulations seem to lead to very non-linear systems of equations which are very well behaved in some regions and very stiff in other regions where the word 'stiff' is used in the mathematical sense. Simple conventional methods of integrating incremental constitutive equations are observed to be totally inadequate. A method of numerically integrating the equations is presented. Automatic step size determination based on accuracy and stability is a necessary expense. In the region where accuracy is the limiting condition the equations can be integrated directly. A forward Euler predictor with a trapezoidal corrector is used in the paper. In the region where stability is the limiting condition, direct integration methods become inefficient and an implicit integrator which is suited to stiff equations must be used. A backward Euler method is used in the paper. It is implemented with a Picard iteration method in which a Newton method is used to predict inelastic strainrate and speed convergence in a Newton-Raphson manner. This allows an analytic expression for the Jacobian to be used, where a full Newton-Raphson would require a numerical approximation to the Jacobian. The starting procedure for the iteration is an adaptation of time independent plasticity ideas. Because of the inherent capability of the unified plasticity-creep formulations, it is felt that these theories will become accepted in the metallurgical community. Structural analysts will then be required to incorporate these formulations and must be prepared to face the difficult implementation inherent in these models. This paper is an attempt to shed some light on the difficulties and expenses involved

Structural Health Monitoring of Tall Buildings with Numerical Integrator and Convex-Concave Hull Classification

Directory of Open Access Journals (Sweden)

Suresh Thenozhi

2012-01-01

Full Text Available An important objective of health monitoring systems for tall buildings is to diagnose the state of the building and to evaluate its possible damage. In this paper, we use our prototype to evaluate our data-mining approach for the fault monitoring. The offset cancellation and high-pass filtering techniques are combined effectively to solve common problems in numerical integration of acceleration signals in real-time applications. The integration accuracy is improved compared with other numerical integrators. Then we introduce a novel method for support vector machine (SVM classification, called convex-concave hull. We use the Jarvis march method to decide the concave (nonconvex hull for the inseparable points. Finally the vertices of the convex-concave hull are applied for SVM training.

Numerical integration of some new unified plasticity-creep formulations

International Nuclear Information System (INIS)

Krieg, R.D.

1977-01-01

The usual constitutive description of metals at high temperature treats creep as a phenomenon which must be added to time independent phenomena. A new approach is now being advocated by some people, principally metallurgists. They all treat the inelastic strain as a unified quantity, incapable of being separated into time dependent and time independent parts. This paper examines the behavior of the differential formulations reported in the literature together with one proposed by the author. These formulations are capable of representing primary and secondary creep, cyclic hardening to a stable cyclic stress-strain loop, a conventional plasticity behavior, and a Bauchinger effect which may be creep induced and discernable either at fast or slow loading rates. The new unified formulations seem to lead to very non-linear systems of equations which are very well behaved in some regions and very stiff in other regions where the word 'stiff' is used in the mathematical sense. Simple conventional methods of integrating incremental constitutive equations are observed to be totally inadequate. A method of numerically integrating the equations is presented. (Auth.)

Integrating spatial and numerical structure in mathematical patterning

Science.gov (United States)

Ni’mah, K.; Purwanto; Irawan, E. B.; Hidayanto, E.

2018-03-01

This paper reports a study monitoring the integrating spatial and numerical structure in mathematical patterning skills of 30 students grade 7th of junior high school. The purpose of this research is to clarify the processes by which learners construct new knowledge in mathematical patterning. Findings indicate that: (1) students are unable to organize the structure of spatial and numerical, (2) students were only able to organize the spatial structure, but the numerical structure is still incorrect, (3) students were only able to organize numerical structure, but its spatial structure is still incorrect, (4) students were able to organize both of the spatial and numerical structure.

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

KAUST Repository

Lyakhov, Dmitry A.

2017-08-29

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\\\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

KAUST Repository

Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Weber, Andreas G.; Michels, Dominik L.

2017-01-01

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

Case studies in the numerical solution of oscillatory integrals

International Nuclear Information System (INIS)

Adam, G.

1992-06-01

A numerical solution of a number of 53,249 test integrals belonging to nine parametric classes was attempted by two computer codes: EAQWOM (Adam and Nobile, IMA Journ. Numer. Anal. (1991) 11, 271-296) and DO1ANF (Mark 13, 1988) from the NAG library software. For the considered test integrals, EAQWOM was found to be superior to DO1ANF as it concerns robustness, reliability, and friendly user information in case of failure. (author). 9 refs, 3 tabs

An energy-stable time-integrator for phase-field models

KAUST Repository

Vignal, Philippe

2016-12-27

We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

An energy-stable time-integrator for phase-field models

KAUST Repository

Vignal, Philippe; Collier, N.; Dalcin, Lisandro; Brown, D.L.; Calo, V.M.

2016-01-01

We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

Science.gov (United States)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

Physics in Design : Real-time Numerical Simulation Integrated into the CAD Environment

NARCIS (Netherlands)

Zwier, Marijn P.; Wits, Wessel W.

2017-01-01

As today's markets are more susceptible to rapid changes and involve global players, a short time to market is required to keep a competitive edge. Concurrently, products are integrating an increasing number of functions and technologies, thus becoming progressively complex. Therefore, efficient and

Integrating numerical computation into the undergraduate education physics curriculum using spreadsheet excel

Science.gov (United States)

Fauzi, Ahmad

2017-11-01

Numerical computation has many pedagogical advantages: it develops analytical skills and problem-solving skills, helps to learn through visualization, and enhances physics education. Unfortunately, numerical computation is not taught to undergraduate education physics students in Indonesia. Incorporate numerical computation into the undergraduate education physics curriculum presents many challenges. The main challenges are the dense curriculum that makes difficult to put new numerical computation course and most students have no programming experience. In this research, we used case study to review how to integrate numerical computation into undergraduate education physics curriculum. The participants of this research were 54 students of the fourth semester of physics education department. As a result, we concluded that numerical computation could be integrated into undergraduate education physics curriculum using spreadsheet excel combined with another course. The results of this research become complements of the study on how to integrate numerical computation in learning physics using spreadsheet excel.

Integration of numerical analysis tools for automated numerical optimization of a transportation package design

International Nuclear Information System (INIS)

Witkowski, W.R.; Eldred, M.S.; Harding, D.C.

1994-01-01

The use of state-of-the-art numerical analysis tools to determine the optimal design of a radioactive material (RAM) transportation container is investigated. The design of a RAM package's components involves a complex coupling of structural, thermal, and radioactive shielding analyses. The final design must adhere to very strict design constraints. The current technique used by cask designers is uncoupled and involves designing each component separately with respect to its driving constraint. With the use of numerical optimization schemes, the complex couplings can be considered directly, and the performance of the integrated package can be maximized with respect to the analysis conditions. This can lead to more efficient package designs. Thermal and structural accident conditions are analyzed in the shape optimization of a simplified cask design. In this paper, details of the integration of numerical analysis tools, development of a process model, nonsmoothness difficulties with the optimization of the cask, and preliminary results are discussed

An integrated numerical protection system (SPIN)

International Nuclear Information System (INIS)

Savornin, J.L.; Bouchet, J.M.; Furet, J.L.; Jover, P.; Sala, A.

1978-01-01

Developments in technology have now made it possible to perform more sophisticated protection functions which follow more closely the physical phenomena to be monitored. For this reason the Commissariat a l'energie atomique, Merlin-Gerin, Cerci and Framatome have embarked on the joint development of an Integrated Numerical Protection System (SPIN) which will fulfil this objective and will improve the safety and availability of power stations. The system described involves the use of programmed numerical techniques and a structure based on multiprocessors. The architecture has a redundancy of four. Throughout the development of the project the validity of the studies was confirmed by experiments. A first numerical model of a protection function was tested in the laboratory and is now in operation in a power station. A set of models was then introduced for checking the main components of the equipment finally chosen prior to building and testing a prototype. (author)

A numerical integration approach suitable for simulating PWR dynamics using a microcomputer system

International Nuclear Information System (INIS)

Zhiwei, L.; Kerlin, T.W.

1983-01-01

It is attractive to use microcomputer systems to simulate nuclear power plant dynamics for the purpose of teaching and/or control system design. An analysis and a comparison of feasibility of existing numerical integration methods have been made. The criteria for choosing the integration step using various numerical integration methods including the matrix exponential method are derived. In order to speed up the simulation, an approach is presented using the Newton recursion calculus which can avoid convergence limitations in choosing the integration step size. The accuracy consideration will dominate the integration step limited. The advantages of this method have been demonstrated through a case study using CBM model 8032 microcomputer to simulate a reduced order linear PWR model under various perturbations. It has been proven theoretically and practically that the Runge-Kutta method and Adams-Moulton method are not feasible. The matrix exponential method is good at accuracy and fairly good at speed. The Newton recursion method can save 3/4 to 4/5 time compared to the matrix exponential method with reasonable accuracy. Vertical Barhis method can be expanded to deal with nonlinear nuclear power plant models and higher order models as well

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

Science.gov (United States)

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved

On the internal resonant modes in marching-on-in-time solution of the time domain electric field integral equation

KAUST Repository

Shi, Yifei; Bagci, Hakan; Lu, Mingyu

2013-01-01

Internal resonant modes are always observed in the marching-on-in-time (MOT) solution of the time domain electric field integral equation (EFIE), although 'relaxed initial conditions,' which are enforced at the beginning of time marching, should in theory prevent these spurious modes from appearing. It has been conjectured that, numerical errors built up during time marching establish the necessary initial conditions and induce the internal resonant modes. However, this conjecture has never been proved by systematic numerical experiments. Our numerical results in this communication demonstrate that, the internal resonant modes' amplitudes are indeed dictated by the numerical errors. Additionally, it is shown that in a few cases, the internal resonant modes can be made 'invisible' by significantly suppressing the numerical errors. These tests prove the conjecture that the internal resonant modes are induced by numerical errors when the time domain EFIE is solved by the MOT method. © 2013 IEEE.

On the internal resonant modes in marching-on-in-time solution of the time domain electric field integral equation

KAUST Repository

Shi, Yifei

2013-08-01

Internal resonant modes are always observed in the marching-on-in-time (MOT) solution of the time domain electric field integral equation (EFIE), although \\'relaxed initial conditions,\\' which are enforced at the beginning of time marching, should in theory prevent these spurious modes from appearing. It has been conjectured that, numerical errors built up during time marching establish the necessary initial conditions and induce the internal resonant modes. However, this conjecture has never been proved by systematic numerical experiments. Our numerical results in this communication demonstrate that, the internal resonant modes\\' amplitudes are indeed dictated by the numerical errors. Additionally, it is shown that in a few cases, the internal resonant modes can be made \\'invisible\\' by significantly suppressing the numerical errors. These tests prove the conjecture that the internal resonant modes are induced by numerical errors when the time domain EFIE is solved by the MOT method. © 2013 IEEE.

Explicit solution of Calderon preconditioned time domain integral equations

KAUST Repository

Ulku, Huseyin Arda

2013-07-01

An explicit marching on-in-time (MOT) scheme for solving Calderon-preconditioned time domain integral equations is proposed. The scheme uses Rao-Wilton-Glisson and Buffa-Christiansen functions to discretize the domain and range of the integral operators and a PE(CE)m type linear multistep to march on in time. Unlike its implicit counterpart, the proposed explicit solver requires the solution of an MOT system with a Gram matrix that is sparse and well-conditioned independent of the time step size. Numerical results demonstrate that the explicit solver maintains its accuracy and stability even when the time step size is chosen as large as that typically used by an implicit solver. © 2013 IEEE.

Analysis of thermal-plastic response of shells of revolution by numerical integration

International Nuclear Information System (INIS)

Leonard, J.W.

1975-01-01

An economic technique for the numerical analysis of the elasto-plastic behaviour of shells of revolution would be of considerable value in the nuclear reactor industry. A numerical method based on the numerical integration of the governing shell equations has been shown, for elastic cases, to be more efficient than the finite element method when applied to shells of revolution. In the numerical integration method, the governing differential equations of motion are converted into a set of initial-value problems. Each initial-value problem is integrated numerically between meridional boundary points and recombined so as to satisfy boundary conditions. For large-deflection elasto-plastic behaviour, the equations are nonlinear and, hence, are recombined in an iterative manner using the Newton-Raphson procedure. Suppression techniques are incorporated in order to eliminate extraneous solutions within the numerical integration procedure. The Reissner-Meissner shell theory for shells of revolution is adopted to account for large deflection and higher-order rotation effects. The computer modelling of the equations is quite general in that specific shell segment geometries, e.g. cylindrical, spherical, toroidal, conical segments, and any combinations thereof can be handled easily. (Auth.)

Integrated numerical platforms for environmental dose assessments of large tritium inventory facilities

International Nuclear Information System (INIS)

Castro, P.; Ardao, J.; Velarde, M.; Sedano, L.; Xiberta, J.

2013-01-01

Related with a prospected new scenario of large inventory tritium facilities [KATRIN at TLK, CANDUs, ITER, EAST, other coming] the prescribed dosimetric limits by ICRP-60 for tritium committed-doses are under discussion requiring, in parallel, to surmount the highly conservative assessments by increasing the refinement of dosimetric-assessments in many aspects. Precise Lagrangian-computations of dosimetric cloud-evolution after standardized (normal/incidental/SBO) tritium cloud emissions are today numerically open to the perfect match of real-time meteorological-data, and patterns data at diverse scales for prompt/early and chronic tritium dose assessments. The trends towards integrated-numerical-platforms for environmental-dose assessments of large tritium inventory facilities under development.

High-accuracy numerical integration of charged particle motion – with application to ponderomotive force

International Nuclear Information System (INIS)

Furukawa, Masaru; Ohkawa, Yushiro; Matsuyama, Akinobu

2016-01-01

A high-accuracy numerical integration algorithm for a charged particle motion is developed. The algorithm is based on the Hamiltonian mechanics and the operator decomposition. The algorithm is made to be time-reversal symmetric, and its order of accuracy can be increased to any order by using a recurrence formula. One of the advantages is that it is an explicit method. An effective way to decompose the time evolution operator is examined; the Poisson tensor is decomposed and non-canonical variables are adopted. The algorithm is extended to a time dependent fields' case by introducing the extended phase space. Numerical tests showing the performance of the algorithm are presented. One is the pure cyclotron motion for a long time period, and the other is a charged particle motion in a rapidly oscillating field. (author)

Numerical Algorithms for Acoustic Integrals - The Devil is in the Details

Science.gov (United States)

Brentner, Kenneth S.

1996-01-01

The accurate prediction of the aeroacoustic field generated by aerospace vehicles or nonaerospace machinery is necessary for designers to control and reduce source noise. Powerful computational aeroacoustic methods, based on various acoustic analogies (primarily the Lighthill acoustic analogy) and Kirchhoff methods, have been developed for prediction of noise from complicated sources, such as rotating blades. Both methods ultimately predict the noise through a numerical evaluation of an integral formulation. In this paper, we consider three generic acoustic formulations and several numerical algorithms that have been used to compute the solutions to these formulations. Algorithms for retarded-time formulations are the most efficient and robust, but they are difficult to implement for supersonic-source motion. Collapsing-sphere and emission-surface formulations are good alternatives when supersonic-source motion is present, but the numerical implementations of these formulations are more computationally demanding. New algorithms - which utilize solution adaptation to provide a specified error level - are needed.

Numerical computation of molecular integrals via optimized (vectorized) FORTRAN code

International Nuclear Information System (INIS)

Scott, T.C.; Grant, I.P.; Saunders, V.R.

1997-01-01

The calculation of molecular properties based on quantum mechanics is an area of fundamental research whose horizons have always been determined by the power of state-of-the-art computers. A computational bottleneck is the numerical calculation of the required molecular integrals to sufficient precision. Herein, we present a method for the rapid numerical evaluation of molecular integrals using optimized FORTRAN code generated by Maple. The method is based on the exploitation of common intermediates and the optimization can be adjusted to both serial and vectorized computations. (orig.)

Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

Science.gov (United States)

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

KAUST Repository

Wang, Yi

2016-07-21

Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.

Analysis of thermal-plastic response of shells of revolution by numerical integration

International Nuclear Information System (INIS)

Leonard, J.W.

1975-01-01

A numerical method based instead on the numerical integration of the governing shell equations has been shown, for elastic cases, to be more efficient than the finite element method when applied to shells of revolution. In the numerical integration method, the governing differential equations of motions are converted into a set of initial-value problems. Each initial-value problem is integrated numerically between meridional boundary points and recombined so as to satisfy boundary conditions. For large-deflection elasto-plastic behavior, the equations are nonlinear and, hence, are recombined in an iterative manner using the Newton-Raphson procedure. Suppression techniques are incorporated in order to eliminate extraneous solutions within the numerical integration procedure. The Reissner-Meissner shell theory for shells of revolution is adopted to account for large deflection and higher-order rotation effects. The computer modelling of the equations is quite general in that specific shell segment geometries, e.g. cylindrical, spherical, toroidal, conical segments, and any combinations thereof can be handled easily. The elasto-plastic constitutive relations adopted are in accordance with currently recommended constitutive equations for inelastic design analysis of FFTF Components. The Von Mises yield criteria and associated flow rule is used and the kinematic hardening law is followed. Examples are considered in which stainless steels common to LMFBR application are used

Mixing-to-eruption timescales: an integrated model combining numerical simulations and high-temperature experiments with natural melts

Science.gov (United States)

Montagna, Chiara; Perugini, Diego; De Campos, Christina; Longo, Antonella; Dingwell, Donald Bruce; Papale, Paolo

2015-04-01

Arrival of magma from depth into shallow reservoirs and associated mixing processes have been documented as possible triggers of explosive eruptions. Quantifying the timing from beginning of mixing to eruption is of fundamental importance in volcanology in order to put constraints about the possible onset of a new eruption. Here we integrate numerical simulations and high-temperature experiment performed with natural melts with the aim to attempt identifying the mixing-to-eruption timescales. We performed two-dimensional numerical simulations of the arrival of gas-rich magmas into shallow reservoirs. We solve the fluid dynamics for the two interacting magmas evaluating the space-time evolution of the physical properties of the mixture. Convection and mingling develop quickly into the chamber and feeding conduit/dyke. Over time scales of hours, the magmas in the reservoir appear to have mingled throughout, and convective patterns become harder to identify. High-temperature magma mixing experiments have been performed using a centrifuge and using basaltic and phonolitic melts from Campi Flegrei (Italy) as initial end-members. Concentration Variance Decay (CVD), an inevitable consequence of magma mixing, is exponential with time. The rate of CVD is a powerful new geochronometer for the time from mixing to eruption/quenching. The mingling-to-eruption time of three explosive volcanic eruptions from Campi Flegrei (Italy) yield durations on the order of tens of minutes. These results are in perfect agreement with the numerical simulations that suggest a maximum mixing time of a few hours to obtain a hybrid mixture. We show that integration of numerical simulation and high-temperature experiments can provide unprecedented results about mixing processes in volcanic systems. The combined application of numerical simulations and CVD geochronometer to the eruptive products of active volcanoes could be decisive for the preparation of hazard mitigation during volcanic unrest.

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

Energy Technology Data Exchange (ETDEWEB)

Liu, Fang, E-mail: fliu@lsec.cc.ac.cn [School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Lin, Lin, E-mail: linlin@math.berkeley.edu [Department of Mathematics, University of California, Berkeley, CA 94720 (United States); Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Vigil-Fowler, Derek, E-mail: vigil@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Lischner, Johannes, E-mail: jlischner597@gmail.com [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kemper, Alexander F., E-mail: afkemper@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sharifzadeh, Sahar, E-mail: ssharifz@bu.edu [Department of Electrical and Computer Engineering and Division of Materials Science and Engineering, Boston University, Boston, MA 02215 (United States); Jornada, Felipe H. da, E-mail: jornada@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Deslippe, Jack, E-mail: jdeslippe@lbl.gov [NERSC, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Yang, Chao, E-mail: cyang@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); and others

2015-04-01

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

Implementation of a revised numerical integration technique into QAD

International Nuclear Information System (INIS)

De Gangi, N.L.

1983-01-01

A technique for numerical integration through a uniform volume source is developed. It is applied to gamma radiation transport shielding problems. The method is based on performing a numerical angular and ray point kernel integration and is incorporated into the QAD-CG computer code (i.e. QAD-UE). Several test problems are analyzed with this technique. Convergence properties of the method are analyzed. Gamma dose rates from a large tank and post LOCA dose rates inside a containment building are evaluated. Results are consistent with data from other methods. The new technique provides several advantages. User setup requirements for large volume source problems are reduced from standard point kernel requirements. Calculational efficiencies are improved. An order of magnitude improvement is seen with a test problem

Evaluation of time integration methods for transient response analysis of nonlinear structures

International Nuclear Information System (INIS)

Park, K.C.

1975-01-01

Recent developments in the evaluation of direct time integration methods for the transient response analysis of nonlinear structures are presented. These developments, which are based on local stability considerations of an integrator, show that the interaction between temporal step size and nonlinearities of structural systems has a pronounced effect on both accuracy and stability of a given time integration method. The resulting evaluation technique is applied to a model nonlinear problem, in order to: 1) demonstrate that it eliminates the present costly process of evaluating time integrator for nonlinear structural systems via extensive numerical experiments; 2) identify the desirable characteristics of time integration methods for nonlinear structural problems; 3) develop improved stiffly-stable methods for application to nonlinear structures. Extension of the methodology for examination of the interaction between a time integrator and the approximate treatment of nonlinearities (such as due to pseudo-force or incremental solution procedures) is also discussed. (Auth.)

Canonical algorithms for numerical integration of charged particle motion equations

Science.gov (United States)

Efimov, I. N.; Morozov, E. A.; Morozova, A. R.

2017-02-01

A technique for numerically integrating the equation of charged particle motion in a magnetic field is considered. It is based on the canonical transformations of the phase space in Hamiltonian mechanics. The canonical transformations make the integration process stable against counting error accumulation. The integration algorithms contain a minimum possible amount of arithmetics and can be used to design accelerators and devices of electron and ion optics.

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

How to integrate divergent integrals: a pure numerical approach to complex loop calculations

International Nuclear Information System (INIS)

Caravaglios, F.

2000-01-01

Loop calculations involve the evaluation of divergent integrals. Usually [G. 't Hooft, M. Veltman, Nucl. Phys. B 44 (1972) 189] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers the Laurent expansion in powers of ε=n-4. In this paper we discuss a method to extract directly all coefficients of this expansion by means of concrete and well defined integrals in a five-dimensional space. We by-pass the formal and symbolic procedure of analytic continuation; instead we can numerically compute the integrals to extract directly both the coefficient of the pole 1/ε and the finite part

Some Comments on the Behavior of the RELAP5 Numerical Scheme at Very Small Time Steps

International Nuclear Information System (INIS)

Tiselj, Iztok; Cerne, Gregor

2000-01-01

The behavior of the RELAP5 code at very short time steps is described, i.e., δt [approximately equal to] 0.01 δx/c. First, the property of the RELAP5 code to trace acoustic waves with 'almost' second-order accuracy is demonstrated. Quasi-second-order accuracy is usually achieved for acoustic waves at very short time steps but can never be achieved for the propagation of nonacoustic temperature and void fraction waves. While this feature may be beneficial for the simulations of fast transients describing pressure waves, it also has an adverse effect: The lack of numerical diffusion at very short time steps can cause typical second-order numerical oscillations near steep pressure jumps. This behavior explains why an automatic halving of the time step, which is used in RELAP5 when numerical difficulties are encountered, in some cases leads to the failure of the simulation.Second, the integration of the stiff interphase exchange terms in RELAP5 is studied. For transients with flashing and/or rapid condensation as the main phenomena, results strongly depend on the time step used. Poor accuracy is achieved with 'normal' time steps (δt [approximately equal to] δx/v) because of the very short characteristic timescale of the interphase mass and heat transfer sources. In such cases significantly different results are predicted with very short time steps because of the more accurate integration of the stiff interphase exchange terms

Numerical evaluation of integrals containing a spherical Bessel function by product integration

International Nuclear Information System (INIS)

Lehman, D.R.; Parke, W.C.; Maximon, L.C.

1981-01-01

A method is developed for numerical evaluation of integrals with k-integration range from 0 to infinity that contain a spherical Bessel function j/sub l/(kr) explicitly. The required quadrature weights are easily calculated and the rate of convergence is rapid: only a relatively small number of quadrature points is needed: for an accurate evaluation even when r is large. The quadrature rule is obtained by the method of product integration. With the abscissas chosen to be those of Clenshaw--Curtis and the Chebyshev polynomials as the interpolating polynomials, quadrature weights are obtained that depend on the spherical Bessel function. An inhomogenous recurrence relation is derived from which the weights can be calculated without accumulation of roundoff error. The procedure is summarized as an easily implementable algorithm. Questions of convergence are discussed and the rate of convergence demonstrated for several test integrals. Alternative procedures are given for generating the integration weights and an error analysis of the method is presented

Parareal algorithms with local time-integrators for time fractional differential equations

Science.gov (United States)

Wu, Shu-Lin; Zhou, Tao

2018-04-01

It is challenge work to design parareal algorithms for time-fractional differential equations due to the historical effect of the fractional operator. A direct extension of the classical parareal method to such equations will lead to unbalance computational time in each process. In this work, we present an efficient parareal iteration scheme to overcome this issue, by adopting two recently developed local time-integrators for time fractional operators. In both approaches, one introduces auxiliary variables to localized the fractional operator. To this end, we propose a new strategy to perform the coarse grid correction so that the auxiliary variables and the solution variable are corrected separately in a mixed pattern. It is shown that the proposed parareal algorithm admits robust rate of convergence. Numerical examples are presented to support our conclusions.

3-D electromagnetic modeling for very early time sounding of shallow targets using integral equations

International Nuclear Information System (INIS)

Xiong, Z.; Tripp, A.C.

1994-01-01

This paper presents an integral equation algorithm for 3D EM modeling at high frequencies for applications in engineering an environmental studies. The integral equation method remains the same for low and high frequencies, but the dominant roles of the displacements currents complicate both numerical treatments and interpretations. With singularity extraction technique they successively extended the application of the Hankel filtering technique to the computation of Hankel integrals occurring in high frequency EM modeling. Time domain results are calculated from frequency domain results via Fourier transforms. While frequency domain data are not obvious for interpretations, time domain data show wave-like pictures that resemble seismograms. Both 1D and 3D numerical results show clearly the layer interfaces

Integral equation approach to time-dependent kinematic dynamos in finite domains

International Nuclear Information System (INIS)

Xu Mingtian; Stefani, Frank; Gerbeth, Gunter

2004-01-01

The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α 2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples - the α 2 dynamo model with radially varying α and the Bullard-Gellman model - illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α 2 dynamo in rectangular domains

Long Pulse Integrator of Variable Integral Time Constant

International Nuclear Information System (INIS)

Wang Yong; Ji Zhenshan; Du Xiaoying; Wu Yichun; Li Shi; Luo Jiarong

2010-01-01

A kind of new long pulse integrator was designed based on the method of variable integral time constant and deducting integral drift by drift slope. The integral time constant can be changed by choosing different integral resistors, in order to improve the signal-to-noise ratio, and avoid output saturation; the slope of integral drift of a certain period of time can be calculated by digital signal processing, which can be used to deduct the drift of original integral signal in real time to reduce the integral drift. The tests show that this kind of long pulse integrator is good at reducing integral drift, which also can eliminate the effects of changing integral time constant. According to experiments, the integral time constant can be changed by remote control and manual adjustment of integral drift is avoided, which can improve the experiment efficiency greatly and can be used for electromagnetic measurement in Tokamak experiment. (authors)

Monograph - The Numerical Integration of Ordinary Differential Equations.

Science.gov (United States)

Hull, T. E.

The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…

Preserving Simplecticity in the Numerical Integration of Linear Beam Optics

Energy Technology Data Exchange (ETDEWEB)

Allen, Christopher K. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2017-07-01

Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms of a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.

Numerical simulation of pseudoelastic shape memory alloys using the large time increment method

Science.gov (United States)

Gu, Xiaojun; Zhang, Weihong; Zaki, Wael; Moumni, Ziad

2017-04-01

The paper presents a numerical implementation of the large time increment (LATIN) method for the simulation of shape memory alloys (SMAs) in the pseudoelastic range. The method was initially proposed as an alternative to the conventional incremental approach for the integration of nonlinear constitutive models. It is adapted here for the simulation of pseudoelastic SMA behavior using the Zaki-Moumni model and is shown to be especially useful in situations where the phase transformation process presents little or lack of hardening. In these situations, a slight stress variation in a load increment can result in large variations of strain and local state variables, which may lead to difficulties in numerical convergence. In contrast to the conventional incremental method, the LATIN method solve the global equilibrium and local consistency conditions sequentially for the entire loading path. The achieved solution must satisfy the conditions of static and kinematic admissibility and consistency simultaneously after several iterations. 3D numerical implementation is accomplished using an implicit algorithm and is then used for finite element simulation using the software Abaqus. Computational tests demonstrate the ability of this approach to simulate SMAs presenting flat phase transformation plateaus and subjected to complex loading cases, such as the quasi-static behavior of a stent structure. Some numerical results are contrasted to those obtained using step-by-step incremental integration.

Numerical evaluation of two-center integrals over Slater type orbitals

Energy Technology Data Exchange (ETDEWEB)

Kurt, S. A., E-mail: slaykurt@gmail.com [Department of Physics, Natural Sciences Institute, Ondokuz Mayıs University, 55139, Samsun (Turkey); Yükçü, N., E-mail: nyukcu@gmail.com [Department of Energy Systems Engineering, Faculty of Technology, Adıyaman University, 02040, Adıyaman (Turkey)

2016-03-25

Slater Type Orbitals (STOs) which one of the types of exponential type orbitals (ETOs) are used usually as basis functions in the multicenter molecular integrals to better understand physical and chemical properties of matter. In this work, we develop algorithms for two-center overlap and two-center two-electron hybrid and Coulomb integrals which are calculated with help of translation method for STOs and some auxiliary functions by V. Magnasco’s group. We use Mathematica programming language to produce algorithms for these calculations. Numerical results for some quantum numbers are presented in the tables. Consequently, we compare our obtained numerical results with the other known literature results and other details of evaluation method are discussed.

Numerical evaluation of two-center integrals over Slater type orbitals

International Nuclear Information System (INIS)

Kurt, S. A.; Yükçü, N.

2016-01-01

Slater Type Orbitals (STOs) which one of the types of exponential type orbitals (ETOs) are used usually as basis functions in the multicenter molecular integrals to better understand physical and chemical properties of matter. In this work, we develop algorithms for two-center overlap and two-center two-electron hybrid and Coulomb integrals which are calculated with help of translation method for STOs and some auxiliary functions by V. Magnasco’s group. We use Mathematica programming language to produce algorithms for these calculations. Numerical results for some quantum numbers are presented in the tables. Consequently, we compare our obtained numerical results with the other known literature results and other details of evaluation method are discussed.

Integration of the time-dependent heat equation in the fuel rod performance program IAMBUS

International Nuclear Information System (INIS)

West, G.

1982-01-01

An iterative numerical method for integration of the time-dependent heat equation is described. No presuppositions are made for the dependency of the thermal conductivity and heat capacity on space, time and temperature. (orig.) [de

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.

Simulating variable-density flows with time-consistent integration of Navier-Stokes equations

Science.gov (United States)

Lu, Xiaoyi; Pantano, Carlos

2017-11-01

In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.

Numerical functional integration method for studying the properties of the physical vacuum

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.

1998-01-01

The new approach to investigate the physical vacuum in quantum theories including its nonperturbative topological structure is discussed. This approach is based on the representation of the matrix element of the evolution operator in Euclidean metrics in a form of the functional integral with a certain measure in the corresponding space and on the use of approximation formulas which we constructed for this kind of integral. No preliminary discretization of space and time is required, as well as no simplifying assumptions like semiclassical approximation, collective excitations, introduction of ''short-time'' propagators, etc. are necessary in this approach. The method allows to use the more preferable deterministic algorithms instead of the traditional stochastic technique. It has been proven that our approach has important advantages over the other known methods, including the higher efficiency of computations. Examples of application of the method to the numerical study of some potential nuclear models and to the computation of the topological susceptibility and the θ-vacua energy are presented. (author)

Methods for enhancing numerical integration

International Nuclear Information System (INIS)

Doncker, Elise de

2003-01-01

We give a survey of common strategies for numerical integration (adaptive, Monte-Carlo, Quasi-Monte Carlo), and attempt to delineate their realm of applicability. The inherent accuracy and error bounds for basic integration methods are given via such measures as the degree of precision of cubature rules, the index of a family of lattice rules, and the discrepancy of uniformly distributed point sets. Strategies incorporating these basic methods often use paradigms to reduce the error by, e.g., increasing the number of points in the domain or decreasing the mesh size, locally or uniformly. For these processes the order of convergence of the strategy is determined by the asymptotic behavior of the error, and may be too slow in practice for the type of problem at hand. For certain problem classes we may be able to improve the effectiveness of the method or strategy by such techniques as transformations, absorbing a difficult part of the integrand into a weight function, suitable partitioning of the domain, transformations and extrapolation or convergence acceleration. Situations warranting the use of these techniques (possibly in an 'automated' way) are described and illustrated by sample applications

Producing complex spoken numerals for time and space

NARCIS (Netherlands)

Meeuwissen, M.H.W.

2004-01-01

This thesis addressed the spoken production of complex numerals for time and space. The production of complex numerical expressions like those involved in telling time (e.g., 'quarter to four') or producing house numbers (e.g., 'two hundred forty-five') has been almost completely ignored. Yet, adult

Time-independent integral equation for Maxwell's system. Application of radar cross section computation

International Nuclear Information System (INIS)

Pujols, Agnes

1991-01-01

We prove that the scattering operator for the wave equation in the exterior of an non-homogeneous obstacle exists. Its distribution kernel is represented by a time-dependent boundary integral equation. A space-time integral variational formulation is developed for determining the current induced by the scattering of an electromagnetic wave by an homogeneous object. The discrete approximation of the variational problem using a finite element method in both space and time leads to stable convergent schemes, giving a numerical code for perfectly conducting cylinders. (author) [fr

Advanced Numerical Integration Techniques for HighFidelity SDE Spacecraft Simulation

Data.gov (United States)

National Aeronautics and Space Administration — Classic numerical integration techniques, such as the ones at the heart of several NASA GSFC analysis tools, are known to work well for deterministic differential...

Trajectory errors of different numerical integration schemes diagnosed with the MPTRAC advection module driven by ECMWF operational analyses

Science.gov (United States)

Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars

2018-02-01

The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration

Microwave Breast Imaging System Prototype with Integrated Numerical Characterization

Directory of Open Access Journals (Sweden)

Mark Haynes

2012-01-01

Full Text Available The increasing number of experimental microwave breast imaging systems and the need to properly model them have motivated our development of an integrated numerical characterization technique. We use Ansoft HFSS and a formalism we developed previously to numerically characterize an S-parameter- based breast imaging system and link it to an inverse scattering algorithm. We show successful reconstructions of simple test objects using synthetic and experimental data. We demonstrate the sensitivity of image reconstructions to knowledge of the background dielectric properties and show the limits of the current model.

Note on the numerical calculation of the Fermi-Dirac integrals

International Nuclear Information System (INIS)

Graef, H.; Pabst, M.

1977-11-01

Expansions of the Fermi-Dirac integrals Fsub(α)(x) are developed, suitable for numerical computation. Only integrals of integer- or half-integer order are treated and expansion coefficients are tabulated for F 1 (x),....,F 9 (x); Fsub(-1/2)(x),...,Fsub(7/2)(x). Maximal relative errors vary with the function and interval considered, but are less than 3 x 10 -6 . (orig.) [de

Experimental research and numerical simulation on flow resistance of integrated valve

International Nuclear Information System (INIS)

Cai Wei; Bo Hanliang; Qin Benke

2008-01-01

The flow resistance of the integrated valve is one of the key parameters for the design of the control rod hydraulic drive system (CRHDS). Experimental research on the improved new integrated valve was performed, and the key data such as pressure difference, volume flow, resistance coefficient and flow coefficient of each flow channel were obtained. With the computational fluid dynamics software CFX, numerical simulation was executed to analyze the effect of Re on the flow resistance. On the basis of experimental and numerical results, fitting empirical formulas of resistance coefficient were obtained, which provide experimental and theoretical foundations for CRHDS's optimized design and theoretical analysis. (authors)

Numerical study of time domain analogy applied to noise prediction from rotating blades

Science.gov (United States)

Fedala, D.; Kouidri, S.; Rey, R.

2009-04-01

Aeroacoustic formulations in time domain are frequently used to model the aerodynamic sound of airfoils, the time data being more accessible. The formulation 1A developed by Farassat, an integral solution of the Ffowcs Williams and Hawkings equation, holds great interest because of its ability to handle surfaces in arbitrary motion. The aim of this work is to study the numerical sensitivity of this model to specified parameters used in the calculation. The numerical algorithms, spatial and time discretizations, and approximations used for far-field acoustic simulation are presented. An approach of quantifying of the numerical errors resulting from implementation of formulation 1A is carried out based on Isom's and Tam's test cases. A helicopter blade airfoil, as defined by Farassat to investigate Isom's case, is used in this work. According to Isom, the acoustic response of a dipole source with a constant aerodynamic load, ρ0c02, is equal to the thickness noise contribution. Discrepancies are observed when the two contributions are computed numerically. In this work, variations of these errors, which depend on the temporal resolution, Mach number, source-observer distance, and interpolation algorithm type, are investigated. The results show that the spline interpolating algorithm gives the minimum error. The analysis is then extended to Tam's test case. Tam's test case has the advantage of providing an analytical solution for the first harmonic of the noise produced by a specific force distribution.

Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

Science.gov (United States)

Nixon, Douglas D.

2009-01-01

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

Numerical approaches to time evolution of complex quantum systems

International Nuclear Information System (INIS)

Fehske, Holger; Schleede, Jens; Schubert, Gerald; Wellein, Gerhard; Filinov, Vladimir S.; Bishop, Alan R.

2009-01-01

We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev polynomials. The Chebyshev approach benefits from two advantages over the standard time-integration Crank-Nicholson scheme: speedup and efficiency. Potential competitors are semiclassical methods such as the Wigner-Moyal or quantum tomographic approaches. We outline the basic concepts of these techniques and benchmark their performance against the Chebyshev approach by monitoring the time evolution of a Gaussian wave packet in restricted one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes and the motion in anharmonic potentials. Finally we apply the prominent Chebyshev technique to two highly non-trivial problems of current interest: (i) the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the spatiotemporal evolution of polaron states in finite quantum systems. Here, depending on the disorder/electron-phonon coupling strength and the device dimensions, we observe transmission or localisation of the matter wave.

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

Science.gov (United States)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

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

Numerical Integration of the Transport Equation For Infinite Homogeneous Media

Energy Technology Data Exchange (ETDEWEB)

Haakansson, Rune

1962-01-15

The transport equation for neutrons in infinite homogeneous media is solved by direct numerical integration. Accounts are taken to the anisotropy and the inelastic scattering. The integration has been performed by means of the trapezoidal rule and the length of the energy intervals are constant in lethargy scale. The machine used is a Ferranti Mercury computer. Results are given for water, heavy water, aluminium water mixture and iron-aluminium-water mixture.

Real time wave forecasting using wind time history and numerical model

Science.gov (United States)

Jain, Pooja; Deo, M. C.; Latha, G.; Rajendran, V.

Operational activities in the ocean like planning for structural repairs or fishing expeditions require real time prediction of waves over typical time duration of say a few hours. Such predictions can be made by using a numerical model or a time series model employing continuously recorded waves. This paper presents another option to do so and it is based on a different time series approach in which the input is in the form of preceding wind speed and wind direction observations. This would be useful for those stations where the costly wave buoys are not deployed and instead only meteorological buoys measuring wind are moored. The technique employs alternative artificial intelligence approaches of an artificial neural network (ANN), genetic programming (GP) and model tree (MT) to carry out the time series modeling of wind to obtain waves. Wind observations at four offshore sites along the east coast of India were used. For calibration purpose the wave data was generated using a numerical model. The predicted waves obtained using the proposed time series models when compared with the numerically generated waves showed good resemblance in terms of the selected error criteria. Large differences across the chosen techniques of ANN, GP, MT were not noticed. Wave hindcasting at the same time step and the predictions over shorter lead times were better than the predictions over longer lead times. The proposed method is a cost effective and convenient option when a site-specific information is desired.

Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation

Directory of Open Access Journals (Sweden)

Berenguer MI

2009-01-01

Full Text Available The authors present a method of numerical approximation of the fixed point of an operator, specifically the integral one associated with a nonlinear Fredholm integral equation, that uses strongly the properties of a classical Schauder basis in the Banach space .

A single-vendor and a single-buyer integrated inventory model with ordering cost reduction dependent on lead time

Science.gov (United States)

Vijayashree, M.; Uthayakumar, R.

2017-09-01

Lead time is one of the major limits that affect planning at every stage of the supply chain system. In this paper, we study a continuous review inventory model. This paper investigates the ordering cost reductions are dependent on lead time. This study addressed two-echelon supply chain problem consisting of a single vendor and a single buyer. The main contribution of this study is that the integrated total cost of the single vendor and the single buyer integrated system is analyzed by adopting two different (linear and logarithmic) types ordering cost reductions act dependent on lead time. In both cases, we develop effective solution procedures for finding the optimal solution and then illustrative numerical examples are given to illustrate the results. The solution procedure is to determine the optimal solutions of order quantity, ordering cost, lead time and the number of deliveries from the single vendor and the single buyer in one production run, so that the integrated total cost incurred has the minimum value. Ordering cost reduction is the main aspect of the proposed model. A numerical example is given to validate the model. Numerical example solved by using Matlab software. The mathematical model is solved analytically by minimizing the integrated total cost. Furthermore, the sensitivity analysis is included and the numerical examples are given to illustrate the results. The results obtained in this paper are illustrated with the help of numerical examples. The sensitivity of the proposed model has been checked with respect to the various major parameters of the system. Results reveal that the proposed integrated inventory model is more applicable for the supply chain manufacturing system. For each case, an algorithm procedure of finding the optimal solution is developed. Finally, the graphical representation is presented to illustrate the proposed model and also include the computer flowchart in each model.

Characteristic times in the English Channel from numerical modelling: supporting decision-making

Energy Technology Data Exchange (ETDEWEB)

Perianez, R [Departamento de Fisica Aplicada 1, Universidad de Sevilla, EUITA, Carretera Utrera km 1, 41013 Sevilla (Spain); Miro, C [Departamento de Fisica Aplicada, Facultad de Veterinaria, Universidad de Extremadura, Avenida de la Universidad s/n, 10071 Caceres (Spain)], E-mail: rperianez@us.es, E-mail: cmiro@unex.es

2009-06-15

A numerical model that simulates the dispersion of radionuclides in the English Channel has been applied to study the dispersion of conservative and non-conservative radionuclides released from the La Hague nuclear fuel reprocessing plant. The model is based upon previous work and now is able to simulate dispersion over long timescales (decades), explicitly including transport by instantaneous tidal currents and variable wind conditions. Wind conditions are obtained from meteorological statistics using a stochastic method. Outputs from the model are treated using time-series analysis techniques. These techniques allow the determination of characteristic times of the system, transport velocities and dispersion factors. This information may be very useful to support the decision-making process after an emergency situation. Thus, we are proposing that time-series analysis can be integrated with numerical modelling for helping decision-making in response to an accident. The model is first validated through its application to actual releases of {sup 99}Tc and {sup 125}Sb, comparing measured and computed concentrations, and characteristic times for three radionuclides are given next: a perfectly conservative one, a very reactive one ({sup 239,240}Pu) and {sup 137}Cs, which has an intermediate behaviour. Characteristic transport velocities and dispersion factors have been calculated as well. Model results are supported by experimental evidence.

A delta-rule model of numerical and non-numerical order processing.

Science.gov (United States)

Verguts, Tom; Van Opstal, Filip

2014-06-01

Numerical and non-numerical order processing share empirical characteristics (distance effect and semantic congruity), but there are also important differences (in size effect and end effect). At the same time, models and theories of numerical and non-numerical order processing developed largely separately. Currently, we combine insights from 2 earlier models to integrate them in a common framework. We argue that the same learning principle underlies numerical and non-numerical orders, but that environmental features determine the empirical differences. Implications for current theories on order processing are pointed out. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Integrated vendor-buyer inventory models with inflation and time value of money in controllable lead time

Directory of Open Access Journals (Sweden)

Prashant Jindal

2016-01-01

Full Text Available In the global critical economic scenario, inflation plays a vital role in deciding optimal pricing of goods in any business entity. This article presents two single-vendor single-buyer integrated supply chain inventory models with inflation and time value of money. Shortage is allowed during the lead-time and it is partially backlogged. Lead time is controllable and can be reduced using crashing cost. In the first model, we consider the demand of lead time follows a normal distribution, and in the second model, it is considered distribution-free. For both cases, our objective is to minimize the integrated system cost by simultaneously optimizing the order quantity, safety factor, lead time and number of lots. The discounted cash flow and classical optimization technique are used to derive the optimal solution for both cases. Numerical examples including the sensitivity analysis of system parameters is provided to validate the results of the supply chain models.

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.

Connection between Feynman integrals having different values of the space-time dimension

International Nuclear Information System (INIS)

Tarasov, O.V.

1996-05-01

A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension d is proposed. The relation between d and d-2 dimensional integrals is given in terms of a differential operator for which an explicit formula can be obtained for each Feynman diagram. We show how the method works for one-, two- and three-loop integrals. The new recurrence relations w.r.t. d are complementary to the recurrence relations which derive from the method of integration by parts. We find that the problem of the irreducible numerators in Feynman integrals can be naturally solved in the framework of the proposed generalized recurrence relations. (orig.)

Integrated optical circuits for numerical computation

Science.gov (United States)

Verber, C. M.; Kenan, R. P.

1983-01-01

The development of integrated optical circuits (IOC) for numerical-computation applications is reviewed, with a focus on the use of systolic architectures. The basic architecture criteria for optical processors are shown to be the same as those proposed by Kung (1982) for VLSI design, and the advantages of IOCs over bulk techniques are indicated. The operation and fabrication of electrooptic grating structures are outlined, and the application of IOCs of this type to an existing 32-bit, 32-Mbit/sec digital correlator, a proposed matrix multiplier, and a proposed pipeline processor for polynomial evaluation is discussed. The problems arising from the inherent nonlinearity of electrooptic gratings are considered. Diagrams and drawings of the application concepts are provided.

Numerical integration methods and layout improvements in the context of dynamic RNA visualization.

Science.gov (United States)

Shabash, Boris; Wiese, Kay C

2017-05-30

RNA visualization software tools have traditionally presented a static visualization of RNA molecules with limited ability for users to interact with the resulting image once it is complete. Only a few tools allowed for dynamic structures. One such tool is jViz.RNA. Currently, jViz.RNA employs a unique method for the creation of the RNA molecule layout by mapping the RNA nucleotides into vertexes in a graph, which we call the detailed graph, and then utilizes a Newtonian mechanics inspired system of forces to calculate a layout for the RNA molecule. The work presented here focuses on improvements to jViz.RNA that allow the drawing of RNA secondary structures according to common drawing conventions, as well as dramatic run-time performance improvements. This is done first by presenting an alternative method for mapping the RNA molecule into a graph, which we call the compressed graph, and then employing advanced numerical integration methods for the compressed graph representation. Comparing the compressed graph and detailed graph implementations, we find that the compressed graph produces results more consistent with RNA drawing conventions. However, we also find that employing the compressed graph method requires a more sophisticated initial layout to produce visualizations that would require minimal user interference. Comparing the two numerical integration methods demonstrates the higher stability of the Backward Euler method, and its resulting ability to handle much larger time steps, a high priority feature for any software which entails user interaction. The work in this manuscript presents the preferred use of compressed graphs to detailed ones, as well as the advantages of employing the Backward Euler method over the Forward Euler method. These improvements produce more stable as well as visually aesthetic representations of the RNA secondary structures. The results presented demonstrate that both the compressed graph representation, as well as the Backward

Calculations of the electromechanical transfer processes using implicit methods of numerical integration

Energy Technology Data Exchange (ETDEWEB)

Pogosyan, T A

1983-01-01

The article is dedicated to the solution of systems of differential equations which describe the transfer processes in an electric power system (EES) by implicit methods of numerical integration. The distinguishing feature of the implicit methods (Euler's reverse method and the trapeze method) is their absolute stability and, consequently, the relatively small accumulation of errors in each step of integration. Therefore, they are found to be very convenient for solving problems of electric power engineering, when the transfer processes are described by a rigid system of differential equations. The rigidity is associated with the range of values of the time constants considered. The advantage of the implicit methods over explicit are shown in a specific example (calculation of the dynamic stability of the simplest electric power system), along with the field of use of the implicit methods and the expedience of their use in power engineering problems.

Modelling of multidimensional quantum systems by the numerical functional integration

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.; Zhidkov, E.P.

1990-01-01

The employment of the numerical functional integration for the description of multidimensional systems in quantum and statistical physics is considered. For the multiple functional integrals with respect to Gaussian measures in the full separable metric spaces the new approximation formulas exact on a class of polynomial functionals of a given summary degree are constructed. The use of the formulas is demonstrated on example of computation of the Green function and the ground state energy in multidimensional Calogero model. 15 refs.; 2 tabs

A theoretical study for the real-time assessment of external gamma exposure using equivalent-volume numerical integration

International Nuclear Information System (INIS)

Han, Moon Hee

1995-02-01

An approximate method for estimating gamma external dose due to an arbitrary distribution of radioactive material has been developed. For the assessment of external gamma dose, the space over which radioactive material is distributed has been assumed to be composed of hexagonal cells. The evaluation of three-dimensional integration over the space is an extremely time-consuming task. Hence, a different approach has been used for the study, i.e., a equivalent-volume spherical approach in which a regular hexahedron is modeled as a equivalent-volume sphere to simplify the integration. For the justification of the current approach, two case studies have been performed: a comparison with a point source approximation and a comparison of external dose rate with the Monte Carlo integration. These comparisons show that the current approach gives reasonable results in a physical sense. Computing times of the developed and Monte Carlo integration method on VAX system have been compared as a function of the number of hexagonal cells. This comparison shows that CPU times for both methods are comparable in the region of small number of cells, but in the region of large number, Monte Carlo integration needs much more computing times. The proposed method is shown to have an accuracy equivalent to Monte Carlo method with an advantage of much shorter calculation time. Then, the method developed here evaluates early off-site consequences of a nuclear accident. An accident consequence assessment model has been integrated using Gaussian puff model which is used to obtain the distribution of radioactive material in the air and on the ground. For this work, the real meteorological data measured at Kori site for 10 years (1976 - 1985) have been statistically analyzed for obtaining site-specific conditions. The short-term external gamma exposures have been assessed for several site-specific meteorological conditions. The results show that the extent and the pattern of short-term external

Numerical Feynman integrals with physically inspired interpolation: Faster convergence and significant reduction of computational cost

Directory of Open Access Journals (Sweden)

Nikesh S. Dattani

2012-03-01

Full Text Available One of the most successful methods for calculating reduced density operator dynamics in open quantum systems, that can give numerically exact results, uses Feynman integrals. However, when simulating the dynamics for a given amount of time, the number of time steps that can realistically be used with this method is always limited, therefore one often obtains an approximation of the reduced density operator at a sparse grid of points in time. Instead of relying only on ad hoc interpolation methods (such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as two time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method. A list of ways in which this proposed method can be further improved is presented in the last section of the article.

On the static loop modes in the marching-on-in-time solution of the time-domain electric field integral equation

KAUST Repository

Shi, Yifei; Bagci, Hakan; Lu, Mingyu

2014-01-01

When marching-on-in-time (MOT) method is applied to solve the time-domain electric field integral equation, spurious internal resonant and static loop modes are always observed in the solution. The internal resonant modes have recently been studied by the authors; this letter investigates the static loop modes. Like internal resonant modes, static loop modes, in theory, should not be observed in the MOT solution since they do not satisfy the zero initial conditions; their appearance is attributed to numerical errors. It is discussed in this letter that the dependence of spurious static loop modes on numerical errors is substantially different from that of spurious internal resonant modes. More specifically, when Rao-Wilton-Glisson functions and Lagrange interpolation functions are used as spatial and temporal basis functions, respectively, errors due to space-time discretization have no discernible impact on spurious static loop modes. Numerical experiments indeed support this discussion and demonstrate that the numerical errors due to the approximate solution of the MOT matrix system have dominant impact on spurious static loop modes in the MOT solution. © 2014 IEEE.

Performance of overlapped shield tunneling through an integrated physical model tests, numerical simulations and real-time field monitoring

Directory of Open Access Journals (Sweden)

Junlong Yang

2017-03-01

Full Text Available In this work, deformations and internal forces of an existing tunnel subjected to a closely overlapped shield tunneling are monitored and analyzed using a series of physical model experiments and numerical simulations. Effects of different excavation sequences and speeds are explicitly considered in the analysis. The results of the physical model experiments show that the bottom-up tunneling procedure is better than the top-down tunneling procedure. The incurred deformations and internal forces of the existing tunnel increase with the excavation speed and the range of influence areas also increase accordingly. For construction process control, real-time monitoring of the power tunnel is used. The monitoring processes feature full automation, adjustable frequency, real-time monitor and dynamic feedback, which are used to guide the construction to achieve micro-disturbance control. In accordance with the situation of crossing construction, a numerical study on the performance of power tunnel is carried out. Construction control measures are given for the undercrossing construction, which helps to accomplish the desired result and meet protection requirements of the existing tunnel structure. Finally, monitoring data and numerical results are compared, and the displacement and joint fracture change models in the power tunnel subject to the overlapped shield tunnel construction are analyzed. Keywords: Overlapped tunnel, Automatic monitoring, Micro-disturbance control

Time's arrow: A numerical experiment

Science.gov (United States)

Fowles, G. Richard

1994-04-01

The dependence of time's arrow on initial conditions is illustrated by a numerical example in which plane waves produced by an initial pressure pulse are followed as they are multiply reflected at internal interfaces of a layered medium. Wave interactions at interfaces are shown to be analogous to the retarded and advanced waves of point sources. The model is linear and the calculation is exact and demonstrably time reversible; nevertheless the results show most of the features expected of a macroscopically irreversible system, including the approach to the Maxwell-Boltzmann distribution, ergodicity, and concomitant entropy increase.

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

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

Molecular radiotherapy: The NUKFIT software for calculating the time-integrated activity coefficient

Energy Technology Data Exchange (ETDEWEB)

Kletting, P.; Schimmel, S.; Luster, M. [Klinik für Nuklearmedizin, Universität Ulm, Ulm 89081 (Germany); Kestler, H. A. [Research Group Bioinformatics and Systems Biology, Institut für Neuroinformatik, Universität Ulm, Ulm 89081 (Germany); Hänscheid, H.; Fernández, M.; Lassmann, M. [Klinik für Nuklearmedizin, Universität Würzburg, Würzburg 97080 (Germany); Bröer, J. H.; Nosske, D. [Bundesamt für Strahlenschutz, Fachbereich Strahlenschutz und Gesundheit, Oberschleißheim 85764 (Germany); Glatting, G. [Medical Radiation Physics/Radiation Protection, Medical Faculty Mannheim, Heidelberg University, Mannheim 68167 (Germany)

2013-10-15

Purpose: Calculation of the time-integrated activity coefficient (residence time) is a crucial step in dosimetry for molecular radiotherapy. However, available software is deficient in that it is either not tailored for the use in molecular radiotherapy and/or does not include all required estimation methods. The aim of this work was therefore the development and programming of an algorithm which allows for an objective and reproducible determination of the time-integrated activity coefficient and its standard error.Methods: The algorithm includes the selection of a set of fitting functions from predefined sums of exponentials and the choice of an error model for the used data. To estimate the values of the adjustable parameters an objective function, depending on the data, the parameters of the error model, the fitting function and (if required and available) Bayesian information, is minimized. To increase reproducibility and user-friendliness the starting values are automatically determined using a combination of curve stripping and random search. Visual inspection, the coefficient of determination, the standard error of the fitted parameters, and the correlation matrix are provided to evaluate the quality of the fit. The functions which are most supported by the data are determined using the corrected Akaike information criterion. The time-integrated activity coefficient is estimated by analytically integrating the fitted functions. Its standard error is determined assuming Gaussian error propagation. The software was implemented using MATLAB.Results: To validate the proper implementation of the objective function and the fit functions, the results of NUKFIT and SAAM numerical, a commercially available software tool, were compared. The automatic search for starting values was successfully tested for reproducibility. The quality criteria applied in conjunction with the Akaike information criterion allowed the selection of suitable functions. Function fit

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)

A hybrid method combining the FDTD and a time domain boundary-integral equation marching-on-in-time algorithm

Directory of Open Access Journals (Sweden)

A. Becker

2003-01-01

Full Text Available In this paper a hybrid method combining the FDTD/FIT with a Time Domain Boundary-Integral Marching-on-in-Time Algorithm (TD-BIM is presented. Inhomogeneous regions are modelled with the FIT-method, an alternative formulation of the FDTD. Homogeneous regions (which is in the presented numerical example the open space are modelled using a TD-BIM with equivalent electric and magnetic currents flowing on the boundary between the inhomogeneous and the homogeneous regions. The regions are coupled by the tangential magnetic fields just outside the inhomogeneous regions. These fields are calculated by making use of a Mixed Potential Integral Formulation for the magnetic field. The latter consists of equivalent electric and magnetic currents on the boundary plane between the homogeneous and the inhomogeneous region. The magnetic currents result directly from the electric fields of the Yee lattice. Electric currents in the same plane are calculated by making use of the TD-BIM and using the electric field of the Yee lattice as boundary condition. The presented hybrid method only needs the interpolations inherent in FIT and no additional interpolation. A numerical result is compared to a calculation that models both regions with FDTD.

Variational Symplectic Integrator for Long-Time Simulations of the Guiding-Center Motion of Charged Particles in General Magnetic Fields

International Nuclear Information System (INIS)

Qin Hong; Guan Xiaoyin

2008-01-01

A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for long-time simulation studies of magnetized plasmas. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure, and has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods

Variational Symplectic Integrator for Long-Time Simulations of the Guiding-Center Motion of Charged Particles in General Magnetic Fields

International Nuclear Information System (INIS)

Qin, H.; Guan, X.

2008-01-01

A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for long-time simulation studies of magnetized plasmas. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure, and has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods.

Molecular radiotherapy: the NUKFIT software for calculating the time-integrated activity coefficient.

Science.gov (United States)

Kletting, P; Schimmel, S; Kestler, H A; Hänscheid, H; Luster, M; Fernández, M; Bröer, J H; Nosske, D; Lassmann, M; Glatting, G

2013-10-01

Calculation of the time-integrated activity coefficient (residence time) is a crucial step in dosimetry for molecular radiotherapy. However, available software is deficient in that it is either not tailored for the use in molecular radiotherapy and/or does not include all required estimation methods. The aim of this work was therefore the development and programming of an algorithm which allows for an objective and reproducible determination of the time-integrated activity coefficient and its standard error. The algorithm includes the selection of a set of fitting functions from predefined sums of exponentials and the choice of an error model for the used data. To estimate the values of the adjustable parameters an objective function, depending on the data, the parameters of the error model, the fitting function and (if required and available) Bayesian information, is minimized. To increase reproducibility and user-friendliness the starting values are automatically determined using a combination of curve stripping and random search. Visual inspection, the coefficient of determination, the standard error of the fitted parameters, and the correlation matrix are provided to evaluate the quality of the fit. The functions which are most supported by the data are determined using the corrected Akaike information criterion. The time-integrated activity coefficient is estimated by analytically integrating the fitted functions. Its standard error is determined assuming Gaussian error propagation. The software was implemented using MATLAB. To validate the proper implementation of the objective function and the fit functions, the results of NUKFIT and SAAM numerical, a commercially available software tool, were compared. The automatic search for starting values was successfully tested for reproducibility. The quality criteria applied in conjunction with the Akaike information criterion allowed the selection of suitable functions. Function fit parameters and their standard

A revised method to calculate the concentration time integral of atmospheric pollutants

International Nuclear Information System (INIS)

Voelz, E.; Schultz, H.

1980-01-01

It is possible to calculate the spreading of a plume in the atmosphere under nonstationary and nonhomogeneous conditions by introducing the ''particle-in-cell'' method (PIC). This is a numerical method by which the transport of and the diffusion in the plume is reproduced in such a way, that particles representing the concentration are moved time step-wise in restricted regions (cells) and separately with the advection velocity and the diffusion velocity. This has a systematical advantage over the steady state Gaussian plume model usually used. The fixed-point concentration time integral is calculated directly instead of being substituted by the locally integrated concentration at a constant time as is done in the Gaussian model. In this way inaccuracies due to the above mentioned computational techniques may be avoided for short-time emissions, as may be seen by the fact that both integrals do not lead to the same results. Also the PIC method enables one to consider the height-dependent wind speed and its variations while the Gaussian model can be used only with averaged wind data. The concentration time integral calculated by the PIC method results in higher maximum values in shorter distances to the source. This is an effect often observed in measurements. (author)

pySecDec: A toolbox for the numerical evaluation of multi-scale integrals

Science.gov (United States)

Borowka, S.; Heinrich, G.; Jahn, S.; Jones, S. P.; Kerner, M.; Schlenk, J.; Zirke, T.

2018-01-01

We present pySECDEC, a new version of the program SECDEC, which performs the factorization of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of the program is now written in the form of python modules, which allow a very flexible usage. The optimization of the C++ code, generated using FORM, is improved, leading to a faster numerical convergence. The new version also creates a library of the integrand functions, such that it can be linked to user-specific codes for the evaluation of matrix elements in a way similar to analytic integral libraries.

High-Order Calderón Preconditioned Time Domain Integral Equation Solvers

KAUST Repository

Valdes, Felipe; Ghaffari-Miab, Mohsen; Andriulli, Francesco P.; Cools, Kristof; Michielssen,

2013-01-01

Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.

High-Order Calderón Preconditioned Time Domain Integral Equation Solvers

KAUST Repository

Valdes, Felipe

2013-05-01

Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions

Science.gov (United States)

Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.

2018-03-01

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

Science.gov (United States)

Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E

2018-03-14

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

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...

NUMERICAL WITHOUT ITERATION METHOD OF MODELING OF ELECTROMECHANICAL PROCESSES IN ASYNCHRONOUS ENGINES

Directory of Open Access Journals (Sweden)

D. G. Patalakh

2018-02-01

Full Text Available Purpose. Development of calculation of electromagnetic and electromechanic transients is in asynchronous engines without iterations. Methodology. Numeral methods of integration of usual differential equations, programming. Findings. As the system of equations, describing the dynamics of asynchronous engine, contents the products of rotor and stator currents and product of rotation frequency of rotor and currents, so this system is nonlinear one. The numeral solution of nonlinear differential equations supposes an iteration process on every step of integration. Time-continuing and badly converging iteration process may be the reason of calculation slowing. The improvement of numeral method by the way of an iteration process removing is offered. As result the modeling time is reduced. The improved numeral method is applied for integration of differential equations, describing the dynamics of asynchronous engine. Originality. The improvement of numeral method allowing to execute numeral integrations of differential equations containing product of functions is offered, that allows to avoid an iteration process on every step of integration and shorten modeling time. Practical value. On the basis of the offered methodology the universal program of modeling of electromechanics processes in asynchronous engines could be developed as taking advantage on fast-acting.

Marching on-in-time solution of the time domain magnetic field integral equation using a predictor-corrector scheme

KAUST Repository

Ulku, Huseyin Arda; Bagci, Hakan; Michielssen, Eric

2013-01-01

An explicit marching on-in-time (MOT) scheme for solving the time-domain magnetic field integral equation (TD-MFIE) is presented. The proposed MOT-TD-MFIE solver uses Rao-Wilton-Glisson basis functions for spatial discretization and a PE(CE)m-type linear multistep method for time marching. Unlike previous explicit MOT-TD-MFIE solvers, the time step size can be chosen as large as that of the implicit MOT-TD-MFIE solvers without adversely affecting accuracy or stability. An algebraic stability analysis demonstrates the stability of the proposed explicit solver; its accuracy and efficiency are established via numerical examples. © 1963-2012 IEEE.

Marching on-in-time solution of the time domain magnetic field integral equation using a predictor-corrector scheme

KAUST Repository

Ulku, Huseyin Arda

2013-08-01

An explicit marching on-in-time (MOT) scheme for solving the time-domain magnetic field integral equation (TD-MFIE) is presented. The proposed MOT-TD-MFIE solver uses Rao-Wilton-Glisson basis functions for spatial discretization and a PE(CE)m-type linear multistep method for time marching. Unlike previous explicit MOT-TD-MFIE solvers, the time step size can be chosen as large as that of the implicit MOT-TD-MFIE solvers without adversely affecting accuracy or stability. An algebraic stability analysis demonstrates the stability of the proposed explicit solver; its accuracy and efficiency are established via numerical examples. © 1963-2012 IEEE.

Conservation properties of numerical integration methods for systems of ordinary differential equations

Science.gov (United States)

Rosenbaum, J. S.

1976-01-01

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Nonlinear dynamics and numerical uncertainties in CFD

Science.gov (United States)

Yee, H. C.; Sweby, P. K.

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

Numerical simulation and experimental research of the integrated high-power LED radiator

Science.gov (United States)

Xiang, J. H.; Zhang, C. L.; Gan, Z. J.; Zhou, C.; Chen, C. G.; Chen, S.

2017-01-01

The thermal management has become an urgent problem to be solved with the increasing power and the improving integration of the LED (light emitting diode) chip. In order to eliminate the contact resistance of the radiator, this paper presented an integrated high-power LED radiator based on phase-change heat transfer, which realized the seamless connection between the vapor chamber and the cooling fins. The radiator was optimized by combining the numerical simulation and the experimental research. The effects of the chamber diameter and the parameters of fin on the heat dissipation performance were analyzed. The numerical simulation results were compared with the measured values by experiment. The results showed that the fin thickness, the fin number, the fin height and the chamber diameter were the factors which affected the performance of radiator from primary to secondary.

Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom

Science.gov (United States)

Ruokosenmäki, Ilkka; Gholizade, Hossein; Kylänpää, Ilkka; Rantala, Tapio T.

2017-01-01

We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.

Time-of-flight depth image enhancement using variable integration time

Science.gov (United States)

Kim, Sun Kwon; Choi, Ouk; Kang, Byongmin; Kim, James Dokyoon; Kim, Chang-Yeong

2013-03-01

Time-of-Flight (ToF) cameras are used for a variety of applications because it delivers depth information at a high frame rate. These cameras, however, suffer from challenging problems such as noise and motion artifacts. To increase signal-to-noise ratio (SNR), the camera should calculate a distance based on a large amount of infra-red light, which needs to be integrated over a long time. On the other hand, the integration time should be short enough to suppress motion artifacts. We propose a ToF depth imaging method to combine advantages of short and long integration times exploiting an imaging fusion scheme proposed for color imaging. To calibrate depth differences due to the change of integration times, a depth transfer function is estimated by analyzing the joint histogram of depths in the two images of different integration times. The depth images are then transformed into wavelet domains and fused into a depth image with suppressed noise and low motion artifacts. To evaluate the proposed method, we captured a moving bar of a metronome with different integration times. The experiment shows the proposed method could effectively remove the motion artifacts while preserving high SNR comparable to the depth images acquired during long integration time.

A purely Lagrangian method for the numerical integration of Fokker-Planck equations

International Nuclear Information System (INIS)

Combis, P.; Fronteau, J.

1986-01-01

A new numerical approach to Fokker-Planck equations is presented, in which the integration grid moves according to the solution of a differential system. The method is purely Lagrangian, the mean effect of the diffusion being inserted into the differential system itself

On the mixed discretization of the time domain magnetic field integral equation

KAUST Repository

Ulku, Huseyin Arda

2012-09-01

Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is proper: Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. © 2012 IEEE.

An efficient explicit marching on in time solver for magnetic field volume integral equation

KAUST Repository

Sayed, Sadeed Bin

2015-07-25

An efficient explicit marching on in time (MOT) scheme for solving the magnetic field volume integral equation is proposed. The MOT system is cast in the form of an ordinary differential equation and is integrated in time using a PE(CE)m multistep scheme. At each time step, a system with a Gram matrix is solved for the predicted/corrected field expansion coefficients. Depending on the type of spatial testing scheme Gram matrix is sparse or consists of blocks with only diagonal entries regardless of the time step size. Consequently, the resulting MOT scheme is more efficient than its implicit counterparts, which call for inversion of fuller matrix system at lower frequencies. Numerical results, which demonstrate the efficiency, accuracy, and stability of the proposed MOT scheme, are presented.

Numerical simulation of a lattice polymer model at its integrable point

International Nuclear Information System (INIS)

Bedini, A; Owczarek, A L; Prellberg, T

2013-01-01

We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Blöte and Nienhuis (1989 J. Phys. A: Math. Gen. 22 1415) and it describes polymers with some attraction, providing thus a model for the polymer collapse transition. At a particular set of Boltzmann weights the model is integrable and the exponents ν = 12/23 ≈ 0.522 and γ = 53/46 ≈ 1.152 have been computed via identification of the scaling dimensions x t = 1/12 and x h = −5/48. We directly investigate the polymer scaling exponents via Monte Carlo simulations using the pruned-enriched Rosenbluth method algorithm. By simulating this polymer model for walks up to length 4096 we find ν = 0.576(6) and γ = 1.045(5), which are clearly different from the predicted values. Our estimate for the exponent ν is compatible with the known θ-point value of 4/7 and in agreement with very recent numerical evaluation by Foster and Pinettes (2012 J. Phys. A: Math. Theor. 45 505003). (paper)

Retarded potentials and time domain boundary integral equations a road map

CERN Document Server

Sayas, Francisco-Javier

2016-01-01

This book offers a thorough and self-contained exposition of the mathematics of time-domain boundary integral equations associated to the wave equation, including applications to scattering of acoustic and elastic waves. The book offers two different approaches for the analysis of these integral equations, including a systematic treatment of their numerical discretization using Galerkin (Boundary Element) methods in the space variables and Convolution Quadrature in the time variable. The first approach follows classical work started in the late eighties, based on Laplace transforms estimates. This approach has been refined and made more accessible by tailoring the necessary mathematical tools, avoiding an excess of generality. A second approach contains a novel point of view that the author and some of his collaborators have been developing in recent years, using the semigroup theory of evolution equations to obtain improved results. The extension to electromagnetic waves is explained in one of the appendices...

Explicit solution of the time domain magnetic field integral equation using a predictor-corrector scheme

KAUST Repository

Ulku, Huseyin Arda; Bagci, Hakan; Michielssen, Eric

2012-01-01

An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.

Explicit solution of the time domain magnetic field integral equation using a predictor-corrector scheme

KAUST Repository

Ulku, Huseyin Arda

2012-09-01

An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.

BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

Science.gov (United States)

Caffo, Michele; Czyż, Henryk; Gunia, Michał; Remiddi, Ettore

2009-03-01

We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations. Program summaryProgram title: BOKASUN Catalogue identifier: AECG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9404 No. of bytes in distributed program, including test data, etc.: 104 123 Distribution format: tar.gz Programming language: FORTRAN77 Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUX Operating system: LINUX RAM: 120 kbytes Classification: 4.4 Nature of problem: Any integral arising in the evaluation of the two-loop sunrise Feynman diagram can be expressed in terms of a given set of Master Integrals, which should be calculated numerically. The program provides a fast and precise evaluation method of the Master Integrals for arbitrary (but not vanishing) masses and arbitrary value of the external momentum. Solution method: The integrals depend on three internal masses and the external momentum squared p. The method is a combination of an accelerated expansion in 1/p in its (pretty large!) region of fast convergence and of a Runge-Kutta numerical solution of a system of linear differential equations. Running time: To obtain 4 Master Integrals on PC with 2 GHz processor it takes 3 μs for series expansion with pre-calculated coefficients, 80 μs for series expansion without pre-calculated coefficients, from a few seconds up to a few minutes for Runge-Kutta method (depending

A hybrid time-domain discontinuous galerkin-boundary integral method for electromagnetic scattering analysis

KAUST Repository

Li, Ping; Shi, Yifei; Jiang, Lijun; Bagci, Hakan

2014-01-01

A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer's shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.

A hybrid time-domain discontinuous galerkin-boundary integral method for electromagnetic scattering analysis

KAUST Repository

Li, Ping

2014-05-01

A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens\\' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer\\'s shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.

Application of Numerical Integration and Data Fusion in Unit Vector Method

Science.gov (United States)

Zhang, J.

2012-01-01

The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of

Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

Directory of Open Access Journals (Sweden)

Zakieh Avazzadeh

2014-01-01

Full Text Available We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.

Scalability of Direct Solver for Non-stationary Cahn-Hilliard Simulations with Linearized time Integration Scheme

KAUST Repository

Woźniak, M.

2016-06-02

We study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzburg-Landau free energy. The numerical simulations are performed by using a parallel multi-frontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.

Time-domain single-source integral equations for analyzing scattering from homogeneous penetrable objects

KAUST Repository

Valdés, Felipe

2013-03-01

Single-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence-and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div-to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. © 2012 IEEE.

New methods for the numerical integration of ordinary differential equations and their application to the equations of motion of spacecraft

Science.gov (United States)

Banyukevich, A.; Ziolkovski, K.

1975-01-01

A number of hybrid methods for solving Cauchy problems are described on the basis of an evaluation of advantages of single and multiple-point numerical integration methods. The selection criterion is the principle of minimizing computer time. The methods discussed include the Nordsieck method, the Bulirsch-Stoer extrapolation method, and the method of recursive Taylor-Steffensen power series.

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

Science.gov (United States)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2015-04-01

The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each

Some applications of perturbation theory to numerical integration methods for the Schroedinger equation

International Nuclear Information System (INIS)

Killingbeck, J.

1979-01-01

By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)

Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques

International Nuclear Information System (INIS)

Rodriguez, Alejandro; Ibanescu, Mihai; Joannopoulos, J. D.; Johnson, Steven G.; Iannuzzi, Davide

2007-01-01

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising nonmonotonic ''lateral'' force from the walls

An integrated framework for SAGD real-time monitoring

Energy Technology Data Exchange (ETDEWEB)

Mohajer, M.; Perez-Damas, C.; Berbin, A.; Al-kinani, A. [Schlumberger, Calgary, AB (Canada)

2009-07-01

This study examined the technologies and workflows for real-time optimization (RTO) of the steam assisted gravity drainage (SAGD) process. Although SAGD operators have tried to control the reservoir's steam chamber distribution to optimize bitumen recovery and minimize steam oil ratios, a true optimization can only be accomplished by implementing RTO workflows. In order for these workflows to be successful, some elements must be properly designed and introduced into the system. Most notably, well completions must ensure the integrity of downhole sensors; the appropriate measuring instruments must be selected; and surface and downhole measurements must be obtained. Operators have not been early adopters of RTO workflows for SAGD because of the numerous parameters that must be monitored, harsh operating conditions, the lack of integration between the different data acquisition systems, and the complex criteria required to optimize SAGD performance. This paper discussed the first stage in the development of a fully integrated RTO workflow for SAGD. An experimental apparatus with fiber optics distributed temperature sensing (DTS) was connected to a data acquisition system, and intra-minute data was streamed directly into an engineering desktop. The paper showed how subcool calculations can be effectively performed along the length of the horizontal well in real time and the results used to improve SAGD operation. Observations were compared against simulated predictions. In the next stage, a more complex set of criteria will be derived and additional data will be incorporated, such as surface heave, cross-well microseismic, multiphase flowmeter, and observation wells. 9 refs., 9 tabs., 13 figs.

Implementation of numerical integration schemes for the simulation of magnetic SMA constitutive response

International Nuclear Information System (INIS)

Kiefer, B; Bartel, T; Menzel, A

2012-01-01

Several constitutive models for magnetic shape memory alloys (MSMAs) have been proposed in the literature. The implementation of numerical integration schemes, which allow the prediction of constitutive response for general loading cases and ultimately the incorporation of MSMA response into numerical solution algorithms for fully coupled magneto-mechanical boundary value problems, however, has received only very limited attention. In this work, we establish two algorithmic implementations of the internal variable model for MSMAs proposed in (Kiefer and Lagoudas 2005 Phil. Mag. Spec. Issue: Recent Adv. Theor. Mech. 85 4289–329, Kiefer and Lagoudas 2009 J. Intell. Mater. Syst. 20 143–70), where we restrict our attention to pure martensitic variant reorientation to limit complexity. The first updating scheme is based on the numerical integration of the reorientation strain evolution equation and represents a classical predictor–corrector-type general return mapping algorithm. In the second approach, the inequality-constrained optimization problem associated with internal variable evolution is converted into an unconstrained problem via Fischer–Burmeister complementarity functions and then iteratively solved in standard Newton–Raphson format. Simulations are verified by comparison to closed-form solutions for experimentally relevant loading cases. (paper)

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

International Nuclear Information System (INIS)

Finn, John M.

2015-01-01

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012

Integrating experimental and numerical methods for a scenario-based quantitative assessment of subsurface energy storage options

Science.gov (United States)

Kabuth, Alina; Dahmke, Andreas; Hagrey, Said Attia al; Berta, Márton; Dörr, Cordula; Koproch, Nicolas; Köber, Ralf; Köhn, Daniel; Nolde, Michael; Tilmann Pfeiffer, Wolf; Popp, Steffi; Schwanebeck, Malte; Bauer, Sebastian

2016-04-01

Within the framework of the transition to renewable energy sources ("Energiewende"), the German government defined the target of producing 60 % of the final energy consumption from renewable energy sources by the year 2050. However, renewable energies are subject to natural fluctuations. Energy storage can help to buffer the resulting time shifts between production and demand. Subsurface geological structures provide large potential capacities for energy stored in the form of heat or gas on daily to seasonal time scales. In order to explore this potential sustainably, the possible induced effects of energy storage operations have to be quantified for both specified normal operation and events of failure. The ANGUS+ project therefore integrates experimental laboratory studies with numerical approaches to assess subsurface energy storage scenarios and monitoring methods. Subsurface storage options for gas, i.e. hydrogen, synthetic methane and compressed air in salt caverns or porous structures, as well as subsurface heat storage are investigated with respect to site prerequisites, storage dimensions, induced effects, monitoring methods and integration into spatial planning schemes. The conceptual interdisciplinary approach of the ANGUS+ project towards the integration of subsurface energy storage into a sustainable subsurface planning scheme is presented here, and this approach is then demonstrated using the examples of two selected energy storage options: Firstly, the option of seasonal heat storage in a shallow aquifer is presented. Coupled thermal and hydraulic processes induced by periodic heat injection and extraction were simulated in the open-source numerical modelling package OpenGeoSys. Situations of specified normal operation as well as cases of failure in operational storage with leaking heat transfer fluid are considered. Bench-scale experiments provided parameterisations of temperature dependent changes in shallow groundwater hydrogeochemistry. As a

A discontinuous galerkin time domain-boundary integral method for analyzing transient electromagnetic scattering

KAUST Repository

Li, Ping

2014-07-01

This paper presents an algorithm hybridizing discontinuous Galerkin time domain (DGTD) method and time domain boundary integral (BI) algorithm for 3-D open region electromagnetic scattering analysis. The computational domain of DGTD is rigorously truncated by analytically evaluating the incoming numerical flux from the outside of the truncation boundary through BI method based on the Huygens\\' principle. The advantages of the proposed method are that it allows the truncation boundary to be conformal to arbitrary (convex/ concave) scattering objects, well-separated scatters can be truncated by their local meshes without losing the physics (such as coupling/multiple scattering) of the problem, thus reducing the total mesh elements. Furthermore, low frequency waves can be efficiently absorbed, and the field outside the truncation domain can be conveniently calculated using the same BI formulation. Numerical examples are benchmarked to demonstrate the accuracy and versatility of the proposed method.

The development and validation of a numerical integration method for non-linear viscoelastic modeling

Science.gov (United States)

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

EVALUATION OF THE POUNDING FORCES DURING EARTHQUAKE USING EXPLICIT DYNAMIC TIME INTEGRATION METHOD

Directory of Open Access Journals (Sweden)

Nica George Bogdan

2017-09-01

Full Text Available Pounding effects during earthquake is a subject of high significance for structural engineers performing in the urban areas. In this paper, two ways to account for structural pounding are used in a MATLAB code, namely classical stereomechanics approach and nonlinear viscoelastic impact element. The numerical study is performed on SDOF structures acted by ELCentro recording. While most of the studies available in the literature are related to Newmark implicit time integration method, in this study the equations of motion are numerical integrated using central finite difference method, an explicit method, having the main advantage that in the displacement at the ith+1 step is calculated based on the loads from the ith step. Thus, the collision is checked and the pounding forces are taken into account into the equation of motion in an easier manner than in an implicit integration method. First, a comparison is done using available data in the literature. Both linear and nonlinear behavior of the structures during earthquake is further investigated. Several layout scenarios are also investigated, in which one or more weak buildings are adjacent to a stiffer building. One of the main findings in this paper is related to the behavior of a weak structure located between two stiff structures.

Carbon Dioxide Dispersion in the Combustion Integrated Rack Simulated Numerically

Science.gov (United States)

Wu, Ming-Shin; Ruff, Gary A.

2004-01-01

When discharged into an International Space Station (ISS) payload rack, a carbon dioxide (CO2) portable fire extinguisher (PFE) must extinguish a fire by decreasing the oxygen in the rack by 50 percent within 60 sec. The length of time needed for this oxygen reduction throughout the rack and the length of time that the CO2 concentration remains high enough to prevent the fire from reigniting is important when determining the effectiveness of the response and postfire procedures. Furthermore, in the absence of gravity, the local flow velocity can make the difference between a fire that spreads rapidly and one that self-extinguishes after ignition. A numerical simulation of the discharge of CO2 from PFE into the Combustion Integrated Rack (CIR) in microgravity was performed to obtain the local velocity and CO2 concentration. The complicated flow field around the PFE nozzle exits was modeled by sources of equivalent mass and momentum flux at a location downstream of the nozzle. The time for the concentration of CO2 to reach a level that would extinguish a fire anywhere in the rack was determined using the Fire Dynamics Simulator (FDS), a computational fluid dynamics code developed by the National Institute of Standards and Technology specifically to evaluate the development of a fire and smoke transport. The simulation shows that CO2, as well as any smoke and combustion gases produced by a fire, would be discharged into the ISS cabin through the resource utility panel at the bottom of the rack. These simulations will be validated by comparing the results with velocity and CO2 concentration measurements obtained during the fire suppression system verification tests conducted on the CIR in March 2003. Once these numerical simulations are validated, portions of the ISS labs and living areas will be modeled to determine the local flow conditions before, during, and after a fire event. These simulations can yield specific information about how long it takes for smoke and

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

Science.gov (United States)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

Numerical simulation of liquid film flow on revolution surfaces with momentum integral method

International Nuclear Information System (INIS)

Bottoni Maurizio

2005-01-01

The momentum integral method is applied in the frame of safety analysis of pressure water reactors under hypothetical loss of coolant accident (LOCA) conditions to simulate numerically film condensation, rewetting and vaporization on the inner surface of pressure water reactor containment. From the conservation equations of mass and momentum of a liquid film arising from condensation of steam upon the inner of the containment during a LOCA in a pressure water reactor plant, an integro-differential equation is derived, referring to an arbitrary axisymmetric surface of revolution. This equation describes the velocity distribution of the liquid film along a meridian of a surface of revolution. From the integro-differential equation and ordinary differential equation of first order for the film velocity is derived and integrated numerically. From the velocity distribution the film thickness distribution is obtained. The solution of the enthalpy equation for the liquid film yields the temperature distribution on the inner surface of the containment. (authors)

Steffensen's Integral Inequality on Time Scales

Directory of Open Access Journals (Sweden)

Ozkan Umut Mutlu

2007-01-01

Full Text Available We establish generalizations of Steffensen's integral inequality on time scales via the diamond- dynamic integral, which is defined as a linear combination of the delta and nabla integrals.

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

Science.gov (United States)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Numerical evaluation of Feynman loop integrals by reduction to tree graphs

International Nuclear Information System (INIS)

Kleinschmidt, T.

2007-12-01

We present a method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. This states that loop graphs can be expressed as a sum of tree graphs with additional external on-shell particles. The original loop integral is replaced by a phase space integration over the additional particles. In cross section calculations and for event generation, this phase space can be sampled simultaneously with the phase space of the original external particles. Since very sophisticated matrix element generators for tree graph amplitudes exist and phase space integrations are generically well understood, this method is suited for a future implementation in a fully automated Monte Carlo event generator. A scheme for renormalization and regularization is presented. We show the construction of subtraction graphs which cancel ultraviolet divergences and present a method to cancel internal on-shell singularities. Real emission graphs can be naturally included in the phase space integral of the additional on-shell particles to cancel infrared divergences. As a proof of concept, we apply this method to NLO Bhabha scattering in QED. Cross sections are calculated and are in agreement with results from conventional methods. We also construct a Monte Carlo event generator and present results. (orig.)

Numerical evaluation of Feynman loop integrals by reduction to tree graphs

Energy Technology Data Exchange (ETDEWEB)

Kleinschmidt, T.

2007-12-15

We present a method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. This states that loop graphs can be expressed as a sum of tree graphs with additional external on-shell particles. The original loop integral is replaced by a phase space integration over the additional particles. In cross section calculations and for event generation, this phase space can be sampled simultaneously with the phase space of the original external particles. Since very sophisticated matrix element generators for tree graph amplitudes exist and phase space integrations are generically well understood, this method is suited for a future implementation in a fully automated Monte Carlo event generator. A scheme for renormalization and regularization is presented. We show the construction of subtraction graphs which cancel ultraviolet divergences and present a method to cancel internal on-shell singularities. Real emission graphs can be naturally included in the phase space integral of the additional on-shell particles to cancel infrared divergences. As a proof of concept, we apply this method to NLO Bhabha scattering in QED. Cross sections are calculated and are in agreement with results from conventional methods. We also construct a Monte Carlo event generator and present results. (orig.)

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

Science.gov (United States)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

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...

On the numerical evaluation of algebro-geometric solutions to integrable equations

International Nuclear Information System (INIS)

Kalla, C; Klein, C

2012-01-01

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations

Time delay systems theory, numerics, applications, and experiments

CERN Document Server

Ersal, Tulga; Orosz, Gábor

2017-01-01

This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike. .

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

Science.gov (United States)

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that

Numerical Simulation and Experimental Validation of an Integrated Sleeve-Wedge Anchorage for CFRP Rods

DEFF Research Database (Denmark)

Schmidt, Jacob Wittrup; Smith, Scott T.; Täljsten, Björn

2011-01-01

. Recently, an integrated sleeve-wedge anchorage has been successfully developed specifically for CFRP rods. This paper in turn presents a numerical simulation of the newly developed anchorage using ABAQUS. The three-dimensional finite element (FE) model, which considers material non-linearity, uses...

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.

H∞ Control of Coronary Artery Input Time-Delay System via the Free-Matrix-Based Integral Inequality

Directory of Open Access Journals (Sweden)

Sha-sha Li

2018-01-01

Full Text Available The issue of H∞ control for the coronary artery input time-delay system with external disturbance is of concern. To further reduce conservation, we utilize the free-matrix-based integral inequality, Wirtinger-based integral inequality, and reciprocal convex combination approach to construct Lyapunov-Krasovskii function (LKF. Then a sufficient condition for controller design which can guarantee robust synchronization the coronary artery system is represented in terms of linear matrix inequality (LMI. Finally, a numerical example is exploited to show the effectiveness of the proposed methods.

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

Science.gov (United States)

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively

A higher order numerical method for time fractional partial differential equations with nonsmooth data

Science.gov (United States)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

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)

An arbitrary-order staggered time integrator for the linear acoustic wave equation

Science.gov (United States)

Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo

2018-02-01

We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.

Fundamental aspects of the integration of seismic monitoring with numerical modelling.

CSIR Research Space (South Africa)

Mendecki, AJ

2001-06-01

Full Text Available of the physical state of the rock- mass. ! It must be equipped with the capability of converting the parameters of a real seismic event into a corresponding model-compatible input in the form of an additional loading on the rock-mass. ! It must allow... for an unambiguous identification and quantification of Aseismic events @ among the model-generated data. Structure of an integrated numerical model The functionality interrelations between the different components of a software package designed to implement...

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

Semi-empirical γ-ray peak efficiency determination including self-absorption correction based on numerical integration

International Nuclear Information System (INIS)

Noguchi, M.; Takeda, K.; Higuchi, H.

1981-01-01

A method of γ-ray efficiency determination for extended (plane or bulk) samples based on numerical integration of point source efficiency is studied. The proposed method is widely applicable to samples of various shapes and materials. The geometrical factor in the peak efficiency can easily be corrected for by simply changing the integration region, and γ-ray self-absorption is also corrected by the absorption coefficients for the sample matrix. (author)

Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

KAUST Repository

Al Jarro, Ahmed

2012-11-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

KAUST Repository

Al Jarro, Ahmed; Salem, Mohamed; Bagci, Hakan; Benson, Trevor; Sewell, Phillip D.; Vuković, Ana

2012-01-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

Formulations by surface integral equations for numerical simulation of non-destructive testing by eddy currents

International Nuclear Information System (INIS)

Vigneron, Audrey

2015-01-01

The thesis addresses the numerical simulation of non-destructive testing (NDT) using eddy currents, and more precisely the computation of induced electromagnetic fields by a transmitter sensor in a healthy part. This calculation is the first step of the modeling of a complete control process in the CIVA software platform developed at CEA LIST. Currently, models integrated in CIVA are restricted to canonical (modal computation) or axially-symmetric geometries. The need for more diverse and complex configurations requires the introduction of new numerical modeling tools. In practice the sensor may be composed of elements with different shapes and physical properties. The inspected parts are conductive and may contain dielectric or magnetic elements. Due to the cohabitation of different materials in one configuration, different regimes (static, quasi-static or dynamic) may coexist. Under the assumption of linear, isotropic and piecewise homogeneous material properties, the surface integral equation (SIE) approach allows to reduce a volume-based problem to an equivalent surface-based problem. However, the usual SIE formulations for the Maxwell's problem generally suffer from numerical noise in asymptotic situations, and especially at low frequencies. The objective of this study is to determine a version that is stable for a range of physical parameters typical of eddy-current NDT applications. In this context, a block-iterative scheme based on a physical decomposition is proposed for the computation of primary fields. This scheme is accurate and well-conditioned. An asymptotic study of the integral Maxwell's problem at low frequencies is also performed, allowing to establish the eddy-current integral problem as an asymptotic case of the corresponding Maxwell problem. (author) [fr

Integrable Time-Dependent Quantum Hamiltonians

Science.gov (United States)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Constraining the thermal conditions of impact environments through integrated low-temperature thermochronometry and numerical modeling

Science.gov (United States)

Kelly, N. M.; Marchi, S.; Mojzsis, S. J.; Flowers, R. M.; Metcalf, J. R.; Bottke, W. F., Jr.

2017-12-01

Impacts have a significant physical and chemical influence on the surface conditions of a planet. The cratering record is used to understand a wide array of impact processes, such as the evolution of the impact flux through time. However, the relationship between impactor size and a resulting impact crater remains controversial (e.g., Bottke et al., 2016). Likewise, small variations in the impact velocity are known to significantly affect the thermal-mechanical disturbances in the aftermath of a collision. Development of more robust numerical models for impact cratering has implications for how we evaluate the disruptive capabilities of impact events, including the extent and duration of thermal anomalies, the volume of ejected material, and the resulting landscape of impacted environments. To address uncertainties in crater scaling relationships, we present an approach and methodology that integrates numerical modeling of the thermal evolution of terrestrial impact craters with low-temperature, (U-Th)/He thermochronometry. The approach uses time-temperature (t-T) paths of crust within an impact crater, generated from numerical simulations of an impact. These t-T paths are then used in forward models to predict the resetting behavior of (U-Th)/He ages in the mineral chronometers apatite and zircon. Differences between the predicted and measured (U-Th)/He ages from a modeled terrestrial impact crater can then be used to evaluate parameters in the original numerical simulations, and refine the crater scaling relationships. We expect our methodology to additionally inform our interpretation of impact products, such as lunar impact breccias and meteorites, providing robust constraints on their thermal histories. In addition, the method is ideal for sample return mission planning - robust "prediction" of ages we expect from a given impact environment enhances our ability to target sampling sites on the Moon, Mars or other solar system bodies where impacts have strongly

Numerical Modelling of Mechanical Integrity of the Copper-Cast Iron Canister. A Literature Review

International Nuclear Information System (INIS)

Lanru Jing

2004-04-01

This review article presents a summary of the research works on the numerical modelling of the mechanical integrity of the composite copper-cast iron canisters for the final disposal of Swedish nuclear wastes, conducted by SKB and SKI since 1992. The objective of the review is to evaluate the outstanding issues existing today about the basic design concepts and premises, fundamental issues on processes, properties and parameters considered for the functions and requirements of canisters under the conditions of a deep geological repository. The focus is placed on the adequacy of numerical modelling approaches adopted in regards to the overall mechanical integrity of the canisters, especially the initial state of canisters regarding defects and the consequences of their evolution under external and internal loading mechanisms adopted in the design premises. The emphasis is the stress-strain behaviour and failure/strength, with creep and plasticity involved. Corrosion, although one of the major concerns in the field of canister safety, was not included

Time-Dependent Heat Conduction Problems Solved by an Integral-Equation Approach

International Nuclear Information System (INIS)

Oberaigner, E.R.; Leindl, M.; Antretter, T.

2010-01-01

Full text: A classical task of mathematical physics is the formulation and solution of a time dependent thermoelastic problem. In this work we develop an algorithm for solving the time-dependent heat conduction equation c p ρ∂ t T-kT, ii =0 in an analytical, exact fashion for a two-component domain. By the Green's function approach the formal solution of the problem is obtained. As an intermediate result an integral-equation for the temperature history at the domain interface is formulated which can be solved analytically. This method is applied to a classical engineering problem, i.e. to a special case of a Stefan-Problem. The Green's function approach in conjunction with the integral-equation method is very useful in cases were strong discontinuities or jumps occur. The initial conditions and the system parameters of the investigated problem give rise to two jumps in the temperature field. Purely numerical solutions are obtained by using the FEM (finite element method) and the FDM (finite difference method) and compared with the analytical approach. At the domain boundary the analytical solution and the FEM-solution are in good agreement, but the FDM results show a signicant smearing effect. (author)

Deep Time Data Infrastructure: Integrating Our Current Geologic and Biologic Databases

Science.gov (United States)

Kolankowski, S. M.; Fox, P. A.; Ma, X.; Prabhu, A.

2016-12-01

As our knowledge of Earth's geologic and mineralogical history grows, we require more efficient methods of sharing immense amounts of data. Databases across numerous disciplines have been utilized to offer extensive information on very specific Epochs of Earth's history up to its current state, i.e. Fossil record, rock composition, proteins, etc. These databases could be a powerful force in identifying previously unseen correlations such as relationships between minerals and proteins. Creating a unifying site that provides a portal to these databases will aid in our ability as a collaborative scientific community to utilize our findings more effectively. The Deep-Time Data Infrastructure (DTDI) is currently being defined as part of a larger effort to accomplish this goal. DTDI will not be a new database, but an integration of existing resources. Current geologic and related databases were identified, documentation of their schema was established and will be presented as a stage by stage progression. Through conceptual modeling focused around variables from their combined records, we will determine the best way to integrate these databases using common factors. The Deep-Time Data Infrastructure will allow geoscientists to bridge gaps in data and further our understanding of our Earth's history.

Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques

NARCIS (Netherlands)

Rodriguez, A.; Ibanescu, M.; Iannuzzi, D.; Joannopoulos, J. D.; Johnson, S.T.

2007-01-01

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the

Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM

Directory of Open Access Journals (Sweden)

Reza Abazari

2013-01-01

Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.

Time-symmetric initial data for binary black holes in numerical relativity

International Nuclear Information System (INIS)

Blanchet, Luc

2003-01-01

We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily static black holes, in the form of a conformal decomposition of the spatial metric. This solution is isometric to the post-Newtonian (PN) metric up to the 2PN order. It represents a nonlinear deformation of the solution of Brill and Lindquist, i.e. an asymptotically flat region is connected to two asymptotically flat (in a certain weak sense) sheets that are the images of the two singularities through appropriate inversion transformations. The total Arnowitt-Deser-Misner mass M as well as the individual masses m 1 and m 2 (when they exist) are computed by surface integrals performed at infinity. Using second order perturbation theory on the Brill-Lindquist background, we prove that the binary's interacting mass-energy M-m 1 -m 2 is well defined at the 2PN order and in agreement with the known post-Newtonian result

Integrated numerical modeling of a laser gun injector

International Nuclear Information System (INIS)

Liu, H.; Benson, S.; Bisognano, J.; Liger, P.; Neil, G.; Neuffer, D.; Sinclair, C.; Yunn, B.

1993-06-01

CEBAF is planning to incorporate a laser gun injector into the linac front end as a high-charge cw source for a high-power free electron laser and nuclear physics. This injector consists of a DC laser gun, a buncher, a cryounit and a chicane. The performance of the injector is predicted based on integrated numerical modeling using POISSON, SUPERFISH and PARMELA. The point-by-point method incorporated into PARMELA by McDonald is chosen for space charge treatment. The concept of ''conditioning for final bunching'' is employed to vary several crucial parameters of the system for achieving highest peak current while maintaining low emittance and low energy spread. Extensive parameter variation studies show that the design will perform beyond the specifications for FEL operations aimed at industrial applications and fundamental scientific research. The calculation also shows that the injector will perform as an extremely bright cw electron source

SOCIAL INTEGRATION: TESTING ANTECEDENTS OF TIME SPENT ONLINE

Directory of Open Access Journals (Sweden)

Lily Suriani Mohd Arif

2013-07-01

Full Text Available The literature on the relationship of social integration and time spent onlineprovides conflicting evidence of the relationship of social integration with timespent online. The study identifies and highlightsthe controversy and attempts toclarify the relationship of social integration withtime spent online bydecomposing the construct social integration into its affective and behavioraldimensions . Thestudy tests antecedents and effects of time spent online in arandom sample of senior level undergraduate students at a public university inMalaysia. The findings indicated that while self-report measures of behavioralsocial integration did not predict time spent online, and, the affective socialintegration had an inverse relationship with time spent online.

Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations

National Research Council Canada - National Science Library

Mitchell, Jason

2002-01-01

A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...

Numerical orbit generators of artificial earth satellites

Science.gov (United States)

Kugar, H. K.; Dasilva, W. C. C.

1984-04-01

A numerical orbit integrator containing updatings and improvements relative to the previous ones that are being utilized by the Departmento de Mecanica Espacial e Controle (DMC), of INPE, besides incorporating newer modellings resulting from the skill acquired along the time is presented. Flexibility and modularity were taken into account in order to allow future extensions and modifications. Characteristics of numerical accuracy, processing quickness, memory saving as well as utilization aspects were also considered. User's handbook, whole program listing and qualitative analysis of accuracy, processing time and orbit perturbation effects were included as well.

Numerical investigation of the late-time Kerr tails

Energy Technology Data Exchange (ETDEWEB)

Racz, Istvan; Toth, Gabor Zs, E-mail: iracz@rmki.kfki.hu, E-mail: tgzs@rmki.kfki.hu [RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)

2011-10-07

The late-time behavior of a scalar field on fixed Kerr background is examined in a numerical framework incorporating the techniques of conformal compactification and hyperbolic initial value formulation. The applied code is 1+(1+2) as it is based on the use of the spectral method in the angular directions while in the time-radial section fourth order finite differencing, along with the method of lines, is applied. The evolution of various types of stationary and non-stationary pure multipole initial states are investigated. The asymptotic decay rates are determined not only in the domain of outer communication but along the event horizon and at future null infinity as well. The decay rates are found to be different for stationary and non-stationary initial data, and they also depend on the fall off properties of the initial data toward future null infinity. The energy and angular momentum transfers are found to show significantly different behavior in the initial phase of the time evolution. The quasinormal ringing phase and the tail phase are also investigated. In the tail phase, the decay exponents for the energy and angular momentum losses at I{sup +} are found to be smaller than at the horizon which is in accordance with the behavior of the field itself and it means that at late times the energy and angular momentum falling into the black hole become negligible in comparison with the energy and angular momentum radiated toward I{sup +}. The energy and angular momentum balances are used as additional verifications of the reliability of our numerical method.

Numerical investigation of the late-time Kerr tails

International Nuclear Information System (INIS)

Racz, Istvan; Toth, Gabor Zs

2011-01-01

The late-time behavior of a scalar field on fixed Kerr background is examined in a numerical framework incorporating the techniques of conformal compactification and hyperbolic initial value formulation. The applied code is 1+(1+2) as it is based on the use of the spectral method in the angular directions while in the time-radial section fourth order finite differencing, along with the method of lines, is applied. The evolution of various types of stationary and non-stationary pure multipole initial states are investigated. The asymptotic decay rates are determined not only in the domain of outer communication but along the event horizon and at future null infinity as well. The decay rates are found to be different for stationary and non-stationary initial data, and they also depend on the fall off properties of the initial data toward future null infinity. The energy and angular momentum transfers are found to show significantly different behavior in the initial phase of the time evolution. The quasinormal ringing phase and the tail phase are also investigated. In the tail phase, the decay exponents for the energy and angular momentum losses at I + are found to be smaller than at the horizon which is in accordance with the behavior of the field itself and it means that at late times the energy and angular momentum falling into the black hole become negligible in comparison with the energy and angular momentum radiated toward I + . The energy and angular momentum balances are used as additional verifications of the reliability of our numerical method.

Digging Back In Time: Integrating Historical Data Into an Operational Ocean Observing System

Science.gov (United States)

McCammon, M.

2016-02-01

Modern technologies allow reporting and display of data near real-time from in situ instrumentation live on the internet. This has given users fast access to critical information for scientific applications, marine safety, planning, and numerous other activities. Equally as valuable is having access to historical data sets. However, it is challenging to identify sources and access of historical data of interest as it exists in many different locations, depending on the funding source and provider. Also, time-varying formats can make it difficult to data-mine and display historical data. There is also the issue of data quality, and having a systematic means of assessing credibility of historical data sets. The Alaska Ocean Observing System (AOOS) data management system demonstrates the successful ingestion of historical data, both old and new (as recent as yesterday) and has integrated numerous historical data streams into user friendly data portals, available for data upload and display on the AOOS Website. An example is the inclusion of non-real-time (e.g. day old) AIS (Automatic Identification System) ship tracking data, important for scientists working in marine mammal migration regions. Other examples include historical sea ice data, and various data streams from previous research projects (e.g. moored time series, HF Radar surface currents, weather, shipboard CTD). Most program or project websites only offer access to data specific to their agency or project alone, but do not have the capacity to provide access to the plethora of other data that might be available for the region and be useful for integration, comparison and synthesis. AOOS offers end users access to a one stop-shop for data in the area they want to research, helping them identify other sources of information and access. Demonstrations of data portals using historical data illustrate these benefits.

A Generalized Technique in Numerical Integration

Science.gov (United States)

Safouhi, Hassan

2018-02-01

Integration by parts is one of the most popular techniques in the analysis of integrals and is one of the simplest methods to generate asymptotic expansions of integral representations. The product of the technique is usually a divergent series formed from evaluating boundary terms; however, sometimes the remaining integral is also evaluated. Due to the successive differentiation and anti-differentiation required to form the series or the remaining integral, the technique is difficult to apply to problems more complicated than the simplest. In this contribution, we explore a generalized and formalized integration by parts to create equivalent representations to some challenging integrals. As a demonstrative archetype, we examine Bessel integrals, Fresnel integrals and Airy functions.

Numerical solutions of the Vlasov equation

International Nuclear Information System (INIS)

Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi

1985-01-01

A numerical procedure is derived for the solutions of the one- and two-dimensional Vlasov-Poisson system equations. This numerical procedure consists of the phase space discretization and the integration of the resulting set of ordinary differential equations. In the phase space discretization, derivatives with respect to the phase space variable are approximated by a weighted sum of the values of the distribution function at properly chosen neighboring points. Then, the resulting set of ordinary differential equations is solved by using an appropriate time integration scheme. The results for linear Landau damping, nonlinear Landau damping and counter-streaming plasmas are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient. (author)

Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind

Directory of Open Access Journals (Sweden)

Mahmoud Paripour

2014-08-01

Full Text Available In this paper, the Bernstein polynomials are used to approximatethe solutions of linear integral equations with multiple time lags (IEMTL through expansion methods (collocation method, partition method, Galerkin method. The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is carried out

Numerical simulations of inertial confinement fusion hohlraum with LARED-integration code

International Nuclear Information System (INIS)

Li Jinghong; Li Shuanggui; Zhai Chuanlei

2011-01-01

In the target design of the Inertial Confinement Fusion (ICF) program, it is common practice to apply radiation hydrodynamics code to study the key physical processes happened in ICF process, such as hohlraum physics, radiation drive symmetry, capsule implosion physics in the radiation-drive approach of ICF. Recently, many efforts have been done to develop our 2D integrated simulation capability of laser fusion with a variety of optional physical models and numerical methods. In order to effectively integrate the existing codes and to facilitate the development of new codes, we are developing an object-oriented structured-mesh parallel code-supporting infrastructure, called JASMIN. Based on two-dimensional three-temperature hohlraum physics code LARED-H and two-dimensional multi-group radiative transfer code LARED-R, we develop a new generation two-dimensional laser fusion code under the JASMIN infrastructure, which enable us to simulate the whole process of laser fusion from the laser beams' entrance into the hohlraum to the end of implosion. In this paper, we will give a brief description of our new-generation two-dimensional laser fusion code, named LARED-Integration, especially in its physical models, and present some simulation results of holhraum. (author)

Tangent modulus in numerical integration of constitutive relations and its influence on convergence of N-R method

Directory of Open Access Journals (Sweden)

Poruba Z.

2009-06-01

Full Text Available For the numerical solution of elasto-plastic problems with use of Newton-Raphson method in global equilibrium equation it is necessary to determine the tangent modulus in each integration point. To reach the parabolic convergence of Newton-Raphson method it is convenient to use so called algorithmic tangent modulus which is consistent with used integration scheme. For more simple models for example Chaboche combined hardening model it is possible to determine it in analytical way. In case of more robust macroscopic models it is in many cases necessary to use the approximation approach. This possibility is presented in this contribution for radial return method on Chaboche model. An example solved in software Ansys corresponds to line contact problem with assumption of Coulomb's friction. The study shows at the end that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N-R method, initial stiffness method.

Experimental and numerical analyses on thermal performance of different typologies of PCMs integrated in the roof space

DEFF Research Database (Denmark)

Elarga, Hagar; Fantucci, Stefano; Serra, Valentina

2017-01-01

portions, one, the bare roof, representing the reference case without PCMs, the other two integrating two PCM's typologies with different melting/solidification temperatures range. A numerical model was furthermore developed implementing the equivalent capacitance numerical method to describe the substance...... peak load between 13% and 59% depending on the PCM typology, highlighting that to reach the expected performance the proper PCM type should be carefully selected....

Numerical modelling of softwood time-dependent behaviour based on microstructure

DEFF Research Database (Denmark)

Engelund, Emil Tang

2010-01-01

The time-dependent mechanical behaviour of softwood such as creep or relaxation can be predicted, from knowledge of the microstructural arrangement of the cell wall, by applying deformation kinetics. This has been done several times before; however, often without considering the constraints defined...... by the basic physical mechanism behind the time-dependent behaviour. The mechanism causing time-dependency is thought to be sliding of the microfibrils past each other as a result breaking and re-bonding of hydrogen bonds. This can be incorporated in a numerical model by only allowing time-dependency in shear...

Experimental and Numerical Investigations in Shallow Cut Grinding by Workpiece Integrated Infrared Thermopile Array.

Science.gov (United States)

Reimers, Marcel; Lang, Walter; Dumstorff, Gerrit

2017-09-30

The purpose of our study is to investigate the heat distribution and the occurring temperatures during grinding. Therefore, we did both experimental and numerical investigations. In the first part, we present the integration of an infrared thermopile array in a steel workpiece. Experiments are done by acquiring data from the thermopile array during grinding of a groove in a workpiece made of steel. In the second part, we present numerical investigations in the grinding process to further understand the thermal characteristic during grinding. Finally, we conclude our work. Increasing the feed speed leads to two things: higher heat flux densities in the workpiece and higher temperature gradients in the material.

Time Domain Surface Integral Equation Solvers for Quantum Corrected Electromagnetic Analysis of Plasmonic Nanostructures

KAUST Repository

Uysal, Ismail Enes

2016-10-01

Plasmonic structures are utilized in many applications ranging from bio-medicine to solar energy generation and transfer. Numerical schemes capable of solving equations of classical electrodynamics have been the method of choice for characterizing scattering properties of such structures. However, as dimensions of these plasmonic structures reduce to nanometer scale, quantum mechanical effects start to appear. These effects cannot be accurately modeled by available classical numerical methods. One of these quantum effects is the tunneling, which is observed when two structures are located within a sub-nanometer distance of each other. At these small distances electrons “jump" from one structure to another and introduce a path for electric current to flow. Classical equations of electrodynamics and the schemes used for solving them do not account for this additional current path. This limitation can be lifted by introducing an auxiliary tunnel with material properties obtained using quantum models and applying a classical solver to the structures connected by this auxiliary tunnel. Early work on this topic focused on quantum models that are generated using a simple one-dimensional wave function to find the tunneling probability and assume a simple Drude model for the permittivity of the tunnel. These tunnel models are then used together with a classical frequency domain solver. In this thesis, a time domain surface integral equation solver for quantum corrected analysis of transient plasmonic interactions is proposed. This solver has several advantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differential equation solvers, it only discretizes surfaces (reducing number of unknowns), enforces the radiation condition implicitly (increasing the accuracy), and allows for time step selection independent of spatial discretization (increasing efficiency). The quantum model

A Stable Marching on-in-time Scheme for Solving the Time Domain Electric Field Volume Integral Equation on High-contrast Scatterers

KAUST Repository

Sayed, Sadeed Bin

2015-05-05

A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.

A Stable Marching on-in-time Scheme for Solving the Time Domain Electric Field Volume Integral Equation on High-contrast Scatterers

KAUST Repository

Sayed, Sadeed Bin; Ulku, Huseyin; Bagci, Hakan

2015-01-01

A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.

A new approach to calculate charge carrier transport mobility in organic molecular crystals from imaginary time path integral simulations

International Nuclear Information System (INIS)

Song, Linze; Shi, Qiang

2015-01-01

We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated

Some considerations on displacement assumed finite elements with the reduced numerical integration technique

International Nuclear Information System (INIS)

Takeda, H.; Isha, H.

1981-01-01

The paper is concerned with the displacement-assumed-finite elements by applying the reduced numerical integration technique in structural problems. The first part is a general consideration on the technique. Its purpose is to examine a variational interpretation of the finite element displacement formulation with the reduced integration technique in structural problems. The formulation is critically studied from a standpoint of the natural stiffness approach. It is shown that these types of elements are equivalent to a certain type of displacement and stress assumed mixed elements. The rank deficiency of the stiffness matrix of these elements is interpreted as a problem in the transformation from the natural system to a Cartesian system. It will be shown that a variational basis of the equivalent mixed formulation is closely related to the Hellinger-Reissner's functional. It is presented that for simple elements, e.g. bilinear quadrilateral plane stress and plate bending there are corresponding mixed elements from the functional. For relatively complex types of these elements, it is shown that they are equivalent to localized mixed elements from the Hellinger-Reissner's functional. In the second part, typical finite elements with the reduced integration technique are studied to demonstrate this equivalence. A bilinear displacement and rotation assumed shear beam element, a bilinear displacement assumed quadrilateral plane stress element and a bilinear deflection and rotation assumed quadrilateral plate bending element are examined to present equivalent mixed elements. Not only the theoretical consideration is presented but numerical studies are shown to demonstrate the effectiveness of these elements in practical analysis. (orig.)

On numerical Bessel transformation

International Nuclear Information System (INIS)

Sommer, B.; Zabolitzky, J.G.

1979-01-01

The authors present a computer program to calculate the three dimensional Fourier or Bessel transforms and definite integrals with Bessel functions. Numerical integration of systems containing Bessel functions occurs in many physical problems, e.g. electromagnetic form factor of nuclei, all transitions involving multipole expansions at high momenta. Filon's integration rule is extended to spherical Bessel functions. The numerical error is of the order of the Simpson error term of the function which has to be transformed. Thus one gets a stable integral even at large arguments of the transformed function. (Auth.)

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.

Sull'Integrazione delle Strutture Numeriche nella Scuola dell'Obbligo (Integrating Numerical Structures in Mandatory School).

Science.gov (United States)

Bonotto, C.

1995-01-01

Attempted to verify knowledge regarding decimal and rational numbers in children ages 10-14. Discusses how pupils can receive and assimilate extensions of the number system from natural numbers to decimals and fractions and later can integrate this extension into a single and coherent numerical structure. (Author/MKR)

Advances in Integrated Vehicle Thermal Management and Numerical Simulation

Directory of Open Access Journals (Sweden)

Yan Wang

2017-10-01

Full Text Available With the increasing demands for vehicle dynamic performance, economy, safety and comfort, and with ever stricter laws concerning energy conservation and emissions, vehicle power systems are becoming much more complex. To pursue high efficiency and light weight in automobile design, the power system and its vehicle integrated thermal management (VITM system have attracted widespread attention as the major components of modern vehicle technology. Regarding the internal combustion engine vehicle (ICEV, its integrated thermal management (ITM mainly contains internal combustion engine (ICE cooling, turbo-charged cooling, exhaust gas recirculation (EGR cooling, lubrication cooling and air conditioning (AC or heat pump (HP. As for electric vehicles (EVs, the ITM mainly includes battery cooling/preheating, electric machines (EM cooling and AC or HP. With the rational effective and comprehensive control over the mentioned dynamic devices and thermal components, the modern VITM can realize collaborative optimization of multiple thermodynamic processes from the aspect of system integration. Furthermore, the computer-aided calculation and numerical simulation have been the significant design methods, especially for complex VITM. The 1D programming can correlate multi-thermal components and the 3D simulating can develop structuralized and modularized design. Additionally, co-simulations can virtualize simulation of various thermo-hydraulic behaviors under the vehicle transient operational conditions. This article reviews relevant researching work and current advances in the ever broadening field of modern vehicle thermal management (VTM. Based on the systematic summaries of the design methods and applications of ITM, future tasks and proposals are presented. This article aims to promote innovation of ITM, strengthen the precise control and the performance predictable ability, furthermore, to enhance the level of research and development (R&D.

On the efficient numerical solution of lattice systems with low-order couplings

International Nuclear Information System (INIS)

Ammon, A.; Genz, A.; Hartung, T.; Jansen, K.; Volmer, J.; Leoevey, H.

2015-10-01

We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling.

Numerical Methods for Pricing American Options with Time-Fractional PDE Models

Directory of Open Access Journals (Sweden)

Zhiqiang Zhou

2016-01-01

Full Text Available In this paper we develop a Laplace transform method and a finite difference method for solving American option pricing problem when the change of the option price with time is considered as a fractal transmission system. In this scenario, the option price is governed by a time-fractional partial differential equation (PDE with free boundary. The Laplace transform method is applied to the time-fractional PDE. It then leads to a nonlinear equation for the free boundary (i.e., optimal early exercise boundary function in Laplace space. After numerically finding the solution of the nonlinear equation, the Laplace inversion is used to transform the approximate early exercise boundary into the time space. Finally the approximate price of the American option is obtained. A boundary-searching finite difference method is also proposed to solve the free-boundary time-fractional PDEs for pricing the American options. Numerical examples are carried out to compare the Laplace approach with the finite difference method and it is confirmed that the former approach is much faster than the latter one.

Experimental and Numerical Investigations in Shallow Cut Grinding by Workpiece Integrated Infrared Thermopile Array

Directory of Open Access Journals (Sweden)

Marcel Reimers

2017-09-01

Full Text Available The purpose of our study is to investigate the heat distribution and the occurring temperatures during grinding. Therefore, we did both experimental and numerical investigations. In the first part, we present the integration of an infrared thermopile array in a steel workpiece. Experiments are done by acquiring data from the thermopile array during grinding of a groove in a workpiece made of steel. In the second part, we present numerical investigations in the grinding process to further understand the thermal characteristic during grinding. Finally, we conclude our work. Increasing the feed speed leads to two things: higher heat flux densities in the workpiece and higher temperature gradients in the material.

A time-spectral approach to numerical weather prediction

Science.gov (United States)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

Energy Technology Data Exchange (ETDEWEB)

Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex (France); Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex (France); Maday, Yvon, E-mail: maday@ann.jussieu.fr [Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions and Institut Universitaire de France, F-75005, Paris (France); Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); Brown Univ, Division of Applied Maths, Providence, RI (United States); Riahi, Mohamed Kamel, E-mail: riahi@cmap.polytechnique.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CMAP, Inria-Saclay and X-Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex (France); Salomon, Julien, E-mail: salomon@ceremade.dauphine.fr [CEREMADE, Univ Paris-Dauphine, Pl. du Mal. de Lattre de Tassigny, F-75016, Paris (France)

2014-12-15

In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.

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…

A higher order space-time Galerkin scheme for time domain integral equations

KAUST Repository

Pray, Andrew J.

2014-12-01

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method\\'s efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

A higher order space-time Galerkin scheme for time domain integral equations

KAUST Repository

Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam

2014-01-01

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

Computation of Green function of the Schroedinger-like partial differential equations by the numerical functional integration

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.; Shahbagian, R.R.; Zhidkov, E.P.

1991-01-01

A new method for numerical solution of the boundary problem for Schroedinger-like partial differential equations in R n is elaborated. The method is based on representation of multidimensional Green function in the form of multiple functional integral and on the use of approximation formulas which are constructed for such integrals. The convergence of approximations to the exact value is proved, the remainder of the formulas is estimated. Method reduces the initial differential problem to quadratures. 16 refs.; 7 tabs

Numerical experiments on unstructured PIC stability.

Energy Technology Data Exchange (ETDEWEB)

Day, David Minot

2011-04-01

Particle-In-Cell (PIC) is a method for plasmas simulation. Particles are pushed with Verlet time integration. Fields are modeled using finite differences on a tensor product mesh (cells). The Unstructured PIC methods studied here use instead finite element discretizations on unstructured (simplicial) meshes. PIC is constrained by stability limits (upper bounds) on mesh and time step sizes. Numerical evidence (2D) and analysis will be presented showing that similar bounds constrain unstructured PIC.

A numerical solution for a class of time fractional diffusion equations with delay

Directory of Open Access Journals (Sweden)

Pimenov Vladimir G.

2017-09-01

Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

Theoretical and numerical investigations of sub-wavelength diffractive optical structures

DEFF Research Database (Denmark)

Dridi, Kim

2000-01-01

The work in this thesis concerns theoretical and numerical investigations of sub-wavelength diffractive optical structures, relying on advanced two-dimensional vectorial numerical models that have applications in Optics and Electromagnetics. Integrated Optics is predicted to play a major role......, such as in dielectric waveguides with gratings and periodic media or photonic crystal structures. The vectorial electromagnetic nature of light is therefore taken into account in the modeling of these diffractive structures. An electromagnetic vector-field model for optical components design based on the classical...... finite-difference time domain method and exact radiation integrals is implemented for the polarization where the electric field vector is perpendicular to the two dimentional plane of symmetry. The computational model solves the full vectorial time domain Maxwell equations with general sources...

Equilibrium and response properties of the integrate-and-fire neuron in discrete time

Directory of Open Access Journals (Sweden)

Moritz Helias

2010-01-01

Full Text Available The integrate-and-fire neuron with exponential postsynaptic potentials is a frequently employed model to study neural networks. Simulations in discrete time still have highest performance at moderate numerical errors, which makes them first choice for long-term simulations of plastic networks. Here we extend the population density approach to investigate how the equilibrium and response properties of the leaky integrate-and-fire neuron are affected by time discretization. We present a novel analytical treatment of the boundary condition at threshold, taking both discretization of time and finite synaptic weights into account. We uncover an increased membrane potential density just below threshold as the decisive property that explains the deviations found between simulations and the classical diffusion approximation. Temporal discretization and finite synaptic weights both contribute to this effect. Our treatment improves the standard formula to calculate the neuron’s equilibrium firing rate. Direct solution of the Markov process describing the evolution of the membrane potential density confirms our analysis and yields a method to calculate the firing rate exactly. Knowing the shape of the membrane potential distribution near threshold enables us to devise the transient response properties of the neuron model to synaptic input. We find a pronounced non-linear fast response component that has not been described by the prevailing continuous time theory for Gaussian white noise input.

Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests

International Nuclear Information System (INIS)

Zilhao, Miguel; Herdeiro, Carlos; Witek, Helvi; Nerozzi, Andrea; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo

2010-01-01

The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.

Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

Science.gov (United States)

Erler, Norbert; Groß, Michael

2015-05-01

Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.

Numerical estimation of structural integrity of salt cavern wells.

NARCIS (Netherlands)

Orlic, B.; Thienen-Visser, K. van; Schreppers, G.J.

2016-01-01

Finite element analyses were performed to estimate axial deformation of cavern wells due to gas storage operations in solution-mined salt caverns. Caverns shrink over time due to salt creep and the cavern roof subsides potentially threatening well integrity. Cavern deformation, deformation of salt

Efficient orbit integration by manifold correction methods.

Science.gov (United States)

Fukushima, Toshio

2005-12-01

Triggered by a desire to investigate, numerically, the planetary precession through a long-term numerical integration of the solar system, we developed a new formulation of numerical integration of orbital motion named manifold correct on methods. The main trick is to rigorously retain the consistency of physical relations, such as the orbital energy, the orbital angular momentum, or the Laplace integral, of a binary subsystem. This maintenance is done by applying a correction to the integrated variables at each integration step. Typical methods of correction are certain geometric transformations, such as spatial scaling and spatial rotation, which are commonly used in the comparison of reference frames, or mathematically reasonable operations, such as modularization of angle variables into the standard domain [-pi, pi). The form of the manifold correction methods finally evolved are the orbital longitude methods, which enable us to conduct an extremely precise integration of orbital motions. In unperturbed orbits, the integration errors are suppressed at the machine epsilon level for an indefinitely long period. In perturbed cases, on the other hand, the errors initially grow in proportion to the square root of time and then increase more rapidly, the onset of which depends on the type and magnitude of the perturbations. This feature is also realized for highly eccentric orbits by applying the same idea as used in KS-regularization. In particular, the introduction of time elements greatly enhances the performance of numerical integration of KS-regularized orbits, whether the scaling is applied or not.

Numerical Solution of Nonlinear Volterra Integral Equations System Using Simpson’s 3/8 Rule

Directory of Open Access Journals (Sweden)

Adem Kılıçman

2012-01-01

Full Text Available The Simpson’s 3/8 rule is used to solve the nonlinear Volterra integral equations system. Using this rule the system is converted to a nonlinear block system and then by solving this nonlinear system we find approximate solution of nonlinear Volterra integral equations system. One of the advantages of the proposed method is its simplicity in application. Further, we investigate the convergence of the proposed method and it is shown that its convergence is of order O(h4. Numerical examples are given to show abilities of the proposed method for solving linear as well as nonlinear systems. Our results show that the proposed method is simple and effective.

A multi-domain spectral method for time-fractional differential equations

Science.gov (United States)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Integration of MDSplus in real-time systems

International Nuclear Information System (INIS)

Luchetta, A.; Manduchi, G.; Taliercio, C.

2006-01-01

RFX-mod makes extensive usage of real-time systems for feedback control and uses MDSplus to interface them to the main Data Acquisition system. For this purpose, the core of MDSplus has been ported to VxWorks, the operating system used for real-time control in RFX. Using this approach, it is possible to integrate real-time systems, but MDSplus is used only for non-real-time tasks, i.e. those tasks which are executed before and after the pulse and whose performance does not affect the system time constraints. More extensive use of MDSplus in real-time systems is foreseen, and a real-time layer for MDSplus is under development, which will provide access to memory-mapped pulse files, shared by the tasks running on the same CPU. Real-time communication will also be integrated in the MDSplus core to provide support for distributed memory-mapped pulse files

Multi-channel time-division integrator in HL-2A

International Nuclear Information System (INIS)

Yan Ji

2008-01-01

HL-2A is China's first Tokamak device with divertor configuration (magnetic confinement controlled nuclear fusion device). To find out the details of on-going fusion reaction at different times is of important significance in achieving controlled nuclear fusion. We developed a new type multi-channel time-division integrator for HL-2A. It has functions of automatic cutting off negative pulse of the input signals, optional integrating time division spacing 0.2-1 ms, TTL starting trigger signal, automatic regularly work 20 s, and integrating 10 channel at the same time. (authors)

Numerical modeling of wind turbine aerodynamic noise in the time domain.

Science.gov (United States)

Lee, Seunghoon; Lee, Seungmin; Lee, Soogab

2013-02-01

Aerodynamic noise from a wind turbine is numerically modeled in the time domain. An analytic trailing edge noise model is used to determine the unsteady pressure on the blade surface. The far-field noise due to the unsteady pressure is calculated using the acoustic analogy theory. By using a strip theory approach, the two-dimensional noise model is applied to rotating wind turbine blades. The numerical results indicate that, although the operating and atmospheric conditions are identical, the acoustical characteristics of wind turbine noise can be quite different with respect to the distance and direction from the wind turbine.

A round robin on numerical analyses for impact problems

International Nuclear Information System (INIS)

Yagawa, G.; Ohtsubo, H.; Toi, Y.; Aizawa, T.; Ikushima, T.

1984-01-01

In this paper, two types of numerical tests are performed using several general- and special-purpose computer codes to understand dynamic behaviors of CASK for nuclear fuel shipping under the impact onto rigid floor due to the accidental fall from the height of 9 m. Discussed are the efficiency and the validity of direct time integration schemes and the effects of material and geometric nonlinearities and contact conditions on the numerical data. (orig.)

Development of Integrated Simulation System for Helical Plasmas

Energy Technology Data Exchange (ETDEWEB)

Nakamura, Y.; Yokoyama, M.; Nakajima, N.; Fukuyama, A.; Watanabe, K. Y.; Funaba, H.; Suzuki, Y.; Murakami, S.; Ida, K.; Sakakibara, S.; Yamada, H.

2005-07-01

Recent progress of computers (parallel/vector-parallel computers, PC clusters, for example) and numerical codes for helical plasmas like three-dimensional MHD equilibrium codes, combined with the development of the plasma diagnostics technique, enable us to do the detailed theoretical analyses of the individual experimental observations. Now, it is pointed out that the experimental data analysis from the viewpoints of integrated physics is an important issue to understand the confinement physics globally. In addition to that, there are international movements towards the integrated numerical simulation study. One is several proposals of integrated modeling of burning tokamak plasmas, motivated by the ITER activity. The integrated numerical simulation will be a good help to draw up new experimental plans especially for burning plasma experiments. Another movement is international collaborations on the confinement database and neoclassical transport in helical plasmas/stellarators. These backgrounds motivate us to start the development of the integrated simulation system which has a modular structure and user-friendly interfaces. The integrated simulation system, which is based on the hierarchical and multi-scale (time and space) modeling, will also be a platform for theoreticians to test their own model such as turbulent transport model. In this paper, we will show the strategy of developing the integrated simulation system and present status of the development. Especially, we discuss the modeling of the time evolution of the plasma net current profile, which is equivalent to the time evolution of the rotational transform profile, in the resistive time scale. (Author)

Numerical investigation of premixed combustion in a porous burner with integrated heat exchanger

Energy Technology Data Exchange (ETDEWEB)

Farzaneh, Meisam; Shafiey, Mohammad; Shams, Mehrzad [K.N. Toosi University of Technology, Department of Mechanical Engineering, Tehran (Iran, Islamic Republic of); Ebrahimi, Reza [K.N. Toosi University of Technology, Department of Aerospace Engineering, Tehran (Iran, Islamic Republic of)

2012-07-15

In this paper, we perform a numerical analysis of a two-dimensional axisymmetric problem arising in premixed combustion in a porous burner with integrated heat exchanger. The physical domain consists of two zones, porous and heat exchanger zones. Two dimensional Navier-Stokes equations, gas and solid energy equations, and chemical species transport equations are solved and heat release is described by a multistep kinetics mechanism. The solid matrix is modeled as a gray medium, and the finite volume method is used to solve the radiative transfer equation to calculate the local radiation source/sink in the solid phase energy equation. Special attention is given to model heat transfer between the hot gas and the heat exchanger tube. Thus, the corresponding terms are added to the energy equations of the flow and the solid matrix. Gas and solid temperature profiles and species mole fractions on the burner centerline, predicted 2D temperature fields, species concentrations and streamlines are presented. Calculated results for temperature profiles are compared to experimental data. It is shown that there is good agreement between the numerical solutions and the experimental data and it is concluded that the developed numerical program is an excellent tool to investigate combustion in porous burner. (orig.)

Self-adaptive numerical integrator for analytic functions

International Nuclear Information System (INIS)

Garribba, S.; Quartapelle, L.; Reina, G.

1978-01-01

A new adaptive algorithm for the integration of analytical functions is presented. The algorithm processes the integration interval by generating local subintervals whose length is controlled through a feedback loop. The control is obtained by means of a relation derived on an analytical basis and valid for an arbitrary integration rule: two different estimates of an integral are used to compute the interval length necessary to obtain an integral estimate with accuracy within the assigned error bounds. The implied method for local generation of subintervals and an effective assumption of error partition among subintervals give rise to an adaptive algorithm provided with a highly accurate and very efficient integration procedure. The particular algorithm obtained by choosing the 6-point Gauss-Legendre integration rule is considered and extensive comparisons are made with other outstanding integration algorithms

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.

Analytical solutions for prediction of the ignition time of wood particles based on a time and space integral method

International Nuclear Information System (INIS)

Haseli, Y.; Oijen, J.A. van; Goey, L.P.H. de

2012-01-01

Highlights: ► A simple model for prediction of the ignition time of a wood particle is presented. ► The formulation is given for both thermally thin and thermally thick particles. ► Transition from thermally thin to thick regime occurs at a critical particle size. ► The model is validated against a numerical model and various experimental data. - Abstract: The main idea of this paper is to establish a simple approach for prediction of the ignition time of a wood particle assuming that the thermo-physical properties remain constant and ignition takes place at a characteristic ignition temperature. Using a time and space integral method, explicit relationships are derived for computation of the ignition time of particles of three common shapes (slab, cylinder and sphere), which may be characterized as thermally thin or thermally thick. It is shown through a dimensionless analysis that the dimensionless ignition time can be described as a function of non-dimensional ignition temperature, reactor temperature or external incident heat flux, and parameter K which represents the ratio of conduction heat transfer to the external radiation heat transfer. The numerical results reveal that for the dimensionless ignition temperature between 1.25 and 2.25 and for values of K up to 8000 (corresponding to woody materials), the variation of the ignition time of a thermally thin particle with K and the dimensionless ignition temperature is linear, whereas the dependence of the ignition time of a thermally thick particle on the above two parameters obeys a quadratic function. Furthermore, it is shown that the transition from the regime of thermally thin to the regime of thermally thick occurs at K cr (corresponding to a critical size of particle) which is found to be independent of the particle shape. The model is validated by comparing the predicted and the measured ignition time of several wood particles obtained from different sources. Good agreement is achieved which

Characterisation of large catastrophic landslides using an integrated field, remote sensing and numerical modelling approach

OpenAIRE

Wolter, Andrea Elaine

2014-01-01

I apply a forensic, multidisciplinary approach that integrates engineering geology field investigations, engineering geomorphology mapping, long-range terrestrial photogrammetry, and a numerical modelling toolbox to two large rock slope failures to study their causes, initiation, kinematics, and dynamics. I demonstrate the significance of endogenic and exogenic processes, both separately and in concert, in contributing to landscape evolution and conditioning slopes for failure, and use geomor...

Application of the numerical Laplace transform inversion to neutron transport theory

International Nuclear Information System (INIS)

Ganapol, B.D.

1989-01-01

A numerical Laplace transform inversion is developed using the Hurwitz-Zweifel method of evaluating the Fourier cosine integral coupled with an Euler-Knopp transformation. The numerical inversion is then applied to problems in linear transport theory concerning slowing down, time-dependence and featuring the determination of the interior scalar flux solution to the one-group stationary transport equation in half-space geometry

The macroevolutionary consequences of phenotypic integration: from development to deep time.

Science.gov (United States)

Goswami, A; Smaers, J B; Soligo, C; Polly, P D

2014-08-19

Phenotypic integration is a pervasive characteristic of organisms. Numerous analyses have demonstrated that patterns of phenotypic integration are conserved across large clades, but that significant variation also exists. For example, heterochronic shifts related to different mammalian reproductive strategies are reflected in postcranial skeletal integration and in coordination of bone ossification. Phenotypic integration and modularity have been hypothesized to shape morphological evolution, and we extended simulations to confirm that trait integration can influence both the trajectory and magnitude of response to selection. We further demonstrate that phenotypic integration can produce both more and less disparate organisms than would be expected under random walk models by repartitioning variance in preferred directions. This effect can also be expected to favour homoplasy and convergent evolution. New empirical analyses of the carnivoran cranium show that rates of evolution, in contrast, are not strongly influenced by phenotypic integration and show little relationship to morphological disparity, suggesting that phenotypic integration may shape the direction of evolutionary change, but not necessarily the speed of it. Nonetheless, phenotypic integration is problematic for morphological clocks and should be incorporated more widely into models that seek to accurately reconstruct both trait and organismal evolution.

Hippocampal “Time Cells”: Time versus Path Integration

Science.gov (United States)

Kraus, Benjamin J.; Robinson, Robert J.; White, John A.; Eichenbaum, Howard; Hasselmo, Michael E.

2014-01-01

SUMMARY Recent studies have reported the existence of hippocampal “time cells,” neurons that fire at particular moments during periods when behavior and location are relatively constant. However, an alternative explanation of apparent time coding is that hippocampal neurons “path integrate” to encode the distance an animal has traveled. Here, we examined hippocampal neuronal firing patterns as rats ran in place on a treadmill, thus “clamping” behavior and location, while we varied the treadmill speed to distinguish time elapsed from distance traveled. Hippocampal neurons were strongly influenced by time and distance, and less so by minor variations in location. Furthermore, the activity of different neurons reflected integration over time and distance to varying extents, with most neurons strongly influenced by both factors and some significantly influenced by only time or distance. Thus, hippocampal neuronal networks captured both the organization of time and distance in a situation where these dimensions dominated an ongoing experience. PMID:23707613

Numerical Asymptotic Solutions Of Differential Equations

Science.gov (United States)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Integrated survival analysis using an event-time approach in a Bayesian framework.

Science.gov (United States)

Walsh, Daniel P; Dreitz, Victoria J; Heisey, Dennis M

2015-02-01

Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.

Integrated survival analysis using an event-time approach in a Bayesian framework

Science.gov (United States)

Walsh, Daniel P.; Dreitz, VJ; Heisey, Dennis M.

2015-01-01

Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.

Incorporating excitation-induced dephasing into the Maxwell-Bloch numerical modeling of photon echoes

International Nuclear Information System (INIS)

Burr, G.W.; Harris, Todd L.; Babbitt, Wm. Randall; Jefferson, C. Michael

2004-01-01

We describe the incorporation of excitation-induced dephasing (EID) into the Maxwell-Bloch numerical simulation of photon echoes. At each time step of the usual numerical integration, stochastic frequency jumps of ions--caused by excitation of neighboring ions--is modeled by convolving each Bloch vector with the Bloch vectors of nearby frequency detunings. The width of this convolution kernel follows the instantaneous change in overall population, integrated over the simulated bandwidth. This approach is validated by extensive comparison against published and original experimental results. The enhanced numerical model is then used to investigate the accuracy of experiments designed to extrapolate to the intrinsic dephasing time T 2 from data taken in the presence of EID. Such a modeling capability offers improved understanding of experimental results, and should allow quantitative analysis of engineering tradeoffs in realistic optical coherent transient applications

Time integration of tensor trains

OpenAIRE

Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart

2014-01-01

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...

Evaluation of wave power by integrating numerical models and measures at the Port of Civitavecchia

International Nuclear Information System (INIS)

Paladini de Mendoza, Francesco; Bonamano, Simone; Carli, Filippo Maria; Marcelli, Marco; Danelli, Andrea; Peviani, Maximo Aurelio; Burgio, Calogero

2015-01-01

An assessment of the available wave power at regional and local scale was carried out. Two hot spots of higher wave power level were identified and characterized along the coastline of northern Latium Region, near the 'Torre Valdaliga' power plant and in proximity of Civitavecchia’s breakwater, where the presence of a harbour and an electric power plant allows wave energy exploitation. The evaluation process was implemented through measurements, and numerical model assessment and validation. The integration of wave gauges measurements with numerical simulations made it possible to estimate the wave power on the extended area near shore. A down scaling process allowed to proceed from regional to local scale providing increased resolution thanks to highly detailed bathymetry.

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

Science.gov (United States)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

Stochastic integrated vendor–buyer model with unstable lead time and setup cost

Directory of Open Access Journals (Sweden)

Chandra K. Jaggi

2011-01-01

Full Text Available This paper presents a new vendor-buyer system where there are different objectives for both sides. The proposed method of this paper is different from the other previously published works since it considers different objectives for both sides. In this paper, the vendor’s emphasis is on the crashing of the setup cost, which not only helps him compete in the market but also provides better services to his customers; and the buyer’s aim is to reduce the lead time, which not only facilitates the buyer to fulfill the customers’ demand on time but also enables him to earn a good reputation in the market or vice versa. In the light of the above stated facts, an integrated vendor-buyer stochastic inventory model is also developed. The propsed model considers two cases for demand during lead time: Case (i Complete demand information, Case (ii Partial demand information. The proposed model jointly optimizes the buyer’s ordered quantity and lead time along with vendor’s setup cost and the number of shipments. The results are demonstrated with the help of numerical examples.

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time.

Science.gov (United States)

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

2017-06-01

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which-as shown on the contact process-provides a significant improvement of the large deviation function estimators compared to the standard one.

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time

Science.gov (United States)

Guevara Hidalgo, Esteban; Nemoto, Takahiro; Lecomte, Vivien

2017-06-01

Rare trajectories of stochastic systems are important to understand because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time and finite population size, effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators, which—as shown on the contact process—provides a significant improvement of the large deviation function estimators compared to the standard one.

Numerical Modeling of Pressurization of Cryogenic Propellant Tank for Integrated Vehicle Fluid System

Science.gov (United States)

Majumdar, Alok K.; LeClair, Andre C.; Hedayat, Ali

2016-01-01

This paper presents a numerical model of pressurization of a cryogenic propellant tank for the Integrated Vehicle Fluid (IVF) system using the Generalized Fluid System Simulation Program (GFSSP). The IVF propulsion system, being developed by United Launch Alliance, uses boiloff propellants to drive thrusters for the reaction control system as well as to run internal combustion engines to develop power and drive compressors to pressurize propellant tanks. NASA Marshall Space Flight Center (MSFC) has been running tests to verify the functioning of the IVF system using a flight tank. GFSSP, a finite volume based flow network analysis software developed at MSFC, has been used to develop an integrated model of the tank and the pressurization system. This paper presents an iterative algorithm for converging the interface boundary conditions between different component models of a large system model. The model results have been compared with test data.

Adaptive numerical modeling of dynamic crack propagation

International Nuclear Information System (INIS)

Adouani, H.; Tie, B.; Berdin, C.; Aubry, D.

2006-01-01

We propose an adaptive numerical strategy that aims at developing reliable and efficient numerical tools to model dynamic crack propagation and crack arrest. We use the cohesive zone theory as behavior of interface-type elements to model crack. Since the crack path is generally unknown beforehand, adaptive meshing is proposed to model the dynamic crack propagation. The dynamic study requires the development of specific solvers for time integration. As both geometry and finite element mesh of the studied structure evolve in time during transient analysis, the stability behavior of dynamic solver becomes a major concern. For this purpose, we use the space-time discontinuous Galerkin finite element method, well-known to provide a natural framework to manage meshes that evolve in time. As an important result, we prove that the space-time discontinuous Galerkin solver is unconditionally stable, when the dynamic crack propagation is modeled by the cohesive zone theory, which is highly non-linear. (authors)

Coarse-grained representation of the quasi adiabatic propagator path integral for the treatment of non-Markovian long-time bath memory

Science.gov (United States)

Richter, Martin; Fingerhut, Benjamin P.

2017-06-01

The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.

Integration Processes of Delay Differential Equation Based on Modified Laguerre Functions

Directory of Open Access Journals (Sweden)

Yeguo Sun

2012-01-01

Full Text Available We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.

Analytical–numerical global model of atmospheric-pressure radio-frequency capacitive discharges

International Nuclear Information System (INIS)

Lazzaroni, C; Chabert, P; Lieberman, M A; Lichtenberg, A J; Leblanc, A

2012-01-01

A one-dimensional hybrid analytical–numerical global model of atmospheric-pressure, radio-frequency (rf) driven capacitive discharges is developed. The feed gas is assumed to be helium with small admixtures of oxygen or nitrogen. The electrical characteristics are modeled analytically as a current-driven homogeneous discharge. The electron power balance is solved analytically to determine a time-varying Maxwellian electron temperature, which oscillates on the rf timescale. Averaging over the rf period yields effective rate coefficients for gas phase activated processes. The particle balance relations for all species are then integrated numerically to determine the equilibrium discharge parameters. The coupling of analytical solutions of the time-varying discharge and electron temperature dynamics, and numerical solutions of the discharge chemistry, allows for a fast solution of the discharge equilibrium. Variations of discharge parameters with discharge composition and rf power are determined. Comparisons are made to more accurate but numerically costly fluid models, with space and time variations, but with the range of parameters limited by computational time. (paper)

Numerical modeling of an enhanced very early time electromagnetic (VETEM) prototype system

Science.gov (United States)

Cui, T.J.; Chew, W.C.; Aydiner, A.A.; Wright, D.L.; Smith, D.V.; Abraham, J.D.

2000-01-01

In this paper, two numerical models are presented to simulate an enhanced very early time electromagnetic (VETEM) prototype system, which is used for buried-object detection and environmental problems. Usually, the VETEM system contains a transmitting loop antenna and a receiving loop antenna, which run on a lossy ground to detect buried objects. In the first numerical model, the loop antennas are accurately analyzed using the Method of Moments (MoM) for wire antennas above or buried in lossy ground. Then, Conjugate Gradient (CG) methods, with the use of the fast Fourier transform (FFT) or MoM, are applied to investigate the scattering from buried objects. Reflected and scattered magnetic fields are evaluated at the receiving loop to calculate the output electric current. However, the working frequency for the VETEM system is usually low and, hence, two magnetic dipoles are used to replace the transmitter and receiver in the second numerical model. Comparing these two models, the second one is simple, but only valid for low frequency or small loops, while the first modeling is more general. In this paper, all computations are performed in the frequency domain, and the FFT is used to obtain the time-domain responses. Numerical examples show that simulation results from these two models fit very well when the frequency ranges from 10 kHz to 10 MHz, and both results are close to the measured data.

A modified precise integration method based on Magnus expansion for transient response analysis of time varying dynamical structure

International Nuclear Information System (INIS)

Yue, Cong; Ren, Xingmin; Yang, Yongfeng; Deng, Wangqun

2016-01-01

This paper provides a precise and efficacious methodology for manifesting forced vibration response with respect to the time-variant linear rotational structure subjected to unbalanced excitation. A modified algorithm based on time step precise integration method and Magnus expansion is developed for instantaneous dynamic problems. The iterative solution is achieved by the ideology of transition and dimensional increment matrix. Numerical examples on a typical accelerating rotation system considering gyroscopic moment and mass unbalance force comparatively demonstrate the validity, effectiveness and accuracy with Newmark-β method. It is shown that the proposed algorithm has high accuracy without loss efficiency.

Real-time numerical simulation with high efficiency for an experimental reactor system

International Nuclear Information System (INIS)

Ding Shuling; Li Fu; Li Sifeng; Chu Xinyuan

2006-01-01

The paper presents a systematic and efficient method for numerical real-time simulation of an experimental reactor. The reactor models were built based on the physical characteristics of the experimental reactor, and several real-time simulation approaches were discussed and compared in the paper. How to implement the real-time reactor simulation system in Windows platform for the sake of hardware-in-loop experiment for the reactor power control system was discussed. (authors)

Conservative fourth-order time integration of non-linear dynamic systems

DEFF Research Database (Denmark)

Krenk, Steen

2015-01-01

An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...

Time variability of X-ray binaries: observations with INTEGRAL. Modeling

International Nuclear Information System (INIS)

Cabanac, Clement

2007-01-01

The exact origin of the observed X and Gamma ray variability in X-ray binaries is still an open debate in high energy astrophysics. Among others, these objects are showing aperiodic and quasi-periodic luminosity variations on timescales as small as the millisecond. This erratic behavior must put constraints on the proposed emission processes occurring in the vicinity of the neutrons star or the stellar mass black-hole held by these objects. We propose here to study their behavior following 3 different ways: first we examine the evolution of a particular X-ray source discovered by INTEGRAL, IGR J19140+0951. Using timing and spectral data given by different instruments, we show that the source type is plausibly consistent with a High Mass X-ray Binary hosting a neutrons star. Subsequently, we propose a new method dedicated to the study of timing data coming from coded mask aperture instruments. Using it on INTEGRAL/ISGRI real data, we detect the presence of periodic and quasi-periodic features in some pulsars and micro-quasars at energies as high as a hundred keV. Finally, we suggest a model designed to describe the low frequency variability of X-ray binaries in their hardest state. This model is based on thermal comptonization of soft photons by a warm corona in which a pressure wave is propagating in cylindrical geometry. By computing both numerical simulations and analytical solution, we show that this model should be suitable to describe some of the typical features observed in X-ray binaries power spectra in their hard state and their evolution such as aperiodic noise and low frequency quasi-periodic oscillations. (author) [fr

System Integration for Real-Time Mobile Manipulation

Directory of Open Access Journals (Sweden)

Reza Oftadeh

2014-03-01

Full Text Available Mobile manipulators are one of the most complicated types of mechatronics systems. The performance of these robots in performing complex manipulation tasks is highly correlated with the synchronization and integration of their low-level components. This paper discusses in detail the mechatronics design of a four wheel steered mobile manipulator. It presents the manipulator's mechanical structure and electrical interfaces, designs low-level software architecture based on embedded PC-based controls, and proposes a systematic solution based on code generation products of MATLAB and Simulink. The remote development environment described here is used to develop real-time controller software and modules for the mobile manipulator under a POSIX-compliant, real-time Linux operating system. Our approach enables developers to reliably design controller modules that meet the hard real-time constraints of the entire low-level system architecture. Moreover, it provides a systematic framework for the development and integration of hardware devices with various communication mediums and protocols, which facilitates the development and integration process of the software controller.

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...

Introduction to numerical analysis

CERN Document Server

Hildebrand, F B

1987-01-01

Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, other topics in lucid presentation. Includes 150 additional problems in this edition. Bibliography.

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

Science.gov (United States)

Dodig, H.

2017-11-01

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

Space-time transformations in radial path integrals

International Nuclear Information System (INIS)

Steiner, F.

1984-09-01

Nonlinear space-time transformations in the radial path integral are discussed. A transformation formula is derived, which relates the original path integral to the Green's function of a new quantum system with an effective potential containing an observable quantum correction proportional(h/2π) 2 . As an example the formula is applied to spherical Brownian motion. (orig.)

Analysis of electromagnetic wave interactions on nonlinear scatterers using time domain volume integral equations

KAUST Repository

Ulku, Huseyin Arda

2014-07-06

and full Schubert-Wilton-Glisson (SWG) functions, respectively. Equations are Galerkin tested in space and the resulting semi-discrete system is integrated in time for the unknown expansion coefficients using the aforementioned predictor-corrector scheme. The explicitness of the MOT scheme allows for incorporation of the nonlinearities as simple discretized function evaluations on the right hand side of the system. Numerical results that demonstrate the accuracy, efficiency, and applicability of the proposed nonlinear MOT-TDVIE solver will be presented.

Improving Music Genre Classification by Short-Time Feature Integration

DEFF Research Database (Denmark)

Meng, Anders; Ahrendt, Peter; Larsen, Jan

2005-01-01

Many different short-time features, using time windows in the size of 10-30 ms, have been proposed for music segmentation, retrieval and genre classification. However, often the available time frame of the music to make the actual decision or comparison (the decision time horizon) is in the range...... of seconds instead of milliseconds. The problem of making new features on the larger time scale from the short-time features (feature integration) has only received little attention. This paper investigates different methods for feature integration and late information fusion for music genre classification...

Multisensory integration: the case of a time window of gesture-speech integration.

Science.gov (United States)

Obermeier, Christian; Gunter, Thomas C

2015-02-01

This experiment investigates the integration of gesture and speech from a multisensory perspective. In a disambiguation paradigm, participants were presented with short videos of an actress uttering sentences like "She was impressed by the BALL, because the GAME/DANCE...." The ambiguous noun (BALL) was accompanied by an iconic gesture fragment containing information to disambiguate the noun toward its dominant or subordinate meaning. We used four different temporal alignments between noun and gesture fragment: the identification point (IP) of the noun was either prior to (+120 msec), synchronous with (0 msec), or lagging behind the end of the gesture fragment (-200 and -600 msec). ERPs triggered to the IP of the noun showed significant differences for the integration of dominant and subordinate gesture fragments in the -200, 0, and +120 msec conditions. The outcome of this integration was revealed at the target words. These data suggest a time window for direct semantic gesture-speech integration ranging from at least -200 up to +120 msec. Although the -600 msec condition did not show any signs of direct integration at the homonym, significant disambiguation was found at the target word. An explorative analysis suggested that gesture information was directly integrated at the verb, indicating that there are multiple positions in a sentence where direct gesture-speech integration takes place. Ultimately, this would implicate that in natural communication, where a gesture lasts for some time, several aspects of that gesture will have their specific and possibly distinct impact on different positions in an utterance.

Time domain numerical calculations of the short electron bunch wakefields in resistive structures

Energy Technology Data Exchange (ETDEWEB)

Tsakanian, Andranik

2010-10-15

The acceleration of electron bunches with very small longitudinal and transverse phase space volume is one of the most actual challenges for the future International Linear Collider and high brightness X-Ray Free Electron Lasers. The exact knowledge on the wake fields generated by the ultra-short electron bunches during its interaction with surrounding structures is a very important issue to prevent the beam quality degradation and to optimize the facility performance. The high accuracy time domain numerical calculations play the decisive role in correct evaluation of the wake fields in advanced accelerators. The thesis is devoted to the development of a new longitudinally dispersion-free 3D hybrid numerical scheme in time domain for wake field calculation of ultra short bunches in structures with walls of finite conductivity. The basic approaches used in the thesis to solve the problem are the following. For materials with high but finite conductivity the model of the plane wave reflection from a conducting half-space is used. It is shown that in the conductive half-space the field components perpendicular to the interface can be neglected. The electric tangential component on the surface contributes to the tangential magnetic field in the lossless area just before the boundary layer. For high conducting media, the task is reduced to 1D electromagnetic problem in metal and the so-called 1D conducting line model can be applied instead of a full 3D space description. Further, a TE/TM (''transverse electric - transverse magnetic'') splitting implicit numerical scheme along with 1D conducting line model is applied to develop a new longitudinally dispersion-free hybrid numerical scheme in the time domain. The stability of the new hybrid numerical scheme in vacuum, conductor and bound cell is studied. The convergence of the new scheme is analyzed by comparison with the well-known analytical solutions. The wakefield calculations for a number of

Implicit time accurate simulation of unsteady flow

Science.gov (United States)

van Buuren, René; Kuerten, Hans; Geurts, Bernard J.

2001-03-01

Implicit time integration was studied in the context of unsteady shock-boundary layer interaction flow. With an explicit second-order Runge-Kutta scheme, a reference solution to compare with the implicit second-order Crank-Nicolson scheme was determined. The time step in the explicit scheme is restricted by both temporal accuracy as well as stability requirements, whereas in the A-stable implicit scheme, the time step has to obey temporal resolution requirements and numerical convergence conditions. The non-linear discrete equations for each time step are solved iteratively by adding a pseudo-time derivative. The quasi-Newton approach is adopted and the linear systems that arise are approximately solved with a symmetric block Gauss-Seidel solver. As a guiding principle for properly setting numerical time integration parameters that yield an efficient time accurate capturing of the solution, the global error caused by the temporal integration is compared with the error resulting from the spatial discretization. Focus is on the sensitivity of properties of the solution in relation to the time step. Numerical simulations show that the time step needed for acceptable accuracy can be considerably larger than the explicit stability time step; typical ratios range from 20 to 80. At large time steps, convergence problems that are closely related to a highly complex structure of the basins of attraction of the iterative method may occur. Copyright

Numerical implementation of the loop-tree duality method

Energy Technology Data Exchange (ETDEWEB)

Buchta, Sebastian; Rodrigo, German [Universitat de Valencia-Consejo Superior de Investigaciones Cientificas, Parc Cientific, Instituto de Fisica Corpuscular, Valencia (Spain); Chachamis, Grigorios [Universidad Autonoma de Madrid, Instituto de Fisica Teorica UAM/CSIC, Madrid (Spain); Draggiotis, Petros [Institute of Nuclear and Particle Physics, NCSR ' ' Demokritos' ' , Agia Paraskevi (Greece)

2017-05-15

We present a first numerical implementation of the loop-tree duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and we present explicit results for scalar and tensor integrals with up to eight external legs (octagons). The LTD method features an excellent performance independently of the number of external legs. (orig.)

Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

Science.gov (United States)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

Numerical simulation of laser resonators

International Nuclear Information System (INIS)

Yoo, J. G.; Jeong, Y. U.; Lee, B. C.; Rhee, Y. J.; Cho, S. O.

2004-01-01

We developed numerical simulation packages for laser resonators on the bases of a pair of integral equations. Two numerical schemes, a matrix formalism and an iterative method, were programmed for finding numeric solutions to the pair of integral equations. The iterative method was tried by Fox and Li, but it was not applicable for high Fresnel numbers since the numerical errors involved propagate and accumulate uncontrollably. In this paper, we implement the matrix method to extend the computational limit further. A great number of case studies are carried out with various configurations of stable and unstable r;esonators to compute diffraction losses, phase shifts, intensity distributions and phases of the radiation fields on mirrors. Our results presented in this paper show not only a good agreement with the results previously obtained by Fox and Li, but also the legitimacy of our numerical procedures for high Fresnel numbers.

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

Application of Taylor-Series Integration to Reentry Problems with Wind

NARCIS (Netherlands)

Bergsma, Michiel; Mooij, E.

2016-01-01

Taylor-series integration is a numerical integration technique that computes the Taylor series of state variables using recurrence relations and uses this series to propagate the state in time. A Taylor-series integration reentry integrator is developed and compared with the fifth-order

Integral and differential methods for the numerical solution of 2-D field problems in high energy physics magnets and electrical machines

International Nuclear Information System (INIS)

Hannalla, A.Y.; Simkin, J.; Trowbridge, C.W.

1979-10-01

Numerical calculations of electromagnetic fields have been performed by solving integral or differential equations. Integral methods are ideally suited to open boundary problems and on the other hand the geometric complexity of electrical machines makes differential methods more attractive. In this paper both integral and differential equation methods are reviewed, and the limitations of the methods are highlighted, in an attempt to show how to select the best method for a particular problem. (author)

Numerical Modeling of an Integrated Vehicle Fluids System Loop for Pressurizing a Cryogenic Tank

Science.gov (United States)

LeClair, A. C.; Hedayat, A.; Majumdar, A. K.

2017-01-01

This paper presents a numerical model of the pressurization loop of the Integrated Vehicle Fluids (IVF) system using the Generalized Fluid System Simulation Program (GFSSP). The IVF propulsion system, being developed by United Launch Alliance to reduce system weight and enhance reliability, uses boiloff propellants to drive thrusters for the reaction control system as well as to run internal combustion engines to develop power and drive compressors to pressurize propellant tanks. NASA Marshall Space Flight Center (MSFC) conducted tests to verify the functioning of the IVF system using a flight-like tank. GFSSP, a finite volume based flow network analysis software developed at MSFC, has been used to support the test program. This paper presents the simulation of three different test series, comparison of numerical prediction and test data and a novel method of presenting data in a dimensionless form. The paper also presents a methodology of implementing a compressor map in a system level code.

A model of interval timing by neural integration.

Science.gov (United States)

Simen, Patrick; Balci, Fuat; de Souza, Laura; Cohen, Jonathan D; Holmes, Philip

2011-06-22

We show that simple assumptions about neural processing lead to a model of interval timing as a temporal integration process, in which a noisy firing-rate representation of time rises linearly on average toward a response threshold over the course of an interval. Our assumptions include: that neural spike trains are approximately independent Poisson processes, that correlations among them can be largely cancelled by balancing excitation and inhibition, that neural populations can act as integrators, and that the objective of timed behavior is maximal accuracy and minimal variance. The model accounts for a variety of physiological and behavioral findings in rodents, monkeys, and humans, including ramping firing rates between the onset of reward-predicting cues and the receipt of delayed rewards, and universally scale-invariant response time distributions in interval timing tasks. It furthermore makes specific, well-supported predictions about the skewness of these distributions, a feature of timing data that is usually ignored. The model also incorporates a rapid (potentially one-shot) duration-learning procedure. Human behavioral data support the learning rule's predictions regarding learning speed in sequences of timed responses. These results suggest that simple, integration-based models should play as prominent a role in interval timing theory as they do in theories of perceptual decision making, and that a common neural mechanism may underlie both types of behavior.

analysis of large electromagnetic pulse simulators using the electric field integral equation method in time domain

International Nuclear Information System (INIS)

Jamali, J.; Aghajafari, R.; Moini, R.; Sadeghi, H.

2002-01-01

A time-domain approach is presented to calculate electromagnetic fields inside a large Electromagnetic Pulse (EMP) simulator. This type of EMP simulator is used for studying the effect of electromagnetic pulses on electrical apparatus in various structures such as vehicles, a reoplanes, etc. The simulator consists of three planar transmission lines. To solve the problem, we first model the metallic structure of the simulator as a grid of conducting wires. The numerical solution of the governing electric field integral equation is then obtained using the method of moments in time domain. To demonstrate the accuracy of the model, we consider a typical EMP simulator. The comparison of our results with those obtained experimentally in the literature validates the model introduced in this paper

INTEGRAL EDUCATION, TIME AND SPACE: PROBLEMATIZING CONCEPTS

Directory of Open Access Journals (Sweden)

Ana Elisa Spaolonzi Queiroz Assis

2018-03-01

Full Text Available Integral Education, despite being the subject of public policy agenda for some decades, still carries disparities related to its concept. In this sense, this article aims to problematize not only the concepts of integral education but also the categories time and space contained in the magazines Em Aberto. They were organized and published by the National Institute of Educational Studies Anísio Teixeira (INEP, numbers 80 (2009 and 88 (2012, respectively entitled "Educação Integral e tempo integral" and " Políticas de educação integral em jornada ampliada". The methodology is based on Bardin’s content analysis, respecting the steps of pre-analysis (research corpus formed by the texts in the journals; material exploration (reading the texts encoding data choosing the registration units for categorization; and processing and interpretation of results, based on Saviani’s Historical-Critical Pedagogy. The work reveals convergent and divergent conceptual multiplicity, provoking a discussion about a critical conception of integral education. Keywords: Integral Education. Historical-Critical Pedagogy. Content Analysis.

Integral reinforcement learning for continuous-time input-affine nonlinear systems with simultaneous invariant explorations.

Science.gov (United States)

Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2015-05-01

This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods.

Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift

Directory of Open Access Journals (Sweden)

Gemechis File

2012-01-01

Full Text Available We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .

Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity.

Science.gov (United States)

Thornburg, Jonathan

2007-01-01

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time : it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Θ. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well

Direct Time Domain Numerical Analysis of Transient Behavior of a VLFS during Unsteady External Loads in Wave Condition

Directory of Open Access Journals (Sweden)

Yong Cheng

2014-01-01

Full Text Available The transient response of the VLFS subjected to arbitrary external load is systematically investigated by a direct time domain modal expansion method, in which the BEM solutions based on time domain Kelvin sources are used for hydrodynamic forces. In the analysis, the time domain free-surface Green functions with sufficient accuracy are rapidly evaluated in finite water depth by the interpolation-tabulation method, and the boundary integral equation with a quarter VLFS model is established taking advantage of symmetry of flow field and structure. The validity of the present method is verified by comparing with the time histories of vertical displacements of the VLFS during a mass drop and airplane landing and takeoff in still water conditions, respectively. Then the developed numerical scheme is used in wave conditions to study the combined action taking into account the mass drop/airplane landing/takeoff loads as well as incident wave action. It is found that the elevation of structural waves due to mass drop load can be significantly changed near the impact region, while the vertical motion of runway in wave conditions is dominant as compared with that only generated by airplane.

Path integral solution for some time-dependent potential

International Nuclear Information System (INIS)

Storchak, S.N.

1989-12-01

The quantum-mechanical problem with a time-dependent potential is solved by the path integral method. The solution is obtained by the application of the previously derived general formula for rheonomic homogeneous point transformation and reparametrization in the path integral. (author). 4 refs

A Lie-admissible method of integration of Fokker-Planck equations with non-linear coefficients (exact and numerical solutions)

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type

Topological transitions at finite temperatures: A real-time numerical approach

International Nuclear Information System (INIS)

Grigoriev, D.Yu.; Rubakov, V.A.; Shaposhnikov, M.E.

1989-01-01

We study topological transitions at finite temperatures within the (1+1)-dimensional abelian Higgs model by a numerical simulation in real time. Basic ideas of the real-time approach are presented and some peculiarities of the Metropolis technique are discussed. It is argued that the processes leading to topological transitions are of classical origin; the transitions can be observed by solving the classical field equations in real time. We show that the topological transitions actually pass via the sphaleron configuration. The transition rate as a function of temperature is found to be in good agreement with the analytical predictions. No extra suppression of the rate is observed. The conditions of applicability of our approach are discussed. The temperature interval where the low-temperature broken phase persists is estimated. (orig.)

Energy drift in reversible time integration

International Nuclear Information System (INIS)

McLachlan, R I; Perlmutter, M

2004-01-01

Energy drift is commonly observed in reversible integrations of systems of molecular dynamics. We show that this drift can be modelled as a diffusion and that the typical energy error after time T is O(√T). (letter to the editor)

Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

Directory of Open Access Journals (Sweden)

Y. Saiki

2007-09-01

Full Text Available An infinite number of unstable periodic orbits (UPOs are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

Analytical-numerical solution for the trajectory of seismic rays in media with vertical heterogeneity

International Nuclear Information System (INIS)

Imhof, Armando Luis; Calvo, Carlos Adolfo; Moyano, Amalia; Sanchez, Manuel

2015-01-01

A determined curve path is followed by the propagation of seismic waves generated in emitters and detected in receivers by the principle of minimum time of Fermat. An ordinary differential equation is derived from the application of the calculation of variations. Due to the compaction of the terrain, the speed usually increases with depth. The experimental laws for each soil have led to this variation leading to a numerical resolution. The adjustment of experimental speed data by an exponential function; the analytical integration of the differential equation and the numerical determination of the integration constants are studied. A geophysical method such as up-hole or down-hole has determined the experimental data. Its main application is centered in the validation of numerical models of curved trajectories. Then time of first arrivals through tomographic algorithms for detection and modeling of anomalies in the first 12 m depth. (author) [es

A numerical solution for the multi-server queue with hyper-exponential service times

NARCIS (Netherlands)

de Smit, J.H.A.

1983-01-01

In this paper we present a numerical method for the queue GI/H2/s, which is based on general results for GI/Hm/s. We give a complete description of the algorithm which yields exact results for the steady distributions of the actual waiting time, the virtual waiting time and the number of customers

The development of efficient numerical time-domain modeling methods for geophysical wave propagation

Science.gov (United States)

Zhu, Lieyuan

This Ph.D. dissertation focuses on the numerical simulation of geophysical wave propagation in the time domain including elastic waves in solid media, the acoustic waves in fluid media, and the electromagnetic waves in dielectric media. This thesis shows that a linear system model can describe accurately the physical processes of those geophysical waves' propagation and can be used as a sound basis for modeling geophysical wave propagation phenomena. The generalized stability condition for numerical modeling of wave propagation is therefore discussed in the context of linear system theory. The efficiency of a series of different numerical algorithms in the time-domain for modeling geophysical wave propagation are discussed and compared. These algorithms include the finite-difference time-domain method, pseudospectral time domain method, alternating directional implicit (ADI) finite-difference time domain method. The advantages and disadvantages of these numerical methods are discussed and the specific stability condition for each modeling scheme is carefully derived in the context of the linear system theory. Based on the review and discussion of these existing approaches, the split step, ADI pseudospectral time domain (SS-ADI-PSTD) method is developed and tested for several cases. Moreover, the state-of-the-art stretched-coordinate perfect matched layer (SCPML) has also been implemented in SS-ADI-PSTD algorithm as the absorbing boundary condition for truncating the computational domain and absorbing the artificial reflection from the domain boundaries. After algorithmic development, a few case studies serve as the real-world examples to verify the capacities of the numerical algorithms and understand the capabilities and limitations of geophysical methods for detection of subsurface contamination. The first case is a study using ground penetrating radar (GPR) amplitude variation with offset (AVO) for subsurface non-aqueous-liquid (NAPL) contamination. The

Time-Lapse Measurement of Wellbore Integrity

Science.gov (United States)

Duguid, A.

2017-12-01

Well integrity is becoming more important as wells are used longer or repurposed. For CO2, shale gas, and other projects it has become apparent that wells represent the most likely unintended migration pathway for fluids out of the reservoir. Comprehensive logging programs have been employed to determine the condition of legacy wells in North America. These studies provide examples of assessment technologies. Logging programs have included pulsed neutron logging, ultrasonic well mapping, and cement bond logging. While these studies provide examples of what can be measured, they have only conducted a single round of logging and cannot show if the well has changed over time. Recent experience with time-lapse logging of three monitoring wells at a US Department of Energy sponsored CO2 project has shown the full value of similar tools. Time-lapse logging has shown that well integrity changes over time can be identified. It has also shown that the inclusion of and location of monitoring technologies in the well and the choice of construction materials must be carefully considered. Two of the wells were approximately eight years old at the time of study; they were constructed with steel and fiberglass casing sections and had lines on the outside of the casing running to the surface. The third well was 68 years old when it was studied and was originally constructed as a production well. Repeat logs were collected six or eight years after initial logging. Time-lapse logging showed the evolution of the wells. The results identified locations where cement degraded over time and locations that showed little change. The ultrasonic well maps show clearly that the lines used to connect the monitoring technology to the surface are visible and have a local effect on cement isolation. Testing and sampling was conducted along with logging. It provided insight into changes identified in the time-lapse log results. Point permeability testing was used to provide an in-situ point

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<

Combined Effects of Numerical Method Type and Time Step on Water Stressed Actual Crop ET

Directory of Open Access Journals (Sweden)

B. Ghahraman

2016-02-01

Full Text Available Introduction: Actual crop evapotranspiration (Eta is important in hydrologic modeling and irrigation water management issues. Actual ET depends on an estimation of a water stress index and average soil water at crop root zone, and so depends on a chosen numerical method and adapted time step. During periods with no rainfall and/or irrigation, actual ET can be computed analytically or by using different numerical methods. Overal, there are many factors that influence actual evapotranspiration. These factors are crop potential evapotranspiration, available root zone water content, time step, crop sensitivity, and soil. In this paper different numerical methods are compared for different soil textures and different crops sensitivities. Materials and Methods: During a specific time step with no rainfall or irrigation, change in soil water content would be equal to evapotranspiration, ET. In this approach, however, deep percolation is generally ignored due to deep water table and negligible unsaturated hydraulic conductivity below rooting depth. This differential equation may be solved analytically or numerically considering different algorithms. We adapted four different numerical methods, as explicit, implicit, and modified Euler, midpoint method, and 3-rd order Heun method to approximate the differential equation. Three general soil types of sand, silt, and clay, and three different crop types of sensitive, moderate, and resistant under Nishaboor plain were used. Standard soil fraction depletion (corresponding to ETc=5 mm.d-1, pstd, below which crop faces water stress is adopted for crop sensitivity. Three values for pstd were considered in this study to cover the common crops in the area, including winter wheat and barley, cotton, alfalfa, sugar beet, saffron, among the others. Based on this parameter, three classes for crop sensitivity was considered, sensitive crops with pstd=0.2, moderate crops with pstd=0.5, and resistive crops with pstd=0

The Cenozoic fold-and-thrust belt of Eastern Sardinia: Evidences from the integration of field data with numerically balanced geological cross section

Science.gov (United States)

Arragoni, S.; Maggi, M.; Cianfarra, P.; Salvini, F.

2016-06-01

Newly collected structural data in Eastern Sardinia (Italy) integrated with numerical techniques led to the reconstruction of a 2-D admissible and balanced model revealing the presence of a widespread Cenozoic fold-and-thrust belt. The model was achieved with the FORC software, obtaining a 3-D (2-D + time) numerical reconstruction of the continuous evolution of the structure through time. The Mesozoic carbonate units of Eastern Sardinia and their basement present a fold-and-thrust tectonic setting, with a westward direction of tectonic transport (referred to the present-day coordinates). The tectonic style of the upper levels is thin skinned, with flat sectors prevailing over ramps and younger-on-older thrusts. Three regional tectonic units are present, bounded by two regional thrusts. Strike-slip faults overprint the fold-and-thrust belt and developed during the Sardinia-Corsica Block rotation along the strike of the preexisting fault ramps, not affecting the numerical section balancing. This fold-and-thrust belt represents the southward prosecution of the Alpine Corsica collisional chain and the missing link between the Alpine Chain and the Calabria-Peloritani Block. Relative ages relate its evolution to the meso-Alpine event (Eocene-Oligocene times), prior to the opening of the Tyrrhenian Sea (Tortonian). Results fill a gap of information about the geodynamic evolution of the European margin in Central Mediterranean, between Corsica and the Calabria-Peloritani Block, and imply the presence of remnants of this double-verging belt, missing in the Southern Tyrrhenian basin, within the Southern Apennine chain. The used methodology proved effective for constraining balanced cross sections also for areas lacking exposures of the large-scale structures, as the case of Eastern Sardinia.

Numerical Simulation of Antennas with Improved Integral Equation Method

International Nuclear Information System (INIS)

Ma Ji; Fang Guang-You; Lu Wei

2015-01-01

Simulating antennas around a conducting object is a challenge task in computational electromagnetism, which is concerned with the behaviour of electromagnetic fields. To analyze this model efficiently, an improved integral equation-fast Fourier transform (IE-FFT) algorithm is presented in this paper. The proposed scheme employs two Cartesian grids with different size and location to enclose the antenna and the other object, respectively. On the one hand, IE-FFT technique is used to store matrix in a sparse form and accelerate the matrix-vector multiplication for each sub-domain independently. On the other hand, the mutual interaction between sub-domains is taken as the additional exciting voltage in each matrix equation. By updating integral equations several times, the whole electromagnetic system can achieve a stable status. Finally, the validity of the presented method is verified through the analysis of typical antennas in the presence of a conducting object. (paper)

Development and successful operation of the enhanced-interlink system of experiment data and numerical simulation in LHD

International Nuclear Information System (INIS)

Emoto, M.; Suzuki, C.; Suzuki, Y.; Yokoyama, M.; Seki, R.; Ida, K.

2014-10-01

The enhanced-interlink system of experiment data and numerical simulation has been developed, and successfully operated routinely in the Large Helical Device (LHD). This system consists of analyzed diagnostic data, real-time coordinate mapping, and automatic data processing. It has enabled automated data handling/transferring between experiment and numerical simulation, to extensively perform experiment analyses. It can be considered as one of the prototypes for a seamless data-centric approach for integrating experiment data and numerical simulation/modellings in fusion experiments. Utilizing this system, experimental analyses by numerical simulations have extensively progressed. The authors believe this data-centric approach for integrating experiment data and numerical simulation/modellings will contribute to not only the LHD but to other plasma fusion projects including DEMO reactor in the future. (author)

Numerical integration of electromagnetic cascade equations, discussion of results for air, copper, iron, and lead

International Nuclear Information System (INIS)

Adler, A.; Fuchs, B.; Thielheim, K.O.

1977-01-01

The longitudinal development of electromagnetic cascades in air, copper, iron, and lead is studied on the basis of results derived recently by numerical integration of the cascade equations applying rather accurate expressions for the cross-sections involved with the interactions of high energy electrons, positrons, and photons in electromagnetic cascades. Special attention is given to scaling properties of transition curves. It is demonstrated that a good scaling may be achieved by means of the depth of maximum cascade development. (author)

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

Science.gov (United States)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Low-temperature baseboard heaters with integrated air supply - An analytical and numerical investigation

Energy Technology Data Exchange (ETDEWEB)

Ploskic, Adnan; Holmberg, Sture [Fluid and Climate Technology, School of Architecture and Built Environment, KTH, Marinens vaeg 30, SE-13640 Handen, Stockholm (Sweden)

2011-01-15

The functioning of a hydronic baseboard heating system with integrated air supply was analyzed. The aim was to investigate thermal performance of the system when cold outdoor (ventilation) airflow was forced through the baseboard heater. The performance of the system was evaluated for different ventilation rates at typical outdoor temperatures during the Swedish winter season. Three different analytical models and Computational Fluid Dynamics (CFD) were used to predict the temperature rise of the airflow inside the baseboard heater. Good agreement between numerical (CFD) and analytical calculations was obtained. Calculations showed that it was fully possible to pre-heat the incoming airflow to the indoor temperature and to cover transmission losses, using 45 C supply water flow. The analytical calculations also showed that the airflow per supply opening in the baseboard heater needed to be limited to 7.0 l/s due to pressure losses inside the channel. At this ventilation rate, the integrated system with one air supply gave about 2.1 more heat output than a conventional baseboard heating system. CFD simulations also showed that the integrated system was capable of countering downdraught created by 2.0 m high glazed areas and a cold outdoor environment. Draught discomfort in the case with the conventional system was slightly above the recommended upper limit, but heat distribution across whole analyzed office space was uniform for both heating systems. It was concluded that low-temperature baseboard heating systems with integrated air supply can meet both international comfort requirements, and lead to energy savings in cold climates. (author)

A numerical integration-based yield estimation method for integrated circuits

International Nuclear Information System (INIS)

Liang Tao; Jia Xinzhang

2011-01-01

A novel integration-based yield estimation method is developed for yield optimization of integrated circuits. This method tries to integrate the joint probability density function on the acceptability region directly. To achieve this goal, the simulated performance data of unknown distribution should be converted to follow a multivariate normal distribution by using Box-Cox transformation (BCT). In order to reduce the estimation variances of the model parameters of the density function, orthogonal array-based modified Latin hypercube sampling (OA-MLHS) is presented to generate samples in the disturbance space during simulations. The principle of variance reduction of model parameters estimation through OA-MLHS together with BCT is also discussed. Two yield estimation examples, a fourth-order OTA-C filter and a three-dimensional (3D) quadratic function are used for comparison of our method with Monte Carlo based methods including Latin hypercube sampling and importance sampling under several combinations of sample sizes and yield values. Extensive simulations show that our method is superior to other methods with respect to accuracy and efficiency under all of the given cases. Therefore, our method is more suitable for parametric yield optimization. (semiconductor integrated circuits)

A numerical integration-based yield estimation method for integrated circuits

Energy Technology Data Exchange (ETDEWEB)

Liang Tao; Jia Xinzhang, E-mail: tliang@yahoo.cn [Key Laboratory of Ministry of Education for Wide Bandgap Semiconductor Materials and Devices, School of Microelectronics, Xidian University, Xi' an 710071 (China)

2011-04-15

A novel integration-based yield estimation method is developed for yield optimization of integrated circuits. This method tries to integrate the joint probability density function on the acceptability region directly. To achieve this goal, the simulated performance data of unknown distribution should be converted to follow a multivariate normal distribution by using Box-Cox transformation (BCT). In order to reduce the estimation variances of the model parameters of the density function, orthogonal array-based modified Latin hypercube sampling (OA-MLHS) is presented to generate samples in the disturbance space during simulations. The principle of variance reduction of model parameters estimation through OA-MLHS together with BCT is also discussed. Two yield estimation examples, a fourth-order OTA-C filter and a three-dimensional (3D) quadratic function are used for comparison of our method with Monte Carlo based methods including Latin hypercube sampling and importance sampling under several combinations of sample sizes and yield values. Extensive simulations show that our method is superior to other methods with respect to accuracy and efficiency under all of the given cases. Therefore, our method is more suitable for parametric yield optimization. (semiconductor integrated circuits)

NUMERICAL SIMULATION OF SHOCK WAVE REFRACTION ON INCLINED CONTACT DISCONTINUITY

Directory of Open Access Journals (Sweden)

P. V. Bulat

2016-05-01

Full Text Available We consider numerical simulation of shock wave refraction on plane contact discontinuity, separating two gases with different density. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes, implemented on unstructured meshes. Integration over time is performed with the use of the third-order Runge–Kutta stepping procedure. The procedure of identification and classification of gas dynamic discontinuities based on conditions of dynamic consistency and image processing methods is applied to visualize and interpret the results of numerical calculations. The flow structure and its quantitative characteristics are defined. The results of numerical and experimental visualization (shadowgraphs, schlieren images, and interferograms are compared.

Zdeněk Kopal: Numerical Analyst

Science.gov (United States)

Křížek, M.

2015-07-01

We give a brief overview of Zdeněk Kopal's life, his activities in the Czech Astronomical Society, his collaboration with Vladimír Vand, and his studies at Charles University, Cambridge, Harvard, and MIT. Then we survey Kopal's professional life. He published 26 monographs and 20 conference proceedings. We will concentrate on Kopal's extensive monograph Numerical Analysis (1955, 1961) that is widely accepted to be the first comprehensive textbook on numerical methods. It describes, for instance, methods for polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations with initial or boundary conditions, and numerical solution of integral and integro-differential equations. Special emphasis will be laid on error analysis. Kopal himself applied numerical methods to celestial mechanics, in particular to the N-body problem. He also used Fourier analysis to investigate light curves of close binaries to discover their properties. This is, in fact, a problem from mathematical analysis.

Time resolved spectroscopy of GRB 030501 using INTEGRAL

DEFF Research Database (Denmark)

Beckmann, V.; Borkowski, J.; Courvoisier, T.J.L.

2003-01-01

The gamma-ray instruments on-board INTEGRAL offer an unique opportunity to perform time resolved analysis on GRBs. The imager IBIS allows accurate positioning of GRBs and broad band spectral analysis, while SPI provides high resolution spectroscopy. GRB 030501 was discovered by the INTEGRAL Burst...... the Ulysses and RHESSI experiments....

An integrated numerical and physical modeling system for an enhanced in situ bioremediation process

International Nuclear Information System (INIS)

Huang, Y.F.; Huang, G.H.; Wang, G.Q.; Lin, Q.G.; Chakma, A.

2006-01-01

Groundwater contamination due to releases of petroleum products is a major environmental concern in many urban districts and industrial zones. Over the past years, a few studies were undertaken to address in situ bioremediation processes coupled with contaminant transport in two- or three-dimensional domains. However, they were concentrated on natural attenuation processes for petroleum contaminants or enhanced in situ bioremediation processes in laboratory columns. In this study, an integrated numerical and physical modeling system is developed for simulating an enhanced in situ biodegradation (EISB) process coupled with three-dimensional multiphase multicomponent flow and transport simulation in a multi-dimensional pilot-scale physical model. The designed pilot-scale physical model is effective in tackling natural attenuation and EISB processes for site remediation. The simulation results demonstrate that the developed system is effective in modeling the EISB process, and can thus be used for investigating the effects of various uncertainties. - An integrated modeling system was developed to enhance in situ bioremediation processes

Implicit and semi-implicit schemes in the Versatile Advection Code : numerical tests

NARCIS (Netherlands)

Tóth, G.; Keppens, R.; Bochev, Mikhail A.

1998-01-01

We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing

Path-integral approach to resonant electron-molecule scattering

International Nuclear Information System (INIS)

Winterstetter, M.; Domcke, W.

1993-01-01

A path-integral formulation of resonant electron-molecule scattering is developed within the framework of the projection-operator formalism of scattering theory. The formation and decay of resonances is treated in real time as a quantum-mechanical electronic-tunneling process, modified by the coupling of the electronic motion with the nuclear degrees of freedom. It is shown that the electronic continuum can be summed over in the path-integral formulation, resulting formally in the path integral for an effective two-state system with coupling to vibrations. The harmonic-oscillator approximation is adopted for the vibrational motion in the present work. Approximation methods are introduced which render the numerical evaluation of the sum over paths feasible for up to ∼10 3 elementary time slices. The theory is numerically realized for simple but nontrivial models representing the 2 Π g d-wave shape resonance in e - +N 2 collisions and the 2 Σ u + p-wave shape resonance in e - +H 2 collisions, respectively. The accuracy of the path-integral results is assessed by comparison with exact numerical reference data for these models. The essential virtue of the path-integral approach is the fact that the computational effort scales at most linearly with the number of vibrational degrees of freedom. The path-integral method is thus well suited to treat electron collisions with polyatomic molecules and molecular aggregates

Integrated Numerical Experiments (INEX) and the Free-Electron Laser Physical Process Code (FELPPC)

International Nuclear Information System (INIS)

Thode, L.E.; Chan, K.C.D.; Schmitt, M.J.; McKee, J.; Ostic, J.; Elliott, C.J.; McVey, B.D.

1990-01-01

The strong coupling of subsystem elements, such as the accelerator, wiggler, and optics, greatly complicates the understanding and design of a free electron laser (FEL), even at the conceptual level. To address the strong coupling character of the FEL the concept of an Integrated Numerical Experiment (INEX) was proposed. Unique features of the INEX approach are consistency and numerical equivalence of experimental diagnostics. The equivalent numerical diagnostics mitigates the major problem of misinterpretation that often occurs when theoretical and experimental data are compared. The INEX approach has been applied to a large number of accelerator and FEL experiments. Overall, the agreement between INEX and the experiments is very good. Despite the success of INEX, the approach is difficult to apply to trade-off and initial design studies because of the significant manpower and computational requirements. On the other hand, INEX provides a base from which realistic accelerator, wiggler, and optics models can be developed. The Free Electron Laser Physical Process Code (FELPPC) includes models developed from INEX, provides coupling between the subsystem models, and incorporates application models relevant to a specific trade-off or design study. In other words, FELPPC solves the complete physical process model using realistic physics and technology constraints. Because FELPPC provides a detailed design, a good estimate for the FEL mass, cost, and size can be made from a piece-part count of the FEL. FELPPC requires significant accelerator and FEL expertise to operate. The code can calculate complex FEL configurations including multiple accelerator and wiggler combinations

Direct numerical simulations of non-premixed ethylene-air flames: Local flame extinction criterion

KAUST Repository

Lecoustre, Vivien R.; Arias, Paul G.; Roy, Somesh P.; Luo, Zhaoyu; Haworth, Daniel C.; Im, Hong G.; Lu, Tianfeng; Trouvé , Arnaud C.

2014-01-01

difference and explicit time integration schemes. The ethylene/air chemistry is simulated with a reduced mechanism that is generated based on the directed relation graph (DRG) based methods along with stiffness removal. The numerical configuration

Global Format for Conservative Time Integration in Nonlinear Dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2014-01-01

The widely used classic collocation-based time integration procedures like Newmark, Generalized-alpha etc. generally work well within a framework of linear problems, but typically may encounter problems, when used in connection with essentially nonlinear structures. These problems are overcome....... In the present paper a conservative time integration algorithm is developed in a format using only the internal forces and the associated tangent stiffness at the specific time integration points. Thus, the procedure is computationally very similar to a collocation method, consisting of a series of nonlinear...... equivalent static load steps, easily implemented in existing computer codes. The paper considers two aspects: representation of nonlinear internal forces in a form that implies energy conservation, and the option of an algorithmic damping with the purpose of extracting energy from undesirable high...

Bridging Numerical and Analytical Models of Transient Travel Time Distributions: Challenges and Opportunities

Science.gov (United States)

Danesh Yazdi, M.; Klaus, J.; Condon, L. E.; Maxwell, R. M.

2017-12-01

Recent advancements in analytical solutions to quantify water and solute time-variant travel time distributions (TTDs) and the related StorAge Selection (SAS) functions synthesize catchment complexity into a simplified, lumped representation. While these analytical approaches are easy and efficient in application, they require high frequency hydrochemical data for parameter estimation. Alternatively, integrated hydrologic models coupled to Lagrangian particle-tracking approaches can directly simulate age under different catchment geometries and complexity at a greater computational expense. Here, we compare and contrast the two approaches by exploring the influence of the spatial distribution of subsurface heterogeneity, interactions between distinct flow domains, diversity of flow pathways, and recharge rate on the shape of TTDs and the relating SAS functions. To this end, we use a parallel three-dimensional variably saturated groundwater model, ParFlow, to solve for the velocity fields in the subsurface. A particle-tracking model, SLIM, is then implemented to determine the age distributions at every real time and domain location, facilitating a direct characterization of the SAS functions as opposed to analytical approaches requiring calibration of such functions. Steady-state results reveal that the assumption of random age sampling scheme might only hold in the saturated region of homogeneous catchments resulting in an exponential TTD. This assumption is however violated when the vadose zone is included as the underlying SAS function gives a higher preference to older ages. The dynamical variability of the true SAS functions is also shown to be largely masked by the smooth analytical SAS functions. As the variability of subsurface spatial heterogeneity increases, the shape of TTD approaches a power-law distribution function, including a broader distribution of shorter and longer travel times. We further found that larger (smaller) magnitude of effective

A conservative, thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

Science.gov (United States)

Nonaka, Andrew; Day, Marcus S.; Bell, John B.

2018-01-01

We present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.

BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

OpenAIRE

Caffo, Michele; Czyz, Henryk; Gunia, Michal; Remiddi, Ettore

2008-01-01

We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations.

Numerical modelling of so-called secondary ultrasonic echoes

International Nuclear Information System (INIS)

Langenberg, K.J.; Fellinger, P.; Hofmann, C.

1994-01-01

The formation of secondary ultrasonic echoes is discussed for a particularly simple testing situation. This discussion is based upon the intuitive visualization of elastic wave propagation as obtained with the numerical EFIT-Code (Elastodynamic Finite Integration Technique). The resulting travel times for the econdary echoes contain well-defined limits as they originate from the simple model of grazing incidence plane longitudinal wave mode conversion. (orig.) [de

Numerical solution of the time dependent neutron transport equation by the method of the characteristics

International Nuclear Information System (INIS)

Talamo, Alberto

2013-01-01

This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps

Numerical solution of the time dependent neutron transport equation by the method of the characteristics

Energy Technology Data Exchange (ETDEWEB)

Talamo, Alberto, E-mail: alby@anl.gov [Nuclear Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439 (United States)

2013-05-01

This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

A CMOS integrated timing discriminator circuit for fast scintillation counters

International Nuclear Information System (INIS)

Jochmann, M.W.

1998-01-01

Based on a zero-crossing discriminator using a CR differentiation network for pulse shaping, a new CMOS integrated timing discriminator circuit is proposed for fast (t r ≥ 2 ns) scintillation counters at the cooler synchrotron COSY-Juelich. By eliminating the input signal's amplitude information by means of an analog continuous-time divider, a normalized pulse shape at the zero-crossing point is gained over a wide dynamic input amplitude range. In combination with an arming comparator and a monostable multivibrator this yields in a highly precise timing discriminator circuit, that is expected to be useful in different time measurement applications. First measurement results of a CMOS integrated logarithmic amplifier, which is part of the analog continuous-time divider, agree well with the corresponding simulations. Moreover, SPICE simulations of the integrated discriminator circuit promise a time walk well below 200 ps (FWHM) over a 40 dB input amplitude dynamic range

An integrated technique for developing real-time systems

NARCIS (Netherlands)

Hooman, J.J.M.; Vain, J.

1995-01-01

The integration of conceptual modeling techniques, formal specification, and compositional verification is considered for real time systems within the knowledge engineering context. We define constructive transformations from a conceptual meta model to a real time specification language and give

Numerical Modelling of Time-Dependent Behaviour of Reinforced Concrete Structure with Use of B3 Model

Directory of Open Access Journals (Sweden)

Koktan Jiří

2014-12-01

Full Text Available The paper proposes an implementation of creep analysis of reinforced concrete structures which utilizes the B3 model and the direct stiffness method for reinforced concrete frames. The analysis is based on a numerical integration and it is implemented in an algorithmic programming language. There is presented a solution with the mentioned approaches which is compared with solution based on the EN 1992-1-1 technical standard.

Path integration on space times with symmetry

International Nuclear Information System (INIS)

Low, S.G.

1985-01-01

Path integration on space times with symmetry is investigated using a definition of path integration of Gaussian integrators. Gaussian integrators, systematically developed using the theory of projective distributions, may be defined in terms of a Jacobi operator Green function. This definition of the path integral yields a semiclassical expansion of the propagator which is valid on caustics. The semiclassical approximation to the free particle propagator on symmetric and reductive homogeneous spaces is computed in terms of the complete solution of the Jacobi equation. The results are used to test the validity of using the Schwinger-DeWitt transform to compute an approximation to the coincidence limit of a field theory Green function from a WKB propagator. The method is found not to be valid except for certain special cases. These cases include manifolds constructed from the direct product of flat space and group manifolds, on which the free particle WKB approximation is exact and two sphere. The multiple geodesic contribution to 2 > on Schwarzschild in the neighborhood of rho = 3M is computed using the transform

Event and Apparent Horizon Finders for 3+1 Numerical Relativity

Directory of Open Access Journals (Sweden)

Thornburg Jonathan

2007-06-01

Full Text Available Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3+1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous null surface in spacetime. The event horizon is defined nonlocally in time: it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part of spacetime has been numerically computed.There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate.In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Theta. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most “apparent horizon” finders actually find MOTSs.There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting

Numerical simulation of low Mach number reacting flows

International Nuclear Information System (INIS)

Bell, J B; Aspden, A J; Day, M S; Lijewski, M J

2007-01-01

Using examples from active research areas in combustion and astrophysics, we demonstrate a computationally efficient numerical approach for simulating multiscale low Mach number reacting flows. The method enables simulations that incorporate an unprecedented range of temporal and spatial scales, while at the same time, allows an extremely high degree of reaction fidelity. Sample applications demonstrate the efficiency of the approach with respect to a traditional time-explicit integration method, and the utility of the methodology for studying the interaction of turbulence with terrestrial and astrophysical flame structures

Real-time 3-D space numerical shake prediction for earthquake early warning

Science.gov (United States)

Wang, Tianyun; Jin, Xing; Huang, Yandan; Wei, Yongxiang

2017-12-01

In earthquake early warning systems, real-time shake prediction through wave propagation simulation is a promising approach. Compared with traditional methods, it does not suffer from the inaccurate estimation of source parameters. For computation efficiency, wave direction is assumed to propagate on the 2-D surface of the earth in these methods. In fact, since the seismic wave propagates in the 3-D sphere of the earth, the 2-D space modeling of wave direction results in inaccurate wave estimation. In this paper, we propose a 3-D space numerical shake prediction method, which simulates the wave propagation in 3-D space using radiative transfer theory, and incorporate data assimilation technique to estimate the distribution of wave energy. 2011 Tohoku earthquake is studied as an example to show the validity of the proposed model. 2-D space model and 3-D space model are compared in this article, and the prediction results show that numerical shake prediction based on 3-D space model can estimate the real-time ground motion precisely, and overprediction is alleviated when using 3-D space model.

A New time Integration Scheme for Cahn-hilliard Equations

KAUST Repository

Schaefer, R.

2015-06-01

In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.

A New time Integration Scheme for Cahn-hilliard Equations

KAUST Repository

Schaefer, R.; Smol-ka, M.; Dalcin, L; Paszyn'ski, M.

2015-01-01

In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.

Numerical solution of continuous-time DSGE models under Poisson uncertainty

DEFF Research Database (Denmark)

Posch, Olaf; Trimborn, Timo

We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We...... classes of models. We illustrate the algorithm simulating both the stochastic neoclassical growth model and the Lucas model under Poisson uncertainty which is motivated by the Barro-Rietz rare disaster hypothesis. We find that, even for non-linear policy functions, the maximum (absolute) error is very...

Continuous integration congestion cost allocation based on sensitivity

International Nuclear Information System (INIS)

Wu, Z.Q.; Wang, Y.N.

2004-01-01

Congestion cost allocation is a very important topic in congestion management. Allocation methods based on the Aumann-Shapley value use the discrete numerical integration method, which needs to solve the incremented OPF solution many times, and as such it is not suitable for practical application to large-scale systems. The optimal solution and its sensitivity change tendency during congestion removal using a DC optimal power flow (OPF) process is analysed. A simple continuous integration method based on the sensitivity is proposed for the congestion cost allocation. The proposed sensitivity analysis method needs a smaller computation time than the method based on using the quadratic method and inner point iteration. The proposed congestion cost allocation method uses a continuous integration method rather than discrete numerical integration. The method does not need to solve the incremented OPF solutions; which allows it use in large-scale systems. The method can also be used for AC OPF congestion management. (author)

On the hydrodynamics of archer fish jumping out of the water: Integrating experiments with numerical simulations

Science.gov (United States)

Sotiropoulos, Fotis; Angelidis, Dionysios; Mendelson, Leah; Techet, Alexandra

2017-11-01

Evolution has enabled fish to develop a range of thrust producing mechanisms to allow skillful movement and give them the ability to catch prey or avoid danger. Several experimental and numerical studies have been performed to investigate how complex maneuvers are executed and develop bioinspired strategies for aquatic robot design. We will discuss recent numerical advances toward the development of a computational framework for performing turbulent, two-phase flow, fluid-structure-interaction (FSI) simulations to investigate the dynamics of aquatic jumpers. We will also discuss the integration of such numerics with high-speed imaging and particle image velocimetry data to reconstruct anatomic fish models and prescribe realistic kinematics of fish motion. The capabilities of our method will be illustrated by applying it to simulate the motion of a small scale archer fish jumping out of the water to capture prey. We will discuss the rich vortex dynamics emerging during the hovering, rapid upward and gliding phases. The simulations will elucidate the thrust production mechanisms by the movement of the pectoral and anal fins and we will show that the fins significantly contribute to the rapid acceleration.

Numerical modeling for saturated-zone groundwater travel time analysis at Yucca Mountain

International Nuclear Information System (INIS)

Arnold, B.W.; Barr, G.E.

1996-01-01

A three-dimensional, site-scale numerical model of groundwater flow in the saturated zone at Yucca Mountain was constructed and linked to particle tracking simulations to produce an estimate of the distribution of groundwater travel times from the potential repository to the boundary of the accessible environment. This effort and associated modeling of groundwater travel times in the unsaturated zone were undertaken to aid in the evaluation of compliance of the site with 10CFR960. These regulations stipulate that pre-waste-emplacement groundwater travel time to the accessible environment shall exceed 1,000 years along any path of likely and significant radionuclide travel

Effects of integration time on in-water radiometric profiles.

Science.gov (United States)

D'Alimonte, Davide; Zibordi, Giuseppe; Kajiyama, Tamito

2018-03-05

This work investigates the effects of integration time on in-water downward irradiance E d , upward irradiance E u and upwelling radiance L u profile data acquired with free-fall hyperspectral systems. Analyzed quantities are the subsurface value and the diffuse attenuation coefficient derived by applying linear and non-linear regression schemes. Case studies include oligotrophic waters (Case-1), as well as waters dominated by Colored Dissolved Organic Matter (CDOM) and Non-Algal Particles (NAP). Assuming a 24-bit digitization, measurements resulting from the accumulation of photons over integration times varying between 8 and 2048ms are evaluated at depths corresponding to: 1) the beginning of each integration interval (Fst); 2) the end of each integration interval (Lst); 3) the averages of Fst and Lst values (Avg); and finally 4) the values weighted accounting for the diffuse attenuation coefficient of water (Wgt). Statistical figures show that the effects of integration time can bias results well above 5% as a function of the depth definition. Results indicate the validity of the Wgt depth definition and the fair applicability of the Avg one. Instead, both the Fst and Lst depths should not be adopted since they may introduce pronounced biases in E u and L u regression products for highly absorbing waters. Finally, the study reconfirms the relevance of combining multiple radiometric casts into a single profile to increase precision of regression products.

A review of some basic aspects related to integration of airplane’s equations of motion

Directory of Open Access Journals (Sweden)

Dan TURCANU

2017-09-01

Full Text Available Numerical integration of the airplane’s equations of motion has long been considered among the most fundamental calculations in airplane’s analysis. Numerical algorithms have been implemented and experimentally validated. However, the need for superior speed and accuracy is still very topical, as, nowadays, various optimization algorithms rely heavily on data generated from the integration of the equations of motion and having access to larger amounts of data can increase the quality of the optimization. Now, for a number of decades, engineers have relied heavily on commercial codes based on automatically selected integration steps. However, optimally chosen constant integration steps can save time and allows for larger numbers of integrations to be performed. Yet, the basic papers that presented the fundamentals of numerical integration, as applied to airplane’s equations of motion are nowadays not easy to locate. Consequently, this paper presents a review of basic aspects related to the integration of airplane’s equation of motion. The discussion covers fundamentals of longitudinal and lateral-directional motion as well as the implementation of some numerical integration methods. The relation between numerical integration steps, accuracy, computational resource usage, numerical stability and their relation with the parameters describing the dynamic response of the airplane is considered and suggestions are presented for a faster yet accurate numerical integration.

Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

Science.gov (United States)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

A numerical approach to the time dependent neutron flux using the Laplace transform technique

International Nuclear Information System (INIS)

El-Demerdash, A; Beynon, T.D.

1979-01-01

In this study a time dependent transport problem in which an isotopic neutron source emits a pulse of neutrons into a finite sphere has been solved by a numerical Laplace transform technique. The object has been to investigate the time behaviour of the neutron field in the moderators at times shortly after the neutron source initiation, that is in the nanosecond time period. The basis of the solution is a numercial evaluation of the Laplace transform of the flux in the linear Boltzmann equation with the use of a modified version of a steady state energy multi-group spatially dependent code. The explicit or direct inversion of the Laplace transformed flux is complicated to be solved numerically due to the ill-conditioned matrix obtained. The suggested method of solutions depends on choice of a function that satisfies the physical condition known from the neutron behaviour and that has a Laplace inversion which is analytically amenable. By employing a least square fitting procedure the function is modified in order to minimize the error in the Laplace transformed values and hence in the time dependent solution. This method has been applied satisfactorily in comparison to analytical and experimental results

Avionics systems integration technology

Science.gov (United States)

Stech, George; Williams, James R.

1988-01-01

A very dramatic and continuing explosion in digital electronics technology has been taking place in the last decade. The prudent and timely application of this technology will provide Army aviation the capability to prevail against a numerically superior enemy threat. The Army and NASA have exploited this technology explosion in the development and application of avionics systems integration technology for new and future aviation systems. A few selected Army avionics integration technology base efforts are discussed. Also discussed is the Avionics Integration Research Laboratory (AIRLAB) that NASA has established at Langley for research into the integration and validation of avionics systems, and evaluation of advanced technology in a total systems context.

An integration time adaptive control method for atmospheric composition detection of occultation

Science.gov (United States)

Ding, Lin; Hou, Shuai; Yu, Fei; Liu, Cheng; Li, Chao; Zhe, Lin

2018-01-01

When sun is used as the light source for atmospheric composition detection, it is necessary to image sun for accurate identification and stable tracking. In the course of 180 second of the occultation, the magnitude of sun light intensity through the atmosphere changes greatly. It is nearly 1100 times illumination change between the maximum atmospheric and the minimum atmospheric. And the process of light change is so severe that 2.9 times per second of light change can be reached. Therefore, it is difficult to control the integration time of sun image camera. In this paper, a novel adaptive integration time control method for occultation is presented. In this method, with the distribution of gray value in the image as the reference variable, and the concepts of speed integral PID control, the integration time adaptive control problem of high frequency imaging. The large dynamic range integration time automatic control in the occultation can be achieved.

Long-time behaviour of discretizations of the simple pendulum equation

Energy Technology Data Exchange (ETDEWEB)

Cieslinski, Jan L [Uniwersytet w Bialymstoku, Wydzial Fizyki, ul. Lipowa 41, 15-424 Bialystok (Poland); Ratkiewicz, Boguslaw [Doctoral Studies, Wydzial Fizyki, Uniwersytet Adama Mickiewicza, Poznan (Poland)], E-mail: janek@alpha.uwb.edu.pl, E-mail: bograt@poczta.onet.pl

2009-03-13

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step.

Long-time behaviour of discretizations of the simple pendulum equation

International Nuclear Information System (INIS)

Cieslinski, Jan L; Ratkiewicz, Boguslaw

2009-01-01

We compare several discretizations of the simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. The chosen numerical schemes are either symplectic maps or integrable (energy-preserving) maps, or both. Therefore, they preserve qualitative features of solutions (such as periodicity). We describe characteristic periodic time dependences of numerical estimates of the period and the amplitude, and explain them as systematic numerical by-effects produced by any method. Finally, we propose a new numerical scheme which is a modification of the discrete gradient method. This modified discrete gradient method preserves (almost exactly) the period of small oscillations for any time step

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.

Long-time predictions in nonlinear dynamics

Science.gov (United States)

Szebehely, V.

1980-01-01

It is known that nonintegrable dynamical systems do not allow precise predictions concerning their behavior for arbitrary long times. The available series solutions are not uniformly convergent according to Poincare's theorem and numerical integrations lose their meaningfulness after the elapse of arbitrary long times. Two approaches are the use of existing global integrals and statistical methods. This paper presents a generalized method along the first approach. As examples long-time predictions in the classical gravitational satellite and planetary problems are treated.

An integrated supply chain inventory model with imperfect-quality items, controllable lead time and distribution-free demand

Directory of Open Access Journals (Sweden)

Lin Hsien-Jen

2013-01-01

Full Text Available In this paper, we consider an integrated vendor-buyer inventory policy for a continuous review model with a random number of defective items and screening process gradually at a fixed screening rate in buyer’s arriving order lot. We assume that shortages are allowed and partially backlogged on the buyer’s side, and that the lead time demand distribution is unknown, except its first two moments. The objective is to apply the minmax distribution free approach to determine the optimal order quantity, reorder point, lead time and the number of lots delivered in one production run simultaneously so that the expected total system cost is minimized. Numerical experiments along with sensitivity analysis were performed to illustrate the effects of parameters on the decision and the total system cost.

Mixed time slicing in path integral simulations

International Nuclear Information System (INIS)

Steele, Ryan P.; Zwickl, Jill; Shushkov, Philip; Tully, John C.

2011-01-01

A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be 'collapsed' in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.

High-precision numerical integration of equations in dynamics

Science.gov (United States)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

An important requirement for the process of solving differential equations in Dynamics, such as the equations of the motion of celestial bodies and, in particular, the motion of cosmic robotic systems is high accuracy at large time intervals. One of effective tools for obtaining such solutions is the Taylor series method. In this connection, we note that it is very advantageous to reduce the given equations of Dynamics to systems with polynomial (in unknowns) right-hand sides. This allows us to obtain effective algorithms for finding the Taylor coefficients, a priori error estimates at each step of integration, and an optimal choice of the order of the approximation used. In the paper, these questions are discussed and appropriate algorithms are considered.

Indirect methods for wake potential integration

International Nuclear Information System (INIS)

Zagorodnov, I.

2006-05-01

The development of the modern accelerator and free-electron laser projects requires to consider wake fields of very short bunches in arbitrary three dimensional structures. To obtain the wake numerically by direct integration is difficult, since it takes a long time for the scattered fields to catch up to the bunch. On the other hand no general algorithm for indirect wake field integration is available in the literature so far. In this paper we review the know indirect methods to compute wake potentials in rotationally symmetric and cavity-like three dimensional structures. For arbitrary three dimensional geometries we introduce several new techniques and test them numerically. (Orig.)

Optimal Real-time Dispatch for Integrated Energy Systems

DEFF Research Database (Denmark)

Anvari-Moghaddam, Amjad; Guerrero, Josep M.; Rahimi-Kian, Ashkan

2016-01-01

With the emerging of small-scale integrated energy systems (IESs), there are significant potentials to increase the functionality of a typical demand-side management (DSM) strategy and typical implementation of building-level distributed energy resources (DERs). By integrating DSM and DERs...... into a cohesive, networked package that fully utilizes smart energy-efficient end-use devices, advanced building control/automation systems, and integrated communications architectures, it is possible to efficiently manage energy and comfort at the end-use location. In this paper, an ontology-driven multi......-agent control system with intelligent optimizers is proposed for optimal real-time dispatch of an integrated building and microgrid system considering coordinated demand response (DR) and DERs management. The optimal dispatch problem is formulated as a mixed integer nonlinear programing problem (MINLP...

An analytical nodal method for time-dependent one-dimensional discrete ordinates problems

International Nuclear Information System (INIS)

Barros, R.C. de

1992-01-01

In recent years, relatively little work has been done in developing time-dependent discrete ordinates (S N ) computer codes. Therefore, the topic of time integration methods certainly deserves further attention. In this paper, we describe a new coarse-mesh method for time-dependent monoenergetic S N transport problesm in slab geometry. This numerical method preserves the analytic solution of the transverse-integrated S N nodal equations by constants, so we call our method the analytical constant nodal (ACN) method. For time-independent S N problems in finite slab geometry and for time-dependent infinite-medium S N problems, the ACN method generates numerical solutions that are completely free of truncation errors. Bsed on this positive feature, we expect the ACN method to be more accurate than conventional numerical methods for S N transport calculations on coarse space-time grids

Real-time numerical simulation of the Carnot cycle

International Nuclear Information System (INIS)

Hurkala, J; Gall, M; Kutner, R; Maciejczyk, M

2005-01-01

We developed a highly interactive, multi-windows Java applet which made it possible to simulate and visualize within any platform and internet the Carnot cycle (or engine) in a real-time computer experiment. We extended our previous model and algorithm (Galant et al 2003 Heat Transfer, Newton's Law of Cooling and the Law of Entropy Increase Simulated by the Real-Time Computer Experiments in Java (Lecture Notes in Computer Science vol 2657) pp 45-53, Gall and Kutner 2005 Molecular mechanisms of heat transfer: Debye relaxation versus power-law Physica A 352 347-78) to simulate not only the heat flow but also the macroscopic movement of the piston. Since in reality it is impossible to construct a reversible Carnot engine, the question arises whether it is possible to simulate it at least in a numerical experiment? The positive answer to this question which we found is related to our model and algorithm which make it possible to omit the many-body problem arising when many gas particles simultaneously interact with the mobile piston. As usual, the considerations of phenomenological thermodynamics began with a study of the basic properties of heat engines, hence our approach, besides intrinsic physical significance, is also important from the educational, technological and even environmental points of view

Numerical modeling of time domain 3-D problems in accelerator physics

International Nuclear Information System (INIS)

Harfoush, F.A.; Jurgens, T.G.

1990-06-01

Time domain analysis is relevant in particle accelerators to study the electromagnetic field interaction of a moving source particle on a lagging test particle as the particles pass an accelerating cavity or some other structure. These fields are called wake fields. The travelling beam inside a beam pipe may undergo more complicated interactions with its environment due to the presence of other irregularities like wires, thin slots, joints and other types of obstacles. Analytical solutions of such problems is impossible and one has to resort to a numerical method. In this paper we present results of our first attempt to model these problems in 3-D using our finite difference time domain (FDTD) code. 10 refs., 9 figs

Complex Langevin simulation of real time quantum evolution

International Nuclear Information System (INIS)

Ilgenfritz, E.M.; Kripfganz, J.

1986-07-01

Complex Langevin methods are used to study the time evolution of quantum mechanical wave packets. We do not need any Feynman ε regularization for the numerical evaluation of the double time path integral. (author)

Monolitic integrated circuit for the strobed charge-to-time converter

International Nuclear Information System (INIS)

Bel'skij, V.I.; Bushnin, Yu.B.; Zimin, S.A.; Punzhin, Yu.N.; Sen'ko, V.A.; Soldatov, M.M.; Tokarchuk, V.P.

1985-01-01

The developed and comercially produced semiconducting circuit - gating charge-to-time converter KR1101PD1 is described. The considered integrated circuit is a short pulse charge-to-time converter with integration of input current. The circuit is designed for construction of time-to-pulse analog-to-digital converters utilized in multichannel detection systems when studying complex topology processes. Input resistance of the circuit is 0.1 Ω permissible input current is 50 mA, maximum measured charge is 300-1000 pC

A Fully Integrated Discrete-Time Superheterodyne Receiver

NARCIS (Netherlands)

Tohidian, M.; Madadi, I.; Staszewski, R.B.

2017-01-01

The zero/low intermediate frequency (IF) receiver (RX) architecture has enabled full CMOS integration. As the technology scales and wireless standards become ever more challenging, the issues related to time-varying dc offsets, the second-order nonlinearity, and flicker noise become more critical.

Numerical simulation of electromagnetic wave propagation using time domain meshless method

International Nuclear Information System (INIS)

Ikuno, Soichiro; Fujita, Yoshihisa; Itoh, Taku; Nakata, Susumu; Nakamura, Hiroaki; Kamitani, Atsushi

2012-01-01

The electromagnetic wave propagation in various shaped wave guide is simulated by using meshless time domain method (MTDM). Generally, Finite Differential Time Domain (FDTD) method is applied for electromagnetic wave propagation simulation. However, the numerical domain should be divided into rectangle meshes if FDTD method is applied for the simulation. On the other hand, the node disposition of MTDM can easily describe the structure of arbitrary shaped wave guide. This is the large advantage of the meshless time domain method. The results of computations show that the damping rate is stably calculated in case with R < 0.03, where R denotes a support radius of the weight function for the shape function. And the results indicate that the support radius R of the weight functions should be selected small, and monomials must be used for calculating the shape functions. (author)

Optimal distribution of integration time for intensity measurements in Stokes polarimetry.

Science.gov (United States)

Li, Xiaobo; Liu, Tiegen; Huang, Bingjing; Song, Zhanjie; Hu, Haofeng

2015-10-19

We consider the typical Stokes polarimetry system, which performs four intensity measurements to estimate a Stokes vector. We show that if the total integration time of intensity measurements is fixed, the variance of the Stokes vector estimator depends on the distribution of the integration time at four intensity measurements. Therefore, by optimizing the distribution of integration time, the variance of the Stokes vector estimator can be decreased. In this paper, we obtain the closed-form solution of the optimal distribution of integration time by employing Lagrange multiplier method. According to the theoretical analysis and real-world experiment, it is shown that the total variance of the Stokes vector estimator can be significantly decreased about 40% in the case discussed in this paper. The method proposed in this paper can effectively decrease the measurement variance and thus statistically improves the measurement accuracy of the polarimetric system.

Optimal order and time-step criterion for Aarseth-type N-body integrators

International Nuclear Information System (INIS)

Makino, Junichiro

1991-01-01

How the selection of the time-step criterion and the order of the integrator change the efficiency of Aarseth-type N-body integrators is discussed. An alternative to Aarseth's scheme based on the direct calculation of the time derivative of the force using the Hermite interpolation is compared to Aarseth's scheme, which uses the Newton interpolation to construct the predictor and corrector. How the number of particles in the system changes the behavior of integrators is examined. The Hermite scheme allows a time step twice as large as that for the standard Aarseth scheme for the same accuracy. The calculation cost of the Hermite scheme per time step is roughly twice as much as that of the standard Aarseth scheme. The optimal order of the integrators depends on both the particle number and the accuracy required. The time-step criterion of the standard Aarseth scheme is found to be inapplicable to higher-order integrators, and a more uniformly reliable criterion is proposed. 18 refs

Evaluating time-lapse ERT for monitoring DNAPL remediation via numerical simulation

Science.gov (United States)

Power, C.; Karaoulis, M.; Gerhard, J.; Tsourlos, P.; Giannopoulos, A.

2012-12-01

Dense non-aqueous phase liquids (DNAPLs) remain a challenging geoenvironmental problem in the near subsurface. Numerous thermal, chemical, and biological treatment methods are being applied at sites but without a non-destructive, rapid technique to map the evolution of DNAPL mass in space and time, the degree of remedial success is difficult to quantify. Electrical resistivity tomography (ERT) has long been presented as highly promising in this context but has not yet become a practitioner's tool due to challenges in interpreting the survey results at real sites where the initial condition (DNAPL mass, DNAPL distribution, subsurface heterogeneity) is typically unknown. Recently, a new numerical model was presented that couples DNAPL and ERT simulation at the field scale, providing a tool for optimizing ERT application and interpretation at DNAPL sites (Power et al., 2011, Fall AGU, H31D-1191). The objective of this study is to employ this tool to evaluate the effectiveness of time-lapse ERT to monitor DNAPL source zone remediation, taking advantage of new inversion methodologies that exploit the differences in the target over time. Several three-dimensional releases of chlorinated solvent DNAPLs into heterogeneous clayey sand at the field scale were generated, varying in the depth and complexity of the source zone (target). Over time, dissolution of the DNAPL in groundwater was simulated with simultaneous mapping via periodic ERT surveys. Both surface and borehole ERT surveys were conducted for comparison purposes. The latest four-dimensional ERT inversion algorithms were employed to generate time-lapse isosurfaces of the DNAPL source zone for all cases. This methodology provided a qualitative assessment of the ability of ERT to track DNAPL mass removal for complex source zones in realistically heterogeneous environments. In addition, it provided a quantitative comparison between the actual DNAPL mass removed and that interpreted by ERT as a function of depth below

Contribution to the asymptotic estimation of the global error of single step numerical integration methods. Application to the simulation of electric power networks; Contribution a l'estimation asymptotique de l'erreur globale des methodes d'integration numerique a un pas. Application a la simulation des reseaux electriques

Energy Technology Data Exchange (ETDEWEB)

Aid, R.

1998-01-07

This work comes from an industrial problem of validating numerical solutions of ordinary differential equations modeling power systems. This problem is solved using asymptotic estimators of the global error. Four techniques are studied: Richardson estimator (RS), Zadunaisky's techniques (ZD), integration of the variational equation (EV), and Solving for the correction (SC). We give some precisions on the relative order of SC w.r.t. the order of the numerical method. A new variant of ZD is proposed that uses the Modified Equation. In the case of variable step-size, it is shown that under suitable restriction, on the hypothesis of the step-size selection, ZD and SC are still valid. Moreover, some Runge-Kutta methods are shown to need less hypothesis on the step-sizes to exhibit a valid order of convergence for ZD and SC. Numerical tests conclude this analysis. Industrial cases are given. Finally, an algorithm to avoid the a priori specification of the integration path for complex time differential equations is proposed. (author)

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)

Integral definition of transition time in the Landau-Zener model

International Nuclear Information System (INIS)

Yan Yue; Wu Biao

2010-01-01

We give a general definition for the transition time in the Landau-Zener model. This definition allows us to compute numerically the Landau-Zener transition time at any sweeping rate without ambiguity in both diabatic and adiabatic bases. With this new definition, analytical results are obtained in both the adiabatic limit and the sudden limit.

An Integrated Numerical Model for the Design of Coastal Protection Structures

Directory of Open Access Journals (Sweden)

Theophanis V. Karambas

2017-10-01

Full Text Available In the present work, an integrated coastal engineering numerical model is presented. The model simulates the linear wave propagation, wave-induced circulation, and sediment transport and bed morphology evolution. It consists of three main modules: WAVE_L, WICIR, and SEDTR. The nearshore wave transformation module WAVE_L (WAVE_Linear is based on the hyperbolic-type mild slope equation and is valid for a compound linear wave field near coastal structures where the waves are subjected to the combined effects of shoaling, refraction, diffraction, reflection (total and partial, and breaking. Radiation stress components (calculated from WAVE_L drive the depth averaged circulation module WICIR (Wave Induced CIRculation for the description of the nearshore wave-induced currents. Sediment transport and bed morphology evolution in the nearshore, surf, and swash zone are simulated by the SEDTR (SEDiment TRansport module. The model is tested against experimental data to study the effect of representative coastal protection structures and is applied to a real case study of a coastal engineering project in North Greece, producing accurate and consistent results for a versatile range of layouts.

Aspects for Run-time Component Integration

DEFF Research Database (Denmark)

Truyen, Eddy; Jørgensen, Bo Nørregaard; Joosen, Wouter

2000-01-01

Component framework technology has become the cornerstone of building a family of systems and applications. A component framework defines a generic architecture into which specialized components can be plugged. As such, the component framework leverages the glue that connects the different inserted...... to dynamically integrate into the architecture of middleware systems new services that support non-functional aspects such as security, transactions, real-time....

Real-Time Numerical Simulation of the Carnot Cycle

International Nuclear Information System (INIS)

Hurkala, J.; Gall, M.; Kutner, R.; Maciejczyk, M.

2005-01-01

We developed a highly interactive, multi-windows Java applet which made it possible to simulate and visualize within any platform and internet the Carnot cycle (or engine) in a real-time computer experiment. We extended our previous model and algorithm to simulate not only the heat flow but also the macroscopic movement of the piston. since in reality it is impossible to construct a reversible Carnot engine, the question arises whether it is possible to simulate it at least in a numerical experiment? The positive answer to this question which we found is related to our model and algorithm which make it possible to omit the many-body problem arising when many gas particles simultaneously interact with the mobile piston. As usually the considerations of phenomenomenological thermodynamics began with a study of the basic properties of heat engines hence our approach, beside intrinsic physical significance, is also important from the educational, technological and even environmental points of view. (author)

Path integral density matrix dynamics: a method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems.

Science.gov (United States)

Habershon, Scott

2013-09-14

We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.

Path integral density matrix dynamics: A method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems

International Nuclear Information System (INIS)

Habershon, Scott

2013-01-01

We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency

Explosion localization and characterization via infrasound using numerical modeling

Science.gov (United States)

Fee, D.; Kim, K.; Iezzi, A. M.; Matoza, R. S.; Jolly, A. D.; De Angelis, S.; Diaz Moreno, A.; Szuberla, C.

2017-12-01

Numerous methods have been applied to locate, detect, and characterize volcanic and anthropogenic explosions using infrasound. Far-field localization techniques typically use back-azimuths from multiple arrays (triangulation) or Reverse Time Migration (RTM, or back-projection). At closer ranges, networks surrounding a source may use Time Difference of Arrival (TDOA), semblance, station-pair double difference, etc. However, at volcanoes and regions with topography or obstructions that block the direct path of sound, recent studies have shown that numerical modeling is necessary to provide an accurate source location. A heterogeneous and moving atmosphere (winds) may also affect the location. The time reversal mirror (TRM) application of Kim et al. (2015) back-propagates the wavefield using a Finite Difference Time Domain (FDTD) algorithm, with the source corresponding to the location of peak convergence. Although it provides high-resolution source localization and can account for complex wave propagation, TRM is computationally expensive and limited to individual events. Here we present a new technique, termed RTM-FDTD, which integrates TRM and FDTD. Travel time and transmission loss information is computed from each station to the entire potential source grid from 3-D Green's functions derived via FDTD. The wave energy is then back-projected and stacked at each grid point, with the maximum corresponding to the likely source. We apply our method to detect and characterize thousands of explosions from Yasur Volcano, Vanuatu and Etna Volcano, Italy, which both provide complex wave propagation and multiple source locations. We compare our results with those from more traditional methods (e.g. semblance), and suggest our method is preferred as it is computationally less expensive than TRM but still integrates numerical modeling. RTM-FDTD could be applied to volcanic other anthropogenic sources at a wide variety of ranges and scenarios. Kim, K., Lees, J.M., 2015. Imaging

Time-dependent generalized Gibbs ensembles in open quantum systems

Science.gov (United States)

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2018-04-01

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

Local linearization methods for the numerical integration of ordinary differential equations: An overview

International Nuclear Information System (INIS)

Jimenez, J.C.

2009-06-01

Local Linearization (LL) methods conform a class of one-step explicit integrators for ODEs derived from the following primary and common strategy: the vector field of the differential equation is locally (piecewise) approximated through a first-order Taylor expansion at each time step, thus obtaining successive linear equations that are explicitly integrated. Hereafter, the LL approach may include some additional strategies to improve that basic affine approximation. Theoretical and practical results have shown that the LL integrators have a number of convenient properties. These include arbitrary order of convergence, A-stability, linearization preserving, regularity under quite general conditions, preservation of the dynamics of the exact solution around hyperbolic equilibrium points and periodic orbits, integration of stiff and high-dimensional equations, low computational cost, and others. In this paper, a review of the LL methods and their properties is presented. (author)

A time-domain finite element boundary integral approach for elastic wave scattering

Science.gov (United States)

Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.

2018-04-01

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.

The Crank Nicolson Time Integrator for EMPHASIS.

Energy Technology Data Exchange (ETDEWEB)

McGregor, Duncan Alisdair Odum; Love, Edward; Kramer, Richard Michael Jack

2018-03-01

We investigate the use of implicit time integrators for finite element time domain approxi- mations of Maxwell's equations in vacuum. We discretize Maxwell's equations in time using Crank-Nicolson and in 3D space using compatible finite elements. We solve the system by taking a single step of Newton's method and inverting the Eddy-Current Schur complement allowing for the use of standard preconditioning techniques. This approach also generalizes to more complex material models that can include the Unsplit PML. We present verification results and demonstrate performance at CFL numbers up to 1000.

Numerical calculation of a class of highly oscillatory integrals with the Mathieu function

International Nuclear Information System (INIS)

Long Yongxing

1992-01-01

The author describes a method for computing highly oscillatory integrals with the Mathieu function. The practice proves that not only the results are highly satisfactory, but also the method is time-saving

Numerical solver of the time-dependent Schroedinger equation with Coulomb singularities

International Nuclear Information System (INIS)

Gordon, Ariel; Jirauschek, Christian; Kaertner, Franz X.

2006-01-01

This paper addresses a very fundamental and important problem in the numerical analysis of atomic and molecular systems: How to discretize Hamiltonians with divergent potential terms, such as Coulomb singularities. At the point of a Coulomb singularity, the wave function cannot be described by a Taylor series expansion, which results in problems when standard discretization schemes are used. We propose using the known asymptotic form of the wave function near the singularity instead of the (nonexistent) Taylor series. This principle, namely discretization by asymptotic behavior correspondence (ABC), is employed in this paper for obtaining grid-discretizations for the Coulomb potential in Cartesian, cylindrical and spherical coordinate systems. We show that computations with the ABC discretization are faster and more precise than with a naive discretization by orders of magnitude. The ABC discretization is well suited for the standard numerical time propagators, such as the Crank-Nicholson, Peaceman-Rachford, and leapfrog schemes. We use the latter, since it is faster and has the same order of accuracy. The leapfrog scheme is generalized to allow absorbing potentials at the grid boundaries

Integrating experimental and simulation length and time scales in mechanistic studies of friction

International Nuclear Information System (INIS)

Sawyer, W G; Perry, S S; Phillpot, S R; Sinnott, S B

2008-01-01

Friction is ubiquitous in all aspects of everyday life and has consequently been under study for centuries. Classical theories of friction have been developed and used to successfully solve numerous tribological problems. However, modern applications that involve advanced materials operating under extreme environments can lead to situations where classical theories of friction are insufficient to describe the physical responses of sliding interfaces. Here, we review integrated experimental and computational studies of atomic-scale friction and wear at solid-solid interfaces across length and time scales. The influence of structural orientation in the case of carbon nanotube bundles, and molecular orientation in the case of polymer films of polytetrafluoroethylene and polyethylene, on friction and wear are discussed. In addition, while friction in solids is generally considered to be athermal, under certain conditions thermally activated friction is observed for polymers, carbon nanotubes and graphite. The conditions under which these transitions occur, and their proposed origins, are discussed. Lastly, a discussion of future directions is presented

Data Integration The Relational Logic Approach

CERN Document Server

Genesereth, Michael

2010-01-01

Data integration is a critical problem in our increasingly interconnected but inevitably heterogeneous world. There are numerous data sources available in organizational databases and on public information systems like the World Wide Web. Not surprisingly, the sources often use different vocabularies and different data structures, being created, as they are, by different people, at different times, for different purposes. The goal of data integration is to provide programmatic and human users with integrated access to multiple, heterogeneous data sources, giving each user the illusion of a sin

Source-rock maturation characteristics of symmetric and asymmetric grabens inferred from integrated analogue and numerical modeling: The southern Viking Graben (North Sea)

NARCIS (Netherlands)

Corver, M.P.; Doust, H.; van Wees, J.D.A.M.; Cloetingh, S.A.P.L.

2011-01-01

We present the results of an integrated analogue and numerical modeling study with a focus on structural, stratigraphic and thermal differences between symmetric and asymmetric grabens. These models enable fault interpretation and subsidence analyses in studies of active rifting and graben

Deterministic computation of functional integrals

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.

1995-09-01

A new method of numerical integration in functional spaces is described. This method is based on the rigorous definition of a functional integral in complete separable metric space and on the use of approximation formulas which we constructed for this kind of integral. The method is applicable to solution of some partial differential equations and to calculation of various characteristics in quantum physics. No preliminary discretization of space and time is required in this method, as well as no simplifying assumptions like semi-classical, mean field approximations, collective excitations, introduction of ''short-time'' propagators, etc are necessary in our approach. The constructed approximation formulas satisfy the condition of being exact on a given class of functionals, namely polynomial functionals of a given degree. The employment of these formulas replaces the evaluation of a functional integral by computation of the ''ordinary'' (Riemannian) integral of a low dimension, thus allowing to use the more preferable deterministic algorithms (normally - Gaussian quadratures) in computations rather than traditional stochastic (Monte Carlo) methods which are commonly used for solution of the problem under consideration. The results of application of the method to computation of the Green function of the Schroedinger equation in imaginary time as well as the study of some models of Euclidean quantum mechanics are presented. The comparison with results of other authors shows that our method gives significant (by an order of magnitude) economy of computer time and memory versus other known methods while providing the results with the same or better accuracy. The funcitonal measure of the Gaussian type is considered and some of its particular cases, namely conditional Wiener measure in quantum statistical mechanics and functional measure in a Schwartz distribution space in two-dimensional quantum field theory are studied in detail. Numerical examples demonstrating the

Direct Numerical Simulation of Turbulent Flow Over Complex Bathymetry

Science.gov (United States)

Yue, L.; Hsu, T. J.

2017-12-01

Direct numerical simulation (DNS) is regarded as a powerful tool in the investigation of turbulent flow featured with a wide range of time and spatial scales. With the application of coordinate transformation in a pseudo-spectral scheme, a parallelized numerical modeling system was created aiming at simulating flow over complex bathymetry with high numerical accuracy and efficiency. The transformed governing equations were integrated in time using a third-order low-storage Runge-Kutta method. For spatial discretization, the discrete Fourier expansion was adopted in the streamwise and spanwise direction, enforcing the periodic boundary condition in both directions. The Chebyshev expansion on Chebyshev-Gauss-Lobatto points was used in the wall-normal direction, assuming there is no-slip on top and bottom walls. The diffusion terms were discretized with a Crank-Nicolson scheme, while the advection terms dealiased with the 2/3 rule were discretized with an Adams-Bashforth scheme. In the prediction step, the velocity was calculated in physical domain by solving the resulting linear equation directly. However, the extra terms introduced by coordinate transformation impose a strict limitation to time step and an iteration method was applied to overcome this restriction in the correction step for pressure by solving the Helmholtz equation. The numerical solver is written in object-oriented C++ programing language utilizing Armadillo linear algebra library for matrix computation. Several benchmarking cases in laminar and turbulent flow were carried out to verify/validate the numerical model and very good agreements are achieved. Ongoing work focuses on implementing sediment transport capability for multiple sediment classes and parameterizations for flocculation processes.

On the relationship between supplier integration and time-to-market

NARCIS (Netherlands)

Perols, J.; Zimmermann, C.; Kortmann, S.

2013-01-01

Recent operations management and innovation management research emphasizes the importance of supplier integration. However, the empirical results as to the relationship between supplier integration and time-to-market are ambivalent. To understand this important relationship, we incorporate two major

Numerical Investigations of Post-Newtonian Hamiltonian Dynamics for Spinning Compact Binaries

Science.gov (United States)

Zhong, S. Y.

2012-03-01

Spinning compact binaries, consisting of neutron stars or black holes, not only have rich dynamic phenomena of resonance and chaos, but also are the most promising source for detecting gravitational waves. There should be a certain relation between the dynamics of the gravitational bodies and the gravitational waveforms. Based on the least-squares correction, several manifold correction schemes like the single-scaling method and the dual-scaling method are designed to suppress numerical errors from 6 integrals of motion in a conservative post-Newtonian (PN) Hamiltonian of spinning compact binaries. Taking a fifth order Runge-Kutta algorithm as a basic integrator, we wonder whether the PN contributions, the spin effects, and the classification of orbits exert some influences on these correction schemes and the Nacozy's approach. It is found that they are almost the same in correcting the integrals for the pure Kepler problem. Once the third-order PN contributions are added to the pure orbital part, there are explicit differences of correction effectiveness among these methods. As an interesting case, the efficiency of correction is better for chaotic eccentric orbits than for quasicircular regular ones. In all cases tested, the new momentum-position dual-scaling scheme does always have the optimal performance. It costs a little but not much expensive additional computational cost when the spin effects exist, and several time-saving techniques are used. The corrected numerical results are more accurate than the uncorrected ones, so that chaos from the numerical errors can be avoided. See Phys. Rev. D 81, 104037 (2010) for more details. Lubich et al. (Phys. Rev. D 81, 104025 (2010)) presented a noncanonically symplectic integrator for the PN Hamiltonian of a spinning compact binary. However, the Euler mixed integrator is problematic because of its bad numerical stability.We improved the work by constructing the second-order and the fourth-order fixed symplectic

Integrals of Motion for Discrete-Time Optimal Control Problems

OpenAIRE

Torres, Delfim F. M.

2003-01-01

We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations are obtained.

Simulating signatures of two-dimensional electronic spectra of the Fenna-Matthews-Olson complex: By using a numerical path integral

International Nuclear Information System (INIS)

Liang, Xian-Ting

2014-01-01

A framework for simulating electronic spectra from photon-echo experiments is constructed by using a numerical path integral technique. This method is non-Markovian and nonperturbative and, more importantly, is not limited by a fixed form of the spectral density functions of the environment. Next, a two-dimensional (2D) third-order electronic spectrum of a dimer system is simulated. The spectrum is in agreement with the experimental and theoretical results previously reported [for example, M. Khalil, N. Demirdöven, and A. Tokmakoff, Phys. Rev. Lett. 90, 047401 (2003)]. Finally, a 2D third-order electronic spectrum of the Fenna-Matthews-Olson (FMO) complex is simulated by using the Debye, Ohmic, and Adolphs and Renger spectral density functions. It is shown that this method can clearly produce the spectral signatures of the FMO complex by using only the Adolphs and Renger spectral density function. Plots of the evolution of the diagonal and cross-peaks show that they are oscillating with the population time

Class Generation for Numerical Wind Atlases

DEFF Research Database (Denmark)

Cutler, N.J.; Jørgensen, B.H.; Ersbøll, Bjarne Kjær

2006-01-01

A new optimised clustering method is presented for generating wind classes for mesoscale modelling to produce numerical wind atlases. It is compared with the existing method of dividing the data in 12 to 16 sectors, 3 to 7 wind-speed bins and dividing again according to the stability...... of the atmosphere. Wind atlases are typically produced using many years of on-site wind observations at many locations. Numerical wind atlases are the result of mesoscale model integrations based on synoptic scale wind climates and can be produced in a number of hours of computation. 40 years of twice daily NCEP...... adapting to the local topography. The purpose of forming classes is to minimise the computational time for the mesoscale model while still representing the synoptic climate features. Only tried briefly in the past, clustering has traits that can be used to improve the existing class generation method...

Numerical methods for the simulation of particle generated electromagnetic fields in acclerator physics

International Nuclear Information System (INIS)

Lau, T.

2006-01-01

In this work modifications of the classical Particle-In-Cell method for the solution of the Maxwell-Vlasov equations are investigated with respect to their application in particle accelerator physics. The aim of the work is to find modifications of the method which minimize and under certain conditions even eliminate the numerical dispersion effect along the beam axis in the numerical solution of Maxwell's equations. This is achieved by the development of dedicated time-integration methods for the Finite Integration Technique and two Finite Volume Methods. The methods are theoretically investigated regarding the conservation of a discrete energy and the existence of a discrete continuity equation. Finally, some of the methods are applied to the simulation of a high frequency rf-gun. (orig.)

A numerical study of two-phase Stokes flow in an axisymmetric flow-focusing device

DEFF Research Database (Denmark)

Jensen, Mads Jakob; Stone, H.A.; Bruus, Henrik

2006-01-01

We present a numerical investigation of the time-dependent dynamics of the creation of gas bubbles in an axisymmetric flow-focusing device. The liquid motion is treated as a Stokes flow, and using a generic framework we implement a second-order time-integration scheme and a free-surface model...... in MATLAB, which interfaces with the finite-element software FEMLAB. We derive scaling laws for the volume of a created bubble and for the gas flow rate, and confirm them numerically. Our results are consistent with existing experimental results by Garstecki et al. [Phys. Rev. Lett. 94, 164501 (2005...

A numerical study on the structural integrity of self-anchored cable-stayed suspension bridges

Directory of Open Access Journals (Sweden)

Paolo Lonetti

2016-10-01

Full Text Available A generalized numerical model for predicting the structural integrity of self-anchored cable-stayed suspension bridges considering both geometric and material nonlinearities is proposed. The bridge is modeled by means of a 3D finite element approach based on a refined displacement-type finite element approximation, in which geometrical nonlinearities are assumed in all components of the structure. Moreover, nonlinearities produced by inelastic material and second order effects in the displacements are considered for girder and pylon elements, which combine gradual yielding theory with CRC tangent modulus concept. In addition, for the elements of the suspension system, i.e. stays, hangers and main cable, a finite plasticity theory is adopted to fully evaluate both geometric and material nonlinearities. In this framework, the influence of geometric and material nonlinearities on the collapse bridge behavior is investigated, by means of a comparative study, which identifies the effects produced on the ultimate bridge behavior of several sources of bridge nonlinearities involved in the bridge components. Results are developed with the purpose to evaluate numerically the influence of the material and geometric characteristics of self-anchored cable-stayed suspension bridges with respect also to conventional bridge based on cablestayed or suspension schemes

Time integration in the code Zgoubi and external usage of PTC's structures

International Nuclear Information System (INIS)

Forest, Etienne; Meot, F.

2006-06-01

The purpose of this note is to describe Zgoubi's integrator and to describe some pitfalls for time based integration when used in accelerators. We show why the convergence rate of an integrator can be affected by an improper treatment at the boundary when time is used as the integration variable. We also point out how the code PTC can be used as a container by other tracking engine. This work is not completed as far as incorporation of Zgoubi is concerned. (authors)

Integrated Harvest and Distribution Scheduling with Time Windows of Perishable Agri-Products in One-Belt and One-Road Context

Directory of Open Access Journals (Sweden)

Yiping Jiang

2018-05-01

Full Text Available The unique characteristics of perishable agri-products are a short lifespan and rapid quality deterioration. This establishes the need to significantly reduce the time from harvest to distribution. These features require reducing the processing time from harvest to distribution to being as short as possible. In this study, we focus on an integrated perishable agri-products scheduling problem that combines harvest and distribution simultaneously, with the purpose of reducing processing time and quality decay. We propose this problem as a mixed integer nonlinear programming model (MINLP to optimize the harvest time and the vehicle routing to consumers, and this MINIP is formulated as a vehicle routing problem with time windows (VRPTW. We introduce a big M method to transform the nonlinear model into a linear model, then apply CPLEX to solve the transformed model. Numerical experiments and sensitive analysis are conducted to verify the efficiency of the proposed model and to provide managerial insights.

Non-integrability of time-dependent spherically symmetric Yang-Mills equations

Energy Technology Data Exchange (ETDEWEB)

Matinyan, S G; Prokhorenko, E B; Savvidy, G K

1988-03-07

The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. It is shown that the motion of this system is ergodic, while the system itself is non-integrable, i.e. manifests dynamical chaos.

A Novel Multiple-Time Scale Integrator for the Hybrid Monte Carlo Algorithm

International Nuclear Information System (INIS)

Kamleh, Waseem

2011-01-01

Hybrid Monte Carlo simulations that implement the fermion action using multiple terms are commonly used. By the nature of their formulation they involve multiple integration time scales in the evolution of the system through simulation time. These different scales are usually dealt with by the Sexton-Weingarten nested leapfrog integrator. In this scheme the choice of time scales is somewhat restricted as each time step must be an exact multiple of the next smallest scale in the sequence. A novel generalisation of the nested leapfrog integrator is introduced which allows for far greater flexibility in the choice of time scales, as each scale now must only be an exact multiple of the smallest step size.

Precise digital integration in wide time range: theory and realization

International Nuclear Information System (INIS)

Batrakov, A.M.; Pavlenko, A.V.

2017-01-01

The digital integration method based on using high-speed precision analog-to-digital converters (ADC) has become widely used over the recent years. The paper analyzes the limitations of this method that are caused by the signal properties, ADC sampling rate and noise spectral density of the ADC signal path. This analysis allowed creating digital integrators with accurate synchronization and achieving an integration error of less than 10 −5 in the time range from microseconds to tens of seconds. The structure of the integrator is described and its basic parameters are presented. The possibilities of different ADC chips in terms of their applicability to digital integrators are discussed. A comparison with other integrating devices is presented.

Numerov iteration method for second order integral-differential equation

International Nuclear Information System (INIS)

Zeng Fanan; Zhang Jiaju; Zhao Xuan

1987-01-01

In this paper, Numerov iterative method for second order integral-differential equation and system of equations are constructed. Numerical examples show that this method is better than direct method (Gauss elimination method) in CPU time and memoy requireing. Therefore, this method is an efficient method for solving integral-differential equation in nuclear physics

Modeling of Electromagnetic Fields in Parallel-Plane Structures: A Unified Contour-Integral Approach

Directory of Open Access Journals (Sweden)

M. Stumpf

2017-04-01

Full Text Available A unified reciprocity-based modeling approach for analyzing electromagnetic fields in dispersive parallel-plane structures of arbitrary shape is described. It is shown that the use of the reciprocity theorem of the time-convolution type leads to a global contour-integral interaction quantity from which novel both time- and frequency-domain numerical schemes can be arrived at. Applications of the numerical method concerning the time-domain radiated interference and susceptibility of parallel-plane structures are discussed and illustrated on numerical examples.

Using a {sigma}-coordinate numerical ocean model for simulating the circulation at Ormen Lange

Energy Technology Data Exchange (ETDEWEB)

Eliassen, Inge K.; Berntsen, Jarle

2000-01-01

This report describes a numerical model for the simulation of circulation at the Ormen Lange oil field. The model uses a topography following vertical coordinate and time split integration procedure. The model is implemented for a 28 km x 46 km area at Ormen Lange. The equations are given in detail and numerical experiments are discussed. The numerical studies investigate how the flow specified at open boundaries surrounding the Ormen Lange area may be interpolated into the interior domain taking into account the conservation laws that are believed to determine the flow and the local topography.

Numerical investigation on exterior conformal mappings with application to airfoils

International Nuclear Information System (INIS)

Mohamad Rashidi Md Razali; Hu Laey Nee

2000-01-01

A numerical method is described in computing a conformal map from an exterior region onto the exterior of the unit disk. The numerical method is based on a boundary integral equation which is similar to the Kerzman-Stein integral equation for interior mapping. Some examples show that numerical results of high accuracy can be obtained provided that the boundaries are smooth. This numerical method has been applied to the mapping airfoils. However, due to the fact that the parametric representation of an air foil is not known, a cubic spline interpolation method has been used. Some numerical examples with satisfying results have been obtained for the symmetrical and cambered airfoils. (Author)

Feasibility of real-time calculation of correlation integral derived statistics applied to EGG time series

NARCIS (Netherlands)

van den Broek, PLC; van Egmond, J; van Rijn, CM; Takens, F; Coenen, AML; Booij, LHDJ

2005-01-01

Background: This study assessed the feasibility of online calculation of the correlation integral (C(r)) aiming to apply C(r)derived statistics. For real-time application it is important to reduce calculation time. It is shown how our method works for EEG time series. Methods: To achieve online

Feasibility of real-time calculation of correlation integral derived statistics applied to EEG time series

NARCIS (Netherlands)

Broek, P.L.C. van den; Egmond, J. van; Rijn, C.M. van; Takens, F.; Coenen, A.M.L.; Booij, L.H.D.J.

2005-01-01

This study assessed the feasibility of online calculation of the correlation integral (C(r)) aiming to apply C(r)-derived statistics. For real-time application it is important to reduce calculation time. It is shown how our method works for EEG time series. Methods: To achieve online calculation of

Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule

Directory of Open Access Journals (Sweden)

P. Krysl

2004-01-01

Full Text Available We address the design of time integrators for mechanical systems that are explicit in the forcing evaluations. Our starting point is the midpoint rule, either in the classical form for the vector space setting, or in the Lie form for the rotation group. By introducing discrete, concentrated impulses we can approximate the forcing impressed upon the system over the time step, and thus arrive at first-order integrators. These can then be composed to yield a second order integrator with very desirable properties: symplecticity and momentum conservation.