Contamination in the Kepler field. Identification of 685 KOIs as false positives via ephemeris matching based ON Q1-Q12 data

Energy Technology Data Exchange (ETDEWEB)

Coughlin, Jeffrey L.; Thompson, Susan E.; Burke, Christopher J.; Caldwell, Douglas A.; Jenkins, Jon M.; Mullally, Fergal R.; Rowe, Jason F. [SETI Institute, 189 Bernardo Avenue, Mountain View, CA 94043 (United States); Bryson, Stephen T.; Haas, Michael R.; Howell, Steve B. [NASA Ames Research Center, M/S 244-30, Moffett Field, CA 94035 (United States); Christiansen, Jessie L. [NASA Exoplanet Science Institute, California Institute of Technology, Pasadena CA 91125 (United States); Kolodziejczak, Jeffery J., E-mail: jeffrey.l.coughlin@nasa.gov [NASA Marshall Space Flight Center, Huntsville, AL 35812 (United States)

2014-05-01

The Kepler mission has to date found almost 6000 planetary transit-like signals, utilizing three years of data for over 170,000 stars at extremely high photometric precision. Due to its design, contamination from eclipsing binaries, variable stars, and other transiting planets results in a significant number of these signals being false positives (FPs). This directly affects the determination of the occurrence rate of Earth-like planets in our Galaxy, as well as other planet population statistics. In order to detect as many of these FPs as possible, we perform ephemeris matching among all transiting planet, eclipsing binary, and variable star sources. We find that 685 Kepler Objects of Interest (KOIs)—12% of all those analyzed—are FPs as a result of contamination, due to 409 unique parent sources. Of these, 118 have not previously been identified by other methods. We estimate that ∼35% of KOIs are FPs due to contamination, when performing a first-order correction for observational bias. Comparing single-planet candidate KOIs to multi-planet candidate KOIs, we find an observed FP fraction due to contamination of 16% and 2.4% respectively, bolstering the existing evidence that multi-planet KOIs are significantly less likely to be FPs. We also analyze the parameter distributions of the ephemeris matches and derive a simple model for the most common type of contamination in the Kepler field. We find that the ephemeris matching technique is able to identify low signal-to-noise FPs that are difficult to identify with other vetting techniques. We expect FP KOIs to become more frequent when analyzing more quarters of Kepler data, and note that many of them will not be able to be identified based on Kepler data alone.

Comparison of pulsar positions from timing and very long baseline astrometry

Science.gov (United States)

Wang, J. B.; Coles, W. A.; Hobbs, G.; Shannon, R. M.; Manchester, R. N.; Kerr, M.; Yuan, J. P.; Wang, N.; Bailes, M.; Bhat, N. D. R.; Dai, S.; Dempsey, J.; Keith, M. J.; Lasky, P. D.; Levin, Y.; Osłowski, S.; Ravi, V.; Reardon, D. J.; Rosado, P. A.; Russell, C. J.; Spiewak, R.; van Straten, W.; Toomey, L.; Wen, L.; You, X.-P.; Zhu, X.-J.

2017-07-01

Pulsar positions can be measured with high precision using both pulsar timing methods and very long baseline interferometry (VLBI). Pulsar timing positions are referenced to a solar-system ephemeris, whereas VLBI positions are referenced to distant quasars. Here, we compare pulsar positions from published VLBI measurements with those obtained from pulsar timing data from the Nanshan and Parkes radio telescopes in order to relate the two reference frames. We find that the timing positions differ significantly from the VLBI positions (and also differ between different ephemerides). A statistically significant change in the obliquity of the ecliptic of 2.16 ± 0.33 mas is found for the JPL ephemeris DE405, but no significant rotation is found in subsequent JPL ephemerides. The accuracy with which we can relate the two frames is limited by the current uncertainties in the VLBI reference source positions and in matching the pulsars to their reference source. Not only do the timing positions depend on the ephemeris used in computing them, but also different segments of the timing data lead to varying position estimates. These variations are mostly common to all ephemerides, but slight changes are seen at the 10 μas level between ephemerides.

Numerical studies of time-independent and time-dependent scattering by several elliptical cylinders

Science.gov (United States)

Nigsch, Martin

2007-07-01

A numerical solution to the problem of time-dependent scattering by an array of elliptical cylinders with parallel axes is presented. The solution is an exact one, based on the separation-of-variables technique in the elliptical coordinate system, the addition theorem for Mathieu functions, and numerical integration. Time-independent solutions are described by a system of linear equations of infinite order which are truncated for numerical computations. Time-dependent solutions are obtained by numerical integration involving a large number of these solutions. First results of a software package generating these solutions are presented: wave propagation around three impenetrable elliptical scatterers. As far as we know, this method described has never been used for time-dependent multiple scattering.

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

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

High-Cadence Transit Timing Variation Monitoring of Extrasolar Planets

Directory of Open Access Journals (Sweden)

Naef D.

2011-02-01

Full Text Available We report ground-based high-cadence transit timing observations of the extrasolar planet WASP-2b. We achieve a typical timing error of 15-30 sec. The data show no significant deviations from the predicted ephemeris.

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

A high-fidelity N-body ephemeris generator for satellites in Earth orbit

Science.gov (United States)

Simmons, David R.

1991-10-01

A program is currently used for mission planning called the Analytic Satellite Ephemeris Program (ASEP), which produces projected data for orbits that remain fairly close to Earth. Lunar and solar perturbations are taken into account in another program called GRAVE. This project is a revision of GRAVE which incorporates more flexible means of input for initial data, provides additional kinds of output information, and makes use of structured programming techniques to make the program more understandable and reliable. The computer program ORBIT was tested against tracking data for the first 313 days of operation of the CRRES satellite. A sample graph is given comparing the semi-major axis calculated by the program with the values supplied by NORAD. When calculated for points at which CRRES passes through the ascending node, the argument of perigee, the right ascension of the ascending node, and the mean anomaly all stay within about a degree of the corresponding values from NORAD; the inclination of the orbital plane is much closer. The program value of the eccentricity is in error by no more than 0.0002.

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.

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.

Continuing Improvement in the Planetary Ephemeris with VLBA Observations of Cassini

Science.gov (United States)

Jones, Dayton L.; Folkner, William M.; Jacobson, Robert A.; Jacobs, Christopher S.; Romney, Jonathan D.; Dhawan, Vivek; Fomalont, Edward B.

2016-06-01

During the past decade a continuing series of measurements of the barycentric position of the Saturn system in the inertial International Celestial Reference Frame (ICRF) has led to a significant improvement in our knowledge of Saturn's orbit. This in turn has improved the current accuracy and time range of the solar system ephemeris produced and maintained by the Jet Propulsion Laboratory. Our observing technique involves high-precision astrometry of the radio signal from Cassini with the NRAO Very Long Baseline Array, combined with solutions for the orbital motion of Cassini about the Saturn barycenter from Doppler tracking by the Deep Space Network. Our VLBA astrometry is done in a phase-referencing mode, providing nrad-level relative positions between Cassini and angularly nearby extragalactic radio sources. The positions of those reference radio sources are tied to the ICRF through dedicated VLBI observations by several groups around the world. We will present recent results from our astrometric observations of Cassini through early 2016. This program will continue until the end of the Cassini mission in 2017, although future improvement in Saturn's orbit will be more incremental because we have already covered more that a quarter of Saturn's orbital period. The Juno mission to Jupiter, which will orbit Jupiter for about 1.5 years starting in July 2016, will provide an excellent opportunity for us to apply the same VLBA astrometry technique to improve the orbit of Jupiter by a factor of several. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work made use of the Swinburne University of Technology software correlator, developed as part of the Australian Major National Research Facilities Program and operated under license. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract

The connection between landscapes and the solar ephemeris in honeybees.

Science.gov (United States)

Towne, William F; Moscrip, Heather

2008-12-01

Honeybees connect the sun's daily pattern of azimuthal movement to some aspect of the landscape around their nests. In the present study, we ask what aspect of the landscape is used in this context--the entire landscape panorama or only sectors seen along familiar flight routes. Previous studies of the solar ephemeris memory in bees have generally used bees that had experience flying a specific route, usually along a treeline, to a feeder. When such bees were moved to a differently oriented treeline on overcast days, the bees oriented their communicative dances as if they were still at the first treeline, based on a memory of the sun's course in relation to some aspect of the site, possibly the familiar route along the treeline or possibly the entire landscape or skyline panorama. Our results show that bees lacking specific flight-route training can nonetheless recall the sun's compass bearing relative to novel flight routes in their natal landscape. Specifically, we moved a hive from one landscape to a differently oriented twin landscape, and only after transplantation under overcast skies did we move a feeder away from the hive. These bees nonetheless danced accurately by memory of the sun's course in relation to their natal landscape. The bees' knowledge of the relationship between the sun and landscape, therefore, is not limited to familiar flight routes and so may encompass, at least functionally, the entire panorama. Further evidence suggests that the skyline in particular may be the bees' preferred reference in this context.

Numerical instability of time-discretized one-point kinetic equations

International Nuclear Information System (INIS)

Hashimoto, Kengo; Ikeda, Hideaki; Takeda, Toshikazu

2000-01-01

The one-point kinetic equations with numerical errors induced by the explicit, implicit and Crank-Nicolson integration methods are derived. The zero-power transfer functions based on the present equations are demonstrated to investigate the numerical stability of the discretized systems. These demonstrations indicate unconditional stability for the implicit and Crank-Nicolson methods but present the possibility of numerical instability for the explicit method. An upper limit of time mesh spacing for the stability is formulated and several numerical calculations are made to confirm the validity of this formula

Numerical time integration for air pollution models

NARCIS (Netherlands)

J.G. Verwer (Jan); W. Hundsdorfer (Willem); J.G. Blom (Joke)

1998-01-01

textabstractDue to the large number of chemical species and the three space dimensions, off-the-shelf stiff ODE integrators are not feasible for the numerical time integration of stiff systems of advection-diffusion-reaction equations [ fracpar{c{t + nabla cdot left( vu{u c right) = nabla cdot left(

Improved timing of the millisecond pulsar PSR 1937+21 using real-time coherent dedispersion

International Nuclear Information System (INIS)

Hankins, T.H.; Stinebring, D.R.; Rawley, L.A.; Princeton Univ., NJ)

1987-01-01

Profiles of the millisecond pulsar PSR 1937+21 have been obtained with 6-micron resolution using a real-time hardware dispersion removal device. This dedisperser has a potential resolution of better than 0.5 microsec and is immune to time-of-arrival jitter caused by scintillation-induced spectral gradients across the receiver passband. It significantly reduces the time-of-arrival residuals when compared with the timing technique currently in use. This increased timing accuracy, when utilized in a long-term timing program of millisec pulsars, will improve the solar system ephemeris and will substantially improve the detection limit of a gravitational wave background. 27 references

Supplement to: Astronomical ephemerides, navigation and war. The astonishing cooperation of the ephemeris institutes of Germany, England, France and the USA during the Second World War based on documents in the archives of the Astronomisches Rechen-Institut. Scans of the documents. (German Title: Supplement zu: Astronomische Ephemeriden, Navigation und Krieg. Die erstaunliche Zusammenarbeit der Ephemeriden-Institute von Deutschland, England, Frankreich und den USA im Zweiten Weltkrieg nach Dokumenten im Archiv des Astronomischen Rechen-Instituts. Scans der Dokumente.)

Science.gov (United States)

Wielen, Roland; Wielen, Ute

In a previous paper (Wielen R. und Wielen U. 2016a: Astronomical Ephemerides, Navigation and War), we have presented the astonishing cooperation of the ephemeris institutes of Germany, England, France and the USA during the Second World War. We were able to use numerous archivalia which we also describe and comment in that paper. In the present paper, we publish colour scans of these archivalia. All the documents shown here are held in the archives of the Astronomisches Rechen-Institut in Heidelberg.

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...

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 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.

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

Space Gravity Spectroscopy - determination of the Earth’s gravitational field by means of Newton interpolated LEO ephemeris Case studies on dynamic (CHAMP Rapid Science Orbit and kinematic orbits

Directory of Open Access Journals (Sweden)

T. Reubelt

2003-01-01

Full Text Available An algorithm for the (kinematic orbit analysis of a Low Earth Orbiting (LEO GPS tracked satellite to determine the spherical harmonic coefficients of the terrestrial gravitational field is presented. A contribution to existing long wavelength gravity field models is expected since the kinematic orbit of a LEO satellite can nowadays be determined with very high accuracy in the range of a few centimeters. To demonstrate the applicability of the proposed method, first results from the analysis of real CHAMP Rapid Science (dynamic Orbits (RSO and kinematic orbits are illustrated. In particular, we take advantage of Newton’s Law of Motion which balances the acceleration vector and the gradient of the gravitational potential with respect to an Inertial Frame of Reference (IRF. The satellite’s acceleration vector is determined by means of the second order functional of Newton’s Interpolation Formula from relative satellite ephemeris (baselines with respect to the IRF. Therefore the satellite ephemeris, which are normally given in a Body fixed Frame of Reference (BRF have to be transformed into the IRF. Subsequently the Newton interpolated accelerations have to be reduced for disturbing gravitational and non-gravitational accelerations in order to obtain the accelerations caused by the Earth’s gravitational field. For a first insight in real data processing these reductions have been neglected. The gradient of the gravitational potential, conventionally expressed in vector-valued spherical harmonics and given in a Body Fixed Frame of Reference, must be transformed from BRF to IRF by means of the polar motion matrix, the precession-nutation matrices and the Greenwich Siderial Time Angle (GAST. The resulting linear system of equations is solved by means of a least squares adjustment in terms of a Gauss-Markov model in order to estimate the spherical harmonics coefficients of the Earth’s gravitational field.Key words. space gravity spectroscopy

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)

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.

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...

NO TIMING VARIATIONS OBSERVED IN THIRD TRANSIT OF SNOW-LINE EXOPLANET KEPLER-421b

International Nuclear Information System (INIS)

Dalba, Paul A.; Muirhead, Philip S.

2016-01-01

We observed Kepler-421 during the anticipated third transit of the snow-line exoplanet Kepler-421b in order to constrain the existence and extent of transit timing variations (TTVs). Previously, the Kepler spacecraft only observed two transits of Kepler-421b, leaving the planet’s transit ephemeris unconstrained. Our visible light, time-series observations from the 4.3 m Discovery Channel Telescope were designed to capture pre-transit baseline and the partial transit of Kepler-421b, barring significant TTVs. We use the light curves to assess the probabilities of various transit models using both the posterior odds ratio and the Bayesian Information Criterion, and find that a transit model with no TTVs is favored to 3.6 σ confidence. These observations suggest that Kepler-421b is either alone in its system or is only experiencing minor dynamic interactions with an unseen companion. With the Kepler-421b ephemeris constrained, we calculate future transit times and discuss the opportunity to characterize the atmosphere of this cold, long-period exoplanet via transmission spectroscopy. Our investigation emphasizes the difficulties associated with observing long-period exoplanet transits and the consequences that arise from failing to refine transit ephemerides.

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.

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 integration of the Teukolsky equation in the time domain

International Nuclear Information System (INIS)

Pazos-Avalos, Enrique; Lousto, Carlos O.

2005-01-01

We present a fourth-order convergent (2+1)-dimensional, numerical formalism to solve the Teukolsky equation in the time domain. Our approach is first to rewrite the Teukolsky equation as a system of first-order differential equations. In this way we get a system that has the form of an advection equation. This is then used in combination with a series expansion of the solution in powers of time. To obtain a fourth-order scheme we kept terms up to fourth derivative in time and use the advectionlike system of differential equations to substitute the temporal derivatives by spatial derivatives. This scheme is applied to evolve gravitational perturbations in the Schwarzschild and Kerr backgrounds. Our numerical method proved to be stable and fourth-order convergent in r* and θ directions. The correct power-law tail, ∼1/t 2l+3 , for general initial data, and ∼1/t 2l+4 , for time-symmetric data, was found in our runs. We noted that it is crucial to resolve accurately the angular dependence of the mode at late times in order to obtain these values of the exponents in the power-law decay. In other cases, when the decay was too fast and round-off error was reached before a tail was developed, then the quasinormal modes frequencies provided a test to determine the validity of our code

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.

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.

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...

Numerical counting ratemeter with variable time constant and integrated circuits

International Nuclear Information System (INIS)

Kaiser, J.; Fuan, J.

1967-01-01

We present here the prototype of a numerical counting ratemeter which is a special version of variable time-constant frequency meter (1). The originality of this work lies in the fact that the change in the time constant is carried out automatically. Since the criterion for this change is the accuracy in the annunciated result, the integration time is varied as a function of the frequency. For the prototype described in this report, the time constant varies from 1 sec to 1 millisec. for frequencies in the range 10 Hz to 10 MHz. This prototype is built entirely of MECL-type integrated circuits from Motorola and is thus contained in two relatively small boxes. (authors) [fr

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.

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 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 Time Integration Methods for a Point Absorber Wave Energy Converter

DEFF Research Database (Denmark)

Zurkinden, Andrew Stephen; Kramer, Morten

2012-01-01

on a discretization of the convolution integral. The calculation of the convolution integral is performed at each time step regardless of the chosen numerical scheme. In the second model the convolution integral is replaced by a system of linear ordinary differential equations. The formulation of the state...

Real Time Precise Point Positioning: Preliminary Results for the Brazilian Region

Science.gov (United States)

Marques, Haroldo; Monico, João.; Hirokazu Shimabukuro, Milton; Aquino, Marcio

2010-05-01

GNSS positioning can be carried out in relative or absolute approach. In the last years, more attention has been driven to the real time precise point positioning (PPP). To achieve centimeter accuracy with this method in real time it is necessary to have available the satellites precise coordinates as well as satellites clocks corrections. The coordinates can be used from the predicted IGU ephemeris, but the satellites clocks must be estimated in a real time. It can be made from a GNSS network as can be seen from EUREF Permanent Network. The infra-structure to realize the PPP in real time is being available in Brazil through the Brazilian Continuous Monitoring Network (RBMC) together with the Sao Paulo State GNSS network which are transmitting GNSS data using NTRIP (Networked Transport of RTCM via Internet Protocol) caster. Based on this information it was proposed a PhD thesis in the Univ. Estadual Paulista (UNESP) aiming to investigate and develop the methodology to estimate the satellites clocks and realize PPP in real time. Then, software is being developed to process GNSS data in the real time PPP mode. A preliminary version of the software was called PPP_RT and is able to process GNSS code and phase data using precise ephemeris and satellites clocks. The PPP processing can be accomplished considering the absolute satellite antenna Phase Center Variation (PCV), Ocean Tide Loading (OTL), Earth Body Tide, among others. The first order ionospheric effects can be eliminated or minimized by ion-free combination or parameterized in the receiver-satellite direction using a stochastic process, e.g. random walk or white noise. In the case of ionosphere estimation, a pseudo-observable is introduced in the mathematical model for each satellite and the initial value can be computed from Klobuchar model or from Global Ionospheric Map (GIM). The adjustment is realized in the recursive mode and the DIA (Detection Identification and Adaptation) is used for quality control. In

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.

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)

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

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.

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.)

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.

Unification of binary star ephemeris solutions

International Nuclear Information System (INIS)

Wilson, R. E.; Van Hamme, W.

2014-01-01

Time-related binary system characteristics such as orbital period, its rate of change, apsidal motion, and variable light-time delay due to a third body, are measured in two ways that can be mutually complementary. The older way is via eclipse timings, while ephemerides by simultaneous whole light and velocity curve analysis have appeared recently. Each has its advantages, for example, eclipse timings typically cover relatively long time spans while whole curves often have densely packed data within specific intervals and allow access to systemic properties that carry additional timing information. Synthesis of the two information sources can be realized in a one step process that combines several data types, with automated weighting based on their standard deviations. Simultaneous light-velocity-timing solutions treat parameters of apsidal motion and the light-time effect coherently with those of period and period change, allow the phenomena to interact iteratively, and produce parameter standard errors based on the quantity and precision of the curves and timings. The logic and mathematics of the unification algorithm are given, including computation of theoretical conjunction times as needed for generation of eclipse timing residuals. Automated determination of eclipse type, recovery from inaccurate starting ephemerides, and automated data weighting are also covered. Computational examples are given for three timing-related cases—steady period change (XY Bootis), apsidal motion (V526 Sagittarii), and the light-time effect due to a binary's reflex motion in a triple system (AR Aurigae). Solutions for all combinations of radial velocity, light curve, and eclipse timing input show consistent results, with a few minor exceptions.

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

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

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.

TRANSIT TIMING OBSERVATIONS FROM KEPLER. VI. POTENTIALLY INTERESTING CANDIDATE SYSTEMS FROM FOURIER-BASED STATISTICAL TESTS

International Nuclear Information System (INIS)

Steffen, Jason H.; Ford, Eric B.; Rowe, Jason F.; Borucki, William J.; Bryson, Steve; Caldwell, Douglas A.; Jenkins, Jon M.; Koch, David G.; Sanderfer, Dwight T.; Seader, Shawn; Twicken, Joseph D.; Fabrycky, Daniel C.; Holman, Matthew J.; Welsh, William F.; Batalha, Natalie M.; Ciardi, David R.; Kjeldsen, Hans; Prša, Andrej

2012-01-01

We analyze the deviations of transit times from a linear ephemeris for the Kepler Objects of Interest (KOI) through quarter six of science data. We conduct two statistical tests for all KOIs and a related statistical test for all pairs of KOIs in multi-transiting systems. These tests identify several systems which show potentially interesting transit timing variations (TTVs). Strong TTV systems have been valuable for the confirmation of planets and their mass measurements. Many of the systems identified in this study should prove fruitful for detailed TTV studies.

Transit timing observations from Kepler. VI. Potentially interesting candidate systems from fourier-based statistical tests

DEFF Research Database (Denmark)

Steffen, J.H.; Ford, E.B.; Rowe, J.F.

2012-01-01

We analyze the deviations of transit times from a linear ephemeris for the Kepler Objects of Interest (KOI) through quarter six of science data. We conduct two statistical tests for all KOIs and a related statistical test for all pairs of KOIs in multi-transiting systems. These tests identify...... several systems which show potentially interesting transit timing variations (TTVs). Strong TTV systems have been valuable for the confirmation of planets and their mass measurements. Many of the systems identified in this study should prove fruitful for detailed TTV studies....

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.

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.

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.

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.

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...

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

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

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

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

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)

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

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)

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

Astronomical ephemerides, navigation and war. The astonishing cooperation of the ephemeris institutes of Germany, England, France and the USA during the Second World War based on documents in the archives of the Astronomisches Rechen-Institut. Edition of the documents. (German Title: Astronomische Ephemeriden, Navigation und Krieg. Die erstaunliche Zusammenarbeit der Ephemeriden-Institute von Deutschland, England, Frankreich und den USA im Zweiten Weltkrieg nach Dokumenten im Archiv des Astronomischen Rechen-Instituts. Edition der Dokumente.)

Science.gov (United States)

Wielen, Roland; Wielen, Ute

During the whole period of the Second World War, England and the USA have exchanged astronomical ephemerides with Germany, even though these data were used for the navigation of warships and aircraft and were therefore of war importance. This astonishing fact is attested by numerous documents which survived in the archives of the Astronomisches Rechen-Institut (ARI). In Germany, the exchange was even explicitly authorized by the ministry which supervised the ARI (i.e. the Reichserziehungsminister). We present here examples of ephemerides for the Sun, the Moon, planets and stars, and explain the position determination by means of astronomical data. Ephemerides were published in almanacs which were computed and issued by special ephemeris institutes. We describe the agreements on the international exchange of ephemerides which were reached in peace times, and the continuation of this exchange during the war using intermediaries in neutral countries, first in the USA (U.S. Naval Observatory, USNO), and, from 1942 onwards, in Sweden (Stockholm Observatory). Involved persons were especially H. Spencer Jones (Astronomer Royal, Greenwich), J. F. Hellweg und W. J. Eckert (USNO), B. Lindblad (Sweden), and A. Kopff (ARI). All those relevant documents which are hold in the archives of the ARI, are described and annotated in detail. Scans of these documents are presented in a separate supplement.

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.

Models and numerical methods for time- and energy-dependent particle transport

Energy Technology Data Exchange (ETDEWEB)

Olbrant, Edgar

2012-04-13

Particles passing through a medium can be described by the Boltzmann transport equation. Therein, all physical interactions of particles with matter are given by cross sections. We compare different analytical models of cross sections for photons, electrons and protons to state-of-the-art databases. The large dimensionality of the transport equation and its integro-differential form make it analytically difficult and computationally costly to solve. In this work, we focus on the following approximative models to the linear Boltzmann equation: (i) the time-dependent simplified P{sub N} (SP{sub N}) equations, (ii) the M{sub 1} model derived from entropy-based closures and (iii) a new perturbed M{sub 1} model derived from a perturbative entropy closure. In particular, an asymptotic analysis for SP{sub N} equations is presented and confirmed by numerical computations in 2D. Moreover, we design an explicit Runge-Kutta discontinuous Galerkin (RKDG) method to the M{sub 1} model of radiative transfer in slab geometry and construct a scheme ensuring the realizability of the moment variables. Among other things, M{sub 1} numerical results are compared with an analytical solution in a Riemann problem and the Marshak wave problem is considered. Additionally, we rigorously derive a new hierarchy of kinetic moment models in the context of grey photon transport in one spatial dimension. For the perturbed M{sub 1} model, we present numerical results known as the two beam instability or the analytical benchmark due to Su and Olson and compare them to the standard M{sub 1} as well as transport solutions.

Combining numerical simulations with time-domain random walk for pathogen risk assessment in groundwater

Science.gov (United States)

Cvetkovic, V.; Molin, S.

2012-02-01

We present a methodology that combines numerical simulations of groundwater flow and advective transport in heterogeneous porous media with analytical retention models for computing the infection risk probability from pathogens in aquifers. The methodology is based on the analytical results presented in [1,2] for utilising the colloid filtration theory in a time-domain random walk framework. It is shown that in uniform flow, the results from the numerical simulations of advection yield comparable results as the analytical TDRW model for generating advection segments. It is shown that spatial variability of the attachment rate may be significant, however, it appears to affect risk in a different manner depending on if the flow is uniform or radially converging. In spite of the fact that numerous issues remain open regarding pathogen transport in aquifers on the field scale, the methodology presented here may be useful for screening purposes, and may also serve as a basis for future studies that would include greater complexity.

Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set

Science.gov (United States)

Pemmaraju, C. D.; Vila, F. D.; Kas, J. J.; Sato, S. A.; Rehr, J. J.; Yabana, K.; Prendergast, David

2018-05-01

The interaction of laser fields with solid-state systems can be modeled efficiently within the velocity-gauge formalism of real-time time dependent density functional theory (RT-TDDFT). In this article, we discuss the implementation of the velocity-gauge RT-TDDFT equations for electron dynamics within a linear combination of atomic orbitals (LCAO) basis set framework. Numerical results obtained from our LCAO implementation, for the electronic response of periodic systems to both weak and intense laser fields, are compared to those obtained from established real-space grid and Full-Potential Linearized Augmented Planewave approaches. Potential applications of the LCAO based scheme in the context of extreme ultra-violet and soft X-ray spectroscopies involving core-electronic excitations are discussed.

Investigation on Reference Frames and Time Systems in Multi-GNSS

Directory of Open Access Journals (Sweden)

Luca Nicolini

2018-01-01

Full Text Available Receivers able to track satellites belonging to different GNSSs (Global Navigation Satellite Systems are available on the market. To compute coordinates and velocities it is necessary to identify all the elements that contribute to interoperability of the different GNSSs. For example the timescales kept by different GNSSs have to be aligned. Receiver-specific biases, or firmware-dependent biases, need to be calibrated. The reference frame used in the representation of the orbits must be unique. In this paper we address the interoperability issues from the standpoint of a Single Point Positioning (SPP user, i.e., using pseudoranges and broadcast ephemeris. The biases between GNSSs timescales and receiver-dependent biases are analyzed for a set of 31 MGEX (Multi-GNSS Experiment stations over a time span of more than three years. Time series of biases between timescales of GPS (Global Positioning System, GLONASS (Global Navigation Satellite System, Galileo, BeiDou, QZSS (Quasi-Zenith Satellite System, SBAS (Satellite Based Augmentation System and NAVIC (Navigation with Indian Constellation are investigated, in addition to the identification of events like discontinuity of receiver-dependent biases due to firmware updating. The GPS broadcast reference frame is shown to be aligned to the one (IGS14 realized by the precise ephemeris of CODE (Center for Orbit Determination in Europe to within 0.1 m and 2 milliarcsec, with values dependent on whether IIR-A, IIR-B/M or IIF satellite blocks are considered. Larger offsets are observed for GLONASS, up to 1 m for GLONASS K satellites. For Galileo the alignment of the broadcast orbit to IGS14/CODE is again at the 0.1 m and several milliarcsec level, with the FOC (Full Operational Capability satellites slightly better than IOV (In Orbit Validation. For BeiDou an alignment of the broadcast frame to IGS14/CODE comparable to GLONASS is observed, regardless of whether IGSO (Inclined Geosynchronous Orbit or MEO

Numerical relativity for D dimensional space-times: Head-on collisions of black holes and gravitational wave extraction

International Nuclear Information System (INIS)

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

2010-01-01

Higher dimensional black holes play an exciting role in fundamental physics, such as high energy physics. In this paper, we use the formalism and numerical code reported in [1] to study the head-on collision of two black holes. For this purpose we provide a detailed treatment of gravitational wave extraction in generic D dimensional space-times, which uses the Kodama-Ishibashi formalism. For the first time, we present the results of numerical simulations of the head-on collision in five space-time dimensions, together with the relevant physical quantities. We show that the total radiated energy, when two black holes collide from rest at infinity, is approximately (0.089±0.006)% of the center of mass energy, slightly larger than the 0.055% obtained in the four-dimensional case, and that the ringdown signal at late time is in very good agreement with perturbative calculations.

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.

TRANSIT TIMING OBSERVATIONS FROM KEPLER. V. TRANSIT TIMING VARIATION CANDIDATES IN THE FIRST SIXTEEN MONTHS FROM POLYNOMIAL MODELS

Energy Technology Data Exchange (ETDEWEB)

Ford, Eric B. [Astronomy Department, University of Florida, 211 Bryant Space Sciences Center, Gainesville, FL 32111 (United States); Ragozzine, Darin; Holman, Matthew J. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Rowe, Jason F.; Barclay, Thomas; Borucki, William J.; Bryson, Stephen T.; Caldwell, Douglas A.; Kinemuchi, Karen; Koch, David G.; Lissauer, Jack J.; Still, Martin; Tenenbaum, Peter [NASA Ames Research Center, Moffett Field, CA 94035 (United States); Steffen, Jason H. [Fermilab Center for Particle Astrophysics, P.O. Box 500, MS 127, Batavia, IL 60510 (United States); Batalha, Natalie M. [Department of Physics and Astronomy, San Jose State University, San Jose, CA 95192 (United States); Fabrycky, Daniel C. [UCO/Lick Observatory, University of California, Santa Cruz, CA 95064 (United States); Gautier, Thomas N. [Jet Propulsion Laboratory/California Institute of Technology, Pasadena, CA 91109 (United States); Ibrahim, Khadeejah A.; Uddin, Kamal [Orbital Sciences Corporation/NASA Ames Research Center, Moffett Field, CA 94035 (United States); Kjeldsen, Hans, E-mail: eford@astro.ufl.edu [Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C (Denmark); and others

2012-09-10

Transit timing variations provide a powerful tool for confirming and characterizing transiting planets, as well as detecting non-transiting planets. We report the results of an updated transit timing variation (TTV) analysis for 1481 planet candidates based on transit times measured during the first sixteen months of Kepler observations. We present 39 strong TTV candidates based on long-term trends (2.8% of suitable data sets). We present another 136 weaker TTV candidates (9.8% of suitable data sets) based on the excess scatter of TTV measurements about a linear ephemeris. We anticipate that several of these planet candidates could be confirmed and perhaps characterized with more detailed TTV analyses using publicly available Kepler observations. For many others, Kepler has observed a long-term TTV trend, but an extended Kepler mission will be required to characterize the system via TTVs. We find that the occurrence rate of planet candidates that show TTVs is significantly increased ({approx}68%) for planet candidates transiting stars with multiple transiting planet candidates when compared to planet candidates transiting stars with a single transiting planet candidate.

Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

A variable timestep generalized Runge-Kutta method for the numerical integration of the space-time diffusion equations

International Nuclear Information System (INIS)

Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.

1991-09-01

A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs

The Transiting System GJ1214: High-Precision Defocused Transit Observations and a Search for Evidence of Transit Timing Variation

DEFF Research Database (Denmark)

Harpsøe, Kennet Bomann West; Hardis, S.; Hinse, T. C.

2012-01-01

Aims: We present 11 high-precision photometric transit observations of the transiting super-Earth planet GJ1214b. Combining these data with observations from other authors, we investigate the ephemeris for possible signs of transit timing variations (TTVs) using a Bayesian approach. Methods......: The observations were obtained using telescope-defocusing techniques, and achieve a high precision with random errors in the photometry as low as 1mmag per point. To investigate the possibility of TTVs in the light curve, we calculate the overall probability of a TTV signal using Bayesian methods. Results...

Numerical Analysis of an H1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

Directory of Open Access Journals (Sweden)

Jinfeng Wang

2014-01-01

Full Text Available We discuss and analyze an H1-Galerkin mixed finite element (H1-GMFE method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H1-GMFE method. Based on the discussion on the theoretical error analysis in L2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H1-norm. Moreover, we derive and analyze the stability of H1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure.

The time-dependent simplified P2 equations: Asymptotic analyses and numerical experiments

International Nuclear Information System (INIS)

Shin, U.; Miller, W.F. Jr.

1998-01-01

Using an asymptotic expansion, the authors found that the modified time-dependent simplified P 2 (SP 2 ) equations are robust, high-order, asymptotic approximations to the time-dependent transport equation in a physical regime in which the conventional time-dependent diffusion equation is the leading-order approximation. Using diffusion limit analysis, they also asymptotically compared three competitive time-dependent equations (the telegrapher's equation, the time-dependent SP 2 equations, and the time-dependent simplified even-parity equation). As a result, they found that the time-dependent SP 2 equations contain higher-order asymptotic approximations to the time-dependent transport equation than the other competitive equations. The numerical results confirm that, in the vast majority of cases, the time-dependent SP 2 solutions are significantly more accurate than the time-dependent diffusion and the telegrapher's solutions. They have also shown that the time-dependent SP 2 equations have excellent characteristics such as rotational invariance (which means no ray effect), good diffusion limit behavior, guaranteed positivity in diffusive regimes, and significant accuracy, even in deep-penetration problems. Through computer-running-time tests, they have shown that the time-dependent SP 2 equations can be solved with significantly less computational effort than the conventionally used, time-dependent S N equations (for N > 2) and almost as fast as the time-dependent diffusion equation. From all these results, they conclude that the time-dependent SP 2 equations should be considered as an important competitor for an improved approximately transport equations solver. Such computationally efficient time-dependent transport models are important for problems requiring enhanced computational efficiency, such as neutronics/fluid-dynamics coupled problems that arise in the analyses of hypothetical nuclear reactor accidents

Tracking target objects orbiting earth using satellite-based telescopes

Science.gov (United States)

De Vries, Willem H; Olivier, Scot S; Pertica, Alexander J

2014-10-14

A system for tracking objects that are in earth orbit via a constellation or network of satellites having imaging devices is provided. An object tracking system includes a ground controller and, for each satellite in the constellation, an onboard controller. The ground controller receives ephemeris information for a target object and directs that ephemeris information be transmitted to the satellites. Each onboard controller receives ephemeris information for a target object, collects images of the target object based on the expected location of the target object at an expected time, identifies actual locations of the target object from the collected images, and identifies a next expected location at a next expected time based on the identified actual locations of the target object. The onboard controller processes the collected image to identify the actual location of the target object and transmits the actual location information to the ground controller.

Theoretical and Numerical Properties of a Gyrokinetic Plasma: Issues Related to Transport Time Scale Simulation

International Nuclear Information System (INIS)

Lee, W.W.

2003-01-01

Particle simulation has played an important role for the recent investigations on turbulence in magnetically confined plasmas. In this paper, theoretical and numerical properties of a gyrokinetic plasma as well as its relationship with magnetohydrodynamics (MHD) are discussed with the ultimate aim of simulating microturbulence in transport time scale using massively parallel computers

Time-dependent magnetization of a type-II superconductor numerically calculated by using the flux-creep equation

International Nuclear Information System (INIS)

Lee, J. H.; Park, I. S.; Ahmad, D.; Kim, D.; Kim, Y. C.; Ko, R. K.; Jeong, D. Y.

2012-01-01

The macroscopic magnetic behaviors of a type-II superconductor, such as the field- or the temperature-dependent magnetization, have been described by using critical state models. However, because the models are time-independent, the magnetic relaxation in a type-II superconductor cannot be described by them, and the time dependence of the magnetization can affect the field or the temperature-dependent magnetization curve described by the models. In order to avoid the time independence of critical state models, we try the numerical calculation used by Qin et al., who mainly calculated the temperature dependence of the ac susceptibility χ(T). Their calculation showed that the frequency-dependent χ(T) could be obtained by using the flux-creep equation. We calculated the field-dependent magnetization and magnetic relaxation by using a numerical method. The calculated field-dependent magnetization M(H) curves shows the shapes of a typical type-II superconductor. The calculated magnetic relaxation do not show a logarithmic decay of the magnetization, but the addition of a surface barrier to the relaxation calculation caused a clear logarithmic decay of the magnetization, producing a crossover at a mid-time. This means that the logarithmic magnetic relaxation is caused by not only flux creep but also a combination of flux creep and a surface barrier.

The influence of time units on the flexibility of the spatial numerical association of response codes effect.

Science.gov (United States)

Zhao, Tingting; He, Xianyou; Zhao, Xueru; Huang, Jianrui; Zhang, Wei; Wu, Shuang; Chen, Qi

2018-05-01

The Spatial Numerical/Temporal Association of Response Codes (SNARC/STEARC) effects are considered evidence of the association between number or time and space, respectively. As the SNARC effect was proposed by Dehaene, Bossini, and Giraux in 1993, several studies have suggested that different tasks and cultural factors can affect the flexibility of the SNARC effect. This study explored the influence of time units on the flexibility of the SNARC effect via materials with Arabic numbers, which were suffixed with time units and subjected to magnitude comparison tasks. Experiment 1 replicated the SNARC effect for numbers and the STEARC effect for time units. Experiment 2 explored the flexibility of the SNARC effect when numbers were attached to time units, which either conflicted with the numerical magnitude or in which the time units were the same or different. Experiment 3 explored whether the SNARC effect of numbers was stable when numbers were near the transition of two adjacent time units. The results indicate that the SNARC effect was flexible when the numbers were suffixed with time units: Time units influenced the direction of the SNARC effect in a way which could not be accounted for by the mathematical differences between the time units and numbers. This suggests that the SNARC effect is not obligatory and can be easily adapted or inhibited based on the current context. © 2017 The Authors. British Journal of Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Real-time numerical shake prediction and updating for earthquake early warning

Science.gov (United States)

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

2017-12-01

Ground motion prediction is important for earthquake early warning systems, because the region's peak ground motion indicates the potential disaster. In order to predict the peak ground motion quickly and precisely with limited station wave records, we propose a real-time numerical shake prediction and updating method. Our method first predicts the ground motion based on the ground motion prediction equation after P waves detection of several stations, denoted as the initial prediction. In order to correct the prediction error of the initial prediction, an updating scheme based on real-time simulation of wave propagation is designed. Data assimilation technique is incorporated to predict the distribution of seismic wave energy precisely. Radiative transfer theory and Monte Carlo simulation are used for modeling wave propagation in 2-D space, and the peak ground motion is calculated as quickly as possible. Our method has potential to predict shakemap, making the potential disaster be predicted before the real disaster happens. 2008 M S8.0 Wenchuan earthquake is studied as an example to show the validity of the proposed method.

Numerical time-dependent partial differential equations for scientists and engineers

CERN Document Server

Brio, Moysey; Zakharian, Aramais R

2010-01-01

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on bas...

Generalized algorithm for control of numerical dispersion in explicit time-domain electromagnetic simulations

Directory of Open Access Journals (Sweden)

Benjamin M. Cowan

2013-04-01

Full Text Available We describe a modification to the finite-difference time-domain algorithm for electromagnetics on a Cartesian grid which eliminates numerical dispersion error in vacuum for waves propagating along a grid axis. We provide details of the algorithm, which generalizes previous work by allowing 3D operation with a wide choice of aspect ratio, and give conditions to eliminate dispersive errors along one or more of the coordinate axes. We discuss the algorithm in the context of laser-plasma acceleration simulation, showing significant reduction—up to a factor of 280, at a plasma density of 10^{23}  m^{-3}—of the dispersion error of a linear laser pulse in a plasma channel. We then compare the new algorithm with the standard electromagnetic update for laser-plasma accelerator stage simulations, demonstrating that by controlling numerical dispersion, the new algorithm allows more accurate simulation than is otherwise obtained. We also show that the algorithm can be used to overcome the critical but difficult challenge of consistent initialization of a relativistic particle beam and its fields in an accelerator simulation.

Helicopter time-domain electromagnetic numerical simulation based on Leapfrog ADI-FDTD

Science.gov (United States)

Guan, S.; Ji, Y.; Li, D.; Wu, Y.; Wang, A.

2017-12-01

We present a three-dimension (3D) Alternative Direction Implicit Finite-Difference Time-Domain (Leapfrog ADI-FDTD) method for the simulation of helicopter time-domain electromagnetic (HTEM) detection. This method is different from the traditional explicit FDTD, or ADI-FDTD. Comparing with the explicit FDTD, leapfrog ADI-FDTD algorithm is no longer limited by Courant-Friedrichs-Lewy(CFL) condition. Thus, the time step is longer. Comparing with the ADI-FDTD, we reduce the equations from 12 to 6 and .the Leapfrog ADI-FDTD method will be easier for the general simulation. First, we determine initial conditions which are adopted from the existing method presented by Wang and Tripp(1993). Second, we derive Maxwell equation using a new finite difference equation by Leapfrog ADI-FDTD method. The purpose is to eliminate sub-time step and retain unconditional stability characteristics. Third, we add the convolution perfectly matched layer (CPML) absorbing boundary condition into the leapfrog ADI-FDTD simulation and study the absorbing effect of different parameters. Different absorbing parameters will affect the absorbing ability. We find the suitable parameters after many numerical experiments. Fourth, We compare the response with the 1-Dnumerical result method for a homogeneous half-space to verify the correctness of our algorithm.When the model contains 107*107*53 grid points, the conductivity is 0.05S/m. The results show that Leapfrog ADI-FDTD need less simulation time and computer storage space, compared with ADI-FDTD. The calculation speed decreases nearly four times, memory occupation decreases about 32.53%. Thus, this algorithm is more efficient than the conventional ADI-FDTD method for HTEM detection, and is more precise than that of explicit FDTD in the late time.

Numerical simulation of homogenization time measurement by probes with different volume size

International Nuclear Information System (INIS)

Thyn, J.; Novy, M.; Zitny, R.; Mostek, M.; Jahoda, M.

2004-01-01

Results of continuous homogenization time measurement of liquid in a stirred tank depend on the scale of scrutiny. Experimental techniques use a probe, which is situated inside as a conductivity method, or outside of the tank as in the case of gamma-radiotracer methods. Expected value of homogenization time evaluated for a given degree of homogenization is higher when using the conductivity method because the conductivity probe measures relatively small volume in contrast to application of radiotracer, when the volume is much greater. Measurement through the wall of tank is a great advantage of radiotracer application but a comparison of the results with another method supposes a determination of measured volume, which is not easy. Simulation of measurement by CFD code can help to solve the problem. Methodology for CFD simulation of radiotracer experiments was suggested. Commercial software was used for simulation of liquid homogenization in mixed vessel with Rushton turbine. Numerical simulation of liquid homogenization time by CFD for different values of detected volume was confronted with measurement of homogenization time with conductivity probe and with different radioisotopes 198 Au, 82 Br and 24 Na. Detected size of the tank volume was affected by different energy of radioisotope used. (author)

Separation of spatial-temporal patterns ('climatic modes') by combined analysis of really measured and generated numerically vector time series

Science.gov (United States)

Feigin, A. M.; Mukhin, D.; Volodin, E. M.; Gavrilov, A.; Loskutov, E. M.

2013-12-01

The new method of decomposition of the Earth's climate system into well separated spatial-temporal patterns ('climatic modes') is discussed. The method is based on: (i) generalization of the MSSA (Multichannel Singular Spectral Analysis) [1] for expanding vector (space-distributed) time series in basis of spatial-temporal empirical orthogonal functions (STEOF), which makes allowance delayed correlations of the processes recorded in spatially separated points; (ii) expanding both real SST data, and longer by several times SST data generated numerically, in STEOF basis; (iii) use of the numerically produced STEOF basis for exclusion of 'too slow' (and thus not represented correctly) processes from real data. The application of the method allows by means of vector time series generated numerically by the INM RAS Coupled Climate Model [2] to separate from real SST anomalies data [3] two climatic modes possessing by noticeably different time scales: 3-5 and 9-11 years. Relations of separated modes to ENSO and PDO are investigated. Possible applications of spatial-temporal climatic patterns concept to prognosis of climate system evolution is discussed. 1. Ghil, M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, et al. (2002) "Advanced spectral methods for climatic time series", Rev. Geophys. 40(1), 3.1-3.41. 2. http://83.149.207.89/GCM_DATA_PLOTTING/GCM_INM_DATA_XY_en.htm 3. http://iridl.ldeo.columbia.edu/SOURCES/.KAPLAN/.EXTENDED/.v2/.ssta/

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

Research in Application of Geodetic GPS Receivers in Time Synchronization

Science.gov (United States)

Zhang, Q.; Zhang, P.; Sun, Z.; Wang, F.; Wang, X.

2018-04-01

In recent years, with the development of satellite orbit and clock parameters accurately determining technology and the popularity of geodetic GPS receivers, Common-View (CV) which proposed in 1980 by Allan has gained widespread application and achieved higher accuracy time synchronization results. GPS Common View (GPS CV) is the technology that based on multi-channel geodetic GPS receivers located in different place and under the same common-view schedule to receiving same GPS satellite signal at the same time, and then calculating the time difference between respective local receiver time and GPST by weighted theory, we will obtain the difference between above local time of receivers that installed in different station with external atomic clock. Multi-channel geodetic GPS receivers have significant advantages such as higher stability, higher accuracy and more common-view satellites in long baseline time synchronization application over the single-channel geodetic GPS receivers. At present, receiver hardware delay and surrounding environment influence are main error factors that affect the accuracy of GPS common-view result. But most error factors will be suppressed by observation data smoothing and using of observation data from different satellites in multi-channel geodetic GPS receiver. After the SA (Selective Availability) cancellation, using a combination of precise satellite ephemeris, ionospheric-free dual-frequency P-code observations and accurately measuring of receiver hardware delay, we can achieve time synchronization result on the order of nanoseconds (ns). In this paper, 6 days observation data of two IGS core stations with external atomic clock (PTB, USNO distance of two stations about 6000 km) were used to verify the GPS common-view theory. Through GPS observation data analysis, there are at least 2-4 common-view satellites and 5 satellites in a few tracking periods between two stations when the elevation angle is 15°, even there will be at least

RESEARCH IN APPLICATION OF GEODETIC GPS RECEIVERS IN TIME SYNCHRONIZATION

Directory of Open Access Journals (Sweden)

Q. Zhang

2018-04-01

Full Text Available In recent years, with the development of satellite orbit and clock parameters accurately determining technology and the popularity of geodetic GPS receivers, Common-View (CV which proposed in 1980 by Allan has gained widespread application and achieved higher accuracy time synchronization results. GPS Common View (GPS CV is the technology that based on multi-channel geodetic GPS receivers located in different place and under the same common-view schedule to receiving same GPS satellite signal at the same time, and then calculating the time difference between respective local receiver time and GPST by weighted theory, we will obtain the difference between above local time of receivers that installed in different station with external atomic clock. Multi-channel geodetic GPS receivers have significant advantages such as higher stability, higher accuracy and more common-view satellites in long baseline time synchronization application over the single-channel geodetic GPS receivers. At present, receiver hardware delay and surrounding environment influence are main error factors that affect the accuracy of GPS common-view result. But most error factors will be suppressed by observation data smoothing and using of observation data from different satellites in multi-channel geodetic GPS receiver. After the SA (Selective Availability cancellation, using a combination of precise satellite ephemeris, ionospheric-free dual-frequency P-code observations and accurately measuring of receiver hardware delay, we can achieve time synchronization result on the order of nanoseconds (ns. In this paper, 6 days observation data of two IGS core stations with external atomic clock (PTB, USNO distance of two stations about 6000 km were used to verify the GPS common-view theory. Through GPS observation data analysis, there are at least 2–4 common-view satellites and 5 satellites in a few tracking periods between two stations when the elevation angle is 15°, even

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.

Time dependent AN neutron transport calculations in finite media using a numerical inverse Laplace transform technique

International Nuclear Information System (INIS)

Ganapol, B.D.; Sumini, M.

1990-01-01

The time dependent space second order discrete form of the monokinetic transport equation is given an analytical solution, within the Laplace transform domain. Th A n dynamic model is presented and the general resolution procedure is worked out. The solution in the time domain is then obtained through the application of a numerical transform inversion technique. The justification of the research relies in the need to produce reliable and physically meaningful transport benchmarks for dynamic calculations. The paper is concluded by a few results followed by some physical comments

The inverse Numerical Computer Program FLUX-BOT for estimating Vertical Water Fluxes from Temperature Time-Series.

Science.gov (United States)

Trauth, N.; Schmidt, C.; Munz, M.

2016-12-01

Heat as a natural tracer to quantify water fluxes between groundwater and surface water has evolved to a standard hydrological method. Typically, time series of temperatures in the surface water and in the sediment are observed and are subsequently evaluated by a vertical 1D representation of heat transport by advection and dispersion. Several analytical solutions as well as their implementation into user-friendly software exist in order to estimate water fluxes from the observed temperatures. Analytical solutions can be easily implemented but assumptions on the boundary conditions have to be made a priori, e.g. sinusoidal upper temperature boundary. Numerical models offer more flexibility and can handle temperature data which is characterized by irregular variations such as storm-event induced temperature changes and thus cannot readily be incorporated in analytical solutions. This also reduced the effort of data preprocessing such as the extraction of the diurnal temperature variation. We developed a software to estimate water FLUXes Based On Temperatures- FLUX-BOT. FLUX-BOT is a numerical code written in MATLAB which is intended to calculate vertical water fluxes in saturated sediments, based on the inversion of measured temperature time series observed at multiple depths. It applies a cell-centered Crank-Nicolson implicit finite difference scheme to solve the one-dimensional heat advection-conduction equation. Besides its core inverse numerical routines, FLUX-BOT includes functions visualizing the results and functions for performing uncertainty analysis. We provide applications of FLUX-BOT to generic as well as to measured temperature data to demonstrate its performance.

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

Investigation of the feasibility of an analytical method of accounting for the effects of atmospheric drag on satellite motion

Science.gov (United States)

Bozeman, Robert E.

1987-01-01

An analytic technique for accounting for the joint effects of Earth oblateness and atmospheric drag on close-Earth satellites is investigated. The technique is analytic in the sense that explicit solutions to the Lagrange planetary equations are given; consequently, no numerical integrations are required in the solution process. The atmospheric density in the technique described is represented by a rotating spherical exponential model with superposed effects of the oblate atmosphere and the diurnal variations. A computer program implementing the process is discussed and sample output is compared with output from program NSEP (Numerical Satellite Ephemeris Program). NSEP uses a numerical integration technique to account for atmospheric drag effects.

Time scales of DNAPL migration in sandy aquifers examined via numerical simulation

Energy Technology Data Exchange (ETDEWEB)

Gerhard, J.I.; Pang, T.; Kueper, B.H. [University of Edinburgh, Edinburgh (United Kingdom). Inst. of Infrastructure & Environmental

2007-03-15

The time required for dense nonaqueous phase liquid (DNAPL) to cease migrating following release to the subsurface is a valuable component of a site conceptual model. This study uses numerical simulation to investigate the migration of six different DNAPLs in sandy aquifers. The most influential parameters governing migration cessation time are the density and viscosity of the DNAPL and the mean hydraulic conductivity of the aquifer. Releases of between 1 and 40 drums of chlorinated solvent DNAPLs, characterized by relatively high density and low viscosity, require on the order of months to a few years to cease migrating in a heterogeneous medium sand aquifer having an average hydraulic conductivity of 7.4 x 10{sup -3} cm/s. In contrast to this, the release of 20 drums of coal tar {rho}{sub D} = 1061 kg/m{sup 3}, {mu}{sub D} = 0.161 Pa(.)s) requires more than 100 years to cease migrating in the same aquifer. Altering the mean hydraulic conductivity of the aquifer results in a proportional change in cessation times. Parameters that exhibit relatively little influence on migration time scales are the DNAPL-water interfacial tension, release volume, source capillary pressure, mean aquifer porosity, and ambient ground water hydraulic gradient. This study also demonstrates that low-density DNAPLs (e.g., coal tar) give rise to greater amounts of lateral spreading and greater amounts of pooling on capillary barriers than high-density DNAPLs such as trichloroethylene or tetrachloroethylene.

Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems

International Nuclear Information System (INIS)

Kotler, Z.; Neria, E.; Nitzan, A.

1991-01-01

The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. We investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one- and two-configuration TDSCF approximations. We also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation. This provides a potentially very useful method to simulate strongly quantum systems coupled to an essentially classical environment. (orig.)

Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems

Energy Technology Data Exchange (ETDEWEB)

Kotler, Z.; Neria, E.; Nitzan, A. (Tel Aviv Univ. (Israel). School of Chemistry)

1991-02-01

The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. We investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one- and two-configuration TDSCF approximations. We also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation. This provides a potentially very useful method to simulate strongly quantum systems coupled to an essentially classical environment. (orig.).

Computational time analysis of the numerical solution of 3D electrostatic Poisson's equation

Science.gov (United States)

Kamboh, Shakeel Ahmed; Labadin, Jane; Rigit, Andrew Ragai Henri; Ling, Tech Chaw; Amur, Khuda Bux; Chaudhary, Muhammad Tayyab

2015-05-01

3D Poisson's equation is solved numerically to simulate the electric potential in a prototype design of electrohydrodynamic (EHD) ion-drag micropump. Finite difference method (FDM) is employed to discretize the governing equation. The system of linear equations resulting from FDM is solved iteratively by using the sequential Jacobi (SJ) and sequential Gauss-Seidel (SGS) methods, simulation results are also compared to examine the difference between the results. The main objective was to analyze the computational time required by both the methods with respect to different grid sizes and parallelize the Jacobi method to reduce the computational time. In common, the SGS method is faster than the SJ method but the data parallelism of Jacobi method may produce good speedup over SGS method. In this study, the feasibility of using parallel Jacobi (PJ) method is attempted in relation to SGS method. MATLAB Parallel/Distributed computing environment is used and a parallel code for SJ method is implemented. It was found that for small grid size the SGS method remains dominant over SJ method and PJ method while for large grid size both the sequential methods may take nearly too much processing time to converge. Yet, the PJ method reduces computational time to some extent for large grid sizes.

Children’s Mapping between Non-Symbolic and Symbolic Numerical Magnitudes and Its Association with Timed and Untimed Tests of Mathematics Achievement

Science.gov (United States)

Brankaer, Carmen; Ghesquière, Pol; De Smedt, Bert

2014-01-01

The ability to map between non-symbolic numerical magnitudes and Arabic numerals has been put forward as a key factor in children’s mathematical development. This mapping ability has been mainly examined indirectly by looking at children’s performance on a symbolic magnitude comparison task. The present study investigated mapping in a more direct way by using a task in which children had to choose which of two choice quantities (Arabic digits or dot arrays) matched the target quantity (dot array or Arabic digit), thereby focusing on small quantities ranging from 1 to 9. We aimed to determine the development of mapping over time and its relation to mathematics achievement. Participants were 36 first graders (M = 6 years 8 months) and 46 third graders (M = 8 years 8 months) who all completed mapping tasks, symbolic and non-symbolic magnitude comparison tasks and standardized timed and untimed tests of mathematics achievement. Findings revealed that children are able to map between non-symbolic and symbolic representations and that this mapping ability develops over time. Moreover, we found that children’s mapping ability is related to timed and untimed measures of mathematics achievement, over and above the variance accounted for by their numerical magnitude comparison skills. PMID:24699664

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

International Nuclear Information System (INIS)

Liao Chaqing

2007-01-01

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

A matter of timing: identifying significant multi-dose radiotherapy improvements by numerical simulation and genetic algorithm search.

Directory of Open Access Journals (Sweden)

Simon D Angus

Full Text Available Multi-dose radiotherapy protocols (fraction dose and timing currently used in the clinic are the product of human selection based on habit, received wisdom, physician experience and intra-day patient timetabling. However, due to combinatorial considerations, the potential treatment protocol space for a given total dose or treatment length is enormous, even for relatively coarse search; well beyond the capacity of traditional in-vitro methods. In constrast, high fidelity numerical simulation of tumor development is well suited to the challenge. Building on our previous single-dose numerical simulation model of EMT6/Ro spheroids, a multi-dose irradiation response module is added and calibrated to the effective dose arising from 18 independent multi-dose treatment programs available in the experimental literature. With the developed model a constrained, non-linear, search for better performing cadidate protocols is conducted within the vicinity of two benchmarks by genetic algorithm (GA techniques. After evaluating less than 0.01% of the potential benchmark protocol space, candidate protocols were identified by the GA which conferred an average of 9.4% (max benefit 16.5% and 7.1% (13.3% improvement (reduction on tumour cell count compared to the two benchmarks, respectively. Noticing that a convergent phenomenon of the top performing protocols was their temporal synchronicity, a further series of numerical experiments was conducted with periodic time-gap protocols (10 h to 23 h, leading to the discovery that the performance of the GA search candidates could be replicated by 17-18 h periodic candidates. Further dynamic irradiation-response cell-phase analysis revealed that such periodicity cohered with latent EMT6/Ro cell-phase temporal patterning. Taken together, this study provides powerful evidence towards the hypothesis that even simple inter-fraction timing variations for a given fractional dose program may present a facile, and highly cost

A matter of timing: identifying significant multi-dose radiotherapy improvements by numerical simulation and genetic algorithm search.

Science.gov (United States)

Angus, Simon D; Piotrowska, Monika Joanna

2014-01-01

Multi-dose radiotherapy protocols (fraction dose and timing) currently used in the clinic are the product of human selection based on habit, received wisdom, physician experience and intra-day patient timetabling. However, due to combinatorial considerations, the potential treatment protocol space for a given total dose or treatment length is enormous, even for relatively coarse search; well beyond the capacity of traditional in-vitro methods. In constrast, high fidelity numerical simulation of tumor development is well suited to the challenge. Building on our previous single-dose numerical simulation model of EMT6/Ro spheroids, a multi-dose irradiation response module is added and calibrated to the effective dose arising from 18 independent multi-dose treatment programs available in the experimental literature. With the developed model a constrained, non-linear, search for better performing cadidate protocols is conducted within the vicinity of two benchmarks by genetic algorithm (GA) techniques. After evaluating less than 0.01% of the potential benchmark protocol space, candidate protocols were identified by the GA which conferred an average of 9.4% (max benefit 16.5%) and 7.1% (13.3%) improvement (reduction) on tumour cell count compared to the two benchmarks, respectively. Noticing that a convergent phenomenon of the top performing protocols was their temporal synchronicity, a further series of numerical experiments was conducted with periodic time-gap protocols (10 h to 23 h), leading to the discovery that the performance of the GA search candidates could be replicated by 17-18 h periodic candidates. Further dynamic irradiation-response cell-phase analysis revealed that such periodicity cohered with latent EMT6/Ro cell-phase temporal patterning. Taken together, this study provides powerful evidence towards the hypothesis that even simple inter-fraction timing variations for a given fractional dose program may present a facile, and highly cost-effecitive means

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.

Seasonal variation of residence time in spring and groundwater evaluated by CFCs and numerical simulation in mountainous headwater catchment

Science.gov (United States)

Tsujimura, Maki; Watanabe, Yasuto; Ikeda, Koichi; Yano, Shinjiro; Abe, Yutaka

2016-04-01

Headwater catchments in mountainous region are the most important recharge area for surface and subsurface waters, additionally time information of the water is principal to understand hydrological processes in the catchments. However, there have been few researches to evaluate variation of residence time of subsurface water in time and space at the mountainous headwaters especially with steep slope. We investigated the temporal variation of the residence time of the spring and groundwater with tracing of hydrological flow processes in mountainous catchments underlain by granite, Yamanashi Prefecture, central Japan. We conducted intensive hydrological monitoring and water sampling of spring, stream and ground waters in high-flow and low-flow seasons from 2008 through 2013 in River Jingu Watershed underlain by granite, with an area of approximately 15 km2 and elevation ranging from 950 m to 2000 m. The CFCs, stable isotopic ratios of oxygen-18 and deuterium, inorganic solute constituent concentrations were determined on all water samples. Also, a numerical simulation was conducted to reproduce of the average residence times of the spring and groundwater. The residence time of the spring water estimated by the CFCs concentration ranged from 10 years to 60 years in space within the watershed, and it was higher (older) during the low flow season and lower (younger) during the high flow season. We tried to reproduce the seasonal change of the residence time in the spring water by numerical simulation, and the calculated residence time of the spring water and discharge of the stream agreed well with the observed values. The groundwater level was higher during the high flow season and the groundwater dominantly flowed through the weathered granite with higher permeability, whereas that was lower during the low flow season and that flowed dominantly through the fresh granite with lower permeability. This caused the seasonal variation of the residence time of the spring

Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method

International Nuclear Information System (INIS)

Onishi, Yuki; Takiyasu, Jumpei; Amaya, Kenji; Yakuwa, Hiroshi; Hayabusa, Keisuke

2012-01-01

Highlights: ► A novel numerical method to analyze time dependent localized corrosion is developed. ► It takes electromigration, mass diffusion, chemical reactions, and moving boundaries. ► Our method perfectly satisfies the conservation of mass and electroneutrality. ► The behavior of typical crevice corrosion is successfully simulated. ► Both verification and validation of our method are carried out. - Abstract: A novel numerical method for time-dependent localized corrosion analysis is presented. Electromigration, mass diffusion, chemical reactions, and moving boundaries are considered in the numerical simulation of localized corrosion of engineering alloys in an underwater environment. Our method combines the finite volume method (FVM) and the voxel method. The FVM is adopted in the corrosion rate calculation so that the conservation of mass is satisfied. A newly developed decoupled algorithm with a projection method is introduced in the FVM to decouple the multiphysics problem into the electrostatic, mass transport, and chemical reaction analyses with electroneutrality maintained. The polarization curves for the corroding metal are used as boundary conditions for the metal surfaces to calculate the corrosion rates. The voxel method is adopted in updating the moving boundaries of cavities without remeshing and mesh-to-mesh solution mapping. Some modifications of the standard voxel method, which represents the boundaries as zigzag-shaped surfaces, are introduced to generate smooth surfaces. Our method successfully reproduces the numerical and experimental results of a capillary electrophoresis problem. Furthermore, the numerical results are qualitatively consistent with the experimental results for several examples of crevice corrosion.

On the complexity of numerical analysis

DEFF Research Database (Denmark)

Miltersen, Peter Bro; Allender, Eric; Burgisser, Peter

2009-01-01

an integer N, decide whether N>0. • In the Blum-Shub-Smale model, polynomial time computation over the reals (on discrete inputs) is polynomial-time equivalent to PosSLP, when there are only algebraic constants. We conjecture that using transcendental constants provides no additional power, beyond nonuniform...... reductions to PosSLP, and we present some preliminary results supporting this conjecture. • The Generic Task of Numerical Computation is also polynomial-time equivalent to PosSLP. We prove that PosSLP lies in the counting hierarchy. Combining this with work of Tiwari, we obtain that the Euclidean Traveling......We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis: • The Blum-Shub-Smale model of computation over the reals. • A problem we call the “Generic Task of Numerical Computation,” which captures an aspect of doing numerical computation...

Probabilistic forecasting of shallow, rainfall-triggered landslides using real-time numerical weather predictions

Directory of Open Access Journals (Sweden)

J. Schmidt

2008-04-01

Full Text Available A project established at the National Institute of Water and Atmospheric Research (NIWA in New Zealand is aimed at developing a prototype of a real-time landslide forecasting system. The objective is to predict temporal changes in landslide probability for shallow, rainfall-triggered landslides, based on quantitative weather forecasts from numerical weather prediction models. Global weather forecasts from the United Kingdom Met Office (MO Numerical Weather Prediction model (NWP are coupled with a regional data assimilating NWP model (New Zealand Limited Area Model, NZLAM to forecast atmospheric variables such as precipitation and temperature up to 48 h ahead for all of New Zealand. The weather forecasts are fed into a hydrologic model to predict development of soil moisture and groundwater levels. The forecasted catchment-scale patterns in soil moisture and soil saturation are then downscaled using topographic indices to predict soil moisture status at the local scale, and an infinite slope stability model is applied to determine the triggering soil water threshold at a local scale. The model uses uncertainty of soil parameters to produce probabilistic forecasts of spatio-temporal landslide occurrence 48~h ahead. The system was evaluated for a damaging landslide event in New Zealand. Comparison with landslide densities estimated from satellite imagery resulted in hit rates of 70–90%.

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

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 study and ex vivo assessment of HIFU treatment time reduction through optimization of focal point trajectory

Science.gov (United States)

Grisey, A.; Yon, S.; Pechoux, T.; Letort, V.; Lafitte, P.

2017-03-01

Treatment time reduction is a key issue to expand the use of high intensity focused ultrasound (HIFU) surgery, especially for benign pathologies. This study aims at quantitatively assessing the potential reduction of the treatment time arising from moving the focal point during long pulses. In this context, the optimization of the focal point trajectory is crucial to achieve a uniform thermal dose repartition and avoid boiling. At first, a numerical optimization algorithm was used to generate efficient trajectories. Thermal conduction was simulated in 3D with a finite difference code and damages to the tissue were modeled using the thermal dose formula. Given an initial trajectory, the thermal dose field was first computed, then, making use of Pontryagin's maximum principle, the trajectory was iteratively refined. Several initial trajectories were tested. Then, an ex vivo study was conducted in order to validate the efficicency of the resulting optimized strategies. Single pulses were performed at 3MHz on fresh veal liver samples with an Echopulse and the size of each unitary lesion was assessed by cutting each sample along three orthogonal planes and measuring the dimension of the whitened area based on photographs. We propose a promising approach to significantly shorten HIFU treatment time: the numerical optimization algorithm was shown to provide a reliable insight on trajectories that can improve treatment strategies. The model must now be improved in order to take in vivo conditions into account and extensively validated.

Numerical methods in software and analysis

CERN Document Server

Rice, John R

1992-01-01

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

Spatial bias and uncertainty in numerical weather predictions for urban runoff forecasts with long time horizons

DEFF Research Database (Denmark)

Pedersen, Jonas Wied; Courdent, Vianney Augustin Thomas; Vezzaro, Luca

2017-01-01

Numerical Weather Predictions (NWP) can be used to forecast urban runoff with long lead times. However, NWP exhibit large spatial uncertainties and using forecasted precipitation directly above the catchment might therefore not be an ideal approach in an online setup. We use the Danish...... Meteorological Institute’s NWP ensemble and investigate a large spatial neighborhood around the catchment over a two-year period. When compared against in-sewer observations, runoff forecasts forced with precipitation from north-east of the catchment are most skillful. This highlights spatial biases...

Numerical models for high beta magnetohydrodynamic flow

International Nuclear Information System (INIS)

Brackbill, J.U.

1987-01-01

The fundamentals of numerical magnetohydrodynamics for highly conducting, high-beta plasmas are outlined. The discussions emphasize the physical properties of the flow, and how elementary concepts in numerical analysis can be applied to the construction of finite difference approximations that capture these features. The linear and nonlinear stability of explicit and implicit differencing in time is examined, the origin and effect of numerical diffusion in the calculation of convective transport is described, and a technique for maintaining solenoidality in the magnetic field is developed. Many of the points are illustrated by numerical examples. The techniques described are applicable to the time-dependent, high-beta flows normally encountered in magnetically confined plasmas, plasma switches, and space and astrophysical plasmas. 40 refs

Numerical study on the matching law between charge caliber and delay time of the rod-shaped explosively formed projectile

Science.gov (United States)

Shen, H. M.; Li, W. B.; Wang, X. M.; Li, W. B.

2017-09-01

To study the application of multi-point initiation technology on shaped charge warhead, numerically simulated the influence of initiating delay time of different charge caliber on detonation wave and performance forming of penetrator. The study found that as charge caliber increased, the allowable initiating delay time also increased. For the commonly used small and medium-charge caliber shaped charge warhead, the charge caliber(Dk ) and the delay time (σ) presented a linear relationship σ = -12.79+1.25Dk . As charge caliber continue increasing, the initiating allowable delay time started to increase exponentially. The study reveals the matching law between charge caliber, initiating delay time and performance forming of penetrator, and it offers guidance for the design of multi-point initiation network for shaped charge.

Numerical simulation of time-dependent deformations under hygral and thermal transient conditions

International Nuclear Information System (INIS)

Roelfstra, P.E.

1987-01-01

Some basic concepts of numerical simulation of the formation of the microstructure of HCP are outlined. The aim is to replace arbitrary terms like aging by more realistic terms like bond density in the xerogel and bonds between hydrating particles of HCP. Actual state parameters such as temperature, humidity and degree of hydration can be determined under transient hygral and thermal conditions by solving numerically a series of appropriate coupled differential equations with given boundary conditions. Shrinkage of a composite structure without crack formation, based on calculated moisture distributions, has been determined with numerical concrete codes. The influence of crack formation, tensile strain-hardening and softening on the total deformation of a quasi-homogeneous drying material has been studied by means of model based on FEM. The difference between shrinkage without crack formation and shrinkage with crack formation can be quantified. Drying shrinkage and creep of concrete cannot be separated. The total deformation depends on the superimposed stress fields. Transient hygral deformation can be realistically predicted if the concept of point properties is applied rigorously. Transient thermal deformation has to be dealt with in the same way. (orig./HP)

MEASURING THE MASS OF SOLAR SYSTEM PLANETS USING PULSAR TIMING

International Nuclear Information System (INIS)

Champion, D. J.; Hobbs, G. B.; Manchester, R. N.; Edwards, R. T.; Burke-Spolaor, S.; Sarkissian, J. M.; Backer, D. C.; Bailes, M.; Bhat, N. D. R.; Van Straten, W.; Coles, W.; Demorest, P. B.; Ferdman, R. D.; Purver, M. B.; Folkner, W. M.; Hotan, A. W.; Kramer, M.; Lommen, A. N.; Nice, D. J.; Stairs, I. H.

2010-01-01

High-precision pulsar timing relies on a solar system ephemeris in order to convert times of arrival (TOAs) of pulses measured at an observatory to the solar system barycenter. Any error in the conversion to the barycentric TOAs leads to a systematic variation in the observed timing residuals; specifically, an incorrect planetary mass leads to a predominantly sinusoidal variation having a period and phase associated with the planet's orbital motion about the Sun. By using an array of pulsars (PSRs J0437-4715, J1744-1134, J1857+0943, J1909-3744), the masses of the planetary systems from Mercury to Saturn have been determined. These masses are consistent with the best-known masses determined by spacecraft observations, with the mass of the Jovian system, 9.547921(2) x10 -4 M sun , being significantly more accurate than the mass determined from the Pioneer and Voyager spacecraft, and consistent with but less accurate than the value from the Galileo spacecraft. While spacecraft are likely to produce the most accurate measurements for individual solar system bodies, the pulsar technique is sensitive to planetary system masses and has the potential to provide the most accurate values of these masses for some planets.

Real-time dynamic control of the Three Gorges Reservoir by coupling numerical weather rainfall prediction and flood forecasting

DEFF Research Database (Denmark)

Wang, Y.; Chen, H.; Rosbjerg, Dan

2013-01-01

In reservoir operation improvement of the accuracy of forecast flood inflow and extension of forecast lead-time can effectively be achieved by using rainfall forecasts from numerical weather predictions with a hydrological catchment model. In this study, the Regional Spectrum Model (RSM), which...... is developed by the Japan Meteorological Agency, was used to forecast rainfall with 5 days lead-time in the upper region of the Three Gorges Reservoir (TGR). A conceptual hydrological model, the Xinanjiang Model, has been set up to forecast the inflow flood of TGR by the Ministry of Water Resources Information...... season 2012 as example, real-time dynamic control of the FLWL was implemented by using the forecasted reservoir flood inflow as input. The forecasted inflow with 5 days lead-time rainfall forecast was evaluated by several performance indices, including the mean relative error of the volumetric reservoir...

Numerical Analysis of Multiscale Computations

CERN Document Server

Engquist, Björn; Tsai, Yen-Hsi R

2012-01-01

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

Time-convolutionless mode-coupling theory near the glass transition: Numerical solutions for the Percus-Yevick model

International Nuclear Information System (INIS)

Kimura, Y.; Tokuyama, M.

2016-01-01

The full numerical solutions of the time-convolutionless modecoupling theory (TMCT) equation recently proposed by Tokuyama are compared with those of the ideal mode-coupling theory (MCT) equation based on the Percus- Yevick static structure factor for hard spheres qualitatively and quantitatively. The ergodic to non-ergodic transition at the critical volume fraction φ_c predicted by MCT is also shown to occur even for TMCT. Thus, φ_c of TMCT is shown to be much higher than that of MCT. The dynamics of coherent-intermediate scattering functions and their two-step relaxation process in a β stage are also discussed.

Alternating-direction implicit numerical solution of the time-dependent, three-dimensional, single fluid, resistive magnetohydrodynamic equations

Energy Technology Data Exchange (ETDEWEB)

Finan, C.H. III

1980-12-01

Resistive magnetohydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are solved simultaneously to avoid syncronization errors.

Numerical

Directory of Open Access Journals (Sweden)

M. Boumaza

2015-07-01

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

On a fast numerical tool for nuclear accidental dynamic phenomenology and application to the real time simulation of Lady Godiva

International Nuclear Information System (INIS)

Bindel, Laurent; Gamess, Andre; Jasserand, Frederic; Laporte, Sebastien

2003-01-01

This paper present a modern numerical method, implemented in a TUI-code named MacDSP, for solving any set of differential equations and in particular phenomenological accidental dynamic calculations. The speed efficiency of such an approach, thanks to the use of the hybrid-level power offered by C++ and an ad-hoc design, make it possible to construct the first kid of a family of real time simulator employing the video games technology DirectX TM : Lady Godiva Real Time Simulator. (author)

Estimation of flushing time in a monsoonal estuary using observational and numerical approaches

Digital Repository Service at National Institute of Oceanography (India)

Manoj, N.T.

and numerical model simulations to correlate TF with monthly mean river discharges. The power regression equation derived from FOS (numerical model) showed good statistical fit with data (r=-0.997 (-1.0)) for any given river discharge compared... was to calculate the TF in the Mandovi during three different seasons in a year. For this purpose, we adopted two approaches, first the computation of TF from FOS. The application of H2N-Model was another approach to calculate the TF in the estuary. The FWF...

Duration and numerical estimation in right brain-damaged patients with and without neglect: Lack of support for a mental time line.

Science.gov (United States)

Masson, Nicolas; Pesenti, Mauro; Dormal, Valérie

2016-08-01

Previous studies have shown that left neglect patients are impaired when they have to orient their attention leftward relative to a standard in numerical comparison tasks. This finding has been accounted for by the idea that numerical magnitudes are represented along a spatial continuum oriented from left to right with small magnitudes on the left and large magnitudes on the right. Similarly, it has been proposed that duration could be represented along a mental time line that shares the properties of the number continuum. By comparing directly duration and numerosity processing, this study investigates whether or not the performance of neglect patients supports the hypothesis of a mental time line. Twenty-two right brain-damaged patients (11 with and 11 without left neglect), as well as 11 age-matched healthy controls, had to judge whether a single dot presented visually lasted shorter or longer than 500 ms and whether a sequence of flashed dots was smaller or larger than 5. Digit spans were also assessed to measure verbal working memory capacities. In duration comparison, no spatial-duration bias was found in neglect patients. Moreover, a significant correlation between verbal working memory and duration performance was observed in right brain-damaged patients, irrespective of the presence or absence of neglect. In numerical comparison, only neglect patients showed an enhanced distance effect for numerical magnitude smaller than the standard. These results do not support the hypothesis of the existence of a mental continuum oriented from left to right for duration. We discuss an alternative account to explain the duration impairment observed in right brain-damaged patients. © 2015 The British Psychological Society.

Numerically robust geometry engine for compound solid geometries

International Nuclear Information System (INIS)

Vlachoudis, V.; Sinuela-Pastor, D.

2013-01-01

Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)

Building X-ray pulsar timing model without the use of radio parameters

Science.gov (United States)

Sun, Hai-feng; Sun, Xiong; Fang, Hai-yan; Shen, Li-rong; Cong, Shao-peng; Liu, Yan-ming; Li, Xiao-ping; Bao, Wei-min

2018-02-01

This paper develops a timing solution for the X-ray pulsar timing model without the use of the initial radio model parameters. First, we address the problem of phase ambiguities for the pre-fit residuals in the construction of pulsar timing model. To improve the estimation accuracy of the pulse time of arrival (TOA), we have deduced the general form of test statistics in Fourier transform, and discussed their estimation performances. Meanwhile, a fast maximum likelihood (FML) technique is presented to estimate the pulse TOA, which outperforms cross correlation (CC) estimator and exhibits a performance comparable with maximum likelihood (ML) estimator in spite of a much less reduced computational complexity. Depending on the strategy of the difference minimum of pre-fit residuals, we present an effective forced phase-connected technique to achieve initial model parameters. Then, we use the observations with the Rossi X-Ray Timing Explorer (RXTE) and X-ray pulsar navigation-I (XPNAV-1) satellites for experimental studies, and discuss main differences for the root mean square (RMS) residuals calculated with the X-ray and radio ephemerides. Finally, a chi-square value (CSV) of pulse profiles is presented as a complementary indicator to the RMS residuals for evaluating the model parameters. The results show that the proposed timing solution is valid and effective, and the obtained model parameters can be a reasonable alternative to the radio ephemeris.

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.

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

precipitation shifts the scale of TTD towards younger (older) travel times, while the shape of the TTD remains untouched. This work constitutes a first step in linking a numerical transport model and analytical solutions of TTD to study their assumptions and limitations, providing physical inferences for empirical parameters.

Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

Science.gov (United States)

Pradipto; Purqon, Acep

2017-07-01

Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.

Numerical relativity

CERN Document Server

Nakamura, T

1993-01-01

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

Validation and Assessment of Multi-GNSS Real-Time Precise Point Positioning in Simulated Kinematic Mode Using IGS Real-Time Service

Directory of Open Access Journals (Sweden)

Liang Wang

2018-02-01

Full Text Available Precise Point Positioning (PPP is a popular technology for precise applications based on the Global Navigation Satellite System (GNSS. Multi-GNSS combined PPP has become a hot topic in recent years with the development of multiple GNSSs. Meanwhile, with the operation of the real-time service (RTS of the International GNSS Service (IGS agency that provides satellite orbit and clock corrections to broadcast ephemeris, it is possible to obtain the real-time precise products of satellite orbits and clocks and to conduct real-time PPP. In this contribution, the real-time multi-GNSS orbit and clock corrections of the CLK93 product are applied for real-time multi-GNSS PPP processing, and its orbit and clock qualities are investigated, first with a seven-day experiment by comparing them with the final multi-GNSS precise product ‘GBM’ from GFZ. Then, an experiment involving real-time PPP processing for three stations in the Multi-GNSS Experiment (MGEX network with a testing period of two weeks is conducted in order to evaluate the convergence performance of real-time PPP in a simulated kinematic mode. The experimental result shows that real-time PPP can achieve a convergence performance of less than 15 min for an accuracy level of 20 cm. Finally, the real-time data streams from 12 globally distributed IGS/MGEX stations for one month are used to assess and validate the positioning accuracy of real-time multi-GNSS PPP. The results show that the simulated kinematic positioning accuracy achieved by real-time PPP on different stations is about 3.0 to 4.0 cm for the horizontal direction and 5.0 to 7.0 cm for the three-dimensional (3D direction.

Numerical simulation in three space dimensions of time-dependent thermal convection in a rotating fluid

International Nuclear Information System (INIS)

Hathaway, D.H.; Somerville, R.C.J.; National Solar Observatory, Sunspot, NM; California Univ., La Jolla)

1985-01-01

Three-dimensional, time-dependent convection in a plane layer of fluid, uniformly heated from below and subject to vertical shear and to rotation about an axis tilted from the vertical, was simulated by the numerical solution of the Boussinesq equations, including all Coriolis terms. Rotation about a vertical axis produces smaller convection cells with diminished heat fluxes and considerable vorticity. When the rotation axis is tilted from the vertical to represent tropical latitudes, the convection cells become elongated in a N-S direction. Imposed flows with constant vertical shear produce convective rolls aligned with the mean flow. When the rotation vector is tilted from the vertical, the competing effects due to rotation and shear can stabilize the convective motions. 15 references

Foundations of children's numerical and mathematical skills: the roles of symbolic and nonsymbolic representations of numerical magnitude.

Science.gov (United States)

Lyons, Ian M; Ansari, Daniel

2015-01-01

Numerical and mathematical skills are critical predictors of academic success. The last three decades have seen a substantial growth in our understanding of how the human mind and brain represent and process numbers. In particular, research has shown that we share with animals the ability to represent numerical magnitude (the total number of items in a set) and that preverbal infants can process numerical magnitude. Further research has shown that similar processing signatures characterize numerical magnitude processing across species and developmental time. These findings suggest that an approximate system for nonsymbolic (e.g., dot arrays) numerical magnitude representation serves as the basis for the acquisition of cultural, symbolic (e.g., Arabic numerals) representations of numerical magnitude. This chapter explores this hypothesis by reviewing studies that have examined the relation between individual differences in nonsymbolic numerical magnitude processing and symbolic math abilities (e.g., arithmetic). Furthermore, we examine the extent to which the available literature provides strong evidence for a link between symbolic and nonsymbolic representations of numerical magnitude at the behavioral and neural levels of analysis. We conclude that claims that symbolic number abilities are grounded in the approximate system for the nonsymbolic representation of numerical magnitude are not strongly supported by the available evidence. Alternative models and future research directions are discussed. © 2015 Elsevier Inc. All rights reserved.

Description of an identification method of thermocouple time constant based on application of recursive numerical filtering to temperature fluctuation

International Nuclear Information System (INIS)

Bernardin, B.; Le Guillou, G.; Parcy, JP.

1981-04-01

Usual spectral methods, based on temperature fluctuation analysis, aiming at thermocouple time constant identification are using an equipment too much sophisticated for on-line application. It is shown that numerical filtering is optimal for this application, the equipment is simpler than for spectral methods and less samples of signals are needed for the same accuracy. The method is described and a parametric study was performed using a temperature noise simulator [fr

The straightforward numerical treatment of the time dependent advection in air pollution problems and its verification

Energy Technology Data Exchange (ETDEWEB)

Hinrichsen, K

1982-01-01

A very simple Lagrangian finite difference scheme has been developed to calculate the time dependent advection of air pollutants. It is mass conserving and avoids numerical pseudo-diffusion. No condition of numerical stability is required. The Eulerian grid used for the diffusion part of the pollutant transport equation remains unchanged. There are no restrictions on temporally and spatially variable emission rates, production and destruction processes, wind velocity, diffusion coefficients, roughness parameters or inversion heights. The only exception is that the wind field should not be too far from being homogeneous in the horizontal direction (test of D. W. Pepper and P. E. Long, 1978, J. appl. Met. 17, 228-233). Steady state solutions are nearly identical with corresponding analytical solutions. The propagation of a pollutant cloud is simulated more realistically as compared with the advection treatment of E. Runca and F. Sardei (1975, Atmospheric Environment 9, 69-80) and M. Dunst (1980, Z. Met. 30, 47-59). The course of a diffusion experiment is modelled to demonstrate the efficiency of the proposed method. Because of its simplicity, the method is especially suited for use in license processes, for control, and for calculating health risks in relation to industrial and power plant accidents with the goal of organizing efficient protection or evacuation.

Gravitational radiation and 3D numerical relativity

International Nuclear Information System (INIS)

Nakamura, T.

1986-01-01

Study of Numerical Relativity in Kyoto is reviewed. Main topics discussed are 2D rotating collapse, phase cancellation effects and perturbation calculation of the gravitational radiation from a particle falling into a black hole. New numerical results on 3D time evolution of pure gravitational waves are also presented

Excel spreadsheet in teaching numerical methods

Science.gov (United States)

Djamila, Harimi

2017-09-01

One of the important objectives in teaching numerical methods for undergraduates’ students is to bring into the comprehension of numerical methods algorithms. Although, manual calculation is important in understanding the procedure, it is time consuming and prone to error. This is specifically the case when considering the iteration procedure used in many numerical methods. Currently, many commercial programs are useful in teaching numerical methods such as Matlab, Maple, and Mathematica. These are usually not user-friendly by the uninitiated. Excel spreadsheet offers an initial level of programming, which it can be used either in or off campus. The students will not be distracted with writing codes. It must be emphasized that general commercial software is required to be introduced later to more elaborated questions. This article aims to report on a teaching numerical methods strategy for undergraduates engineering programs. It is directed to students, lecturers and researchers in engineering field.

PIV quantification of the flow induced by an ultrasonic horn and numerical modeling of the flow and related processing times.

Science.gov (United States)

Schenker, M C; Pourquié, M J B M; Eskin, D G; Boersma, B J

2013-01-01

The flow in a confined container induced by an ultrasonic horn is measured by Particle Image Velocimetry (PIV). This flow is caused by acoustic streaming and highly influenced by the presence of cavitation. The jet-like experimentally observed flow is compared with the available theoretical solution for a turbulent free round jet. The similarity between both flows enables a simplified numerical model to be made, whilst the phenomenon is very difficult to simulate otherwise. The numerical model requires only two parameters, i.e. the flow momentum and turbulent kinetic energy at the position of the horn tip. The simulated flow is used as a basis for the calculation of the time required for the entire liquid volume to pass through the active cavitation region. Copyright © 2012 Elsevier B.V. All rights reserved.

Noninvariance of Space and Time Scale Ranges under a Lorentz Transformation and the Implications for the Numerical Study of Relativistic Systems

International Nuclear Information System (INIS)

Vay, J.-L.; Vay, J.-L.

2007-01-01

We present an analysis which shows that the ranges of space and time scales spanned by a system are not invariant under the Lorentz transformation. This implies the existence of a frame of reference which minimizes an aggregate measure of the range of space and time scales. Such a frame is derived for example cases: free electron laser, laser-plasma accelerator, and particle beam interacting with electron clouds. Implications for experimental, theoretical and numerical studies are discussed. The most immediate relevance is the reduction by orders of magnitude in computer simulation run times for such systems

Numerical modeling of time-dependent deformation and induced stresses in concrete pipes constructed in Queenston shale using micro-tunneling technique

Directory of Open Access Journals (Sweden)

Hayder Mohammed Salim Al-Maamori

2018-04-01

Full Text Available Effects of time-dependent deformation (TDD on a tunnel constructed using the micro-tunneling technique in Queenston shale (QS are investigated employing the finite element method. The TDD and strength parameters of the QS were measured from tests conducted on QS specimens soaked in water and lubricant fluids (LFs used in micro-tunneling such as bentonite and polymer solutions. The numerical model was verified using the results of TDD tests performed on QS samples, field measurements of some documented projects, and the closed-form solutions to circular tunnels in swelling rock. The verified model was then employed to conduct a parametric study considering important micro-tunneling design parameters, such as depth and diameter of the tunnel, in situ stress ratio (Ko, and the time lapse prior to replacing LFs with permanent cement grout around the tunnel. It was revealed that the time lapse plays a vital role in controlling deformations and associated stresses developed in the tunnel lining. The critical case of a pipe or tunnel in which the maximum tensile stress develops at its springline occurs when it is constructed at shallow depths in the QS layer. The results of the parametric study were used to suggest recommendations for the construction of tunnels in QS employing micro-tunneling. Keywords: Numerical model, Micro-tunneling, Queenston shale (QS, Lubricant fluids (LFs

Numerical solution of ordinary differential equations

CERN Document Server

Fox, L

1987-01-01

Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numeri...

An improved grey model for the prediction of real-time GPS satellite clock bias

Science.gov (United States)

Zheng, Z. Y.; Chen, Y. Q.; Lu, X. S.

2008-07-01

In real-time GPS precise point positioning (PPP), real-time and reliable satellite clock bias (SCB) prediction is a key to implement real-time GPS PPP. It is difficult to hold the nuisance and inenarrable performance of space-borne GPS satellite atomic clock because of its high-frequency, sensitivity and impressionable, it accords with the property of grey model (GM) theory, i. e. we can look on the variable process of SCB as grey system. Firstly, based on limits of quadratic polynomial (QP) and traditional GM to predict SCB, a modified GM (1,1) is put forward to predict GPS SCB in this paper; and then, taking GPS SCB data for example, we analyzed clock bias prediction with different sample interval, the relationship between GM exponent and prediction accuracy, precision comparison of GM to QP, and concluded the general rule of different type SCB and GM exponent; finally, to test the reliability and validation of the modified GM what we put forward, taking IGS clock bias ephemeris product as reference, we analyzed the prediction precision with the modified GM, It is showed that the modified GM is reliable and validation to predict GPS SCB and can offer high precise SCB prediction for real-time GPS PPP.

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.

Composite body movements modulate numerical cognition: Evidence from the motion–numerical compatibility effect

Directory of Open Access Journals (Sweden)

Xiaorong eCheng

2015-11-01

Full Text Available A recent hierarchical model of numerical processing, initiated by Fischer and Brugger (2011 and Fisher (2012, suggested that situated factors, such as different body postures and body movements, can influence the magnitude representation and bias numerical processing. Indeed, Loetscher and colleagues (2008 found that participants’ behavior in a random number generation (RNG task was biased by head rotations. More small numbers were reported after leftward than rightward head turns, i.e. a motion–numerical compatibility effect. Here, by carrying out two experiments, we explored whether similar motion–numerical compatibility effects exist for movements of other important body components, e.g. arms, and for composite body movements as well, which are basis for complex human activities in many ecologically meaningful situations. In Experiment 1, a motion-numerical compatibility effect was observed for lateral rotations of two body components, i.e., the head and arms. Relatively large numbers were reported after making rightward compared to leftward movements for both lateral head and arm turns. The motion-numerical compatibility effect was observed again in Experiment 2 when participants were asked to perform composite body movements of congruent movement directions, e.g., simultaneous head left turns and arm left turns. However, it disappeared when the movement directions were incongruent, e.g., simultaneous head left turns and arm right turns. Taken together, our results extended Loetscher et al.'s (2008 finding by demonstrating that their effect is effector-general and exists for arm movements. Moreover, our study reveals for the first time that the impact of spatial information on numerical processing induced by each of the two sensorimotor-based situated factors, e.g., a lateral head turn and a lateral arm turn, can cancel each other out.

Real-Time Estimation of Volcanic ASH/SO2 Cloud Height from Combined Uv/ir Satellite Observations and Numerical Modeling

Science.gov (United States)

Vicente, Gilberto A.

An efficient iterative method has been developed to estimate the vertical profile of SO2 and ash clouds from volcanic eruptions by comparing near real-time satellite observations with numerical modeling outputs. The approach uses UV based SO2 concentration and IR based ash cloud images, the volcanic ash transport model PUFF and wind speed, height and directional information to find the best match between the simulated and the observed displays. The method is computationally fast and is being implemented for operational use at the NOAA Volcanic Ash Advisory Centers (VAACs) in Washington, DC, USA, to support the Federal Aviation Administration (FAA) effort to detect, track and measure volcanic ash cloud heights for air traffic safety and management. The presentation will show the methodology, results, statistical analysis and SO2 and Aerosol Index input products derived from the Ozone Monitoring Instrument (OMI) onboard the NASA EOS/Aura research satellite and from the Global Ozone Monitoring Experiment-2 (GOME-2) instrument in the MetOp-A. The volcanic ash products are derived from AVHRR instruments in the NOAA POES-16, 17, 18, 19 as well as MetOp-A. The presentation will also show how a VAAC volcanic ash analyst interacts with the system providing initial condition inputs such as location and time of the volcanic eruption, followed by the automatic real-time tracking of all the satellite data available, subsequent activation of the iterative approach and the data/product delivery process in numerical and graphical format for operational applications.

Long-time behavior in numerical solutions of certain dynamical systems

International Nuclear Information System (INIS)

Vazquez, L.

1987-01-01

A general discretization of the ordinary nonlinear differential equations d 2 v/dt 2 =f(v) and dv/dt=g(v) is studied. The discrete scheme conserves the discrete analogous of a quantity that is conserved by the corresponding equations. This method is applied to two cases and no ''ghost solutions'' were observed for the long range calculation. In these cases we analyze the stability of the corresponding numerical scheme as a dynamical system and in the sense studied by Kuo Pen-Yu and Stetter. In particular we find a correspondence between both kinds of stability. (author)

A transit timing analysis with combined ground- and space-based photometry

Directory of Open Access Journals (Sweden)

Raetz St.

2015-01-01

The CoRoT satellite looks back on six years of high precision photometry of a very high number of stars. Thousands of transiting events are detected from which 27 were confirmed to be transiting planets so far. In my research I search and analyze TTVs in the CoRoT sample and combine the unprecedented precision of the light curves with ground-based follow-up photometry. Because CoRoT can observe transiting planets only for a maximum duration of 150 days the ground-based follow-up can help to refine the ephemeris. Here we present first examples.

3-D time-dependent numerical model of flow patterns within a large-scale Czochralski system

Science.gov (United States)

Nam, Phil-Ouk; O, Sang-Kun; Yi, Kyung-Woo

2008-04-01

Silicon single crystals grown through the Czochralski (Cz) method have increased in size to 300 mm, resulting in the use of larger crucibles. The objective of this study is to investigate the continuous Cz method in a large crucible (800 mm), which is performed by inserting a polycrystalline silicon rod into the melt. The numerical model is based on a time-dependent and three-dimensional standard k- ɛ turbulent model using the analytical software package CFD-ACE+, version 2007. Wood's metal melt, which has a low melting point ( Tm=70 °C), was used as the modeling fluid. Crystal rotation given in the clockwise direction with rotation rates varying from 0 to 15 rpm, while the crucible was rotated counter-clockwise, with rotation rates between 0 and 3 rpm. The results show that asymmetrical phenomena of fluid flow arise as results of crystal and crucible rotation, and that these phenomena move with the passage of time. Near the crystal, the flow moves towards the crucible at the pole of the asymmetrical phenomena. Away from the poles, a vortex begins to form, which is strongly pronounced in the region between the poles.

High speed numerical integration algorithm using FPGA | Razak ...

African Journals Online (AJOL)

Conventionally, numerical integration algorithm is executed in software and time consuming to accomplish. Field Programmable Gate Arrays (FPGAs) can be used as a much faster, very efficient and reliable alternative to implement the numerical integration algorithm. This paper proposed a hardware implementation of four ...

Numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1982-01-01

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

A dynamical approach in exploring the unknown mass in the Solar system using pulsar timing arrays

Science.gov (United States)

Guo, Y. J.; Lee, K. J.; Caballero, R. N.

2018-04-01

The error in the Solar system ephemeris will lead to dipolar correlations in the residuals of pulsar timing array for widely separated pulsars. In this paper, we utilize such correlated signals, and construct a Bayesian data-analysis framework to detect the unknown mass in the Solar system and to measure the orbital parameters. The algorithm is designed to calculate the waveform of the induced pulsar-timing residuals due to the unmodelled objects following the Keplerian orbits in the Solar system. The algorithm incorporates a Bayesian-analysis suit used to simultaneously analyse the pulsar-timing data of multiple pulsars to search for coherent waveforms, evaluate the detection significance of unknown objects, and to measure their parameters. When the object is not detectable, our algorithm can be used to place upper limits on the mass. The algorithm is verified using simulated data sets, and cross-checked with analytical calculations. We also investigate the capability of future pulsar-timing-array experiments in detecting the unknown objects. We expect that the future pulsar-timing data can limit the unknown massive objects in the Solar system to be lighter than 10-11-10-12 M⊙, or measure the mass of Jovian system to a fractional precision of 10-8-10-9.

Computer-Aided Numerical Inversion of Laplace Transform

Directory of Open Access Journals (Sweden)

Umesh Kumar

2000-01-01

Full Text Available This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

Introduction to the numerical solutions of Markov chains

CERN Document Server

Stewart, Williams J

1994-01-01

A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse - and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here, Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing metho...

Simulation and Analysis of Autonomous Time Synchronization Based on Asynchronism Two-way Inter-satellite Link

Science.gov (United States)

Fang, L.; Yang, X. H.; Sun, B. Q.; Qin, W. J.; Kong, Y.

2013-09-01

The measurement of the inter-satellite link is one of the key techniques in the autonomous operation of satellite navigation system. Based on the asynchronism inter-satellite two-way measurement mode in GPS constellation, the reduction formula of the inter-satellite time synchronization is built in this paper. Moreover, the corrective method of main systematic errors is proposed. Inter-satellite two-way time synchronization is simulated on the basis of IGS (International GNSS Service) precise ephemeris. The impacts of the epoch domestication of asynchronism inter-satellite link pseudo-range, the initial orbit, and the main systematic errors on satellite time synchronization are analyzed. Furthermore, the broadcast clock error of each satellite is calculated by the ``centralized'' inter-satellite autonomous time synchronization. Simulation results show that the epoch domestication of asynchronism inter-satellite link pseudo-range and the initial orbit have little impact on the satellite clock errors, and thus they needn't be taken into account. The errors caused by the relativistic effect and the asymmetry of path travel have large impact on the satellite clock errors. These should be corrected with theoretical formula. Compared with the IGS precise clock error, the root mean square of the broadcast clock error of each satellite is about 0.4 ns.

The effects of static quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent harmonic frequency: Perturbative analysis and numerical calculations

International Nuclear Information System (INIS)

Sarkar, P.; Bhattacharyya, S.P.

1995-01-01

The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2.4, 6 ... ) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K t . However, it depends upon the rate at which K t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H 0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab

Numerical resolution of the time-domain three-dimensional Maxwell equations by a conform finite element approximation. Part II: numerical results

International Nuclear Information System (INIS)

Heintze, E.

1993-01-01

The aim of this report is to validate the program MAX3D built up from the discretization of the formulation (FB) established in part 1. A qualitative and quantitative analysis is carried out on numerical results obtained with various test cases of which, for most of them, analytical solutions are known. 32 figs., 3 refs

Numerical relativity

CERN Document Server

Shibata, Masaru

2016-01-01

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

Numerical analysis

CERN Document Server

Khabaza, I M

1960-01-01

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

Numerical discrepancy between serial and MPI parallel computations

Directory of Open Access Journals (Sweden)

Sang Bong Lee

2016-09-01

Full Text Available Numerical simulations of 1D Burgers equation and 2D sloshing problem were carried out to study numerical discrepancy between serial and parallel computations. The numerical domain was decomposed into 2 and 4 subdomains for parallel computations with message passing interface. The numerical solution of Burgers equation disclosed that fully explicit boundary conditions used on subdomains of parallel computation was responsible for the numerical discrepancy of transient solution between serial and parallel computations. Two dimensional sloshing problems in a rectangular domain were solved using OpenFOAM. After a lapse of initial transient time sloshing patterns of water were significantly different in serial and parallel computations although the same numerical conditions were given. Based on the histograms of pressure measured at two points near the wall the statistical characteristics of numerical solution was not affected by the number of subdomains as much as the transient solution was dependent on the number of subdomains.

Rework of the ERA software system: ERA-8

Science.gov (United States)

Pavlov, D.; Skripnichenko, V.

2015-08-01

The software system that has been powering many products of the IAA during decades has undergone a major rework. ERA has capabilities for: processing tables of observations of different kinds, fitting parameters to observations, integrating equations of motion of the Solar system bodies. ERA comprises a domain-specific language called SLON, tailored for astronomical tasks. SLON provides a convenient syntax for reductions of observations, choosing of IAU standards to use, applying rules for filtering observations or selecting parameters for fitting. Also, ERA includes a table editor and a graph plotter. ERA-8 has a number of improvements over previous versions such as: integration of the Solar system and TT xA1 TDB with arbitrary number of asteroids; option to use different ephemeris (including DE and INPOP); integrator with 80-bit floating point. The code of ERA-8 has been completely rewritten from Pascal to C (for numerical computations) and Racket (for running SLON programs and managing data). ERA-8 is portable across major operating systems. The format of tables in ERA-8 is based on SQLite. The SPICE format has been chosen as the main format for ephemeris in ERA-8.

TEMPEST: A three-dimensional time-dependent computer program for hydrothermal analysis: Volume 1, Numerical methods and input instructions

International Nuclear Information System (INIS)

Trent, D.S.; Eyler, L.L.; Budden, M.J.

1983-09-01

This document describes the numerical methods, current capabilities, and the use of the TEMPEST (Version L, MOD 2) computer program. TEMPEST is a transient, three-dimensional, hydrothermal computer program that is designed to analyze a broad range of coupled fluid dynamic and heat transfer systems of particular interest to the Fast Breeder Reactor thermal-hydraulic design community. The full three-dimensional, time-dependent equations of motion, continuity, and heat transport are solved for either laminar or turbulent fluid flow, including heat diffusion and generation in both solid and liquid materials. 10 refs., 22 figs., 2 tabs

Numerical and experimental investigations on the time dependent behavior of a salt dome with a high-level waste repository

International Nuclear Information System (INIS)

Prij, J.; Vons, L.H.

1984-01-01

Results are presented of in-situ measurements, performed in a 300 m deep dry-drilled borehole, in the ASSE-mine. Convergence measurements at ambient as well as elevated temperatures and pressure measurements at elevated temperatures are discussed. Creep equations derived from these experiments are used for the numerical analysis of the time dependent behavior of a salt dome with a HLW repository. The analyses show that the total stresses in the salt remain compressive with deviatoric components smaller than 3 MPa. 9 references, 6 figures, 1 table

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)

Formation Number Of Laminar Vortex Rings. Numerical Simulations

International Nuclear Information System (INIS)

Rosenfeld, M.; Rambod, E.; Gharib, M.

1998-01-01

The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the formation number, are confirmed. The formation number is indicative of the time a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found experimentally to be approximately 4. Numerical extension of the experimental study to thick shear layers indicates that the scaled circulation of the pinched-off vortex is relatively insensitive of the details of the formation process, such as the velocity program, velocity profile or vortex generator geometry. In contrast, the formation number does depend on the velocity profile

The Physical Basis of the Leap Second

Science.gov (United States)

2008-10-07

ralentissement du mouvement de rotation de la terre, (Paris: G. Baillière) Explanatory Supplement 1961, Explanatory Supplement to the Astronomical Ephemeris...Beard, R. L., & Bartholomew, T. R. 2001, Metrologia , 38, 509 Newcomb, S. 1895a, Astronomical Papers Prepared for the Use of the American Ephemeris and

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)

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.

Self-similar radiation from numerical Rosenau-Hyman compactons

International Nuclear Information System (INIS)

Rus, Francisco; Villatoro, Francisco R.

2007-01-01

The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically induced radiation, which is illustrated here using four numerical methods applied to the Rosenau-Hyman K(p, p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated graphically by the proper scaling. A grid refinement study shows that the amplitude of the radiations decreases as the grid size does, confirming its numerical origin. The front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters. The amplitude of the radiations decreases exponentially in time, being characterized by a nearly constant scaling exponent. An ansatz for both the backward and forward radiations corresponding to a self-similar function characterized by the scaling exponent is suggested by the present numerical results

Observations of Mars 1950-1976 compared to ephemerides

International Nuclear Information System (INIS)

Duncombe, R.L.; Kubo, Y.

1979-01-01

The present basis for the ephemeris of Mars in the National Ephemerides is the theory of S. Newcomb (1898) as amended by the corrections of Ross (1971). These amendments by Ross, however, are empirical in nature and therefore the present ephemeris of Mars does not have a strictly gravitational basis. In order to provide a gravitationally consistent basis for the ephemeris of Mars, Clemence (1949,1961) constructed a new general perturbation theory based on the final elements of Mars as derived by Newcomb for the epoch 1850. To test the adequacy and accuracy of this new theory, Clemence compared it against 87 observations from 1802-1839 and 1931-1950. This provided provisional values of the constraints (without secular, variation) for his new theory. These provisional elements and Clemence's theory were used to produce a heliocentric ephemeris of Mars for the period 1800-2000 (Duncombe and Clemence 1960, Duncombe 1964). The authors provide a comparison from data between 1950-1976. (Auth.)

Numerical study of fractional nonlinear Schrodinger equations

KAUST Repository

Klein, Christian

2014-10-08

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.

Numerical simulation of single bubble boiling behavior

Directory of Open Access Journals (Sweden)

Junjie Liu

2017-06-01

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

Numerical calculation of two-phase flows

International Nuclear Information System (INIS)

Travis, J.R.; Harlow, F.H.; Amsden, A.A.

1975-06-01

The theoretical study of time-varying two-phase flow problems in several space dimensions introduces such a complicated set of coupled nonlinear partial differential equations that numerical solution procedures for high-speed computers are required in almost all but the simplest examples. Efficient attainment of realistic solutions for practical problems requires a finite- difference formulation that is simultaneously implicit in the treatment of mass convection, equations of state, and the momentum coupling between phases. Such a method is described, the equations on which it is based are discussed, and its properties are illustrated by means of examples. In particular, the capability for calculating physical instabilities and other time-varying dynamics, at the same time avoiding numerical instability is emphasized. The computer code is applicable to problems in reactor safety analysis, the dynamics of fluidized dust beds, raindrops or aerosol transport, and a variety of similar circumstances, including the effects of phase transitions and the release of latent heat or chemical energy. (U.S.)

Numerical studies of the linear theta pinch

International Nuclear Information System (INIS)

Brackbill, J.U.; Menzel, M.T.; Barnes, D.C.

1975-01-01

Aspects of several physical problems associated with linear theta pinches were studied using recently developed numerical methods for the solution of the nonlinear equations for time-dependent magnetohydrodynamic flow in two- and three-dimensions. The problems studied include the propagation of end-loss produced rarefaction waves, the flow produced in a proposed injection experiment geometry, and the linear growth and nonlinear saturation of instabilities in rotating plasmas, all in linear geometries. The studies illustrate how numerical computations aid in flow visualization, and how the small amplitude behavior and nonlinear fate of plasmas in unstable equilibria can be connected through the numerical solution of the dynamical equations. (auth)

Numerical investigations of Z-pinch plasma instabilities

International Nuclear Information System (INIS)

Duan Yaoyong; Guo Yonghui; Wang Wensheng; Qiu Aici

2004-01-01

A two-dimensional, radiation magneto-hydrodynamics model is applied to the simulation of Z-pinch plasma sausage instability. Different implosion mechanisms in the cases of the existence and the non-existence of instability are analyzed, and the effects of various initial density perturbation levels on the x-ray power and energy are investigated. Numerical results show that x-ray energy output is not susceptive to sausage instabilities in a certain extent but x-ray power versus time is evidently dependent on the instabilities. In addition, this paper also studies the effects of numerical treatment of extreme low density in Z-pinch simulations on numerical results

Numerical modeling of time-dependent bio-convective stagnation flow of a nanofluid in slip regime

Directory of Open Access Journals (Sweden)

Rakesh Kumar

Full Text Available A numerical investigation of unsteady stagnation point flow of bioconvective nanofluid due to an exponential deforming surface is made in this research. The effects of Brownian diffusion, thermophoresis, slip velocity and thermal jump are incorporated in the nanofluid model. By utilizing similarity transformations, the highly nonlinear partial differential equations governing present nano-bioconvective boundary layer phenomenon are reduced into ordinary differential system. The resultant expressions are solved for numerical solution by employing a well-known implicit finite difference approach termed as Keller-box method (KBM. The influence of involved parameters (unsteadiness, bioconvection Schmidt number, velocity slip, thermal jump, thermophoresis, Schmidt number, Brownian motion, bioconvection Peclet number on the distributions of velocity, temperature, nanoparticle and motile microorganisms concentrations, the coefficient of local skin-friction, rate of heat transport, Sherwood number and local density motile microorganisms are exhibited through graphs and tables. Keywords: Unsteadiness, Bio-convection, Slip regime, Stagnation point flow, Numerical modeling

Numerical precision control and GRACE

International Nuclear Information System (INIS)

Fujimoto, J.; Hamaguchi, N.; Ishikawa, T.; Kaneko, T.; Morita, H.; Perret-Gallix, D.; Tokura, A.; Shimizu, Y.

2006-01-01

The control of the numerical precision of large-scale computations like those generated by the GRACE system for automatic Feynman diagram calculations has become an intrinsic part of those packages. Recently, Hitachi Ltd. has developed in FORTRAN a new library HMLIB for quadruple and octuple precision arithmetic where the number of lost-bits is made available. This library has been tested with success on the 1-loop radiative correction to e + e - ->e + e - τ + τ - . It is shown that the approach followed by HMLIB provides an efficient way to track down the source of numerical significance losses and to deliver high-precision results yet minimizing computing time

The nitrate time bomb: a numerical way to investigate nitrate storage and lag time in the unsaturated zone.

Science.gov (United States)

Wang, L; Butcher, A S; Stuart, M E; Gooddy, D C; Bloomfield, J P

2013-10-01

Nitrate pollution in groundwater, which is mainly from agricultural activities, remains an international problem. It threatens the environment, economics and human health. There is a rising trend in nitrate concentrations in many UK groundwater bodies. Research has shown it can take decades for leached nitrate from the soil to discharge into groundwater and surface water due to the 'store' of nitrate and its potentially long travel time in the unsaturated and saturated zones. However, this time lag is rarely considered in current water nitrate management and policy development. The aim of this study was to develop a catchment-scale integrated numerical method to investigate the nitrate lag time in the groundwater system, and the Eden Valley, UK, was selected as a case study area. The method involves three models, namely the nitrate time bomb-a process-based model to simulate the nitrate transport in the unsaturated zone (USZ), GISGroundwater--a GISGroundwater flow model, and N-FM--a model to simulate the nitrate transport in the saturated zone. This study answers the scientific questions of when the nitrate currently in the groundwater was loaded into the unsaturated zones and eventually reached the water table; is the rising groundwater nitrate concentration in the study area caused by historic nitrate load; what caused the uneven distribution of groundwater nitrate concentration in the study area; and whether the historic peak nitrate loading has reached the water table in the area. The groundwater nitrate in the area was mainly from the 1980s to 2000s, whilst the groundwater nitrate in most of the source protection zones leached into the system during 1940s-1970s; the large and spatially variable thickness of the USZ is one of the major reasons for unevenly distributed groundwater nitrate concentrations in the study area; the peak nitrate loading around 1983 has affected most of the study area. For areas around the Bowscar, Beacon Edge, Low Plains, Nord Vue

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

Science.gov (United States)

Kou, Baoquan; Xing, Feng; Zhang, Lu; Zhou, Yiheng; Liu, Jiaqi

2017-05-01

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 processing of ultrasonic holographic data

International Nuclear Information System (INIS)

Langenberg, K.J.; Kiefer, R.; Wosnitza, M.; Schmitz, V.; Fraunhofer-Gesellschaft zur Foerderung der Angewandten Forschung e.V., Saarbruecken

1980-01-01

Reconstructing ultrasonic holographic data numerically, the well-known Fresnel approximation is a first step in evaluating the Rayleigh-Sommerfeld diffraction formula, that is to say, a one- or two-dimensional Fourier-transform of the holographic data multiplied by a complex phase factor has to be computed. The present contribution investigates the relation between flaw depth and aperture size yielding the more advantageous use of the spatial frequency approach where the advantage is in terms of the number of samples and hence computation time in evaluating Fourier transforms numerically. (orig.) [de

Comment on 'Shang S. 2012. Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step. Hydrological Processes 26: 3338-3343. DOI: 10.1002/hyp.8405'

Science.gov (United States)

Yatheendradas, Soni; Narapusetty, Balachandrudu; Peters-Lidard, Christa; Funk, Christopher; Verdin, James

2014-01-01

A previous study analyzed errors in the numerical calculation of actual crop evapotranspiration (ET(sub a)) under soil water stress. Assuming no irrigation or precipitation, it constructed equations for ET(sub a) over limited soil-water ranges in a root zone drying out due to evapotranspiration. It then used a single crop-soil composite to provide recommendations about the appropriate usage of numerical methods under different values of the time step and the maximum crop evapotranspiration (ET(sub c)). This comment reformulates those ET(sub a) equations for applicability over the full range of soil water values, revealing a dependence of the relative error in numerical ET(sub a) on the initial soil water that was not seen in the previous study. It is shown that the recommendations based on a single crop-soil composite can be invalid for other crop-soil composites. Finally, a consideration of the numerical error in the time-cumulative value of ET(sub a) is discussed besides the existing consideration of that error over individual time steps as done in the previous study. This cumulative ET(sub a) is more relevant to the final crop yield.

Numerical Simulation of the Time Evolution of Small-Scale Irregularities in the F-Layer Ionospheric Plasma

Directory of Open Access Journals (Sweden)

O. V. Mingalev

2011-01-01

Full Text Available Dynamics of magnetic field-aligned small-scale irregularities in the electron concentration, existing in the F-layer ionospheric plasma, is investigated with the help of a mathematical model. The plasma is assumed to be a rarefied compound consisting of electrons and positive ions and being in a strong, external magnetic field. In the applied model, kinetic processes in the plasma are simulated by using the Vlasov-Poisson system of equations. The system of equations is numerically solved applying a macroparticle method. The time evolution of a plasma irregularity, having initial cross-section dimension commensurable with a Debye length, is simulated during the period sufficient for the irregularity to decay completely. The results of simulation indicate that the small-scale irregularity, created initially in the F-region ionosphere, decays accomplishing periodic damped vibrations, with the process being collisionless.

Measuring multi-joint stiffness during single movements: numerical validation of a novel time-frequency approach.

Science.gov (United States)

Piovesan, Davide; Pierobon, Alberto; DiZio, Paul; Lackner, James R

2012-01-01

This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

Measuring multi-joint stiffness during single movements: numerical validation of a novel time-frequency approach.

Directory of Open Access Journals (Sweden)

Davide Piovesan

Full Text Available This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

Numerical differential protection

CERN Document Server

Ziegler, Gerhard

2012-01-01

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

Numerical calculations in elementary quantum mechanics using Feynman path integrals

International Nuclear Information System (INIS)

Scher, G.; Smith, M.; Baranger, M.

1980-01-01

We show that it is possible to do numerical calculations in elementary quantum mechanics using Feynman path integrals. Our method involves discretizing both time and space, and summing paths through matrix multiplication. We give numerical results for various one-dimensional potentials. The calculations of energy levels and wavefunctions take approximately 100 times longer than with standard methods, but there are other problems for which such an approach should be more efficient

Numerical Analysis of Electromagnetic Fields in Multiscale Model

International Nuclear Information System (INIS)

Ma Ji; Fang Guang-You; Ji Yi-Cai

2015-01-01

Modeling technique for electromagnetic fields excited by antennas is an important topic in computational electromagnetics, which is concerned with the numerical solution of Maxwell's equations. In this paper, a novel hybrid technique that combines method of moments (MoM) with finite-difference time-domain (FDTD) method is presented to handle the problem. This approach employed Huygen's principle to realize the hybridization of the two classical numerical algorithms. For wideband electromagnetic data, the interpolation scheme is used in the MoM based on the dyadic Green's function. On the other hand, with the help of equivalence principle, the scattered electric and magnetic fields on the Huygen's surface calculated by MoM are taken as the sources for FDTD. Therefore, the electromagnetic fields in the environment can be obtained by employing finite-difference time-domain method. Finally, numerical results show the validity of the proposed technique by analyzing two canonical samples. (paper)

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.

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...

Numerical Simulation of Partially-Coherent Broadband Optical Imaging Using the FDTD Method

Science.gov (United States)

Çapoğlu, İlker R.; White, Craig A.; Rogers, Jeremy D.; Subramanian, Hariharan; Taflove, Allen; Backman, Vadim

2012-01-01

Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially-coherent and unpolarized illumination. The scattering of light from the sample is calculated using the finite-difference time-domain (FDTD) numerical method. Geometrical optics principles are applied to the scattered light to obtain the intensity distribution at the image plane. Multilayered object spaces are also supported by our algorithm. For the first time, numerical FDTD calculations are directly compared to and shown to agree well with broadband experimental microscopy results. PMID:21540939

Numerical simulation in astrophysics

International Nuclear Information System (INIS)

Miyama, Shoken

1985-01-01

There have been many numerical simulations of hydrodynamical problems in astrophysics, e.g. processes of star formation, supernova explosion and formation of neutron stars, and general relativistic collapse of star to form black hole. The codes are made to be suitable for computing such problems. In astrophysical hydrodynamical problems, there are the characteristics: problems of self-gravity or external gravity acting, objects of scales very large or very short, objects changing by short period or long time scale, problems of magnetic force and/or centrifugal force acting. In this paper, we present one of methods of numerical simulations which may satisfy these requirements, so-called smoothed particle methods. We then introduce the methods briefly. Then, we show one of the applications of the methods to astrophysical problem (fragmentation and collapse of rotating isothermal cloud). (Mori, K.)

A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models

International Nuclear Information System (INIS)

Echard, B.; Gayton, N.; Lemaire, M.; Relun, N.

2013-01-01

Applying reliability methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable method called AK-IS for active learning and Kriging-based Importance Sampling. This new method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the method is, first, proved on two academic applications. It is then conducted for assessing the reliability of a challenging aerospace case study submitted to fatigue.

On the characteristics of a numerical fluid dynamics simulator

International Nuclear Information System (INIS)

Winkler, K.H.A.; Norman, M.L.; Norton, J.L.

1986-01-01

John von Neumann envisioned scientists and mathematicians analyzing and controlling their numerical experiments on nonlinear dynamic systems interactively. The authors describe their concept of a real-time Numerical Fluid Dynamics Simulator NFDS. The authors envision the NFDS to be composed of simulation processors, data storage devices, and image processing devices of extremely high power and capacity, interconnected by very high throughput communication channels. They present individual component performance requirements for both real-time and playback operating modes of the NFDS, using problems of current interest in fluid dynamics as examples. Scaling relations are derived showing the dependence of system requirements on the dimensionality and complexity of the numerical model. The authors conclude by extending their analysis to the system requirements posed in modeling the more involved physics of radiation hydrodynamics

Rossi X-Ray Timing Explorer Observation of PSR B0656+14

International Nuclear Information System (INIS)

Chang, H.; Ho, C.

1999-01-01

PSR B0656+14 was observed by the Rossi X-Ray Timing Explorer (RXTE) with the proportional counter array (PCA) and the high-energy X-ray timing experiment (HEXTE) for 160 ks during 1997 August 22 - September 3. No pulsation was firmly found in the timing analysis, during which the contemporaneous radio ephemeris and various statistical tests were applied in searching for evidence of pulsation. A marginal detection of pulsation at a confidence level of 95.5% based on the H test was found with data in the whole HEXTE energy band. In the energy band of 2-10 keV the RXTE PCA upper limits are about 1 order of magnitude lower than that from ASCA GIS data. If the Compton Gamma Ray Observatory EGRET detection of this pulsar is real, considering the common trait that most EGRET-detected pulsars have a cooling spectrum in hard X-ray and gamma-ray energy bands, the estimated RXTE upper limits indicate a deviation (low-energy turnover) from a cooling spectrum starting from 20 keV or higher. This in turn suggests an outer magnetospheric synchrotron radiation origin for high-energy emissions from PSR B0656+14. The RXTE PCA upper limits also suggest that a reported power-law component based on ASCA SIS data in 1-10 keV fitted jointly with ROSAT data, if real, should be mainly unpulsed. copyright copyright 1999. The American Astronomical Society

Time lens for high-resolution neutron time-of-flight spectrometers

International Nuclear Information System (INIS)

Baumann, K.; Gaehler, R.; Grigoriev, P.; Kats, E.I.

2005-01-01

We examine in analytic and numeric ways the imaging effects of temporal neutron lenses created by traveling magnetic fields. For fields of parabolic shape we derive the imaging equations, investigate the time magnification, the evolution of the phase-space element, the gain factor, and the effect of finite beam size. The main aberration effects are calculated numerically. The system is technologically feasible and should convert neutron time-of-flight instruments from pinhole to imaging configuration in time, thus enhancing intensity and/or time resolution. Further fields of application for high-resolution spectrometry may be opened

Examples of the nonlinear dynamics of ballistic capture and escape in the earth-moon system

Science.gov (United States)

Belbruno, Edward A.

1990-01-01

An example of a trajectory is given which is initially captured in an elliptic resonant orbit about the earth and then ballistically escapes the earth-moon system. This is demonstrated by a numerical example in three-dimensions using a planetary ephemeris. Another example shows a mechanism of how an elliptic orbit about the earth can increase its energy by performing a complex nonlinear transition to an elliptic orbit of a larger semi-major axis. Capture is also considered. An application of ballistic capture at the moon via an unstable periodic orbit using the four-body sun-earth-moon-S/C interaction is described.

Numerical investigations of gravitational collapse

Energy Technology Data Exchange (ETDEWEB)

Csizmadia, Peter; Racz, Istvan, E-mail: iracz@rmki.kfki.h [RMKI, Budapest, Konkoly Thege Miklos ut 29-33, H-1121 (Hungary)

2010-03-01

Some properties of a new framework for simulating generic 4-dimensional spherically symmetric gravitating systems are discussed. The framework can be used to investigate spacetimes that undergo complete gravitational collapse. The analytic setup is chosen to ensure that our numerical method is capable to follow the time evolution everywhere, including the black hole region.

Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

Energy Technology Data Exchange (ETDEWEB)

Klein, R I; Stone, J M

2007-11-20

We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.

Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

International Nuclear Information System (INIS)

Klein, R I; Stone, J M

2007-01-01

We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments

Abort Options for Human Missions to Earth-Moon Halo Orbits

Science.gov (United States)

Jesick, Mark C.

2013-01-01

Abort trajectories are optimized for human halo orbit missions about the translunar libration point (L2), with an emphasis on the use of free return trajectories. Optimal transfers from outbound free returns to L2 halo orbits are numerically optimized in the four-body ephemeris model. Circumlunar free returns are used for direct transfers, and cislunar free returns are used in combination with lunar gravity assists to reduce propulsive requirements. Trends in orbit insertion cost and flight time are documented across the southern L2 halo family as a function of halo orbit position and free return flight time. It is determined that the maximum amplitude southern halo incurs the lowest orbit insertion cost for direct transfers but the maximum cost for lunar gravity assist transfers. The minimum amplitude halo is the most expensive destination for direct transfers but the least expensive for lunar gravity assist transfers. The on-orbit abort costs for three halos are computed as a function of abort time and return time. Finally, an architecture analysis is performed to determine launch and on-orbit vehicle requirements for halo orbit missions.

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.

Hybrid TE-TM scheme for time domain numerical calculations of wakefields in structures with walls of finite conductivity

Directory of Open Access Journals (Sweden)

Andranik Tsakanian

2012-05-01

Full Text Available In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.

A numerical algorithm to evaluate the transient response for a synchronous scanning streak camera using a time-domain Baum–Liu–Tesche equation

Energy Technology Data Exchange (ETDEWEB)

Pei, Chengquan [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi’an 710049 (China); Tian, Jinshou [Xi' an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi' an 710119 (China); Wu, Shengli, E-mail: slwu@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi’an 710049 (China); He, Jiai [School of Computer and Communication, Lanzhou University of Technology, Lanzhou, Gansu 730050 (China); Liu, Zhen [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi’an 710049 (China)

2016-10-01

The transient response is of great influence on the electromagnetic compatibility of synchronous scanning streak cameras (SSSCs). In this paper we propose a numerical method to evaluate the transient response of the scanning deflection plate (SDP). First, we created a simplified circuit model for the SDP used in an SSSC, and then derived the Baum–Liu–Tesche (BLT) equation in the frequency domain. From the frequency-domain BLT equation, its transient counterpart was derived. These parameters, together with the transient-BLT equation, were used to compute the transient load voltage and load current, and then a novel numerical method to fulfill the continuity equation was used. Several numerical simulations were conducted to verify this proposed method. The computed results were then compared with transient responses obtained by a frequency-domain/fast Fourier transform (FFT) method, and the accordance was excellent for highly conducting cables. The benefit of deriving the BLT equation in the time domain is that it may be used with slight modifications to calculate the transient response and the error can be controlled by a computer program. The result showed that the transient voltage was up to 1000 V and the transient current was approximately 10 A, so some protective measures should be taken to improve the electromagnetic compatibility.

A numerical algorithm to evaluate the transient response for a synchronous scanning streak camera using a time-domain Baum–Liu–Tesche equation

International Nuclear Information System (INIS)

Pei, Chengquan; Tian, Jinshou; Wu, Shengli; He, Jiai; Liu, Zhen

2016-01-01

The transient response is of great influence on the electromagnetic compatibility of synchronous scanning streak cameras (SSSCs). In this paper we propose a numerical method to evaluate the transient response of the scanning deflection plate (SDP). First, we created a simplified circuit model for the SDP used in an SSSC, and then derived the Baum–Liu–Tesche (BLT) equation in the frequency domain. From the frequency-domain BLT equation, its transient counterpart was derived. These parameters, together with the transient-BLT equation, were used to compute the transient load voltage and load current, and then a novel numerical method to fulfill the continuity equation was used. Several numerical simulations were conducted to verify this proposed method. The computed results were then compared with transient responses obtained by a frequency-domain/fast Fourier transform (FFT) method, and the accordance was excellent for highly conducting cables. The benefit of deriving the BLT equation in the time domain is that it may be used with slight modifications to calculate the transient response and the error can be controlled by a computer program. The result showed that the transient voltage was up to 1000 V and the transient current was approximately 10 A, so some protective measures should be taken to improve the electromagnetic compatibility.

Playing Linear Numerical Board Games Promotes Low-Income Children's Numerical Development

Science.gov (United States)

Siegler, Robert S.; Ramani, Geetha B.

2008-01-01

The numerical knowledge of children from low-income backgrounds trails behind that of peers from middle-income backgrounds even before the children enter school. This gap may reflect differing prior experience with informal numerical activities, such as numerical board games. Experiment 1 indicated that the numerical magnitude knowledge of…

Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations

Science.gov (United States)

Liang, Fayun; Chen, Haibing; Huang, Maosong

2017-07-01

To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

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.

THE BENEFITS OF VLBI ASTROMETRY TO PULSAR TIMING ARRAY SEARCHES FOR GRAVITATIONAL RADIATION

Energy Technology Data Exchange (ETDEWEB)

Madison, D. R.; Chatterjee, S.; Cordes, J. M. [Department of Astronomy and Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14850 (United States)

2013-11-10

Precision astrometry is an integral component of successful pulsar timing campaigns. Astrometric parameters are commonly derived by fitting them as parameters of a timing model to a series of pulse times of arrival (TOAs). TOAs measured to microsecond precision over spans of several years can yield position measurements with sub-milliarcsecond precision. However, timing-based astrometry can become biased if a pulsar displays any red spin noise or a red signal produced by the stochastic gravitational wave background. We investigate how noise of different spectral types is absorbed by timing models, leading to significant estimation biases in the astrometric parameters. We find that commonly used techniques for fitting timing models in the presence of red noise (Cholesky whitening) prevent the absorption of noise into the timing model remarkably well if the time baseline of observations exceeds several years, but are inadequate for dealing with shorter pulsar data sets. Independent of timing, pulsar-optimized very long baseline interferometry (VLBI) is capable of providing position estimates precise to the sub-milliarcsecond levels needed for high-precision timing. In order to make VLBI astrometric parameters useful in pulsar timing models, the transformation between the International Celestial Reference Frame (ICRF) and the dynamical solar system ephemeris used for pulsar timing must be constrained to within a few microarcseconds. We compute a transformation between the ICRF and pulsar timing frames and quantitatively discuss how the transformation will improve in coming years. We find that incorporating VLBI astrometry into the timing models of pulsars for which only a couple of years of timing data exist will lead to more realistic assessments of red spin noise and could enhance the amplitude of gravitational wave signatures in post-fit timing residuals by factors of 20 or more.

Identification of Genetic Loci Jointly Influencing Schizophrenia Risk and the Cognitive Traits of Verbal-Numerical Reasoning, Reaction Time, and General Cognitive Function.

Science.gov (United States)

Smeland, Olav B; Frei, Oleksandr; Kauppi, Karolina; Hill, W David; Li, Wen; Wang, Yunpeng; Krull, Florian; Bettella, Francesco; Eriksen, Jon A; Witoelar, Aree; Davies, Gail; Fan, Chun C; Thompson, Wesley K; Lam, Max; Lencz, Todd; Chen, Chi-Hua; Ueland, Torill; Jönsson, Erik G; Djurovic, Srdjan; Deary, Ian J; Dale, Anders M; Andreassen, Ole A

2017-10-01

Schizophrenia is associated with widespread cognitive impairments. Although cognitive deficits are one of the factors most strongly associated with functional outcome in schizophrenia, current treatment strategies largely fail to ameliorate these impairments. To develop more efficient treatment strategies in patients with schizophrenia, a better understanding of the pathogenesis of these cognitive deficits is needed. Accumulating evidence indicates that genetic risk of schizophrenia may contribute to cognitive dysfunction. To identify genomic regions jointly influencing schizophrenia and the cognitive domains of reaction time and verbal-numerical reasoning, as well as general cognitive function, a phenotype that captures the shared variation in performance across cognitive domains. Combining data from genome-wide association studies from multiple phenotypes using conditional false discovery rate analysis provides increased power to discover genetic variants and could elucidate shared molecular genetic mechanisms. Data from the following genome-wide association studies, published from July 24, 2014, to January 17, 2017, were combined: schizophrenia in the Psychiatric Genomics Consortium cohort (n = 79 757 [cases, 34 486; controls, 45 271]); verbal-numerical reasoning (n = 36 035) and reaction time (n = 111 483) in the UK Biobank cohort; and general cognitive function in CHARGE (Cohorts for Heart and Aging Research in Genomic Epidemiology) (n = 53 949) and COGENT (Cognitive Genomics Consortium) (n = 27 888). Genetic loci identified by conditional false discovery rate analysis. Brain messenger RNA expression and brain expression quantitative trait locus functionality were determined. Among the participants in the genome-wide association studies, 21 loci jointly influencing schizophrenia and cognitive traits were identified: 2 loci shared between schizophrenia and verbal-numerical reasoning, 6 loci shared between schizophrenia and

Numerical analysis of the big bounce in loop quantum cosmology

International Nuclear Information System (INIS)

Laguna, Pablo

2007-01-01

Loop quantum cosmology (LQC) homogeneous models with a massless scalar field show that the big-bang singularity can be replaced by a big quantum bounce. To gain further insight on the nature of this bounce, we study the semidiscrete loop quantum gravity Hamiltonian constraint equation from the point of view of numerical analysis. For illustration purposes, we establish a numerical analogy between the quantum bounces and reflections in finite difference discretizations of wave equations triggered by the use of nonuniform grids or, equivalently, reflections found when solving numerically wave equations with varying coefficients. We show that the bounce is closely related to the method for the temporal update of the system and demonstrate that explicit time-updates in general yield bounces. Finally, we present an example of an implicit time-update devoid of bounces and show back-in-time, deterministic evolutions that reach and partially jump over the big-bang singularity

The solar UV exposure time required for vitamin D3 synthesis in the human body estimated by numerical simulation and observation in Japan

Science.gov (United States)

Nakajima, Hideaki; Miyauchi, Masaatsu; Hirai, Chizuko

2013-04-01

After the discovery of Antarctic ozone hole, the negative effect of exposure of human body to harmful solar ultraviolet (UV) radiation is widely known. However, there is positive effect of exposure to UV radiation, i.e., vitamin D synthesis. Although the importance of solar UV radiation for vitamin D3 synthesis in the human body is well known, the solar exposure time required to prevent vitamin D deficiency has not been well determined. This study attempted to identify the time of solar exposure required for vitamin D3 synthesis in the body by season, time of day, and geographic location (Sapporo, Tsukuba, and Naha, in Japan) using both numerical simulations and observations. According to the numerical simulation for Tsukuba at noon in July under a cloudless sky, 2.3 min of solar exposure are required to produce 5.5 μg vitamin D3 per 600 cm2 skin. This quantity of vitamin D represents the recommended intake for an adult by the Ministry of Health, Labour and Welfare, and the 2010 Japanese Dietary Reference Intakes (DRIs). In contrast, it took 49.5 min to produce the same amount of vitamin D3 at Sapporo in the northern part of Japan in December, at noon under a cloudless sky. The necessary exposure time varied considerably with the time of the day. For Tsukuba at noon in December, 14.5 min were required, but at 09:00 68.7 min were required and at 15:00 175.8 min were required for the same meteorological conditions. Naha receives high levels of UV radiation allowing vitamin D3 synthesis almost throughout the year. According to our results, we are further developing an index to quantify the necessary time of UV radiation exposure to produce required amount of vitamin D3 from a UV radiation data.

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

Direct numerical methods of mathematical modeling in mechanical structural design

International Nuclear Information System (INIS)

Sahili, Jihad; Verchery, Georges; Ghaddar, Ahmad; Zoaeter, Mohamed

2002-01-01

Full text.Structural design and numerical methods are generally interactive; requiring optimization procedures as the structure is analyzed. This analysis leads to define some mathematical terms, as the stiffness matrix, which are resulting from the modeling and then used in numerical techniques during the dimensioning procedure. These techniques and many others involve the calculation of the generalized inverse of the stiffness matrix, called also the 'compliance matrix'. The aim of this paper is to introduce first, some different existing mathematical procedures, used to calculate the compliance matrix from the stiffness matrix, then apply direct numerical methods to solve the obtained system with the lowest computational time, and to compare the obtained results. The results show a big difference of the computational time between the different procedures

Prediction of the time course of callus stiffness as a function of mechanical parameters in experimental rat fracture healing studies--a numerical study.

Directory of Open Access Journals (Sweden)

Tim Wehner

Full Text Available Numerous experimental fracture healing studies are performed on rats, in which different experimental, mechanical parameters are applied, thereby prohibiting direct comparison between each other. Numerical fracture healing simulation models are able to predict courses of fracture healing and offer support for pre-planning animal experiments and for post-hoc comparison between outcomes of different in vivo studies. The aims of this study are to adapt a pre-existing fracture healing simulation algorithm for sheep and humans to the rat, to corroborate it using the data of numerous different rat experiments, and to provide healing predictions for future rat experiments. First, material properties of different tissue types involved were adjusted by comparing experimentally measured callus stiffness to respective simulated values obtained in three finite element (FE models. This yielded values for Young's moduli of cortical bone, woven bone, cartilage, and connective tissue of 15,750 MPa, 1,000 MPa, 5 MPa, and 1 MPa, respectively. Next, thresholds in the underlying mechanoregulatory tissue differentiation rules were calibrated by modifying model parameters so that predicted fracture callus stiffness matched experimental data from a study that used rigid and flexible fixators. This resulted in strain thresholds at higher magnitudes than in models for sheep and humans. The resulting numerical model was then used to simulate numerous fracture healing scenarios from literature, showing a considerable mismatch in only 6 of 21 cases. Based on this corroborated model, a fit curve function was derived which predicts the increase of callus stiffness dependent on bodyweight, fixation stiffness, and fracture gap size. By mathematically predicting the time course of the healing process prior to the animal studies, the data presented in this work provides support for planning new fracture healing experiments in rats. Furthermore, it allows one to transfer and

Multi-hump potentials for efficient wave absorption in the numerical solution of the time-dependent Schrödinger equation

Science.gov (United States)

Silaev, A. A.; Romanov, A. A.; Vvedenskii, N. V.

2018-03-01

In the numerical solution of the time-dependent Schrödinger equation by grid methods, an important problem is the reflection and wrap-around of the wave packets at the grid boundaries. Non-optimal absorption of the wave function leads to possible large artifacts in the results of numerical simulations. We propose a new method for the construction of the complex absorbing potentials for wave suppression at the grid boundaries. The method is based on the use of the multi-hump imaginary potential which contains a sequence of smooth and symmetric humps whose widths and amplitudes are optimized for wave absorption in different spectral intervals. We show that this can ensure a high efficiency of absorption in a wide range of de Broglie wavelengths, which includes wavelengths comparable to the width of the absorbing layer. Therefore, this method can be used for high-precision simulations of various phenomena where strong spreading of the wave function takes place, including the phenomena accompanying the interaction of strong fields with atoms and molecules. The efficiency of the proposed method is demonstrated in the calculation of the spectrum of high-order harmonics generated during the interaction of hydrogen atoms with an intense infrared laser pulse.

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.

Numerical analysis in electromagnetics the TLM method

CERN Document Server

Saguet, Pierre

2013-01-01

The aim of this book is to give a broad overview of the TLM (Transmission Line Matrix) method, which is one of the "time-domain numerical methods". These methods are reputed for their significant reliance on computer resources. However, they have the advantage of being highly general.The TLM method has acquired a reputation for being a powerful and effective tool by numerous teams and still benefits today from significant theoretical developments. In particular, in recent years, its ability to simulate various situations with excellent precision, including complex materials, has been

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.

Two dimensional numerical simulations of carrier dynamics during time-resolved photoluminescence decays in two-photon microscopy measurements in semiconductors

International Nuclear Information System (INIS)

Kanevce, Ana; Kuciauskas, Darius; Levi, Dean H.; Johnston, Steven W.; Allende Motz, Alyssa M.

2015-01-01

We use two-dimensional numerical simulations to analyze high spatial resolution time-resolved spectroscopy data. This analysis is applied to two-photon excitation time-resolved photoluminescence (2PE-TRPL) but is broadly applicable to all microscopic time-resolved techniques. By solving time-dependent drift-diffusion equations, we gain insight into carrier dynamics and transport characteristics. Accurate understanding of measurement results establishes the limits and potential of the measurement and enhances its value as a characterization method. Diffusion of carriers outside of the collection volume can have a significant impact on the measured decay but can also provide an estimate of carrier mobility as well as lifetime. In addition to material parameters, the experimental conditions, such as spot size and injection level, can impact the measurement results. Although small spot size provides better resolution, it also increases the impact of diffusion on the decay; if the spot size is much smaller than the diffusion length, it impacts the entire decay. By reproducing experimental 2PE-TRPL decays, the simulations determine the bulk carrier lifetime from the data. The analysis is applied to single-crystal and heteroepitaxial CdTe, material important for solar cells, but it is also applicable to other semiconductors where carrier diffusion from the excitation volume could affect experimental measurements

Numerical modeling of slow shocks

International Nuclear Information System (INIS)

Winske, D.

1987-01-01

This paper reviews previous attempt and the present status of efforts to understand the structure of slow shocks by means of time dependent numerical calculations. Studies carried out using MHD or hybrid-kinetic codes have demonstrated qualitative agreement with theory. A number of unresolved issues related to hybrid simulations of the internal shock structure are discussed in some detail. 43 refs., 8 figs

GNSS global real-time augmentation positioning: Real-time precise satellite clock estimation, prototype system construction and performance analysis

Science.gov (United States)

Chen, Liang; Zhao, Qile; Hu, Zhigang; Jiang, Xinyuan; Geng, Changjiang; Ge, Maorong; Shi, Chuang

2018-01-01

for BeiDou GEO satellites. The real-time positioning results prove that the GPS + BeiDou + Galileo RT-PPP comparing to GPS-only can effectively accelerate convergence time by about 60%, improve the positioning accuracy by about 30% and obtain averaged RMS 4 cm in horizontal and 6 cm in vertical; additionally RT-SPP accuracy in the prototype system can realize positioning accuracy with about averaged RMS 1 m in horizontal and 1.5-2 m in vertical, which are improved by 60% and 70% to SPP based on broadcast ephemeris, respectively.

Numerical solution of High-kappa model of superconductivity

Energy Technology Data Exchange (ETDEWEB)

Karamikhova, R. [Univ. of Texas, Arlington, TX (United States)

1996-12-31

We present formulation and finite element approximations of High-kappa model of superconductivity which is valid in the high {kappa}, high magnetic field setting and accounts for applied magnetic field and current. Major part of this work deals with steady-state and dynamic computational experiments which illustrate our theoretical results numerically. In our experiments we use Galerkin discretization in space along with Backward-Euler and Crank-Nicolson schemes in time. We show that for moderate values of {kappa}, steady states of the model system, computed using the High-kappa model, are virtually identical with results computed using the full Ginzburg-Landau (G-L) equations. We illustrate numerically optimal rates of convergence in space and time for the L{sup 2} and H{sup 1} norms of the error in the High-kappa solution. Finally, our numerical approximations demonstrate some well-known experimentally observed properties of high-temperature superconductors, such as appearance of vortices, effects of increasing the applied magnetic field and the sample size, and the effect of applied constant current.

Numerical Methods for a Class of Differential Algebraic Equations

Directory of Open Access Journals (Sweden)

Lei Ren

2017-01-01

Full Text Available This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs. At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs.

Period, epoch, and prediction errors of ephemerides from continuous sets of timing measurements

Science.gov (United States)

Deeg, H. J.

2015-06-01

Space missions such as Kepler and CoRoT have led to large numbers of eclipse or transit measurements in nearly continuous time series. This paper shows how to obtain the period error in such measurements from a basic linear least-squares fit, and how to correctly derive the timing error in the prediction of future transit or eclipse events. Assuming strict periodicity, a formula for the period error of these time series is derived, σP = σT (12 / (N3-N))1 / 2, where σP is the period error, σT the timing error of a single measurement, and N the number of measurements. Compared to the iterative method for period error estimation by Mighell & Plavchan (2013), this much simpler formula leads to smaller period errors, whose correctness has been verified through simulations. For the prediction of times of future periodic events, usual linear ephemeris were epoch errors are quoted for the first time measurement, are prone to an overestimation of the error of that prediction. This may be avoided by a correction for the duration of the time series. An alternative is the derivation of ephemerides whose reference epoch and epoch error are given for the centre of the time series. For long continuous or near-continuous time series whose acquisition is completed, such central epochs should be the preferred way for the quotation of linear ephemerides. While this work was motivated from the analysis of eclipse timing measures in space-based light curves, it should be applicable to any other problem with an uninterrupted sequence of discrete timings for which the determination of a zero point, of a constant period and of the associated errors is needed.

Numerical simulation of onshore separation processes - residence time optimization

Energy Technology Data Exchange (ETDEWEB)

Fonte, Clarissa Bergman; Oliveira Junior, Joao Americo Aguirre [Engineering Simulation and Scientific Software (ESSS), Florianopolis, SC (Brazil)], E-mails: clarissa@esss.com.br, joao.aguirre@esss.com.br; Dutra, Eduardo Stein Soares [PETROBRAS E e P Engenharia de Producao, Rio de Janeiro, RJ (Brazil). Gerencia de Engenharia de Instalacoes de Superficie e Automacao], E-mail: eduardodutra@petrobras.com.br

2011-04-15

Cylindrical tanks are commonly used in onshore facilities to process and treat oil and water streams. These tanks generate a gravitational separation and, when sedimentation velocity is reached, the residence time inside the tank is crucial to guarantee proper separation. The ideal geometry for a tank maximizes the effective residence time by providing the largest possible fluid path, along which sedimentation of the denser phase occurs. Large volume tanks can be used for this purpose. However, internal devices, which increase the effective residence time and decrease undesirable hydrodynamic effects, are a commonly used alternative, allowing a reduction in tank size. This study focuses on the application of computational fluid dynamics as a tool to analyze four geometries found in gravitational separation tanks to identify that which offers the highest residence time values. (author)

Numerical shaping of the ultrasonic wavelet

International Nuclear Information System (INIS)

Bonis, M.

1991-01-01

Improving the performance and the quality of ultrasonic testing requires the numerical control of the shape of the driving signal applied to the piezoelectric transducer. This allows precise shaping of the ultrasonic field wavelet and corrections for the physical defects of the transducer, which are mainly due to the damper or the lens. It also does away with the need for an accurate electric matching. It then becomes feasible to characterize, a priori, the ultrasonic wavelet by means of temporal and/or spectral specifications and to use, subsequently, an adaptative algorithm to calculate the corresponding driving wavelet. Moreover, the versatility resulting from the numerical control of this wavelet allows it to be changed in real time during a test

Dynamic load synthesis for shock numerical simulation in space structure design

Science.gov (United States)

Monti, Riccardo; Gasbarri, Paolo

2017-08-01

Pyroshock loads are the most stressing environments that a space equipment experiences during its operating life from a mechanical point of view. In general, the mechanical designer considers the pyroshock analysis as a very demanding constraint. Unfortunately, due to the non-linear behaviour of the structure under such loads, only the experimental tests can demonstrate if it is able to withstand these dynamic loads. By taking all the previous considerations into account, some preliminary information about the design correctness could be done by performing ;ad-hoc; numerical simulations, for example via commercial finite element software (i.e. MSC Nastran). Usually these numerical tools face the shock solution in two ways: 1) a direct mode, by using a time dependent enforcement and by evaluating the time-response and space-response as well as the internal forces; 2) a modal basis approach, by considering a frequency dependent load and of course by evaluating internal forces in the frequency domain. This paper has the main aim to develop a numerical tool to synthetize the time dependent enforcement based on deterministic and/or genetic algorithm optimisers. In particular starting from a specified spectrum in terms of SRS (Shock Response Spectrum) a time dependent discrete function, typically an acceleration profile, will be obtained to force the equipment by simulating the shock event. The synthetizing time and the interface with standards numerical codes will be two of the main topics dealt with in the paper. In addition a congruity and consistency methodology will be presented to ensure that the identified time dependent loads fully match the specified spectrum.

No variations in transit times for Qatar-1 b

Science.gov (United States)

Maciejewski, G.; Fernández, M.; Aceituno, F. J.; Ohlert, J.; Puchalski, D.; Dimitrov, D.; Seeliger, M.; Kitze, M.; Raetz, St.; Errmann, R.; Gilbert, H.; Pannicke, A.; Schmidt, J.-G.; Neuhäuser, R.

2015-05-01

Aims: The transiting hot-Jupiter planet Qatar-1 b exhibits variations in transit times that could be perturbative. A hot Jupiter with a planetary companion on a nearby orbit would constitute an unprecedented planetary configuration, which is important for theories of the formation and evolution of planetary systems. We performed a photometric follow-up campaign to confirm or refute transit timing variations. Methods: We extend the baseline of transit observations by acquiring 18 new transit light curves acquired with 0.6-2.0 m telescopes. These photometric time series, together with data available in the literature, were analyzed in a homogenous way to derive reliable transit parameters and their uncertainties. Results: We show that the dataset of transit times is consistent with a linear ephemeris leaving no hint of any periodic variations with a range of 1 min. We find no compelling evidence of a close-in planetary companion to Qatar-1 b. This finding is in line with a paradigm that hot Jupiters are not components of compact multiplanetary systems. Based on dynamical simulations, we place tighter constraints on the mass of any fictitious nearby planet in the system. Furthermore, new transit light curves allowed us to redetermine system parameters with better precision than reported in previous studies. Our values generally agree with previous determinations. Partly based on (1) data collected with telescopes at the Rozhen National Astronomical Observatory and (2) observations obtained with telescopes of the University Observatory Jena, which is operated by the Astrophysical Institute of the Friedrich-Schiller-University.Tables of light curve data are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/577/A109

Time-domain numerical computations of electromagnetic fields in cylindrical co-ordinates using the transmission line matrix: evaluation of radiaion losses from a charge bunch passing through a pill-box resonator

International Nuclear Information System (INIS)

Sarma, J.; Robson, P.N.

1979-01-01

The two dimensional transmission line matrix (TLM) numerical method has been adapted to compute electromagnetic field distributions in cylindrical co-ordinates and it is applied to evaluate the radiation loss from a charge bunch passing through a 'pill-box' resonator. The computer program has been developed to calculate not only the total energy loss to the resonator but also that component of it which exists in the TM 010 mode. The numerically computed results are shown to agree very well with the analytically derived values as found in the literature which, therefore, established the degree of accuracy that is obtained with the TLM method. The particular features of computational simplicity, numerical stability and the inherently time-domain solutions produced by the TLM method are cited as additional, attractive reasons for using this numerical procedure in solving such problems. (Auth.)

Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling

Science.gov (United States)

Dobronets, B. S.; Popova, O. A.

2018-05-01

Data aggregation issues for numerical modeling are reviewed in the present study. The authors discuss data aggregation procedures as preprocessing for subsequent numerical modeling. To calculate the data aggregation, the authors propose using numerical probabilistic analysis (NPA). An important feature of this study is how the authors represent the aggregated data. The study shows that the offered approach to data aggregation can be interpreted as the frequency distribution of a variable. To study its properties, the density function is used. For this purpose, the authors propose using the piecewise polynomial models. A suitable example of such approach is the spline. The authors show that their approach to data aggregation allows reducing the level of data uncertainty and significantly increasing the efficiency of numerical calculations. To demonstrate the degree of the correspondence of the proposed methods to reality, the authors developed a theoretical framework and considered numerical examples devoted to time series aggregation.

Numerical analysis

CERN Document Server

Scott, L Ridgway

2011-01-01

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

Design of heat exchangers by numerical methods

International Nuclear Information System (INIS)

Konuk, A.A.

1981-01-01

Differential equations describing the heat tranfer in shell - and tube heat exchangers are derived and solved numerically. The method of ΔT sub(lm) is compared with the proposed method in cases where the specific heat at constant pressure, Cp and the overall heat transfer coefficient, U, vary with temperature. The error of the method of ΔT sub (lm) for the computation of the exchanger lenght is less than + 10%. However, the numerical method, being more accurate and at the same time easy to use and economical, is recommended for the design of shell-and-tube heat exchangers. (Author) [pt

A Numerical Study of Quantization-Based Integrators

Directory of Open Access Journals (Sweden)

Barros Fernando

2014-01-01

Full Text Available Adaptive step size solvers are nowadays considered fundamental to achieve efficient ODE integration. While, traditionally, ODE solvers have been designed based on discrete time machines, new approaches based on discrete event systems have been proposed. Quantization provides an efficient integration technique based on signal threshold crossing, leading to independent and modular solvers communicating through discrete events. These solvers can benefit from the large body of knowledge on discrete event simulation techniques, like parallelization, to obtain efficient numerical integration. In this paper we introduce new solvers based on quantization and adaptive sampling techniques. Preliminary numerical results comparing these solvers are presented.

Decoupled Scheme for Time-Dependent Natural Convection Problem II: Time Semidiscreteness

Directory of Open Access Journals (Sweden)

Tong Zhang

2014-01-01

stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem.

Nonspinning numerical relativity waveform surrogates: assessing the model

Science.gov (United States)

Field, Scott; Blackman, Jonathan; Galley, Chad; Scheel, Mark; Szilagyi, Bela; Tiglio, Manuel

2015-04-01

Recently, multi-modal gravitational waveform surrogate models have been built directly from data numerically generated by the Spectral Einstein Code (SpEC). I will describe ways in which the surrogate model error can be quantified. This task, in turn, requires (i) characterizing differences between waveforms computed by SpEC with those predicted by the surrogate model and (ii) estimating errors associated with the SpEC waveforms from which the surrogate is built. Both pieces can have numerous sources of numerical and systematic errors. We make an attempt to study the most dominant error sources and, ultimately, the surrogate model's fidelity. These investigations yield information about the surrogate model's uncertainty as a function of time (or frequency) and parameter, and could be useful in parameter estimation studies which seek to incorporate model error. Finally, I will conclude by comparing the numerical relativity surrogate model to other inspiral-merger-ringdown models. A companion talk will cover the building of multi-modal surrogate models.

Numerical methods to solve the two-dimensional heat conduction equation

International Nuclear Information System (INIS)

Santos, R.S. dos.

1981-09-01

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

Search across Different Media: Numeric Data Sets and Text Files

Directory of Open Access Journals (Sweden)

Michael Buckland

2006-12-01

Full Text Available Digital technology encourages the hope of searching across and between different media forms (text, sound, image, numeric data. Topic searches are described in two different media: text files and socioeconomic numeric databases and also for transverse searching, whereby retrieved text is used to find topically related numeric data and vice versa. Direct transverse searching across different media is impossible. Descriptive metadata provide enabling infrastructure, but usually require mappings between different vocabularies and a search-term recommender system. Statistical association techniques and natural-language processing can help. Searches in socioeconomic numeric databases ordinarily require that place and time be specified.

On the numerical simulation of tracer flows in porous media

International Nuclear Information System (INIS)

Aquino, J.; Pereira, F.; Amaral Souto, H.P.; Francisco, A.S.

2007-01-01

We discuss in detail a new Lagrangian, locally conservative procedure which has been proposed for the numerical solution of linear transport problems in porous media. The new scheme is computationally efficient, virtually free of numerical diffusion, and can be applied to investigate numerically the time evolution of radionuclide contaminant plumes. Results of two-dimensional simulations of tracer flows will be presented to show the influence on the computed solutions of distinct interpolation functions for evaluating the velocity field at any position of the physical domain, as required by the Lagrangian scheme. (author)

EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY

Energy Technology Data Exchange (ETDEWEB)

FRANCOIS, MARIANNE M. [Los Alamos National Laboratory; DENDY, EDWARD D. [Los Alamos National Laboratory; LOWRIE, ROBERT B. [Los Alamos National Laboratory; LIVESCU, DANIEL [Los Alamos National Laboratory; STEINKAMP, MICHAEL J. [Los Alamos National Laboratory

2007-01-11

The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.

The numerical multiconfiguration self-consistent field approach for atoms

International Nuclear Information System (INIS)

Stiehler, Johannes

1995-12-01

The dissertation uses the Multiconfiguration Self-Consistent Field Approach to specify the electronic wave function of N electron atoms in a static electrical field. It presents numerical approaches to describe the wave functions and introduces new methods to compute the numerical Fock equations. Based on results computed with an implemented computer program the universal application, flexibility and high numerical precision of the presented approach is shown. RHF results and for the first time MCSCF results for polarizabilities and hyperpolarizabilities of various states of the atoms He to Kr are discussed. In addition, an application to interpret a plasma spectrum of gallium is presented. (orig.)

Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

International Nuclear Information System (INIS)

Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi

2015-01-01

Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM

Numerical vs. turbulent diffusion in geophysical flow modelling

International Nuclear Information System (INIS)

D'Isidoro, M.; Maurizi, A.; Tampieri, F.

2008-01-01

Numerical advection schemes induce the spreading of passive tracers from localized sources. The effects of changing resolution and Courant number are investigated using the WAF advection scheme, which leads to a sub-diffusive process. The spreading rate from an instantaneous source is compared with the physical diffusion necessary to simulate unresolved turbulent motions. The time at which the physical diffusion process overpowers the numerical spreading is estimated, and is shown to reduce as the resolution increases, and to increase as the wind velocity increases.

Elements of calculation of reactivity by numerical processing

International Nuclear Information System (INIS)

Hedde, J.

1968-01-01

In order to explore the new opportunities provided by numerical techniques, the author describes the theoretical optimal conditions of a calculation in real time of reactivity from counting samples produced by a nuclear reactor. These optimal conditions can be the better approached if a more complex processing is adopted. A compromise is to be searched between the desired precision and simplicity of the numerical processing hardware. An example is reported to assess result accuracy on a wide power evolution range with a structure of reduced complexity [fr

A new numerical scheme for the simulation of active magnetic regenerators

DEFF Research Database (Denmark)

Torregrosa-Jaime, B.; Engelbrecht, Kurt; Payá, J.

2014-01-01

A 1D model of a parallel-plate active magnetic regenerator (AMR) has been developed based on a new numerical scheme. With respect to the implicit scheme, the new scheme achieves accurate results, minimizes computational time and prevents numerical errors. The model has been used to check the boun...

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…

Numerical Optimization in Microfluidics

DEFF Research Database (Denmark)

Jensen, Kristian Ejlebjærg

2017-01-01

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

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.)

Application of symplectic integrator to numerical fluid analysis

International Nuclear Information System (INIS)

Tanaka, Nobuatsu

2000-01-01

This paper focuses on application of the symplectic integrator to numerical fluid analysis. For the purpose, we introduce Hamiltonian particle dynamics to simulate fluid behavior. The method is based on both the Hamiltonian formulation of a system and the particle methods, and is therefore called Hamiltonian Particle Dynamics (HPD). In this paper, an example of HPD applications, namely the behavior of incompressible inviscid fluid, is solved. In order to improve accuracy of HPD with respect to space, CIVA, which is a highly accurate interpolation method, is combined, but the combined method is subject to problems in that the invariants of the system are not conserved in a long-time computation. For solving the problems, symplectic time integrators are introduced and the effectiveness is confirmed by numerical analyses. (author)

Hindi Numerals.

Science.gov (United States)

Bright, William

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

Comparison of groundwater residence time using isotope techniques and numerical groundwater flow model in Gneissic Terrain, Korea

International Nuclear Information System (INIS)

Bae, D.S.; Kim, C.S.; Koh, Y.K.; Kim, K.S.; Song, M.Y.

1997-01-01

The prediction of groundwater flow affecting the migration of radionuclides is an important component of the performance assessment of radioactive waste disposal. Groundwater flow in fractured rock mass is controlled by fracture networks, transmissivity and hydraulic gradient. Furthermore the scale-dependent and anisotropic properties of hydraulic parameters are resulted mainly from irregular patterns of fracture system, which are very complex to evaluate properly with the current techniques available. For the purpose of characterizing a groundwater flow in fractured rock mass, the discrete fracture network (DFN) concept is available on the basis of assumptions of groundwater flowing only along fractures and flowpaths in rock mass formed by interconnected fractures. To increase the reliability of assessment in groundwater flow phenomena, numerical groundwater flow model and isotopic techniques were applied. Fracture mapping, borehole acoustic scanning were performed to identify conductive fractures in gneissic terrane. Tracer techniques, using deuterium, oxygen-18 and tritium were applied to evaluate the recharge area and groundwater residence time

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)

Methods of numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1983-01-01

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

Numerical modelling of random walk one-dimensional diffusion

International Nuclear Information System (INIS)

Vamos, C.; Suciu, N.; Peculea, M.

1996-01-01

The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies

Strategy for a numerical Rock Mechanics Site Descriptive Model. Further development of the theoretical/numerical approach

International Nuclear Information System (INIS)

Olofsson, Isabelle; Fredriksson, Anders

2005-05-01

The Swedish Nuclear and Fuel Management Company (SKB) is conducting Preliminary Site Investigations at two different locations in Sweden in order to study the possibility of a Deep Repository for spent fuel. In the frame of these Site Investigations, Site Descriptive Models are achieved. These products are the result of an interaction of several disciplines such as geology, hydrogeology, and meteorology. The Rock Mechanics Site Descriptive Model constitutes one of these models. Before the start of the Site Investigations a numerical method using Discrete Fracture Network (DFN) models and the 2D numerical software UDEC was developed. Numerical simulations were the tool chosen for applying the theoretical approach for characterising the mechanical rock mass properties. Some shortcomings were identified when developing the methodology. Their impacts on the modelling (in term of time and quality assurance of results) were estimated to be so important that the improvement of the methodology with another numerical tool was investigated. The theoretical approach is still based on DFN models but the numerical software used is 3DEC. The main assets of the programme compared to UDEC are an optimised algorithm for the generation of fractures in the model and for the assignment of mechanical fracture properties. Due to some numerical constraints the test conditions were set-up in order to simulate 2D plane strain tests. Numerical simulations were conducted on the same data set as used previously for the UDEC modelling in order to estimate and validate the results from the new methodology. A real 3D simulation was also conducted in order to assess the effect of the '2D' conditions in the 3DEC model. Based on the quality of the results it was decided to update the theoretical model and introduce the new methodology based on DFN models and 3DEC simulations for the establishment of the Rock Mechanics Site Descriptive Model. By separating the spatial variability into two parts, one

Time processing in dyscalculia

Directory of Open Access Journals (Sweden)

marinella eCappelletti

2011-12-01

Full Text Available To test whether atypical number development may affect other types of quantity processing, we investigated temporal discrimination in adults with developmental dyscalculia (DD. This also allowed us to test whether (1 number and time may be sub-served by a common quantity system or decision mechanisms –in which case they may both be impaired, or (2 whether number and time are distinct –and therefore they may dissociate. Participants judged which of two successively presented horizontal lines was longer in duration, the first line being preceded by either a small or a large number prime (‘1’ or ‘9’ or by a neutral symbol (‘#’, or in third task decide which of two Arabic numbers (either ‘1’, ‘5’, ’9’ lasted longer. Results showed that (i DD’s temporal discriminability was normal as long as numbers were not part of the experimental design even as task-irrelevant stimuli; however (ii task-irrelevant numbers dramatically disrupted DD’s temporal discriminability, the more their salience increased, though the actual magnitude of the numbers had no effect; and in contrast (iii controls’ time perception was robust to the presence of numbers but modulated by numerical quantity such that small number primes or numerical stimuli made durations appear shorter than veridical and the opposite for larger numerical prime or numerical stimuli. This study is the first to investigate continuous quantity as time in a population with a congenital number impairment and to show that atypical development of numerical competence leaves continuous quantity processing spared. Our data support the idea of a partially shared quantity system across numerical and temporal dimensions, which allows dissociations and interactions among dimensions; furthermore, they suggest that impaired number in DD is unlikely to originate from systems initially dedicated to continuous quantity processing like time.

Cloud-Based Numerical Weather Prediction for Near Real-Time Forecasting and Disaster Response

Science.gov (United States)

Molthan, Andrew; Case, Jonathan; Venners, Jason; Schroeder, Richard; Checchi, Milton; Zavodsky, Bradley; Limaye, Ashutosh; O'Brien, Raymond

2015-01-01

activities in environmental monitoring and prediction across a growing number of regional hubs throughout the world. Capacity-building applications that extend numerical weather prediction to developing countries are intended to provide near real-time applications to benefit public health, safety, and economic interests, but may have a greater impact during disaster events by providing a source for local predictions of weather-related hazards, or impacts that local weather events may have during the recovery phase.

Numerical treatment of the unsteady hydromagnetic thermal boundary layer problem

International Nuclear Information System (INIS)

Drymonitou, M.A.; Geroyannis, V.S.; Goudas, C.L.

1980-01-01

This paper presents a suitable numerical method for the treatment of the unsteady hydromagnetic thermal boundary layer problem for flows past an infinite porous flat plate, the motion of which is governed by a general time-dependent law, under the influence of a transverse externally set magnetic field. The normal velocity of suction/injection at the plate is also assumed to be time-dependent. The results obtained on the basis of numerical approximations seem to compare favourably with earlier results (Pande et al., 1976; Tokis, 1978). Analytical approximations are given for the cases of a plate (i) generally accelerated and (ii) harmonically oscillating. The direct numerical treatment is obviously advantageous since it allows handling of cases where the known methods for analytical approximations are not applicable. This problem is closely related to the motions and heat transfer occurring locally on the surfaces of stars. (orig.)

Three dimensional numerical modeling for ground penetrating radar using finite difference time domain (FDTD) method; Jikan ryoiki yugen sabunho ni yoru chika radar no sanjigen suchi modeling

Energy Technology Data Exchange (ETDEWEB)

Sanada, Y; Ashida, Y; Sassa, K [Kyoto University, Kyoto (Japan)

1996-10-01

3-D numerical modeling by FDTD method was studied for ground penetrating radar. Radar radiates electromagnetic wave, and determines the existence and distance of objects by reflection wave. Ground penetrating radar uses the above functions for underground surveys, however, its resolution and velocity analysis accuracy are problems. In particular, propagation characteristics of electromagnetic wave in media such as heterogeneous and anisotropic soil and rock are essential. The behavior of electromagnetic wave in the ground could be precisely reproduced by 3-D numerical modeling using FDTD method. FDTD method makes precise analysis in time domain and electric and magnetic fields possible by sequentially calculating the difference equation of Maxwell`s equation. Because of the high calculation efficiency of FDTD method, more precise complicated analysis can be expected by using the latest advanced computers. The numerical model and calculation example are illustrated for surface type electromagnetic pulse ground penetrating radar assuming the survey of steel pipes of 1m deep. 4 refs., 3 figs., 1 tab.

The role of similarity in updating numerical information in working memory: decomposing the numerical distance effect.

Science.gov (United States)

Lendínez, Cristina; Pelegrina, Santiago; Lechuga, M Teresa

2014-01-01

The present study investigates the process of updating representations in working memory (WM) and how similarity between the information involved influences this process. In WM updating tasks, the similarity in terms of numerical distance between the number to be substituted and the new one facilitates the updating process. We aimed to disentangle the possible effect of two dimensions of similarity that may contribute to this numerical effect: numerical distance itself and common digits shared between the numbers involved. Three experiments were conducted in which different ranges of distances and the coincidence between the digits of the two numbers involved in updating were manipulated. Results showed that the two dimensions of similarity had an effect on updating times. The greater the similarity between the information maintained in memory and the new information that substituted it, the faster the updating. This is consistent both with the idea of distributed representations based on features, and with a selective updating process based on a feature overwriting mechanism. Thus, updating in WM can be understood as a selective substitution process influenced by similarity in which only certain parts of the representation stored in memory are changed.

Numerical solution of non-linear diffusion problems

International Nuclear Information System (INIS)

Carmen, A. del; Ferreri, J.C.

1998-01-01

This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs

Numerical simulation of fire vortex

Science.gov (United States)

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

2018-05-01

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

Numerical solver for compressible two-fluid flow

NARCIS (Netherlands)

J. Naber (Jorick)

2005-01-01

textabstractThis report treats the development of a numerical solver for the simulation of flows of two non-mixing fluids described by the two-dimensional Euler equations. A level-set equation in conservative form describes the interface. After each time step the deformed level-set function is

Numerical methods for stochastic partial differential equations with white noise

CERN Document Server

Zhang, Zhongqiang

2017-01-01

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...

A numerical investigation of phytoplankton and Pseudocalanus elongatus dynamics in the spring bloom time in the Gdańsk Gulf

Science.gov (United States)

Dzierzbicka-Głowacka, Lidia

2005-01-01

A nutrient-phytoplankton-zooplankton-detritus (1D-NPZD) `phytoplankton {Phyt} and Pseudocalanus elongatus {Zoop} dynamics in the spring bloom time in the Gdańsk Gulf. The 1D-NPZD model consists of three coupled, partial second-order differential equations of the diffusion type for phytoplankton {Phyt}, zooplankton {Zoop}, nutrients {Nutr} and one ordinary first-order differential equation for benthic detritus pool {Detr}, together with initial and boundary conditions. In this model, the {Zoop} is presented by only one species of copepod ( P. elongatus) and {Zoop} is composed of six cohorts of copepods with weights ( Wi) and numbers ( Zi); where Zoop= limit∑i=16W iZ i. The calculations were made for 90 days (March, April, May) for two stations at Gdańsk Gulf with a vertical space step of 0.5m and a time step of 900 s. The flow field and water temperature used as the inputs in the biological model 1D-NPZD were reproduced by the prognostic numerical simulation technique using hydrographic climatological data. The results of the numerical investigations described here were compared with the mean observed values of surface chlorophyll- a and depth integrated P. elongatus biomass for 10 years, 1980-1990. The slight differences between the calculated and mean observed values of surface chlorophyll- a and zooplankton biomass are ca. 10-60 mg C m -3 and ca. 5-23 mg C m -2, respectively, depending on the location of the hydrographic station. The 1D-NPZD model with a high-resolution zooplankton module for P. elongatus can be used to describe the temporal patterns for phytoplankton biomass and P. elongatus in the centre of the Gdańsk Gulf.

Two-fluid Numerical Simulations of Solar Spicules

Energy Technology Data Exchange (ETDEWEB)

Kuźma, Błażej; Murawski, Kris; Kayshap, Pradeep; Wójcik, Darek [Group of Astrophysics, University of Maria Curie-Skłodowska, ul. Radziszewskiego 10, 20-031 Lublin (Poland); Srivastava, Abhishek Kumar; Dwivedi, Bhola N., E-mail: blazejkuzma1@gmail.com [Department of Physics, Indian Institute of Technology (BHU), Varanasi-221005 (India)

2017-11-10

We aim to study the formation and evolution of solar spicules by means of numerical simulations of the solar atmosphere. With the use of newly developed JOANNA code, we numerically solve two-fluid (for ions + electrons and neutrals) equations in 2D Cartesian geometry. We follow the evolution of a spicule triggered by the time-dependent signal in ion and neutral components of gas pressure launched in the upper chromosphere. We use the potential magnetic field, which evolves self-consistently, but mainly plays a passive role in the dynamics. Our numerical results reveal that the signal is steepened into a shock that propagates upward into the corona. The chromospheric cold and dense plasma lags behind this shock and rises into the corona with a mean speed of 20–25 km s{sup −1}. The formed spicule exhibits the upflow/downfall of plasma during its total lifetime of around 3–4 minutes, and it follows the typical characteristics of a classical spicule, which is modeled by magnetohydrodynamics. The simulated spicule consists of a dense and cold core that is dominated by neutrals. The general dynamics of ion and neutral spicules are very similar to each other. Minor differences in those dynamics result in different widths of both spicules with increasing rarefaction of the ion spicule in time.

Finger-Based Numerical Skills Link Fine Motor Skills to Numerical Development in Preschoolers.

Science.gov (United States)

Suggate, Sebastian; Stoeger, Heidrun; Fischer, Ursula

2017-12-01

Previous studies investigating the association between fine-motor skills (FMS) and mathematical skills have lacked specificity. In this study, we test whether an FMS link to numerical skills is due to the involvement of finger representations in early mathematics. We gave 81 pre-schoolers (mean age of 4 years, 9 months) a set of FMS measures and numerical tasks with and without a specific finger focus. Additionally, we used receptive vocabulary and chronological age as control measures. FMS linked more closely to finger-based than to nonfinger-based numerical skills even after accounting for the control variables. Moreover, the relationship between FMS and numerical skill was entirely mediated by finger-based numerical skills. We concluded that FMS are closely related to early numerical skill development through finger-based numerical counting that aids the acquisition of mathematical mental representations.

Numerical solution of dynamic equilibrium models under Poisson uncertainty

DEFF Research Database (Denmark)

Posch, Olaf; Trimborn, Timo

2013-01-01

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retar...... solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households....

Numerical methods for axisymmetric and 3D nonlinear beams

Science.gov (United States)

Pinton, Gianmarco F.; Trahey, Gregg E.

2005-04-01

Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.

A Space-Time Finite Element Approach to the Numerical Simulation of Vascular Fluid-Solid Interaction

NARCIS (Netherlands)

Vlijm, E.J.; Van Brummelen, E.H.

2008-01-01

Numerical studies of cardiovascular diseases like arteriosclerosis have gained increasing attention the last decade. The modeling of blood, blood vessel and their coupling, shows to be a challenging problem. In this thesis a two-dimensional model has been constructed and its behaviour has been

Experimental and Numerical Investigation of Flow Structures around Cylindrical Bluff Bodies

Directory of Open Access Journals (Sweden)

Yagmur Sercan

2015-01-01

Full Text Available The understanding and quantitative prediction of velocity and pressure fluctuations in turbulent flows around such bluff bodies have been evolving over the years. The main aim of the present work is to investigate experimentally and numerically the flow field in the wake region of different bluff bodies such as circular, square and triangle cross section cylinders placed horizontally perpendicular to the uniform flow. The experimental studies were performed by Particle Image Velocimetry (PIV method in an open water channel at Reynolds numbers 5000 and 10000 defined according to the characteristic lengths of the cylinders in the facilities of Selcuk University of Advanced Technology Research and Application Center in Turkey. The experimental results are compared to the numerical results obtained by means of transient simulation with LES turbulence model of ANSYS-Fluent Software. It is shown that the numerical and experimental results have a good agreement in respect of the instantaneous and time-averaged flow field patterns of vorticity, velocity component streamwise direction and streamline topology. In addition, drag coefficient of the geometries were also numerically calculated. For all geometries the wake length in x and y directions and size of the foci of the streamlines are decreasing by increasing Reynolds numbers in time-averaged results. The time-averaged flow patterns of both experimental and numerical results have considerable symmetry with respect to the centerline of each cylinder. Contours of the time-averaged stream wise velocity for Re=10000 demonstrate that the stagnation point around the symmetry plane moves further upstream for all cylinders in accordance with Re=5000. The maximum drag coefficient value was yielded for the square cross-section cylinder as 1.78 due to the sharp-edged geometry.

Numerical method for three dimensional steady-state two-phase flow calculations

International Nuclear Information System (INIS)

Raymond, P.; Toumi, I.

1992-01-01

This paper presents the numerical scheme which was developed for the FLICA-4 computer code to calculate three dimensional steady state two phase flows. This computer code is devoted to steady state and transient thermal hydraulics analysis of nuclear reactor cores 1,3 . The first section briefly describes the FLICA-4 flow modelling. Then in order to introduce the numerical method for steady state computations, some details are given about the implicit numerical scheme based upon an approximate Riemann solver which was developed for calculation of flow transients. The third section deals with the numerical method for steady state computations, which is derived from this previous general scheme and its optimization. We give some numerical results for steady state calculations and comparisons on required CPU time and memory for various meshing and linear system solvers

Black-Hole Binaries, Gravitational Waves, and Numerical Relativity

Science.gov (United States)

Kelly, Bernard J.; Centrella, Joan; Baker, John G.; Kelly, Bernard J.; vanMeter, James R.

2010-01-01

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events ' releasing tremendous amounts of energy in the form of gravitational radiation ' and are key sources for both ground- and spacebased gravitational wave detectors. The black-hole merger dynamics and the resulting gravitational waveforms can only he calculated through numerical simulations of Einstein's equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit cnuld be simulated. Recently ' however, a series of dramatic advances in numerical relativity has ' for the first time, allowed stable / robust black hole merger simulations. We chronicle this remarkable progress in the rapidly maturing field of numerical relativity, and the new understanding of black-hole binary dynamics that is emerging. We also discuss important applications of these fundamental physics results to astrophysics, to gravitationalwave astronomy, and in other areas.

Representation of Numerical and Non-Numerical Order in Children

Science.gov (United States)

Berteletti, Ilaria; Lucangeli, Daniela; Zorzi, Marco

2012-01-01

The representation of numerical and non-numerical ordered sequences was investigated in children from preschool to grade 3. The child's conception of how sequence items map onto a spatial scale was tested using the Number-to-Position task (Siegler & Opfer, 2003) and new variants of the task designed to probe the representation of the alphabet…

Lattice Boltzmann model for numerical relativity.

Science.gov (United States)

Ilseven, E; Mendoza, M

2016-02-01

In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

Towards numerical simulations of supersonic liquid jets using ghost fluid method

International Nuclear Information System (INIS)

Majidi, Sahand; Afshari, Asghar

2015-01-01

Highlights: • A ghost fluid method based solver is developed for numerical simulation of compressible multiphase flows. • The performance of the numerical tool is validated via several benchmark problems. • Emergence of supersonic liquid jets in quiescent gaseous environment is simulated using ghost fluid method for the first time. • Bow-shock formation ahead of the liquid jet is clearly observed in the obtained numerical results. • Radiation of mach waves from the phase-interface witnessed experimentally is evidently captured in our numerical simulations. - Abstract: A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid

Numerical characterization of thermo-mechanical performance of breeder pebble beds

International Nuclear Information System (INIS)

An, Zhiyong; Ying, Alice; Abdou, Mohamed

2007-01-01

A numerical approach using the discrete element method (DEM) has been applied to study the thermo-mechanical properties of ceramic breeder pebble beds. This numerical scheme is able to predict the inelastic behavior observed in a loading and unloading operation. In addition, it demonstrates that the average value of contact force increases linearly with overall pressure, but at a much faster rate, about 3.4 times the overall pressure increase rate. In this paper, the thermal creep properties of two different ceramic breeder pebble materials, Li 4 SiO 4 and Li 2 O, are also examined by the current numerical code. The difference found in the properties of candidate materials is reflected numerically in the overall strain in the pebble bed when the stress magnitude becomes smaller

Numerical characterization of thermo-mechanical performance of breeder pebble beds

International Nuclear Information System (INIS)

An, Zhiyong; Ying, Alice; Abdou, Mohamed

2008-01-01

A numerical approach using the discrete element method (DEM) has been applied to study the thermo-mechanical properties of ceramic breeder pebble beds. This numerical scheme is able to predict the inelastic behavior observed in a loading and unloading operation. In addition, it demonstrates that the average value of contact force increases linearly with overall pressure, but at a much faster rate, about 3.4 times the overall pressure increase rate. In this paper, the thermal creep properties of two different ceramic breeder pebble materials, Li 4 SiO 4 and Li 2 O, are also examined by the current numerical code. The difference found in the properties of candidate materials is reflected numerically in the overall strain in the pebble bed when the stress magnitude becomes smaller. (author)

Mitigation of numerical noise for beam loss simulations

CERN Document Server

Kesting, Frederik

2017-01-01

Numerical noise emerges in self-consistent simulations of charged particles, and its mitigation is investigated since the first numerical studies in plasma physics. In accelerator physics, recent studies find an artificial diffusion of the particle beam due to numerical noise in particle-in-cell tracking, which is of particular importance for high intensity machines with a long storage time, as the SIS100 at FAIR or in context of the LIU upgrade at CERN. In beam loss simulations for these projects artificial effects must be distinguished from physical beam loss. Therefore, it is important to relate artificial diffusion to artificial beam loss, and to choose simulation parameters such that physical beam loss is well resolved. As a practical tool, we therefore suggest a scaling law to find optimal simulation parameters for a given maximum percentage of acceptable artificial beam loss.

Numerical analysis of resonances induced by s wave neutrons in transmission time-of-flight experiments with a computer IBM 7094 II

International Nuclear Information System (INIS)

Corge, Ch.

1969-01-01

Numerical analysis of transmission resonances induced by s wave neutrons in time-of-flight experiments can be achieved in a fairly automatic way on an IBM 7094/II computer. The involved computations are carried out following a four step scheme: 1 - experimental raw data are processed to obtain the resonant transmissions, 2 - values of experimental quantities for each resonance are derived from the above transmissions, 3 - resonance parameters are determined using a least square method to solve the over determined system obtained by equalling theoretical functions to the correspondent experimental values. Four analysis methods are gathered in the same code, 4 - graphical control of the results is performed. (author) [fr

Numerical simulation of trapped dipolar quantum gases: Collapse studies and vortex dynamics

KAUST Repository

Sparber, Christof; Markowich, Peter; Huang, Zhongyi

2010-01-01

We numerically study the three dimensional Gross-Pitaevskii equation for dipolar quantum gases using a time-splitting algorithm. We are mainly concerned with numerical investigations of the possible blow-up of solutions, i.e. collapse of the condensate, and the dynamics of vortices. © American Institute of Mathematical Sciences.

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.

Numerical Prediction of a Bi-Directional Micro Thermal Flow Sensors

Directory of Open Access Journals (Sweden)

M. Al-Amayrah

2011-09-01

Full Text Available Thermal flow sensors such as hot-wire anemometer (HWA can be used to measure the flow velocity with certain accuracy. However, HWA can measure the flow velocity without determining the flow direction. Pulsed-Wire Anemometer (PWA with 3 wires can be used to measure flow velocity and flow directions. The present study aims to develop a numerical analysis of unsteady flow around a pulsed hot-wire anemometer using three parallel wires. The pulsed wire which is called the heated wire is located in the middle and the two sensor wires are installed upstream and downstream of the pulsed wire. 2-D numerical models were built and simulated using different wires arrangements. The ratio of the separation distance between the heated wire and sensor wire (x to the diameter of the heated wire (D ratios (x/D was varied between 3.33 and 183.33. The output results are plotted as a function of Peclet number (convection time / diffusion time. It was found that as the ratio of x/D increases, the sensitivity of PWA device to the time of flight decreases. But at the same the reading of the time of flight becomes more accurate, because the effects of the diffusion and wake after the heated wire decrease. Also, a very good agreement has been obtained between the present numerical simulation and the previous experimental data.

Theory and numerics of gravitational waves from preheating after inflation

International Nuclear Information System (INIS)

Dufaux, Jean-Francois; Kofman, Lev; Bergman, Amanda; Felder, Gary; Uzan, Jean-Philippe

2007-01-01

Preheating after inflation involves large, time-dependent field inhomogeneities, which act as a classical source of gravitational radiation. The resulting spectrum might be probed by direct detection experiments if inflation occurs at a low enough energy scale. In this paper, we develop a theory and algorithm to calculate, analytically and numerically, the spectrum of energy density in gravitational waves produced from an inhomogeneous background of stochastic scalar fields in an expanding universe. We derive some generic analytical results for the emission of gravity waves by stochastic media of random fields, which can test the validity/accuracy of numerical calculations. We contrast our method with other numerical methods in the literature, and then we apply it to preheating after chaotic inflation. In this case, we are able to check analytically our numerical results, which differ significantly from previous works. We discuss how the gravity-wave spectrum builds up with time and find that the amplitude and the frequency of its peak depend in a relatively simple way on the characteristic spatial scale amplified during preheating. We then estimate the peak frequency and amplitude of the spectrum produced in two models of preheating after hybrid inflation, which for some parameters may be relevant for gravity-wave interferometric experiments

STELLAR ACTIVITY AND EXCLUSION OF THE OUTER PLANET IN THE HD 99492 SYSTEM

Energy Technology Data Exchange (ETDEWEB)

Kane, Stephen R.; Thirumalachari, Badrinath; Hinkel, Natalie R. [Department of Physics and Astronomy, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132 (United States); Henry, Gregory W. [Center of Excellence in Information Systems, Tennessee State University, 3500 John A. Merritt Blvd., Box 9501, Nashville, TN 37209 (United States); Jensen, Eric L. N. [Dept of Physics and Astronomy, Swarthmore College, Swarthmore, PA 19081 (United States); Boyajian, Tabetha S.; Fischer, Debra A. [Department of Astronomy, Yale University, New Haven, CT 06511 (United States); Howard, Andrew W. [Institute for Astronomy, University of Hawaii, Honolulu, HI 96822 (United States); Isaacson, Howard T. [Astronomy Department, University of California, Berkeley, CA 94720 (United States); Wright, Jason T., E-mail: skane@sfsu.edu [Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802 (United States)

2016-03-20

A historical problem for indirect exoplanet detection has been contending with the intrinsic variability of the host star. If the variability is periodic, it can easily mimic various exoplanet signatures, such as radial velocity (RV) variations that originate with the stellar surface rather than the presence of a planet. Here we present an update for the HD 99492 planetary system, using new RV and photometric measurements from the Transit Ephemeris Refinement and Monitoring Survey. Our extended time series and subsequent analyses of the Ca ii H and K emission lines show that the host star has an activity cycle of ∼13 years. The activity cycle correlates with the purported orbital period of the outer planet, the signature of which is thus likely due to the host star activity. We further include a revised Keplerian orbital solution for the remaining planet, along with a new transit ephemeris. Our transit-search observations were inconclusive.

Numerical study on anaerobic digestion of fruit and vegetable waste: Biogas generation

Science.gov (United States)

Wardhani, Puteri Kusuma; Watanabe, Masaji

2016-02-01

The study provides experimental results and numerical results concerning anaerobic digestion of fruit and vegetable waste. Experiments were carried out by using batch floating drum type digester without mixing and temperature setting. The retention time was 30 days. Numerical results based on Monod type model with influence of temperature is introduced. Initial value problems were analyzed numerically, while kinetic parameters were analyzed by using trial error methods. The numerical results for the first five days seems appropriate in comparison with the experimental outcomes. However, numerical results shows that the model is inappropriate for 30 days of fermentation. This leads to the conclusion that Monod type model is not suitable for describe the mixture degradation of fruit and vegetable waste and horse dung.

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

Monotone numerical methods for finite-state mean-field games

KAUST Repository

Gomes, Diogo A.; Saude, Joao

2017-01-01

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

Monotone numerical methods for finite-state mean-field games

KAUST Repository

Gomes, Diogo A.

2017-04-29

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

Advanced approach to numerical forecasting using artificial neural networks

Directory of Open Access Journals (Sweden)

Michael Štencl

2009-01-01

Full Text Available Current global market is driven by many factors, such as the information age, the time and amount of information distributed by many data channels it is practically impossible analyze all kinds of incoming information flows and transform them to data with classical methods. New requirements could be met by using other methods. Once trained on patterns artificial neural networks can be used for forecasting and they are able to work with extremely big data sets in reasonable time. The patterns used for learning process are samples of past data. This paper uses Radial Basis Functions neural network in comparison with Multi Layer Perceptron network with Back-propagation learning algorithm on prediction task. The task works with simplified numerical time series and includes forty observations with prediction for next five observations. The main topic of the article is the identification of the main differences between used neural networks architectures together with numerical forecasting. Detected differences then verify on practical comparative example.

Towards High Resolution Numerical Algorithms for Wave Dominated Physical Phenomena

Science.gov (United States)

2009-01-30

Modelling and Numerical Analysis, 40(5):815-841, 2006. [31] Michael Dumbser, Martin Kaser, and Eleuterio F. Toro. An arbitrary high-order Discontinuous...proximation of PML, SIAM J. Numer. Anal., 41 (2003), pp. 287-305. [60] E. BECACHE, S. FAUQUEUX, AND P. JOLY , Stability of perfectly matched layers, group...time-domain performance analysis, IEEE Trans, on Magnetics, 38 (2002), pp. 657- 660. [64] J. DIAZ AND P. JOLY , An analysis of higher-order boundary

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing

Science.gov (United States)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko

2007-10-01

The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak secondary wave reproduction in some cases) consistency of the numerical modelling results with known stationary linear test solutions. Numerical stability of the developed model is investigated with respect to the reference state choice, modelling dynamics of a stationary front. The horizontally area-mean reference temperature proves to be the optimal stability warrant. The numerical scheme with explicit residual in the vertical forcing term becomes unstable for cross-frontal temperature differences exceeding 30 K. Stability is restored, if the vertical forcing is treated implicitly, which enables to use time steps, comparable with the hydrostatic SISL.

Costs of travel time uncertainty and benefits of travel time information: Conceptual model and numerical examples

NARCIS (Netherlands)

Ettema, D.F.; Timmermans, H.J.P.

2006-01-01

A negative effect of congestion that tends to be overlooked is travel time uncertainty. Travel time uncertainty causes scheduling costs due to early or late arrival. The negative effects of travel time uncertainty can be reduced by providing travellers with travel time information, which improves

Molecular dynamics with deterministic and stochastic numerical methods

CERN Document Server

Leimkuhler, Ben

2015-01-01

This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications.  Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method...

The distance effect in numerical memory-updating tasks.

Science.gov (United States)

Lendínez, Cristina; Pelegrina, Santiago; Lechuga, Teresa

2011-05-01

Two experiments examined the role of numerical distance in updating numerical information in working memory. In the first experiment, participants had to memorize a new number only when it was smaller than a previously memorized number. In the second experiment, updating was based on an external signal, which removed the need to perform any numerical comparison. In both experiments, distance between the memorized number and the new one was manipulated. The results showed that smaller distances between the new and the old information led to shorter updating times. This graded facilitation suggests that the process by which information is substituted in the focus of attention involves maintaining the shared features between the new and the old number activated and selecting other new features to be activated. Thus, the updating cost may be related to amount of new features to be activated in the focus of attention.

Efficient numerical simulation of heat storage in subsurface georeservoirs

Science.gov (United States)

Boockmeyer, A.; Bauer, S.

2015-12-01

The transition of the German energy market towards renewable energy sources, e.g. wind or solar power, requires energy storage technologies to compensate for their fluctuating production. Large amounts of energy could be stored in georeservoirs such as porous formations in the subsurface. One possibility here is to store heat with high temperatures of up to 90°C through borehole heat exchangers (BHEs) since more than 80 % of the total energy consumption in German households are used for heating and hot water supply. Within the ANGUS+ project potential environmental impacts of such heat storages are assessed and quantified. Numerical simulations are performed to predict storage capacities, storage cycle times, and induced effects. For simulation of these highly dynamic storage sites, detailed high-resolution models are required. We set up a model that accounts for all components of the BHE and verified it using experimental data. The model ensures accurate simulation results but also leads to large numerical meshes and thus high simulation times. In this work, we therefore present a numerical model for each type of BHE (single U, double U and coaxial) that reduces the number of elements and the simulation time significantly for use in larger scale simulations. The numerical model includes all BHE components and represents the temporal and spatial temperature distribution with an accuracy of less than 2% deviation from the fully discretized model. By changing the BHE geometry and using equivalent parameters, the simulation time is reduced by a factor of ~10 for single U-tube BHEs, ~20 for double U-tube BHEs and ~150 for coaxial BHEs. Results of a sensitivity study that quantify the effects of different design and storage formation parameters on temperature distribution and storage efficiency for heat storage using multiple BHEs are then shown. It is found that storage efficiency strongly depends on the number of BHEs composing the storage site, their distance and

First passage time problems in time-dependent fields

International Nuclear Information System (INIS)

Fletcher, J.E.; Havlin, S.; Weiss, G.H.

1988-01-01

This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency omega* for which the mean residence time on the line segment in a minimum. It is shown that for a random walk on a line segment of length L the mean residence time goes like L 2 for large L when omega omega*, but when omega = omega* the dependence is proportional to L. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation

Analysis of control rod behavior based on numerical simulation

International Nuclear Information System (INIS)

Ha, D. G.; Park, J. K.; Park, N. G.; Suh, J. M.; Jeon, K. L.

2010-01-01

The main function of a control rod is to control core reactivity change during operation associated with changes in power, coolant temperature, and dissolved boron concentration by the insertion and withdrawal of control rods from the fuel assemblies. In a scram, the control rod assemblies are released from the CRDMs (Control Rod Drive Mechanisms) and, due to gravity, drop rapidly into the fuel assemblies. The control rod insertion time during a scram must be within the time limits established by the overall core safety analysis. To assure the control rod operational functions, the guide thimbles shall not obstruct the insertion and withdrawal of the control rods or cause any damage to the fuel assembly. When fuel assembly bow occurs, it can affect both the operating performance and the core safety. In this study, the drag forces of the control rod are estimated by a numerical simulation to evaluate the guide tube bow effect on control rod withdrawal. The contact condition effects are also considered. A full scale 3D model is developed for the evaluation, and ANSYS - commercial numerical analysis code - is used for this numerical simulation. (authors)

Longitudinal Brain Development of Numerical Skills in Typically Developing Children and Children with Developmental Dyscalculia

Directory of Open Access Journals (Sweden)

Ursina McCaskey

2018-01-01

Full Text Available Developmental dyscalculia (DD is a learning disability affecting the acquisition of numerical-arithmetical skills. Studies report persistent deficits in number processing and aberrant functional activation of the fronto-parietal numerical network in DD. However, the neural development of numerical abilities has been scarcely investigated. The present paper provides a first attempt to investigate behavioral and neural trajectories of numerical abilities longitudinally in typically developing (TD and DD children. During a study period of 4 years, 28 children (8–11 years were evaluated twice by means of neuropsychological tests and a numerical order fMRI paradigm. Over time, TD children improved in numerical abilities and showed a consistent and well-developed fronto-parietal network. In contrast, DD children revealed persistent deficits in number processing and arithmetic. Brain imaging results of the DD group showed an age-related activation increase in parietal regions (intraparietal sulcus, pointing to a delayed development of number processing areas. Besides, an activation increase in frontal areas was observed over time, indicating the use of compensatory mechanisms. In conclusion, results suggest a continuation in neural development of number representation in DD, whereas the neural network for simple ordinal number estimation seems to be stable or show only subtle changes in TD children over time.

Longitudinal Brain Development of Numerical Skills in Typically Developing Children and Children with Developmental Dyscalculia.

Science.gov (United States)

McCaskey, Ursina; von Aster, Michael; Maurer, Urs; Martin, Ernst; O'Gorman Tuura, Ruth; Kucian, Karin

2017-01-01

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Studies report persistent deficits in number processing and aberrant functional activation of the fronto-parietal numerical network in DD. However, the neural development of numerical abilities has been scarcely investigated. The present paper provides a first attempt to investigate behavioral and neural trajectories of numerical abilities longitudinally in typically developing (TD) and DD children. During a study period of 4 years, 28 children (8-11 years) were evaluated twice by means of neuropsychological tests and a numerical order fMRI paradigm. Over time, TD children improved in numerical abilities and showed a consistent and well-developed fronto-parietal network. In contrast, DD children revealed persistent deficits in number processing and arithmetic. Brain imaging results of the DD group showed an age-related activation increase in parietal regions (intraparietal sulcus), pointing to a delayed development of number processing areas. Besides, an activation increase in frontal areas was observed over time, indicating the use of compensatory mechanisms. In conclusion, results suggest a continuation in neural development of number representation in DD, whereas the neural network for simple ordinal number estimation seems to be stable or show only subtle changes in TD children over time.

Numerical distance protection

CERN Document Server

Ziegler, Gerhard

2011-01-01

Distance protection provides the basis for network protection in transmission systems and meshed distribution systems. This book covers the fundamentals of distance protection and the special features of numerical technology. The emphasis is placed on the application of numerical distance relays in distribution and transmission systems.This book is aimed at students and engineers who wish to familiarise themselves with the subject of power system protection, as well as the experienced user, entering the area of numerical distance protection. Furthermore it serves as a reference guide for s

SPICE Module for the Satellite Orbit Analysis Program (SOAP)

Science.gov (United States)

Coggi, John; Carnright, Robert; Hildebrand, Claude

2008-01-01

A SPICE module for the Satellite Orbit Analysis Program (SOAP) precisely represents complex motion and maneuvers in an interactive, 3D animated environment with support for user-defined quantitative outputs. (SPICE stands for Spacecraft, Planet, Instrument, Camera-matrix, and Events). This module enables the SOAP software to exploit NASA mission ephemeris represented in the JPL Ancillary Information Facility (NAIF) SPICE formats. Ephemeris types supported include position, velocity, and orientation for spacecraft and planetary bodies including the Sun, planets, natural satellites, comets, and asteroids. Entire missions can now be imported into SOAP for 3D visualization, playback, and analysis. The SOAP analysis and display features can now leverage detailed mission files to offer the analyst both a numerically correct and aesthetically pleasing combination of results that can be varied to study many hypothetical scenarios. The software provides a modeling and simulation environment that can encompass a broad variety of problems using orbital prediction. For example, ground coverage analysis, communications analysis, power and thermal analysis, and 3D visualization that provide the user with insight into complex geometric relations are included. The SOAP SPICE module allows distributed science and engineering teams to share common mission models of known pedigree, which greatly reduces duplication of effort and the potential for error. The use of the software spans all phases of the space system lifecycle, from the study of future concepts to operations and anomaly analysis. It allows SOAP software to correctly position and orient all of the principal bodies of the Solar System within a single simulation session along with multiple spacecraft trajectories and the orientation of mission payloads. In addition to the 3D visualization, the user can define numeric variables and x-y plots to quantitatively assess metrics of interest.

Numerical methods using Matlab

CERN Document Server

Lindfield, George

2012-01-01

Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board. Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of use

Solution to the monoenergetic time-dependent neutron transport equation with a time-varying source

International Nuclear Information System (INIS)

Ganapol, B.D.

1986-01-01

Even though fundamental time-dependent neutron transport problems have existed since the inception of neutron transport theory, it has only been recently that a reliable numerical solution to one of the basic problems has been obtained. Experience in generating numerical solutions to time-dependent transport equations has indicated that the multiple collision formulation is the most versatile numerical technique for model problems. The formulation coupled with a moment reconstruction of each collided flux component has led to benchmark-quality (four- to five-digit accuracy) numerical evaluation of the neutron flux in plane infinite geometry for any degree of scattering anisotropy and for both pulsed isotropic and beam sources. As will be shown in this presentation, this solution can serve as a Green's function, thus extending the previous results to more complicated source situations. Here we will be concerned with a time-varying source at the center of an infinite medium. If accurate, such solutions have both pedagogical and practical uses as benchmarks against which other more approximate solutions designed for a wider class of problems can be compared

Transiting Exoplanet Monitoring Project (TEMP). IV. Refined System Parameters, Transit Timing Variations, and Orbital Stability of the Transiting Planetary System HAT-P-25

Science.gov (United States)

Wang, Xian-Yu; Wang, Songhu; Hinse, Tobias C.; Li, Kai; Wang, Yong-Hao; Laughlin, Gregory; Liu, Hui-Gen; Zhang, Hui; Wu, Zhen-Yu; Zhou, Xu; Zhou, Ji-Lin; Hu, Shao-Ming; Wu, Dong-Hong; Peng, Xi-Yan; Chen, Yuan-Yuan

2018-06-01

We present eight new light curves of the transiting extra-solar planet HAT-P-25b obtained from 2013 to 2016 with three telescopes at two observatories. We use the new light curves, along with recent literature material, to estimate the physical and orbital parameters of the transiting planet. Specifically, we determine the mid-transit times (T C ) and update the linear ephemeris, T C[0] = 2456418.80996 ± 0.00025 [BJDTDB] and P = 3.65281572 ± 0.00000095 days. We carry out a search for transit timing variations (TTVs), and find no significant TTV signal at the ΔT = 80 s-level, placing a limit on the possible strength of planet–planet interactions (TTVG). In the course of our analysis, we calculate the upper mass-limits of the potential nearby perturbers. Near the 1:2, 2:1, and 3:1 resonances with HAT-P-25b, perturbers with masses greater than 0.5, 0.3, and 0.5 M ⊕ respectively, can be excluded. Furthermore, based on the analysis of TTVs caused by light travel time effect (LTTE) we also eliminate the possibility that a long-period perturber exists with M p > 3000 MJ within a = 11.2 au of the parent star.

Numerical approach of the quantum circuit theory

Energy Technology Data Exchange (ETDEWEB)

Silva, J.J.B., E-mail: jaedsonfisica@hotmail.com; Duarte-Filho, G.C.; Almeida, F.A.G.

2017-03-15

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

Numerical approach of the quantum circuit theory

International Nuclear Information System (INIS)

Silva, J.J.B.; Duarte-Filho, G.C.; Almeida, F.A.G.

2017-01-01

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

Numerical approach of the quantum circuit theory

Science.gov (United States)

Silva, J. J. B.; Duarte-Filho, G. C.; Almeida, F. A. G.

2017-03-01

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

Numerical modeling and experimental validation of thermoplastic composites induction welding

Science.gov (United States)

Palmieri, Barbara; Nele, Luigi; Galise, Francesco

2018-05-01

In this work, a numerical simulation and experimental test of the induction welding of continuous fibre-reinforced thermoplastic composites (CFRTPCs) was provided. The thermoplastic Polyamide 66 (PA66) with carbon fiber fabric was used. Using a dedicated software (JMag Designer), the influence of the fundamental process parameters such as temperature, current and holding time was investigated. In order to validate the results of the simulations, and therefore the numerical model used, experimental tests were carried out, and the temperature values measured during the tests were compared with the aid of an optical pyrometer, with those provided by the numerical simulation. The mechanical properties of the welded joints were evaluated by single lap shear tests.

Numerical modelling of moisture migration in non-uniformly heated concrete

International Nuclear Information System (INIS)

Khoylou, N.; England, G.L.

1995-01-01

This paper describes a numerical modelling procedure, capable of predicting temperature-dependent moisture flow in concrete. The flow direction is not defined by the sign of the temperature gradient. Irreversible thermodynamic process based on the production of entropy are used to check the course of the numerical calculations which take place in a stepwise manner in time. Numerical results indicate that thick walls will take many years to dry significantly. They also show that if venting to atmosphere is introduced at locations within the wall, the pore-water pressure, the water migration behaviour and the drying rate will be changed. This behaviour has also been experimentally observed. (author). 7 refs., 10 figs

Soundness of Timed-Arc Workflow Nets in Discrete and Continuous-Time Semantics

DEFF Research Database (Denmark)

Mateo, Jose Antonio; Srba, Jiri; Sørensen, Mathias Grund

2015-01-01

Analysis of workflow processes with quantitative aspectslike timing is of interest in numerous time-critical applications. We suggest a workflow model based on timed-arc Petri nets and studythe foundational problems of soundness and strong (time-bounded) soundness.We first consider the discrete-t...

Space-time accessibility under conditions of uncertain travel times: theory and numerical simulations

NARCIS (Netherlands)

Ettema, D.F.; Timmermans, H.J.P.

2007-01-01

Recently, several accessibility measures using the space–time prism concept have been suggested in the literature. These measures fail to take into account (i) the ability of individuals to adjust their activity–travel patterns in coping with constrained choice sets, (ii) uncertainty in the

Automated smoother for the numerical decoupling of dynamics models.

Science.gov (United States)

Vilela, Marco; Borges, Carlos C H; Vinga, Susana; Vasconcelos, Ana Tereza R; Santos, Helena; Voit, Eberhard O; Almeida, Jonas S

2007-08-21

Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure. In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from in-vivo NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations. The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental

Numerical Study on Critical Wedge Angle of Cellular Detonation Reflections

International Nuclear Information System (INIS)

Gang, Wang; Kai-Xin, Liu; De-Liang, Zhang

2010-01-01

The critical wedge angle (CWA) for the transition from regular reflection (RR) to Mach reflection (MR) of a cellular detonation wave is studied numerically by an improved space-time conservation element and solution element method together with a two-step chemical reaction model. The accuracy of that numerical way is verified by simulating cellular detonation reflections at a 19.3° wedge. The planar and cellular detonation reflections over 45°–55° wedges are also simulated. When the cellular detonation wave is over a 50° wedge, numerical results show a new phenomenon that RR and MR occur alternately. The transition process between RR and MR is investigated with the local pressure contours. Numerical analysis shows that the cellular structure is the essential reason for the new phenomenon and the CWA of detonation reflection is not a certain angle but an angle range. (fundamental areas of phenomenology(including applications))

Numerical solutions of the monoenergetic neutron transport equation with anisotropic scattering

International Nuclear Information System (INIS)

Dahl, B.

1985-01-01

The Boltzmann equation for monoenergetic neutrons has been solved numerically with high accuracy for homogeneous slabs and spheres with various degree of linear anisotropy. Vacuum boundary conditions are used. The numerical method is based on previous work by Carlvik. Benchmark values of the criticality factor and higher order eigenvalues are given for multiplying systems of thickness or diameter from 10 -5 to 20 mean free paths and with anisotropy coefficients from 0.0 to 0.3. For slab geometry, both even and odd mode eigenvalues are treated. With increasing anisotropy, an increasing number of complex eigenvalues is observer. The total flux is calculated from the eigenvector and tables of the fundamental mode flux are given. Accurate extrapolation distances are derived for various dimensions and anisotropy coefficients from our eigenvalue results on slabs and spheres and from the work by Sanchez on infinite cylinders.The time eigenvalue spectrum in subcritical systems has also been studied. First, the connection between the eigenvalues arising from the time dependent and stationary transport equation is established. Based on this, the spectrum of real time eigenvalues in slabs and spheres is calculated. For spheres, the existence of complex time eigenvalues in the region beyond the value corresponding to the Corngold limit is numerically established. The presence of such eigenvalues has earlier not been proved. It is further shown that the Boltzmann equation for a sphere is significantly simplified when the decay constant is at the Corngold limit. The spectrum of sphere diameters corresponding to this decay constant is calculated for various linear anisotropies, and detailed numerical results are given. (Author)

Reactions, accuracy and response complexity of numerical typing on touch screens.

Science.gov (United States)

Lin, Cheng-Jhe; Wu, Changxu

2013-01-01

Touch screens are popular nowadays as seen on public kiosks, industrial control panels and personal mobile devices. Numerical typing is one frequent task performed on touch screens, but this task on touch screen is subject to human errors and slow responses. This study aims to find innate differences of touch screens from standard physical keypads in the context of numerical typing by eliminating confounding issues. Effects of precise visual feedback and urgency of numerical typing were also investigated. The results showed that touch screens were as accurate as physical keyboards, but reactions were indeed executed slowly on touch screens as signified by both pre-motor reaction time and reaction time. Provision of precise visual feedback caused more errors, and the interaction between devices and urgency was not found on reaction time. To improve usability of touch screens, designers should focus more on reducing response complexity and be cautious about the use of visual feedback. The study revealed that slower responses on touch screens involved more complex human cognition to formulate motor responses. Attention should be given to designing precise visual feedback appropriately so that distractions or visual resource competitions can be avoided to improve human performance on touch screens.

Numerical and Experimental Study of Pump Sump Flows

Directory of Open Access Journals (Sweden)

Wei-Liang Chuang

2014-01-01

Full Text Available The present study analyzes pump sump flows with various discharges and gate submergence. Investigations using a three-dimensional large eddy simulation model and an acoustic Doppler velocimeter are performed. Flow patterns and velocity profiles in the approaching flow are shown to describe the flow features caused by various discharges and gate submergence. The variation of a large-scale spanwise vortex behind a sluice gate is examined and discussed. The suction effect on approaching flow near the pipe column is examined using numerical modeling. To gain more understanding of the vortices variation, a comparison between time-averaged and instantaneous flow patterns is numerically conducted. Additionally, swirl angle, a widely used index for evaluating pump efficiency, is experimentally and numerically examined under various flow conditions. The results indicate that the pump becomes less efficient with increasing discharge and gate submergence. The fluctuation of the free surface over the pump sump is also discussed.

Numerical Simulation of Wind Turbine Blade-Tower Interaction

Institute of Scientific and Technical Information of China (English)

Qiang Wang; Hu Zhou; Decheng Wan

2012-01-01

Numerical simulations of wind turbine blade-tower interaction by using the open source OpenFOAM tools coupled with arbitrary mesh interface (AMI) method were presented.The governing equations were the unsteady Reynolds-averaged Navier-Stokes (PANS) which were solved by the pimpleDyMFoam solver,and the AMI method was employed to handle mesh movements.The National Renewable Energy Laboratory (NREL) phase Ⅵ wind turbine in upwind configuration was selected for numerical tests with different incoming wind speeds (5,10,15,and 25 m/s) at a fixed blade pitch and constant rotational speed.Detailed numerical results of vortex structure,time histories of thrust,and pressure distribution on the blade and tower were presented.The findings show that the wind turbine tower has little effect on the whole aerodynamic performance of an upwind wind turbine,while the rotating rotor will induce an obvious cyclic drop in the front pressure of the tower.Also,strong interaction of blade tip vortices with separation from the tower was observed.

Numerical Analysis of Ginzburg-Landau Models for Superconductivity.

Science.gov (United States)

Coskun, Erhan

Thin film conventional, as well as High T _{c} superconductors of various geometric shapes placed under both uniform and variable strength magnetic field are studied using the universially accepted macroscopic Ginzburg-Landau model. A series of new theoretical results concerning the properties of solution is presented using the semi -discrete time-dependent Ginzburg-Landau equations, staggered grid setup and natural boundary conditions. Efficient serial algorithms including a novel adaptive algorithm is developed and successfully implemented for solving the governing highly nonlinear parabolic system of equations. Refinement technique used in the adaptive algorithm is based on modified forward Euler method which was also developed by us to ease the restriction on time step size for stability considerations. Stability and convergence properties of forward and modified forward Euler schemes are studied. Numerical simulations of various recent physical experiments of technological importance such as vortes motion and pinning are performed. The numerical code for solving time-dependent Ginzburg-Landau equations is parallelized using BlockComm -Chameleon and PCN. The parallel code was run on the distributed memory multiprocessors intel iPSC/860, IBM-SP1 and cluster of Sun Sparc workstations, all located at Mathematics and Computer Science Division, Argonne National Laboratory.

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<

Practical considerations in developing numerical simulators for thermal recovery

Energy Technology Data Exchange (ETDEWEB)

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

1996-08-15

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

Time processing in dyscalculia.

Science.gov (United States)

Cappelletti, Marinella; Freeman, Elliot D; Butterworth, Brian L

2011-01-01

To test whether atypical number development may affect other types of quantity processing, we investigated temporal discrimination in adults with developmental dyscalculia (DD). This also allowed us to test whether number and time may be sub-served by a common quantity system or decision mechanisms: if they do, both should be impaired in dyscalculia, but if number and time are distinct they should dissociate. Participants judged which of two successively presented horizontal lines was longer in duration, the first line being preceded by either a small or a large number prime ("1" or "9") or by a neutral symbol ("#"), or in a third task participants decided which of two Arabic numbers (either "1," "5," "9") lasted longer. Results showed that (i) DD's temporal discriminability was normal as long as numbers were not part of the experimental design, even as task-irrelevant stimuli; however (ii) task-irrelevant numbers dramatically disrupted DD's temporal discriminability the more their salience increased, though the actual magnitude of the numbers had no effect; in contrast (iii) controls' time perception was robust to the presence of numbers but modulated by numerical quantity: therefore small number primes or numerical stimuli seemed to make durations appear shorter than veridical, but longer for larger numerical prime or numerical stimuli. This study is the first to show spared temporal discrimination - a dimension of continuous quantity - in a population with a congenital number impairment. Our data reinforce the idea of a partially shared quantity system across numerical and temporal dimensions, which supports both dissociations and interactions among dimensions; however, they suggest that impaired number in DD is unlikely to originate from systems initially dedicated to continuous quantity processing like 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...

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...

Experimental and Numerical Analysis of Steel Joints in Round Wood

Directory of Open Access Journals (Sweden)

Mikolášek David

2014-12-01

Full Text Available The paper analyses a drawn steel joint in round logs for which several types of reinforcements have been proposed. The load-carrying capacity of the reinforcements have been tested in laboratories. At the same time, numerical modelling has been performed - it has focused, in particular, on rigidity of the joints during the loading process. Physical and geometrical nonlinearities have been taken into account. The Finite Element Method and 3D computation models have been used in the numerical calculations.

Numeral-Incorporating Roots in Numeral Systems: A Comparative Analysis of Two Sign Languages

Science.gov (United States)

Fuentes, Mariana; Massone, Maria Ignacia; Fernandez-Viader, Maria del Pilar; Makotrinsky, Alejandro; Pulgarin, Francisca

2010-01-01

Numeral-incorporating roots in the numeral systems of Argentine Sign Language (LSA) and Catalan Sign Language (LSC), as well as the main features of the number systems of both languages, are described and compared. Informants discussed the use of numerals and roots in both languages (in most cases in natural contexts). Ten informants took part in…

Polyhedral meshing in numerical analysis of conjugate heat transfer

Science.gov (United States)

Sosnowski, Marcin; Krzywanski, Jaroslaw; Grabowska, Karolina; Gnatowska, Renata

2018-06-01

Computational methods have been widely applied in conjugate heat transfer analysis. The very first and crucial step in such research is the meshing process which consists in dividing the analysed geometry into numerous small control volumes (cells). In Computational Fluid Dynamics (CFD) applications it is desirable to use the hexahedral cells as the resulting mesh is characterized by low numerical diffusion. Unfortunately generating such mesh can be a very time-consuming task and in case of complicated geometry - it may not be possible to generate cells of good quality. Therefore tetrahedral cells have been implemented into commercial pre-processors. Their advantage is the ease of its generation even in case of very complex geometry. On the other hand tetrahedrons cannot be stretched excessively without decreasing the mesh quality factor, so significantly larger number of cells has to be used in comparison to hexahedral mesh in order to achieve a reasonable accuracy. Moreover the numerical diffusion of tetrahedral elements is significantly higher. Therefore the polyhedral cells are proposed within the paper in order to combine the advantages of hexahedrons (low numerical diffusion resulting in accurate solution) and tetrahedrons (rapid semi-automatic generation) as well as to overcome the disadvantages of both the above mentioned mesh types. The major benefit of polyhedral mesh is that each individual cell has many neighbours, so gradients can be well approximated. Polyhedrons are also less sensitive to stretching than tetrahedrons which results in better mesh quality leading to improved numerical stability of the model. In addition, numerical diffusion is reduced due to mass exchange over numerous faces. This leads to a more accurate solution achieved with a lower cell count. Therefore detailed comparison of numerical modelling results concerning conjugate heat transfer using tetrahedral and polyhedral meshes is presented in the paper.

Finite-difference time-domain analysis of time-resolved terahertz spectroscopy experiments

DEFF Research Database (Denmark)

Larsen, Casper; Cooke, David G.; Jepsen, Peter Uhd

2011-01-01

In this paper we report on the numerical analysis of a time-resolved terahertz (THz) spectroscopy experiment using a modified finite-difference time-domain method. Using this method, we show that ultrafast carrier dynamics can be extracted with a time resolution smaller than the duration of the T...

Disruptive Innovation in Numerical Hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Waltz, Jacob I. [Los Alamos National Laboratory

2012-09-06

We propose the research and development of a high-fidelity hydrodynamic algorithm for tetrahedral meshes that will lead to a disruptive innovation in the numerical modeling of Laboratory problems. Our proposed innovation has the potential to reduce turnaround time by orders of magnitude relative to Advanced Simulation and Computing (ASC) codes; reduce simulation setup costs by millions of dollars per year; and effectively leverage Graphics Processing Unit (GPU) and future Exascale computing hardware. If successful, this work will lead to a dramatic leap forward in the Laboratory's quest for a predictive simulation capability.

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

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

Science.gov (United States)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

Numerical studies of pair creation in counterpropagating laser fields

Energy Technology Data Exchange (ETDEWEB)

Ruf, Matthias

2009-05-27

Pair creation from vacuum induced by electromagnetic fields is probably one of the most intriguing phenomena in physics. If the fields are sufficiently strong, the QED vacuum become unstable. Due to the remarkable progress in laser technology during recent years an experimental investigation of pair creation by pure laser light is coming into reach. The focus of this thesis is on pair creation in counterpropagating laser beams. The pair creation probability is calculated employing the numerically obtained solutions of the Dirac equation. This numerical ansatz has the capability of calculating the momentum distribution of the created pairs in a single propagation, for pure time dependent field configurations. Furthermore, it allows to take the magnetic component of the laser fields into account, which is usually neglected. The latter strongly affects the creation process at high laser frequency. The involved numerical calculations are rather time consuming, therefore the second project of this thesis was to develop a highly efficient code for solving relativistic quantum mechanical problems. This is accomplished by adopting the split-operator method to the Klein-Gordon equation. Here the possibility arises to use parallel computing. However the corresponding spin-statistics becomes crucial in the case of pair creation, demonstrated in several examples. (orig.)

Numerical studies of pair creation in counterpropagating laser fields

International Nuclear Information System (INIS)

Ruf, Matthias

2009-01-01

Pair creation from vacuum induced by electromagnetic fields is probably one of the most intriguing phenomena in physics. If the fields are sufficiently strong, the QED vacuum become unstable. Due to the remarkable progress in laser technology during recent years an experimental investigation of pair creation by pure laser light is coming into reach. The focus of this thesis is on pair creation in counterpropagating laser beams. The pair creation probability is calculated employing the numerically obtained solutions of the Dirac equation. This numerical ansatz has the capability of calculating the momentum distribution of the created pairs in a single propagation, for pure time dependent field configurations. Furthermore, it allows to take the magnetic component of the laser fields into account, which is usually neglected. The latter strongly affects the creation process at high laser frequency. The involved numerical calculations are rather time consuming, therefore the second project of this thesis was to develop a highly efficient code for solving relativistic quantum mechanical problems. This is accomplished by adopting the split-operator method to the Klein-Gordon equation. Here the possibility arises to use parallel computing. However the corresponding spin-statistics becomes crucial in the case of pair creation, demonstrated in several examples. (orig.)

Adapted all-numerical correlator for face recognition applications

Science.gov (United States)

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

2013-03-01

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

Numerical Modeling and Mechanical Analysis of Flexible Risers

Directory of Open Access Journals (Sweden)

J. Y. Li

2015-01-01

Full Text Available ABAQUS is used to create a detailed finite element model for a 10-layer unbonded flexible riser to simulate the riser’s mechanical behavior under three load conditions: tension force and internal and external pressure. It presents a technique to create detailed finite element model and to analyze flexible risers. In FEM model, all layers are modeled separately with contact interfaces; interaction between steel trips in certain layers has been considered as well. FEM model considering contact interaction, geometric nonlinearity, and friction has been employed to accurately simulate the structural behavior of riser. The model includes the main features of the riser geometry with very little simplifying assumptions. The model was solved using a fully explicit time-integration scheme implemented in a parallel environment on an eight-processor cluster and 24 G memory computer. There is a very good agreement obtained from numerical and analytical comparisons, which validates the use of numerical model here. The results from the numerical simulation show that the numerical model takes into account various details of the riser. It has been shown that the detailed finite element model can be used to predict riser’s mechanics behavior under various load cases and bound conditions.

A New Language Design for Prototyping Numerical Computation

Directory of Open Access Journals (Sweden)

Thomas Derby

1996-01-01

Full Text Available To naturally and conveniently express numerical algorithms, considerable expressive power is needed in the languages in which they are implemented. The language Matlab is widely used by numerical analysts for this reason. Expressiveness or ease-of-use can also result in a loss of efficiency, as is the case with Matlab. In particular, because numerical analysts are highly interested in the performance of their algorithms, prototypes are still often implemented in languages such as Fortran. In this article we describe a language design that is intended to both provide expressiveness for numerical computation, and at the same time provide performance guarantees. In our language, EQ, we attempt to include both syntactic and semantic features that correspond closely to the programmer's model of the problem, including unordered equations, large-granularity state transitions, and matrix notation. The resulting language does not fit into standard language categories such as functional or imperative but has features of both paradigms. We also introduce the notion of language dependability, which is the idea that a language should guarantee that certain program transformations are performed by all implementations. We first describe the interesting features of EQ, and then present three examples of algorithms written using it. We also provide encouraging performance results from an initial implementation of our language.

Black holes in a box: Toward the numerical evolution of black holes in AdS space-times

International Nuclear Information System (INIS)

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

2010-01-01

The evolution of black holes in ''confining boxes'' is interesting for a number of reasons, particularly because it mimics the global structure of anti-de Sitter geometries. These are nonglobally hyperbolic space-times and the Cauchy problem may only be well defined if the initial data are supplemented by boundary conditions at the timelike conformal boundary. Here, we explore the active role that boundary conditions play in the evolution of a bulk black hole system, by imprisoning a black hole binary in a box with mirrorlike boundary conditions. We are able to follow the post-merger dynamics for up to two reflections off the boundary of the gravitational radiation produced in the merger. We estimate that about 15% of the radiation energy is absorbed by the black hole per interaction, whereas transfer of angular momentum from the radiation to the black hole is observed only in the first interaction. We discuss the possible role of superradiant scattering for this result. Unlike the studies with outgoing boundary conditions, both of the Newman-Penrose scalars Ψ 4 and Ψ 0 are nontrivial in our setup, and we show that the numerical data verifies the expected relations between them.

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

Science.gov (United States)

Warnez, M. T.; Johnsen, E.

2015-06-01

Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller-Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin-Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time.

Numerical investigation of power requirements for ultra-high-speed serial-to-parallel conversion

DEFF Research Database (Denmark)

Lillieholm, Mads; Mulvad, Hans Christian Hansen; Palushani, Evarist

2012-01-01

We present a numerical bit-error rate investigation of 160-640 Gbit/s serial-to-parallel conversion by four-wave mixing based time-domain optical Fourier transformation, showing an inverse scaling of the required pump energy per bit with the bit rate.......We present a numerical bit-error rate investigation of 160-640 Gbit/s serial-to-parallel conversion by four-wave mixing based time-domain optical Fourier transformation, showing an inverse scaling of the required pump energy per bit with the bit rate....

Numerical methods for characterization of synchrotron radiation based on the Wigner function method

Directory of Open Access Journals (Sweden)

Takashi Tanaka

2014-06-01

Full Text Available Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.

Numerical Simulation of Sloshing Phenomena in Cubic Tank with Multiple Baffles

Directory of Open Access Journals (Sweden)

Mi-An Xue

2012-01-01

Full Text Available A two-phase fluid flow model solving Navier-Stokes equations was employed in this paper to investigate liquid sloshing phenomena in cubic tank with horizontal baffle, perforated vertical baffle, and their combinatorial configurations under the harmonic motion excitation. Laboratory experiment of liquid sloshing in cubic tank with perforated vertical baffle was carried out to validate the present numerical model. Fairly good agreements were obtained from the comparisons between the present numerical results and the present experimental data, available numerical data. Liquid sloshing in cubic tank with multiple baffles was investigated numerically in detail under different external excitation frequencies. Power spectrum of the time series of free surface elevation was presented with the aid of fast Fourier transform technique. The dynamic impact pressures acting on the normal and parallel sidewalls were discussed in detail.

Numerically pricing American options under the generalized mixed fractional Brownian motion model

Science.gov (United States)

Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying

2016-06-01

In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.

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

Numerical Optimization Design of Dynamic Quantizer via Matrix Uncertainty Approach

Directory of Open Access Journals (Sweden)

Kenji Sawada

2013-01-01

Full Text Available In networked control systems, continuous-valued signals are compressed to discrete-valued signals via quantizers and then transmitted/received through communication channels. Such quantization often degrades the control performance; a quantizer must be designed that minimizes the output difference between before and after the quantizer is inserted. In terms of the broadbandization and the robustness of the networked control systems, we consider the continuous-time quantizer design problem. In particular, this paper describes a numerical optimization method for a continuous-time dynamic quantizer considering the switching speed. Using a matrix uncertainty approach of sampled-data control, we clarify that both the temporal and spatial resolution constraints can be considered in analysis and synthesis, simultaneously. Finally, for the slow switching, we compare the proposed and the existing methods through numerical examples. From the examples, a new insight is presented for the two-step design of the existing continuous-time optimal quantizer.

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

Science.gov (United States)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

Real-time numerical processing for HPGE detectors signals

International Nuclear Information System (INIS)

Eric Barat; Thomas Dautremer; Laurent Laribiere; Jean Christophe Trama

2006-01-01

Full text of publication follows: Concerning the gamma spectrometry, technology progresses in the processor field makes very conceivable and attractive executing complex real-time digital process. Only some simplified and rigid treatments can be find in the market up to now. Indeed, the historical solution used for 50 years consists of performing a so-called 'cusp' filtering and disturbing the optimal shape in order to shrink and/or truncate it. This tuning largely determined by the input count rate (ICR) the user expects to measure is then a compromise between the resolution and the throughput. Because it is not possible to tune it for each pulse, that is a kind of 'leveling down' which is made: the energy of each pulse is not as well estimated as it could be. The new approach proposed here avoids totally this restricting hand tuning. The innovation lies in the modelling of the shot-noise signal as a Jump Markov Linear System. The jump is the occurrence of a pulse in the signal. From this model, we developed an algorithm which makes possible the on-line estimation of the energies without having to temporally enlarge the pulses as the cusp filter does. The algorithm first determines whether there is a pulse or not at each time, then conditionally to this information, it performs an optimal Kalman smoother. Thanks to this global optimization, this allows us to dramatically increase the compromise throughput versus resolution, gaining an important factor on a commercial device concerning the admissible ICR (more than 1 million counts per second admissible). A huge advantage of the absence of hand tuning is that the system accepts fluctuating ICR. To validate the concept we built a real time demonstrator. First, our equipment is composed of an electronic stage which prepared the signal coming from the preamplifier of the detector and optimized the signal-to-noise ratio. Then the signal is sampled at 10 MHz and the powerful of two Pentium running at 3 GHz is enough to

The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

Science.gov (United States)

Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung

2016-01-01

Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

Three-dimensional numerical simulation during laser processing of CFRP

Science.gov (United States)

Ohkubo, Tomomasa; Sato, Yuji; Matsunaga, Ei-ichi; Tsukamoto, Masahiro

2017-09-01

We performed three-dimensional numerical simulation about laser processing of carbon-fiber-reinforced plastic (CFRP) using OpenFOAM as libraries of finite volume method (FVM). Although a little theoretical or numerical studies about heat affected zone (HAZ) formation were performed, there is no research discussing how HAZ is generated considering time development about removal of each material. It is important to understand difference of removal speed of carbon fiber and resin in order to improve quality of cut surface of CFRP. We demonstrated how the carbon fiber and resin are removed by heat of ablation plume by our simulation. We found that carbon fiber is removed faster than resin at first stage because of the difference of thermal conductivity, and after that, the resin is removed faster because of its low combustion temperature. This result suggests the existence of optimal contacting time of the laser ablation and kerf of the target.

Numeral Incorporation in Japanese Sign Language

Science.gov (United States)

Ktejik, Mish

2013-01-01

This article explores the morphological process of numeral incorporation in Japanese Sign Language. Numeral incorporation is defined and the available research on numeral incorporation in signed language is discussed. The numeral signs in Japanese Sign Language are then introduced and followed by an explanation of the numeral morphemes which are…

Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity

Directory of Open Access Journals (Sweden)

Font José A.

2008-09-01

Full Text Available This article presents a comprehensive overview of numerical hydrodynamics and magnetohydrodynamics (MHD in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003, most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable

Numerical Investigation of Pressure Losses in Axisymmetric Sudden Expansion with a Chamfer

Energy Technology Data Exchange (ETDEWEB)

Bae, Youngmin; Kim, Youngin; Kim, Keung Koo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2014-05-15

In this paper, the pressure losses through axisymmetric sudden expansions with a chamfer are analyzed by means of numerical simulation, with an emphasis on the effect of the Reynolds number. In this study, we investigate numerically the turbulent flow in axisymmetric sudden expansions having a slight chamfer on the edge. With the aim of investigating the impact of Reynolds number on the expansion losses in a time-averaged sense, an extensive set of simulations is carried out. On the basis of numerical results, we also propose a general correlation to estimate the local loss coefficient in sudden expansions with a chamfer.

Numerical Investigation of Pressure Losses in Axisymmetric Sudden Expansion with a Chamfer

International Nuclear Information System (INIS)

Bae, Youngmin; Kim, Youngin; Kim, Keung Koo

2014-01-01

In this paper, the pressure losses through axisymmetric sudden expansions with a chamfer are analyzed by means of numerical simulation, with an emphasis on the effect of the Reynolds number. In this study, we investigate numerically the turbulent flow in axisymmetric sudden expansions having a slight chamfer on the edge. With the aim of investigating the impact of Reynolds number on the expansion losses in a time-averaged sense, an extensive set of simulations is carried out. On the basis of numerical results, we also propose a general correlation to estimate the local loss coefficient in sudden expansions with a chamfer

Numerical modeling of the creep behavior of clays with emphasis on tunnels and underground openings

International Nuclear Information System (INIS)

1990-02-01

This report presents an interpretive overview and critical assessment of the state-of-the-art for numerical modeling of the creep behavior of clays. The overview and assessment is focused upon application to underground openings. Field and laboratory observations of time-dependent behavior, constitutive modeling of creep behavior, and numerical implementation of constitutive equations are addressed. A critical assessment of the ability of existing models to predict aspects of creep behavior relevant to waste repository design and suggestions for improved analyses that can be developed with existing technology are provided. Both heuristic and mathematical constitutive models are reviewed. Heuristic models provide a basis for evaluation of the required parameters for the continuum mechanics based mathematical models. The continuum mechanics models are required for numerical analysis. It has been demonstrated that, by using iterative and incremental analysis, virtually any viscous or inviscid continuum mechanics material model can be adapted to consider time-dependent behavior. Available numerical models for numerical analysis of geotechnical problems involving creep deformations are reviewed. Models for thermo-mechanical coupling are also addressed in this review. Cases where creep-inclusive analyses have been applied to analysis of prototype behavior are cited. However, the lack of well documented case histories of time-dependent deformations over significant time spans is identified as a major obstacle to model verification. Recommendations are made for an alternative design approach capable of guaranteeing the very long term mechanical integrity of the liner. 167 refs., 22 figs., 6 tabs

A new scheme to treat the numerical Tcherenkov instability for electromagnetic particle simulations

International Nuclear Information System (INIS)

Assous, F.; Degond, P.; Segre, J.; Degond, P.

1997-10-01

The aim of this paper is to present a new explicit time scheme for electromagnetic particle simulations. The main property of this new scheme, which depends on a parameter, is to reduce and in some cases to suppress numerical instabilities that can appear in this context, and are widely described in the literature. Other numerical properties are also investigated, and a numerical example is finally given to illustrate our purpose. This scheme is expected to be useful in the field of plasma modelling. (authors)

Direct Numerical Simulation and Visualization of Subcooled Pool Boiling

Directory of Open Access Journals (Sweden)

Tomoaki Kunugi

2014-01-01

Full Text Available A direct numerical simulation of the boiling phenomena is one of the promising approaches in order to clarify their heat transfer characteristics and discuss the mechanism. During these decades, many DNS procedures have been developed according to the recent high performance computers and computational technologies. In this paper, the state of the art of direct numerical simulation of the pool boiling phenomena during mostly two decades is briefly summarized at first, and then the nonempirical boiling and condensation model proposed by the authors is introduced into the MARS (MultiInterface Advection and Reconstruction Solver developed by the authors. On the other hand, in order to clarify the boiling bubble behaviors under the subcooled conditions, the subcooled pool boiling experiments are also performed by using a high speed and high spatial resolution camera with a highly magnified telescope. Resulting from the numerical simulations of the subcooled pool boiling phenomena, the numerical results obtained by the MARS are validated by being compared to the experimental ones and the existing analytical solutions. The numerical results regarding the time evolution of the boiling bubble departure process under the subcooled conditions show a very good agreement with the experimental results. In conclusion, it can be said that the proposed nonempirical boiling and condensation model combined with the MARS has been validated.

Phase Evolution of the Crab Pulsar between Radio and X-Ray

Energy Technology Data Exchange (ETDEWEB)

Yan, L. L.; Ge, M. Y.; Zheng, S. J.; Lu, F. J.; Tuo, Y. L.; Zhang, S. N.; Lu, Y. [Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Yuan, J. P.; Tong, H. [Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi, Xinjiang 830011 (China); Han, J. L. [National Astronomical Observatory, Chinese Academy of Sciences, Jia 20 Datun Road, Beijing 100012 (China); Du, Y. J., E-mail: yanlinli@ihep.ac.cn [Qian Xuesen Laboratory of Space Technology, No. 104, Youyi Road, Haidian District, Beijing 100094 (China)

2017-08-20

We study the X-ray phases of the Crab pulsar utilizing the 11-year observations from the Rossi X-ray Timing Explorer , 6-year radio observations from Nanshan Telescope, and the ephemeris from Jodrell Bank Observatory. It is found that the X-ray phases in different energy bands and the radio phases from the Nanshan Telescope show similar behaviors, including long-time evolution and short-time variations. Such strong correlations between the X-ray and radio phases imply that the radio and X-ray timing noises are both generated from the pulsar spin that cannot be well described by the the monthly ephemeris from the Jodrell Bank observatory. When using the Nanshan phases as references to study the X-ray timing noise, it has a significantly smaller variation amplitude and shows no long-time evolution, with a change rate of (−1.1 ± 1.1) × 10{sup −7} periods per day. These results show that the distance of the X-ray and radio emission regions on the Crab pulsar has no detectable secular change, and it is unlikely that the timing noises resulted from any unique physical processes in the radio or X-ray emitting regions. The similar behaviors of the X-ray and radio timing noises also imply that the variation of the interstellar medium is not the origin of the Crab pulsar’s timing noises, which is consistent with the results obtained from the multi-frequency radio observations of PSR B1540−06.

Numerical modeling of the pulsar wind interaction with ISM

NARCIS (Netherlands)

Bogovalov, S. V.; Chechetkin, V. M.; Koldoba, A. V.; Ustyugova, G. V.; Battiston, R; Shea, MA; Rakowski, C; Chatterjee, S

2006-01-01

Time dependent numerical simulation of relativistic wind interaction with interstellar medium was performed. The winds are ejected from magnetosphere of rotation powered pulsars. The particle flux in the winds is assumed to be isotropic. The energy flux is taken as strongly anisotropic in accordance

Numerical evaluation of a robust self-triggered MPC algorithm

NARCIS (Netherlands)

Brunner, F.D.; Heemels, W.P.M.H.; Allgöwer, F.

2016-01-01

We present numerical examples demonstrating the efficacy of a recently proposed self-triggered model predictive control scheme for disturbed linear discrete-time systems with hard constraints on the input and state. In order to reduce the amount of communication between the controller and the

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

Science.gov (United States)

Alves, E. Paulo; Mori, Warren; Fiuza, Frederico

2017-10-01

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect. This work is supported by DOE FES under FWP 100237 and 100182.

Numerical and experimental analysis of time-dependent load transfer in reinforced concrete columns

Directory of Open Access Journals (Sweden)

L. T. Kataoka

Full Text Available A study was conducted to assess the influence of the steel reinforcement ratio in concrete columns on their properties of creep and shrinkage. Experimental tests and three-dimensional finite element-based simulations of the experimental curves from plain concrete cylinders and plain concrete columns derived by curve fitting were performed using the ACI 209 model available in DIANA 9.3. Columns with longitudinal reinforcement ratios of 0%, 1.4% and 2.8%, loaded to 30% and 40% of their 7-day compressive strength, were investigated. The results indicated that numerical simulation does not predict experimental data for a long period. However, simulations fitted with experimental curves derived from plain concrete columns presented values close to those of experimental data for 91 days.

Numerical Simulation of Moving Load on Concrete Pavements

Directory of Open Access Journals (Sweden)

Lajčáková Gabriela

2015-06-01

Full Text Available The knowledge of the development with time of the strain and stress states in pavement structures is needed in the solution of various engineering tasks as the design fatigue lifetime reliability maintenance and structure development. The space computing model of the truck TATRA 815 is introduced. The pavement computing model is created in the sense of Kirchhof theory of the thin slab on elastic foundation. The goal of the calculation is to obtain the vertical deflection in the middle of the slab and the time courses of vertical tire forces. The equations of motion are derived in the form of differential equations. The assumption about the shape of the slab deflection area is adopted. The equations of the motion are solved numerically in the environment of program system MATLAB. The dependences following the influence of various parameters (speed of vehicle motion, stiffness of subgrade, slab thickness, road profile on the pavement vertical deflections and the vertical tire forces are introduced. The results obtained from the plate computing model are compared with the results obtained by the FEM analysis. The outputs of the numerical solution in the time domain can be transformed into a frequency domain and subsequently used to solve various engineering tasks.

Elimination of numerical diffusion in 1 - phase and 2 - phase flows

Energy Technology Data Exchange (ETDEWEB)

Rajamaeki, M. [VTT Energy (Finland)

1997-07-01

The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods.

Elimination of numerical diffusion in 1 - phase and 2 - phase flows

International Nuclear Information System (INIS)

Rajamaeki, M.

1997-01-01

The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods

TE/TM field solver for particle beam simulations without numerical Cherenkov radiation

Directory of Open Access Journals (Sweden)

Igor Zagorodnov

2005-04-01

Full Text Available The Yee finite-difference time domain method (FDTD is commonly used in wake field and particle-in-cell simulations. However, in accelerator modeling the high energy particles can travel in vacuum faster than their own radiation. This effect is commonly referred to as numerical Cherenkov radiation and is a consequence of numerical grid dispersion. Several numerical approaches are proposed to reduce the dispersion for all angles and for a given frequency range, that justifies itself for domains big in all three directions. On the contrary, in accelerator modeling the transverse dimensions and transverse beam velocity are small, but it is extremely important to eliminate the dispersion error in the well-defined direction of the beam motion for all frequencies. In this paper we propose a new two-level economical conservative scheme for electromagnetic field calculations in three dimensions. The scheme does not have dispersion in the longitudinal direction and is staircase-free (second order convergent. Unlike the FDTD method, it is based on a “transversal-electric/transversal-magnetic” (TE/TM-like splitting of the field components in time. The scheme assures energy and charge conservation. Additionally, the usage of damping terms allows suppressing high frequency noise generated due to the transverse dispersion and the current fluctuations. The dispersion relation of the damping scheme is analyzed. As numerical examples show, the new scheme is much more accurate on the long-time scale than the conventional FDTD approach.

Numerical simulation of convection and heat transfer in Czochralski crystal growth by multiple-relaxation-time LBM

Science.gov (United States)

Liu, Ding; Huang, Weichao; Zhang, Ni

2017-07-01

A two-dimensional axisymmetric swirling model based on the lattice Boltzmann method (LBM) in a pseudo Cartesian coordinate system is posited to simulate Czochralski (Cz) crystal growth in this paper. Specifically, the multiple-relaxation-time LBM (MRT-LBM) combined with the finite difference method (FDM) is used to analyze the melt convection and heat transfer in the process of Cz crystal growth. An incompressible axisymmetric swirling MRT-LB D2Q9 model is applied to solve for the axial and radial velocities by inserting thermal buoyancy and rotational inertial force into the two-dimensional lattice Boltzmann equation. In addition, the melt temperature and the azimuthal velocity are solved by MRT-LB D2Q5 models, and the crystal temperature is solved by FDM. The comparison results of stream functions values of different methods demonstrate that our hybrid model can be used to simulate the fluid-thermal coupling in the axisymmetric swirling model correctly and effectively. Furthermore, numerical simulations of melt convection and heat transfer are conducted under the conditions of high Grashof (Gr) numbers, within the range of 105 ˜ 107, and different high Reynolds (Re) numbers. The experimental results show our hybrid model can obtain the exact solution of complex crystal-growth models and analyze the fluid-thermal coupling effectively under the combined action of natural convection and forced convection.

Stabilization of numerical interchange in spectral-element magnetohydrodynamics

Science.gov (United States)

Sovinec, C. R.

2016-08-01

Auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. The projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code Sovinec et al. [17], provided that the projections introduce numerical dissipation.

Intelligent numerical methods applications to fractional calculus

CERN Document Server

Anastassiou, George A

2016-01-01

In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.

Artificial Boundary Conditions for the Numerical Simulation of Unsteady Acoustic Waves

National Research Council Canada - National Science Library

Tsynkov, S. V

2003-01-01

We construct non-local artificial boundary conditions (ABCs) for the numerical simulation of genuinely time-dependent acoustic waves that propagate from a compact source in an unbounded unobstructed space...

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

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

Development of numerical processing in children with typical and dyscalculic arithmetic skills—a longitudinal study

Science.gov (United States)

Landerl, Karin

2013-01-01

Numerical processing has been demonstrated to be closely associated with arithmetic skills, however, our knowledge on the development of the relevant cognitive mechanisms is limited. The present longitudinal study investigated the developmental trajectories of numerical processing in 42 children with age-adequate arithmetic development and 41 children with dyscalculia over a 2-year period from beginning of Grade 2, when children were 7; 6 years old, to beginning of Grade 4. A battery of numerical processing tasks (dot enumeration, non-symbolic and symbolic comparison of one- and two-digit numbers, physical comparison, number line estimation) was given five times during the study (beginning and middle of each school year). Efficiency of numerical processing was a very good indicator of development in numerical processing while within-task effects remained largely constant and showed low long-term stability before middle of Grade 3. Children with dyscalculia showed less efficient numerical processing reflected in specifically prolonged response times. Importantly, they showed consistently larger slopes for dot enumeration in the subitizing range, an untypically large compatibility effect when processing two-digit numbers, and they were consistently less accurate in placing numbers on a number line. Thus, we were able to identify parameters that can be used in future research to characterize numerical processing in typical and dyscalculic development. These parameters can also be helpful for identification of children who struggle in their numerical development. PMID:23898310

Numerical analysis of fragmentation mechanisms in vapor explosions

Energy Technology Data Exchange (ETDEWEB)

Koshizuka, Seiichi; Ikeda, Hirokazu; Oka, Yoshiaki [Tokyo Univ., Tokai, Ibaraki (Japan). Nuclear Engineering Research Lab.

1998-01-01

Fragmentation of molten metal is the key process in vapor explosions. However this process is so rapid that the mechanisms have not been clarified yet in the experimental studies. Besides, numerical simulation is difficult because we have to analyze water, steam and molten metal simultaneously with evaporation and fragmentation. The authors have been developing a new numerical method, the Moving Particle Semi-implicit (MPS) method, based on moving particles and their interactions. Grids are not necessary. Incompressible flows with fragmentation on free surfaces have been calculated successfully using the MPS method. In the present study numerical simulation of the fragmentation processes using the MPS method is carried out to investigate the mechanisms. A numerical model to calculate evaporation from water to steam is developed. In this model, new particles are generated on water-steam interfaces. Effect of evaporation is also investigated. Growth of the filament is not accelerated when the normal evaporation is considered. This is because the normal evaporation needs a longer time than the moment of the jet impingement, though the filament growth is decided in this moment. Next, rapid evaporation based on spontaneous nucleation is considered. The filament growth is markedly accelerated. This result is consistent with the experimental fact that the spontaneous nucleation temperature is a necessary condition of small-scale vapor explosions. (J.P.N.)

Numerical simulations for radiation hydrodynamics. 2: Transport limit

International Nuclear Information System (INIS)

Dai, W.W.; Woodward, P.R.

2000-01-01

A finite difference scheme is proposed for two-dimensional radiation hydrodynamical equations in the transport limit. The scheme is of Godunov-type, in which the set of time-averaged flux needed in the scheme is calculated through Riemann problems solved. In the scheme, flow signals are explicitly treated, while radiation signals are implicitly treated. Flow fields and radiation fields are updated simultaneously. An iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implicitness of the scheme. The sweeping method used in the scheme significantly reduces the number of iterations or computer CPU time needed. A new approach to further accelerate the convergence is proposed, which further reduces the number of iterations needed by more than one order. No matter how many cells radiation signals propagate in one time step, only an extremely small number of iterations are needed in the scheme, and each iteration costs only about 0.8% of computer CPU time which is needed for one time step of a second order accurate and fully explicit scheme. Two-dimensional problems are treated through a dimensionally split technique. Therefore, iterations for solving the set of algebraic equations are carried out only in each one-dimensional sweep. Through numerical examples it is shown that the scheme keeps the principle advantages of Godunov schemes for flow motion. In the time scale of flow motion numerical results are the same as those obtained from a second order accurate and fully explicit scheme. The acceleration of the convergence proposed in this paper may be directly applied to other hyperbolic systems. This study is important for laser fusion and astrophysics

Linear polarization of BY Draconis

International Nuclear Information System (INIS)

Koch, R.H.; Pfeiffer, R.J.

1976-01-01

Linear polarization measurements are reported in four bandpasses for the flare star BY Dra. The red polarization is intrinsically variable at a confidence level greater than 99 percent. On a time scale of many months, the variability is not phase-locked to either a rotational or a Keplerian ephemeris. The observations of the three other bandpasses are useful principally to indicate a polarization spectrum rising toward shorter wavelengths

Numerical solution of critical state in superconductivity by finite element software

Energy Technology Data Exchange (ETDEWEB)

Hong, Z; Campbell, A M; Coombs, T A [Cambridge University Engineering Department, Trumpington Street, Cambridge CB2 1PZ (United Kingdom)

2006-12-15

A numerical method is proposed to analyse the electromagnetic behaviour of systems including high-temperature superconductors (HTSCs) in time-varying external fields and superconducting cables carrying AC transport current. The E-J constitutive law together with an H-formulation is used to calculate the current distribution and electromagnetic fields in HTSCs, and the magnetization of HTSCs; then the forces in the interaction between the electromagnet and the superconductor and the AC loss of the superconducting cable can be obtained. This numerical method is based on solving the partial differential equations time dependently and is adapted to the commercial finite element software Comsol Multiphysics 3.2. The advantage of this method is to make the modelling of the superconductivity simple, flexible and extendable.

Numerical perturbative methods in the quantum theory of physical systems

International Nuclear Information System (INIS)

Adam, G.

1980-01-01

During the last two decades, development of digital electronic computers has led to the deployment of new, distinct methods in theoretical physics. These methods, based on the advances of modern numerical analysis as well as on specific equations describing physical processes, enabled to perform precise calculations of high complexity which have completed and sometimes changed our image of many physical phenomena. Our efforts have concentrated on the development of numerical methods with such intrinsic performances as to allow a successful approach of some Key issues in present theoretical physics on smaller computation systems. The basic principle of such methods is to translate, in numerical analysis language, the theory of perturbations which is suited to numerical rather than to analytical computation. This idea has been illustrated by working out two problems which arise from the time independent Schroedinger equation in the non-relativistic approximation, within both quantum systems with a small number of particles and systems with a large number of particles, respectively. In the first case, we are led to the numerical solution of some quadratic ordinary differential equations (first section of the thesis) and in the second case, to the solution of some secular equations in the Brillouin area (second section). (author)

Numerical Modeling and Analysis of Transient Electromagnetic Wave Propagation and Scattering

National Research Council Canada - National Science Library

Petropoulos, Peter

2000-01-01

.... We are continuing with analysis and numerical comparisons with exact ABC's in ABC's instead of the simpler Dirichlet boundary condition to terminate the sponge layers in the time-domain is desirable...

Fast numerical solution of KKR-CPA equations: Testing new algorithms

Energy Technology Data Exchange (ETDEWEB)

Bruno, E.; Florio, G.M.; Ginatempo, B.; Giuliano, E.S. (Universita di Messina (Italy))

1994-04-01

Some numerical methods for the solution of KKR-CPA equations are discussed and tested. New, efficient, computational algorithms are proposed, allowing a remarkable reduction of computing time and a good reliability in evaluating spectral quantities. 16 refs., 7 figs.

Numerical simulation of flow-induced vibrations in tube bundles

International Nuclear Information System (INIS)

Elisabeth Longatte; Zaky Bendjeddou; Mhamed Souli

2005-01-01

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

Numerical solution of neutron transport equations in discrete ordinates and slab geometry

International Nuclear Information System (INIS)

Serrano Pedraza, F.

1985-01-01

An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used

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.

Numerical modeling and experimental testing of a wave energy converter: deliverable D4.2

Energy Technology Data Exchange (ETDEWEB)

Zurkinden, A.S.; Kramer, M.; Ferri, F.; Kofoed, J.P.

2013-05-15

The objective of this document is to summarize the outcome of the research which has been carried out during the period May 2011 until June 2012 i.e. during the first year of the PhD study. The work has been done in collaboration with the co-authors. The aim of the project was primarily to provide numerical values for comparison with the experimental test results which were carried out in the same time. It is for this reason why Chapter 4 does consist exclusively of numerical values. Experimental values and measured time series of wave elevations have been used throughout the report in order to a) validate the numerical model and b) preform stochastic analysis. The latter technique is introduced in order to optimize the control parameters of the power take off system. (Author)

NUMERICAL DETERMINATION OF HORIZONTAL SETTLERS PERFORMANCE

Directory of Open Access Journals (Sweden)

M. M. Biliaiev

2015-08-01

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

Exploring the time-saving bias: How drivers misestimate time saved when increasing speed

Directory of Open Access Journals (Sweden)

Eyal Peer

2010-12-01

Full Text Available According to the time-saving bias, drivers underestimate the time saved when increasing from a low speed and overestimate the time saved when increasing from a relatively high speed. Previous research used a specific type of task --- drivers were asked to estimate time saved when increasing speed and to give a numeric response --- to show this. The present research conducted two studies with multiple questions to show that the time-saving bias occurs in other tasks. Study 1 found that drivers committed the time-saving bias when asked to estimate (a the time saved when increasing speed or (b the distance that can be completed at a given time when increasing speed or (c the speed required to complete a given distance in decreasing times. Study 2 showed no major differences in estimations of time saved compared to estimations of the remaining journey time and also between responses given on a numeric scale versus a visual analog scale. Study 3 tested two possible explanations for the time-saving bias: a Proportion heuristic and a Differences heuristic. Some evidence was found for use of the latter.

On the numerical solution of fault trees

International Nuclear Information System (INIS)

Demichela, M.; Piccinini, N.; Ciarambino, I.; Contini, S.

2003-01-01

In this paper an account will be given of the numerical solution of the logic trees directly extracted from the Recursive Operability Analysis. Particular attention will be devoted to the use of the NOT and INH logic gates for correct logical representation of Fault Trees prior to their quantitative resolution. The NOT gate is needed for correct logical representation of events when both non-intervention and correct intervention of a protective system may lead to a Top Event. The INH gate must be used to correctly represent the time link between two events that are both necessary, but must occur in sequence. Some numerical examples will be employed to show both the correct identification of the events entering the INH gates and how use of the AND gate instead of the INH gate leads to overestimation of the probability of occurrence of a Top Event

Numerical and Experimental Study of Amplitude Modulated Positive Corona Discharge

Directory of Open Access Journals (Sweden)

Pablo Martín GOMEZ

2014-12-01

Full Text Available The electrical behavior of a modulated positive corona discharge loudspeaker was studied. A coaxial transducer in air was built using a central copper wire of 75 mm radius (inner electrode and a perforated tube of 11 mm (outer electrode. A high voltage DC supply provided the bias current and a sinusoidal signal was superimposed to measure the discharge admittance. The experimental results could not be matched to previously reported equivalent circuits with fixed components. Using the basic equations that describe the ion motion, a numerical model was proposed. The computed values matched well the experimental data and suggested an equivalent circuit composed of frequency dependent conductance and capacitance. This dependence is closely related to the ion travel time between electrodes (transit time. Simulations carried out at several inter-electrode distances could be synthesized in a single plot where the different results overlap and further emphasize the role of the transit time. This numerical model proved to be an efficient tool to simulate and design modulated corona transducers.

A Dynamical Systems Approach to the Design of the Science Orbit Around Europa

Science.gov (United States)

Gomez, Gerard; Lara, Martin; Russell, Ryan P.

2006-01-01

The science orbit for a future mission to Europa requires low eccentricity, low altitude, and high inclination. However, high inclination orbits around planetary satellites are unstable due to third-body perturbations. Without control, the orbiter impacts Europa after few weeks. To minimize control, a tour over the stable-unstable, averaged manifolds of unstable frozen orbits has been suggested. We proceed with the unaveraged equations and study the manifolds of unstable orbits that are periodic in a rotating frame attached to Europa. Massive numerical computation helps in understanding the unstable dynamics close to Europa, and, thus, in selecting long lifetime high inclination orbits. A final test of a selected set of initial conditions on a high fidelity, ephemeris model, validate the results.

Numerical Hydrodynamics in General Relativity

Directory of Open Access Journals (Sweden)

Font José A.

2003-01-01

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

Uralic numerals : is the evolution of numeral system reconstructable? : (Reading new Václav Balzhek's book on numerals in Eurasia) / Vladimir Napolskich

Index Scriptorium Estoniae

Napolskich, Vladimir

2003-01-01

Rmt.: Balzhek, Václav. Numerals. Comparative-etymological analyses of numeral systems and their implications (saharan, nubian, egyptian, berber, kartvelian, ralic, altaic and indo-european languages). Brno, 1999. (Spisy Masarykovy Univerzity v Brné. Filozofická fakulta; 322). Ülevaade uurali keelte arvsõnu käsitlevast osast

Numerical relativity beyond astrophysics

Science.gov (United States)

Garfinkle, David

2017-01-01

Though the main applications of computer simulations in relativity are to astrophysical systems such as black holes and neutron stars, nonetheless there are important applications of numerical methods to the investigation of general relativity as a fundamental theory of the nature of space and time. This paper gives an overview of some of these applications. In particular we cover (i) investigations of the properties of spacetime singularities such as those that occur in the interior of black holes and in big bang cosmology. (ii) investigations of critical behavior at the threshold of black hole formation in gravitational collapse. (iii) investigations inspired by string theory, in particular analogs of black holes in more than 4 spacetime dimensions and gravitational collapse in spacetimes with a negative cosmological constant.

Numerical relativity beyond astrophysics.

Science.gov (United States)

Garfinkle, David

2017-01-01

Though the main applications of computer simulations in relativity are to astrophysical systems such as black holes and neutron stars, nonetheless there are important applications of numerical methods to the investigation of general relativity as a fundamental theory of the nature of space and time. This paper gives an overview of some of these applications. In particular we cover (i) investigations of the properties of spacetime singularities such as those that occur in the interior of black holes and in big bang cosmology. (ii) investigations of critical behavior at the threshold of black hole formation in gravitational collapse. (iii) investigations inspired by string theory, in particular analogs of black holes in more than 4 spacetime dimensions and gravitational collapse in spacetimes with a negative cosmological constant.

MHD turbulent dynamo in astrophysics: Theory and numerical simulation

Science.gov (United States)

Chou, Hongsong

2001-10-01

This thesis treats the physics of dynamo effects through theoretical modeling of magnetohydrodynamic (MHD) systems and direct numerical simulations of MHD turbulence. After a brief introduction to astrophysical dynamo research in Chapter 1, the following issues in developing dynamic models of dynamo theory are addressed: In Chapter 2, nonlinearity that arises from the back reaction of magnetic field on velocity field is considered in a new model for the dynamo α-effect. The dependence of α-coefficient on magnetic Reynolds number, kinetic Reynolds number, magnetic Prandtl number and statistical properties of MHD turbulence is studied. In Chapter 3, the time-dependence of magnetic helicity dynamics and its influence on dynamo effects are studied with a theoretical model and 3D direct numerical simulations. The applicability of and the connection between different dynamo models are also discussed. In Chapter 4, processes of magnetic field amplification by turbulence are numerically simulated with a 3D Fourier spectral method. The initial seed magnetic field can be a large-scale field, a small-scale magnetic impulse, and a combination of these two. Other issues, such as dynamo processes due to helical Alfvénic waves and the implication and validity of the Zeldovich relation, are also addressed in Appendix B and Chapters 4 & 5, respectively. Main conclusions and future work are presented in Chapter 5. Applications of these studies are intended for astrophysical magnetic field generation through turbulent dynamo processes, especially when nonlinearity plays central role. In studying the physics of MHD turbulent dynamo processes, the following tools are developed: (1)A double Fourier transform in both space and time for the linearized MHD equations (Chapter 2 and Appendices A & B). (2)A Fourier spectral numerical method for direct simulation of 3D incompressible MHD equations (Appendix C).

Numerical semigroups and applications

CERN Document Server

Assi, Abdallah

2016-01-01

This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher leve...

Modeling and numerical simulation of multi-component flow in porous media

International Nuclear Information System (INIS)

Saad, B.

2011-01-01

This work deals with the modelization and numerical simulation of two phase multi-component flow in porous media. The study is divided into two parts. First we study and prove the mathematical existence in a weak sense of two degenerate parabolic systems modeling two phase (liquid and gas) two component (water and hydrogen) flow in porous media. In the first model, we assume that there is a local thermodynamic equilibrium between both phases of hydrogen by using the Henry's law. The second model consists of a relaxation of the previous model: the kinetic of the mass exchange between dissolved hydrogen and hydrogen in the gas phase is no longer instantaneous. The second part is devoted to the numerical analysis of those models. Firstly, we propose a numerical scheme to compare numerical solutions obtained with the first model and numerical solutions obtained with the second model where the characteristic time to recover the thermodynamic equilibrium goes to zero. Secondly, we present a finite volume scheme with a phase-by-phase upstream weighting scheme without simplified assumptions on the state law of gas densities. We also validate this scheme on a 2D test cases. (author)

Numerical solution of the Navier--Stokes equations at high Reynolds numbers

International Nuclear Information System (INIS)

Shestakov, A.I.

1974-01-01

A numerical method is presented which is designed to solve the Navier-Stokes equations for two-dimensional, incompressible flow. The method is intended for use on problems with high Reynolds numbers for which calculations via finite difference methods have been unattainable or unreliable. The proposed scheme is a hybrid utilizing a time-splitting finite difference method in areas away from the boundaries. In areas neighboring the boundaries, the equations of motion are solved by the newly proposed vortex method by Chorin. The major accomplishment of the new scheme is that it contains a simple way for merging the two methods at the interface of the two subdomains. The proposed algorithm is designed for use on the time-dependent equations but can be used on steady state problems as well. The method is tested on the popular, time-independent, square cavity problem, an example of a separated flow with closed streamlines. Numerical results are presented for a Reynolds number of 10 3 . (auth)

Numerical solution of boundary-integral equations for molecular electrostatics.

Science.gov (United States)

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

Numerical studies on divertor experiments

International Nuclear Information System (INIS)

Ueda, N.; Itoh, K.; Itoh, S.-I.; Tanaka, M.; Hasegawa, M.; Shoji, T.; Sugihara, M.

1988-04-01

Numerical analysis on the divertor experiments such as JFT-2M tokamak is made by use of the two-dimensional time-dependent simulation code. The plasma in the scrape-off layer (SOL) and divertor region is solved for the given particle and heat sources from the main plasma, Γ p and Q T . Effect of the direction of the toroidal magnetic field is studied. It is found that the heat flux which is proportional to b vector x ∇T i has influences on the divertor plasmas, but has a small effect on the parameters on the midplane in the framework of the fluid model. Parameter survey on Γ p and Q T is made. The transient response of the SOL/divertor plasma to the sudden change of Γ p and Q T is studied. Time delay in the SOL and divertor region is calculated. (author)

Numerical solution of the polymer system

Energy Technology Data Exchange (ETDEWEB)

Haugse, V.; Karlsen, K.H.; Lie, K.-A.; Natvig, J.R.

1999-05-01

The paper describes the application of front tracking to the polymer system, an example of a nonstrictly hyperbolic system. Front tracking computes piecewise constant approximations based on approximate Remain solutions and exact tracking of waves. It is well known that the front tracking method may introduce a blow-up of the initial total variation for initial data along the curve where the two eigenvalues of the hyperbolic system are identical. It is demonstrated by numerical examples that the method converges to the correct solution after a finite time that decreases with the discretization parameter. For multidimensional problems, front tracking is combined with dimensional splitting and numerical experiments indicate that large splitting steps can be used without loss of accuracy. Typical CFL numbers are in the range of 10 to 20 and comparisons with the Riemann free, high-resolution method confirm the high efficiency of front tracking. The polymer system, coupled with an elliptic pressure equation, models two-phase, tree-component polymer flooding in an oil reservoir. Two examples are presented where this model is solved by a sequential time stepping procedure. Because of the approximate Riemann solver, the method is non-conservative and CFL members must be chosen only moderately larger than unity to avoid substantial material balance errors generated in near-well regions after water breakthrough. Moreover, it is demonstrated that dimensional splitting may introduce severe grid orientation effects for unstable displacements that are accentuated for decreasing discretization parameters. 9 figs., 2 tabs., 26 refs.

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

Numerical implementation of the Dirac equation on hypercube multicomputers

International Nuclear Information System (INIS)

Wells, J.C.

1991-01-01

Motivated by an interest in nonperturbative electromagnetic lepton-pair production in relativistic heavy-ion collisions, we discuss the numerical methods used in implementing a lattice solution of the time-dependent Dirac equation in three-dimensional Cartesian coordinates. Discretization is obtained using the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions, and represented on a spatial lattice. All numerical procedures reduce to a series of matrix-vector operations which we perform on the Intel iPSC/860 hypercube multicomputer. We discuss solutions to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data parallel computers

The Finite Element Numerical Modelling of 3D Magnetotelluric

Directory of Open Access Journals (Sweden)

Ligang Cao

2014-01-01

Full Text Available The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.

Monoenergetic time-dependent neutron transport in an infinite medium with time-varying cross sections

International Nuclear Information System (INIS)

Ganapol, B.D.

1987-01-01

For almost 20 yr, the main thrust of the author's research has been the generation of as many benchmark solutions to the time-dependent monoenergetic neutron transport equation as possible. The major motivation behind this effort has been to provide code developers with highly accurate numerical solutions to serve as standards in the assessment of numerical transport algorithms. In addition, these solutions provide excellent educational tools since the important physical features of neutron transport are still present even though the problems solved are idealized. A secondary motivation, though of equal importance, is the intellectual stimulation and understanding provided by the combination of the analytical, numerical, and computational techniques required to obtain these solutions. Therefore, to further the benchmark development, the added complication of time-dependent cross sections in the one-group transport equation is considered here

Numerical problems in physics

CERN Document Server

Singh, Devraj

2015-01-01

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

Influence of mesh non-orthogonality on numerical simulation of buoyant jet flows

International Nuclear Information System (INIS)

Ishigaki, Masahiro; Abe, Satoshi; Sibamoto, Yasuteru; Yonomoto, Taisuke

2017-01-01

Highlights: • Influence of mesh non-orthogonality on numerical solution of buoyant jet flows. • Buoyant jet flows are simulated with hexahedral and prismatic meshes. • Jet instability with prismatic meshes may be overestimated compared to that with hexahedral meshes. • Modified solvers that can reduce the influence of mesh non-orthogonality and reduce computation time are proposed. - Abstract: In the present research, we discuss the influence of mesh non-orthogonality on numerical solution of a type of buoyant flow. Buoyant jet flows are simulated numerically with hexahedral and prismatic mesh elements in an open source Computational Fluid Dynamics (CFD) code called “OpenFOAM”. Buoyant jet instability obtained with the prismatic meshes may be overestimated compared to that obtained with the hexahedral meshes when non-orthogonal correction is not applied in the code. Although the non-orthogonal correction method can improve the instability generated by mesh non-orthogonality, it may increase computation time required to reach a convergent solution. Thus, we propose modified solvers that can reduce the influence of mesh non-orthogonality and reduce the computation time compared to the existing solvers in OpenFOAM. It is demonstrated that calculations for a buoyant jet with a large temperature difference are performed faster by the modified solver.

Influence of mesh non-orthogonality on numerical simulation of buoyant jet flows

Energy Technology Data Exchange (ETDEWEB)

Ishigaki, Masahiro, E-mail: ishigaki.masahiro@jaea.go.jp; Abe, Satoshi; Sibamoto, Yasuteru; Yonomoto, Taisuke

2017-04-01

Highlights: • Influence of mesh non-orthogonality on numerical solution of buoyant jet flows. • Buoyant jet flows are simulated with hexahedral and prismatic meshes. • Jet instability with prismatic meshes may be overestimated compared to that with hexahedral meshes. • Modified solvers that can reduce the influence of mesh non-orthogonality and reduce computation time are proposed. - Abstract: In the present research, we discuss the influence of mesh non-orthogonality on numerical solution of a type of buoyant flow. Buoyant jet flows are simulated numerically with hexahedral and prismatic mesh elements in an open source Computational Fluid Dynamics (CFD) code called “OpenFOAM”. Buoyant jet instability obtained with the prismatic meshes may be overestimated compared to that obtained with the hexahedral meshes when non-orthogonal correction is not applied in the code. Although the non-orthogonal correction method can improve the instability generated by mesh non-orthogonality, it may increase computation time required to reach a convergent solution. Thus, we propose modified solvers that can reduce the influence of mesh non-orthogonality and reduce the computation time compared to the existing solvers in OpenFOAM. It is demonstrated that calculations for a buoyant jet with a large temperature difference are performed faster by the modified solver.

Transient productivity index for numerical well test simulations

Energy Technology Data Exchange (ETDEWEB)

Blanc, G.; Ding, D.Y.; Ene, A. [Institut Francais du Petrole, Pau (France)] [and others

1997-08-01

The most difficult aspect of numerical simulation of well tests is the treatment of the Bottom Hole Flowing (BHF) Pressure. In full field simulations, this pressure is derived from the Well-block Pressure (WBP) using a numerical productivity index which accounts for the grid size and permeability, and for the well completion. This productivity index is calculated assuming a pseudo-steady state flow regime in the vicinity of the well and is therefore constant during the well production period. Such a pseudo-steady state assumption is no longer valid for the early time of a well test simulation as long as the pressure perturbation has not reached several grid-blocks around the well. This paper offers two different solutions to this problem: (1) The first one is based on the derivation of a Numerical Transient Productivity Index (NTPI) to be applied to Cartesian grids; (2) The second one is based on the use of a Corrected Transmissibility and Accumulation Term (CTAT) in the flow equation. The representation of the pressure behavior given by both solutions is far more accurate than the conventional one as shown by several validation examples which are presented in the following pages.

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.

Radiation transport in numerical astrophysics

International Nuclear Information System (INIS)

Lund, C.M.

1983-02-01

In this article, we discuss some of the numerical techniques developed by Jim Wilson and co-workers for the calculation of time-dependent radiation flow. Difference equations for multifrequency transport are given for both a discrete-angle representation of radiation transport and a Fick's law-like representation. These methods have the important property that they correctly describe both the streaming and diffusion limits of transport theory in problems where the mean free path divided by characteristic distances varies from much less than one to much greater than one. They are also stable for timesteps comparable to the changes in physical variables, rather than being limited by stability requirements

Numerical double layer solutions with ionization

International Nuclear Information System (INIS)

Andersson, D.; Soerensen, J.

1982-08-01

Maxwell's equation div D = ro in one dimension is solved numerically, taking ionization into account. Time independent anode sheath and double layer solutions are obtained. By varying voltage, neutral gas pressure, temperature of the trapped ions on the cathode side and density and temperature of the trapped electrones on the anode side, diagrams are constructed that show permissible combinations of these parameters. Results from a recent experiment form a subset. Distribution functions, the Langmuir condition, some scaling laws and a possible application to the lower ionosphere are discussed. (Authors)

Numerical method for partial equilibrium flow

International Nuclear Information System (INIS)

Ramshaw, J.D.; Cloutman, L.D.; Los Alamos, New Mexico 87545)

1981-01-01

A numerical method is presented for chemically reactive fluid flow in which equilibrium and nonequilibrium reactions occur simultaneously. The equilibrium constraints on the species concentrations are established by a quadratic iterative procedure. If the equilibrium reactions are uncoupled and of second or lower order, the procedure converges in a single step. In general, convergence is most rapid when the reactions are weakly coupled. This can frequently be achieved by a judicious choice of the independent reactions. In typical transient calculations, satisfactory accuracy has been achieved with about five iterations per time step

Numerical analysis using Sage

CERN Document Server

Anastassiou, George A

2015-01-01

This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application.  Answers may be verified using Sage.  The presented code, written in core components of Sage, are backward compatible, i.e., easily applicable to other software systems such as Mathematica®.  Sage is  open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity with any programming language is a p...

Development of numerical processing in children with typical and dyscalculic arithmetic skills – a longitudinal study

Directory of Open Access Journals (Sweden)

Karin eLanderl

2013-07-01

Full Text Available Numerical processing has been demonstrated to be closely associated with arithmetic skills, however, our knowledge on the development of the relevant cognitive mechanisms is limited. The present longitudinal study investigated the developmental trajectories of numerical processing in 42 children with age-adequate arithmetic development and 41 children with dyscalculia over a two-year period from beginning of Grade 2, when children were 7;6 years old, to beginning of Grade 4. A battery of numerical processing tasks (dot enumeration, non-symbolic and symbolic comparison of one- and two-digit numbers, physical comparison, number line estimation was given five times during the study (beginning and middle of each school year. Efficiency of numerical processing was a very good indicator of development in numerical processing while within-task effects remained largely constant and showed low long-term stability before middle of Grade 3. Children with dyscalculia showed less efficient numerical processing reflected in specifically prolonged response times. Importantly, they showed consistently larger slopes for dot enumeration in the subitizing range, an untypically large compatibility effect when processing two-digit numbers, and they were consistently less accurate in placing numbers on a number line. Thus, we were able to identify parameters that can be used in future research to characterize numerical processing in typical and dyscalculic development. These parameters can also be helpful for identification of children who struggle in their numerical development.

Numerical simulation of runaway electron effect on Plasma Facing Components

International Nuclear Information System (INIS)

Ezato, Koichiro; Suzuki, Satoshi; Akiba, Masato; Kunugi, Tomoaki

1998-07-01

The runaway electron effects on Plasma Facing Components (PFCs) are studied by the numerical analyses. The present study is the first investigation of time-dependent thermal response of PFCs caused by runaway electron impact. For this purpose, we developed a new integrated numerical code, which consists of the Monte Carlo code for the coupled electrons and photons transport analysis and the finite element code for the thermo-mechanical analysis. In this code, we apply the practical incident parameters and distribution of runaway electrons recently proposed by S. Putvinski, which can express the time-dependent behavior of runaway electrons impact. The incident parameters of electrons in this study are the energy density ranging from 10 to 75 MJ/m 2 , the average electrons' energy of 12.5 MeV, the incident angle of 0.01deg and the characteristic time constant for decay of runaway electrons event of 0.15sec. The numerical results showed that the divertor with CFC (Carbon-Fiber-Composite) armor did not suffer serious damage. On the other hand, maximum temperatures at the surface of the divertor with tungsten armor and the first wall with beryllium armor exceed the melting point in case of the incident energy density of 20 and 50 MJ/m 2 . Within the range of the incident condition of runaway electrons, the cooling pipe of each PFCs can be prevented from the melting or burn-out caused by runaway electrons impact, which is one of the possible consequences of runaway electrons event so far. (author)

Numerical and experimental investigation of the melt casting of explosives

Energy Technology Data Exchange (ETDEWEB)

Sun, Dawei; Garimella, Suresh V. [School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088 (United States); Singh, Sanjeev; Naik, Neelam [US Army Armaments Research, Development and Engineering Center, Picatinny Arsenal, NJ 07806 (United States)

2005-10-01

Melt casting of energetic materials is investigated, and a numerical model is formulated for the analysis of the coupled fluid flow, heat transfer, and stress fields involved in this phase-change process. The numerical model is based on a conservative multi block control volume method. The SIMPLE algorithm is employed along with an enthalpy method approach to model the solidification process. Results from the model are verified against analytical solutions, experimental results, and published numerical results for simplified cases. In the melt casting of RDX-binder mixtures, the very high viscosity of the melt limits the influence of melt convection. The impacts of different cooling conditions on the velocity, temperature and stress distributions, as well as on the solidification time, are discussed. The present model can be used to improve the quality of cast explosives, by optimizing and controlling the processing conditions. (Abstract Copyright [2005], Wiley Periodicals, Inc.)

7th International Conference on Hyperbolic Problems Theory, Numerics, Applications

CERN Document Server

Jeltsch, Rolf

1999-01-01

These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phe...

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 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.

On the elimination of numerical Cerenkov radiation in PIC simulations

International Nuclear Information System (INIS)

Greenwood, Andrew D.; Cartwright, Keith L.; Luginsland, John W.; Baca, Ernest A.

2004-01-01

Particle-in-cell (PIC) simulations are a useful tool in modeling plasma in physical devices. The Yee finite difference time domain (FDTD) method is commonly used in PIC simulations to model the electromagnetic fields. However, in the Yee FDTD method, poorly resolved waves at frequencies near the cut off frequency of the grid travel slower than the physical speed of light. These slowly traveling, poorly resolved waves are not a problem in many simulations because the physics of interest are at much lower frequencies. However, when high energy particles are present, the particles may travel faster than the numerical speed of their own radiation, leading to non-physical, numerical Cerenkov radiation. Due to non-linear interaction between the particles and the fields, the numerical Cerenkov radiation couples into the frequency band of physical interest and corrupts the PIC simulation. There are two methods of mitigating the effects of the numerical Cerenkov radiation. The computational stencil used to approximate the curl operator can be altered to improve the high frequency physics, or a filtering scheme can be introduced to attenuate the waves that cause the numerical Cerenkov radiation. Altering the computational stencil is more physically accurate but is difficult to implement while maintaining charge conservation in the code. Thus, filtering is more commonly used. Two previously published filters by Godfrey and Friedman are analyzed and compared to ideally desired filter properties

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.

A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

Directory of Open Access Journals (Sweden)

Rongwu Lu

2017-01-01

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

Interactive Numerical and Symbolic Analysis: A New Paradigm for Teaching Electronics

Directory of Open Access Journals (Sweden)

Jean-Claude Thomassian

2008-09-01

Full Text Available Analog Insydes, Mathematica’s symbolic circuit analysis toolbox, uses modern algorithms of expression simplification depending on comparisons with a numerical reference solution of the circuit under investigation. Some insight is offered on how the complexity of an expression barrier is overcome followed by two classical examples, a BJT emitter follower and a MOSFET common-gate amplifier stage to illustrate the proposed method at work. A concluding section discusses that time spent teaching introductory electronics by computer-aided circuit analysis, interactive numerical and symbolic, is a worthwhile investment.

A Numerical Method for Analyzing Electromagnetic Scattering Properties of a Moving Conducting Object

Directory of Open Access Journals (Sweden)

Lei Kuang

2014-01-01

Full Text Available A novel numerical approach is developed to analyze electromagnetic scattering properties of a moving conducting object based on the finite-difference time-domain (FDTD algorithm. Relativistic boundary conditions are implemented into the FDTD algorithm to calculate the electromagnetic field on the moving boundary. An improved technique is proposed to solve the scattered field in order to improve the computational efficiency and stability of solutions. The time-harmonic scattered field from a one-dimensional moving conducting surface is first simulated by the proposed approach. Numerical results show that the amplitude and frequency of the scattered field suffer a modulation shift. Then the transient scattered field is calculated, and broadband electromagnetic scattering properties of the moving conducting surface are obtained by the fast Fourier transform (FFT. Finally, the scattered field from a two-dimensional moving square cylinder is analyzed. The numerical results demonstrate the Doppler effect of a moving conducting object. The simulated results agree well with analytical results.

Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

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Fei Chen

2013-01-01

Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

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)

JDiffraction: A GPGPU-accelerated JAVA library for numerical propagation of scalar wave fields

Science.gov (United States)

Piedrahita-Quintero, Pablo; Trujillo, Carlos; Garcia-Sucerquia, Jorge

2017-05-01

JDiffraction, a GPGPU-accelerated JAVA library for numerical propagation of scalar wave fields, is presented. Angular spectrum, Fresnel transform, and Fresnel-Bluestein transform are the numerical algorithms implemented in the methods and functions of the library to compute the scalar propagation of the complex wavefield. The functionality of the library is tested with the modeling of easy to forecast numerical experiments and also with the numerical reconstruction of a digitally recorded hologram. The performance of JDiffraction is contrasted with a library written for C++, showing great competitiveness in the apparently less complex environment of JAVA language. JDiffraction also includes JAVA easy-to-use methods and functions that take advantage of the computation power of the graphic processing units to accelerate the processing times of 2048×2048 pixel images up to 74 frames per second.

Numerical model for the thermal behavior of thermocline storage tanks

Science.gov (United States)

Ehtiwesh, Ismael A. S.; Sousa, Antonio C. M.

2018-03-01

Energy storage is a critical factor in the advancement of solar thermal power systems for the sustained delivery of electricity. In addition, the incorporation of thermal energy storage into the operation of concentrated solar power systems (CSPs) offers the potential of delivering electricity without fossil-fuel backup even during peak demand, independent of weather conditions and daylight. Despite this potential, some areas of the design and performance of thermocline systems still require further attention for future incorporation in commercial CSPs, particularly, their operation and control. Therefore, the present study aims to develop a simple but efficient numerical model to allow the comprehensive analysis of thermocline storage systems aiming better understanding of their dynamic temperature response. The validation results, despite the simplifying assumptions of the numerical model, agree well with the experiments for the time evolution of the thermocline region. Three different cases are considered to test the versatility of the numerical model; for the particular type of a storage tank with top round impingement inlet, a simple analytical model was developed to take into consideration the increased turbulence level in the mixing region. The numerical predictions for the three cases are in general good agreement against the experimental results.

An Experimental-Numerical Study of Small Scale Flow Interaction with Bioluminescent Plankton

National Research Council Canada - National Science Library

Latz, Michael

1998-01-01

Numerical and experimental approaches were used to investigate the effects of quantified flow stimuli on bioluminescence sUmulatidn at the small length and time scales appropriate for individual plankton...

A semi-implicit, second-order-accurate numerical model for multiphase underexpanded volcanic jets

Directory of Open Access Journals (Sweden)

S. Carcano

2013-11-01

Full Text Available An improved version of the PDAC (Pyroclastic Dispersal Analysis Code, Esposti Ongaro et al., 2007 numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation of multiphase volcanic jets in supersonic regimes. The present version of PDAC includes second-order time- and space discretizations and fully multidimensional advection discretizations in order to reduce numerical diffusion and enhance the accuracy of the original model. The model is tested on the problem of jet decompression in both two and three dimensions. For homogeneous jets, numerical results are consistent with experimental results at the laboratory scale (Lewis and Carlson, 1964. For nonequilibrium gas–particle jets, we consider monodisperse and bidisperse mixtures, and we quantify nonequilibrium effects in terms of the ratio between the particle relaxation time and a characteristic jet timescale. For coarse particles and low particle load, numerical simulations well reproduce laboratory experiments and numerical simulations carried out with an Eulerian–Lagrangian model (Sommerfeld, 1993. At the volcanic scale, we consider steady-state conditions associated with the development of Vulcanian and sub-Plinian eruptions. For the finest particles produced in these regimes, we demonstrate that the solid phase is in mechanical and thermal equilibrium with the gas phase and that the jet decompression structure is well described by a pseudogas model (Ogden et al., 2008. Coarse particles, on the other hand, display significant nonequilibrium effects, which associated with their larger relaxation time. Deviations from the equilibrium regime, with maximum velocity and temperature differences on the order of 150 m s−1 and 80 K across shock waves, occur especially during the rapid acceleration phases, and are able to modify substantially the jet dynamics with respect to the homogeneous case.

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

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

Science.gov (United States)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Direct numerical simulation of axisymmetric laminar low-density jets

Science.gov (United States)

Gomez Lendinez, Daniel; Coenen, Wilfried; Sevilla, Alejandro

2017-11-01

The stability of submerged laminar axisymmetric low-density jets has been investigated experimentally (Kyle & Sreenivasan 1993, Hallberg & Strykowski 2006) and with linear analysis (Jendoubi & Strykowski 1994, Coenen & Sevilla 2012, Coenen et al. 2017). These jets become globally unstable when the Reynolds number is larger than a certain critical value which depends on the density ratio and on the velocity profile at the injector outlet. In this work, Direct Numerical Simulations using FreeFEM + + (Hecht 2012) with P1 elements for pressure and P2 for velocity and density are performed to complement the above mentioned studies. Density and velocity fields are analyzed at long time showing the unforced space-time evolution of nonlinear disturbances propagating along the jet. Using the Stuart-Landau model to fit the numerical results for the self-excited oscillations we have computed a neutral stability curve that shows good agreement with experiments and stability theory. Thanks to Spanish MINECO under projects DPI2014-59292-C3-1-P and DPI2015-71901-REDT for financial support.

Numerical modeling and optimization of the Iguassu gas centrifuge

Science.gov (United States)

Bogovalov, S. V.; Borman, V. D.; Borisevich, V. D.; Tronin, V. N.; Tronin, I. V.

2017-07-01

The full procedure of the numerical calculation of the optimized parameters of the Iguassu gas centrifuge (GC) is under discussion. The procedure consists of a few steps. On the first step the problem of a hydrodynamical flow of the gas in the rotating rotor of the GC is solved numerically. On the second step the problem of diffusion of the binary mixture of isotopes is solved. The separation power of the gas centrifuge is calculated after that. On the last step the time consuming procedure of optimization of the GC is performed providing us the maximum of the separation power. The optimization is based on the BOBYQA method exploring the results of numerical simulations of the hydrodynamics and diffusion of the mixture of isotopes. Fast convergence of calculations is achieved due to exploring of a direct solver at the solution of the hydrodynamical and diffusion parts of the problem. Optimized separative power and optimal internal parameters of the Iguassu GC with 1 m rotor were calculated using the developed approach. Optimization procedure converges in 45 iterations taking 811 minutes.

GPU based numerical simulation of core shooting process

Directory of Open Access Journals (Sweden)

Yi-zhong Zhang

2017-11-01

Full Text Available Core shooting process is the most widely used technique to make sand cores and it plays an important role in the quality of sand cores. Although numerical simulation can hopefully optimize the core shooting process, research on numerical simulation of the core shooting process is very limited. Based on a two-fluid model (TFM and a kinetic-friction constitutive correlation, a program for 3D numerical simulation of the core shooting process has been developed and achieved good agreements with in-situ experiments. To match the needs of engineering applications, a graphics processing unit (GPU has also been used to improve the calculation efficiency. The parallel algorithm based on the Compute Unified Device Architecture (CUDA platform can significantly decrease computing time by multi-threaded GPU. In this work, the program accelerated by CUDA parallelization method was developed and the accuracy of the calculations was ensured by comparing with in-situ experimental results photographed by a high-speed camera. The design and optimization of the parallel algorithm were discussed. The simulation result of a sand core test-piece indicated the improvement of the calculation efficiency by GPU. The developed program has also been validated by in-situ experiments with a transparent core-box, a high-speed camera, and a pressure measuring system. The computing time of the parallel program was reduced by nearly 95% while the simulation result was still quite consistent with experimental data. The GPU parallelization method can successfully solve the problem of low computational efficiency of the 3D sand shooting simulation program, and thus the developed GPU program is appropriate for engineering applications.

Time-dependent scattering in resonance lines

International Nuclear Information System (INIS)

Kunasz, P.B.

1983-01-01

A numerical finite-difference method is presented for the problem of time-dependent line transfer in a finite slab in which material density is sufficiently low that the time of flight between scatterings greatly exceeds the relaxation time of the upper state of the scattering transition. The medium is assumed to scatter photons isotropically, with complete frequency redistribution. Numerical solutions are presented for a homogeneous, time-independent slab illuminated by an externally imposed radiation field which enters the slab at t = 0. Graphical results illustrate relaxation to steady state of trapped internal radiation, emergent energy, and emergent profiles. A review of the literature is also given in which the time-dependent line transfer problem is discussed in the context of recent analytical work

Numerical solution of the radionuclide transport equation

International Nuclear Information System (INIS)

Hadermann, J.; Roesel, F.

1983-11-01

A numerical solution of the one-dimensional geospheric radionuclide chain transport equation based on the pseudospectral method is developed. The advantages of this approach are flexibility in incorporating space and time dependent migration parameters, arbitrary boundary conditions and solute rock interactions as well as efficiency and reliability. As an application the authors investigate the impact of non-linear sorption isotherms on migration in crystalline rock. It is shown that non-linear sorption, in the present case a Freundlich isotherm, may reduce concentration at the geosphere outlet by orders of magnitude provided the migration time is comparable or larger than the half-life of the nuclide in question. The importance of fixing dispersivity within the continuum approach is stressed. (Auth.)

Numerical Gram-Schmidt orthonormalization

International Nuclear Information System (INIS)

Werneth, Charles M; Dhar, Mallika; Maung, Khin Maung; Sirola, Christopher; Norbury, John W