Calculation and modular properties of multiloop superstring amplitudes
Danilov, G. S.
2013-01-01
Multiloop superstring amplitudes are calculated within an extensively used gauge where the two-dimensional gravitino field carries Grassmann moduli. In general, the amplitudes possess, instead of modular symmetry, symmetry with respect to modular transformation supplemented with appropriate transformations of two-dimensional local supersymmetry. If the number of loops is larger than three, the integrationmeasures are notmodular forms, while the expression for the amplitude contains integrals along the boundary of the fundamental region of the modular group.
Calculation and modular properties of multi-loop superstring amplitudes
Danilov, G S
2012-01-01
Multi-loop superstring amplitude is calculated in the conventional gauge where Grassmann moduli are carried by the 2D gravitino field. Generally, instead of the modular symmetry, the amplitudes hold the symmetry under modular transformations added by relevant transformations of the 2D local supersymmetry. If a number of loops are larger than 3, the integration measures are not modular forms. In this case the expression for the amplitude contains an integral over the bound of the fundamental region of the modular group. (paper)
Technology of multiloop calculations for closed bosonic strings
Ramachandran, R.
1986-03-01
In this article, we trace the essentials of the technology of multiloop computations in the covariant Polyakov formalism of the closed bosonic string theory in the critical dimension. We discuss how we may isolate the divergences in the multiloop vacuum amplitude and show that they are interpreted as due to tadpole diagrams in which the dilaton goes into vacuum. (author)
Results and techniques of multi-loop calculations
Steinhauser, M.
2002-01-01
In this review some recent multi-loop results obtained in the framework of perturbative quantum chromodynamics (QCD) and quantum electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore the connection to observables involving a scalar Higgs boson is worked out in detail. An all-order low energy v theorem is derived which establishes a relation between the coefficient functions in the hadronic Higgs decay and the decoupling constants. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order α s 4 and α s 3 , respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Pade approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass-dependence. In particular, we concentrate on the evaluation of the total cross section for the production of hadrons in e + e - annihilation. The knowledge of the complete mass dependence at order α s 2 has triggered a bunch of theory-driven analyses of the hadronic contribution to the electromagnetic coupling evaluated at high energy scales. The status is summarized in this review. In a further application four-loop diagrams are considered which contribute to the order α 2 QED corrections to the μ decay. Its relevance for the determination of the Fermi constant G F is discussed. Finally the calculation of the three-loop relation between the anti M anti S and on
Radial electromagnetic force calculation of induction motor based on multi-loop theory
HE Haibo
2017-12-01
Full Text Available [Objectives] In order to study the vibration and noise of induction motors, a method of radial electromagnetic force calculation is established on the basis of the multi-loop model.[Methods] Based on the method of calculating air-gap magneto motive force according to stator and rotor fundamental wave current, the analytic formulas are deduced for calculating the air-gap magneto motive force and radial electromagnetic force generated in accordance with any stator winding and rotor conducting bar current. The multi-loop theory and calculation method for the electromagnetic parameters of a motor are introduced, and a dynamic simulation model of an induction motor built to achieve the current of the stator winding and rotor conducting bars, and obtain the calculation formula of radial electromagnetic force. The radial electromagnetic force and vibration are then estimated.[Results] The experimental results indicate that the vibration acceleration frequency and amplitude of the motor are consistent with the experimental results.[Conclusions] The results and calculation method can support the low noise design of converters.
Calculation of chiral determinants and multiloop amplitudes by cutting and sewing method
Losev, A.
1989-01-01
Functional integrals over fermions on open Riemann surfaces are determined up to a multiplicative constant by conservation laws. Using a cutting and sewing method these constants are found. Multiloop statsums and amplitudes as a product of anomaly-free expressions in Schottky parametrization and statsums on spheres are obtained. 5 refs
Paradoxes in numerical calculations
Brandts, J.; Křížek, Michal; Zhang, Z.
2016-01-01
Roč. 26, č. 3 (2016), s. 317-330 ISSN 1210-0552 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : round-off errors * numerical instability * recurrence formulae Subject RIV: BA - General Mathematics Impact factor: 0.394, year: 2016
Numerical calculations near spatial infinity
Zenginoglu, Anil
2007-01-01
After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied. The reduced conformal field equations based on the conformal Gauss gauge allow us in spherical symmetry to calculate numerically the entire Schwarzschild-Kruskal spacetime in a smooth way including spacelike, null and timelike infinity and the domain close to the singularity
Numerical calculations in quantum field theories
Rebbi, C.
1984-01-01
Four lecture notes are included: (1) motivation for numerical calculations in Quantum Field Theory; (2) numerical simulation methods; (3) Monte Carlo studies of Quantum Chromo Dynamics; and (4) systems with fermions. 23 references
Reactor Thermal Hydraulic Numerical Calculation And Modeling
Duong Ngoc Hai; Dang The Ba
2008-01-01
In the paper the results of analysis of thermal hydraulic state models using the numerical codes such as COOLOD, EUREKA and RELAP5 for simulation of the reactor thermal hydraulic states are presented. The calculations, analyses of reactor thermal hydraulic state and safety were implemented using different codes. The received numerical results, which were compared each to other, to experiment measurement of Dalat (Vietnam) research reactor and published results, show their appropriateness and capacity for analyses of different appropriate cases. (author)
A numerical method for resonance integral calculations
Tanbay, Tayfun; Ozgener, Bilge
2013-01-01
A numerical method has been proposed for resonance integral calculations and a cubic fit based on least squares approximation to compute the optimum Bell factor is given. The numerical method is based on the discretization of the neutron slowing down equation. The scattering integral is approximated by taking into account the location of the upper limit in energy domain. The accuracy of the method has been tested by performing computations of resonance integrals for uranium dioxide isolated rods and comparing the results with empirical values. (orig.)
Hidden beauty in multiloop amplitudes
Cachazo, Freddy; Spradlin, Marcus; Volovich, Anastasia
2006-01-01
Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric Yang-Mills theory are believed to possess the remarkable property of satisfying iteration relations in L. We propose a simple new method for studying iteration relations for four-particle amplitudes which involves the use of certain linear differential operators and eliminates the need to fully evaluate any loop integrals. We carry out this procedure in explicit detail for the two-loop amplitude and prove that this method can be applied to any multiloop integral, allowing a conjectured iteration relation for any given amplitude to be tested up to polynomials in logarithms
Numerical calculation of impurity charge state distributions
Crume, E.C.; Arnurius, D.E.
1977-09-01
The numerical calculation of impurity charge state distributions using the computer program IMPDYN is discussed. The time-dependent corona atomic physics model used in the calculations is reviewed, and general and specific treatments of electron impact ionization and recombination are referenced. The complete program and two examples relating to tokamak plasmas are given on a microfiche so that a user may verify that his version of the program is working properly. In the discussion of the examples, the corona steady-state approximation is shown to have significant defects when the plasma environment, particularly the electron temperature, is changing rapidly
Hybrid numerical calculation method for bend waveguides
Garnier , Lucas; Saavedra , C.; Castro-Beltran , Rigoberto; Lucio , José Luis; Bêche , Bruno
2017-01-01
National audience; The knowledge of how the light will behave in a waveguide with a radius of curvature becomes more and more important because of the development of integrated photonics, which include ring micro-resonators, phasars, and other devices with a radius of curvature. This work presents a numerical calculation method to determine the eigenvalues and eigenvectors of curved waveguides. This method is a hybrid method which uses at first conform transformation of the complex plane gene...
Multiloop stringlike formulas for QED
Lam, C.S.
1993-01-01
Multiloop gauge-theory amplitudes written in the Feynman-parameter representation are poised to take advantage of two important developments of the past decade: the spinor-helicity technique and the superstring reorganization. The former has been considered in a previous paper; the latter will be elaborated in this paper. We show here how to write multiloop stringlike formulas in the Feynman-parameter representation for any diagram in QED, including those involving other nonelectromagnetic interactions, provided the internal photon lines are not adjacent to any external photon line. The general connection between the Feynman-parameter approach and the superstring and/or first-quantized approach is discussed. In the special case of a one-loop multiphoton amplitude, these formulas reduce to the ones obtained by the superstring and the first-quantized methods. The stringlike formulas exhibit a simple gauge structure which makes the Ward-Takahashi identity apparent, and enables the integration-by-parts technique of Bern and Kosower to be applied, so that gauge-invariant parts can be extracted diagram by diagram with the seagull vertex neglected
Numerical calculations on heterogeneity of groundwater flow
Follin, S.
1992-01-01
The upscaling of model parameters is a key issue in many research fields concerned with parameter heterogeneity. The upscaling process allows for fewer model blocks and relaxes the numerical problems caused by high contrasts in the hydraulic conductivity. The trade-offs are dependent on the object but the general drawback is an increasing uncertainty about the representativeness. The present study deals with numerical calculations of heterogeneity of groundwater flow and solute transport in hypothetical blocks of fractured hard rock in a '3m scale' and addresses both conceptual and practical problems in numerical simulation. Evidence that the hydraulic conductivity (K) of the rock mass between major fracture zones is highly heterogeneous in a 3m scale is provided by a large number of field investigations. The present uses the documented heterogeneity and investigates flow and transport in a two-dimensional stochastic continuum characterized by a variance in Y = In(K) of σ y 2 = 16, corresponding to about 12 log 10 cycles in K. The study considers anisotropy, channelling, non-Fickian and Fickian transport, and conditional simulation. The major conclusions are: * heterogeneity gives rise to anisotropy in the upscaling process, * the choice of support scale is crucial for the modelling of solute transport. As a consequence of the obtained results, a two-dimensional stochastic discontinuum model is presented, which provides a tool for linking stochastic continuum models to discrete fracture network models. (au) (14 figs., 136 refs.)
Numerical precision calculations for LHC physics
Reuschle, Christian Andreas
2013-02-05
In this thesis I present aspects of QCD calculations, which are related to the fully numerical evaluation of next-to-leading order (NLO) QCD amplitudes, especially of the one-loop contributions, and the efficient computation of associated collider observables. Two interrelated topics have thereby been of concern to the thesis at hand, which give rise to two major parts. One large part is focused on the general group-theoretical behavior of one-loop QCD amplitudes, with respect to the underlying SU(N{sub c}) theory, in order to correctly and efficiently handle the color degrees of freedom in QCD one-loop amplitudes. To this end a new method is introduced that can be used in order to express color-ordered partial one-loop amplitudes with multiple quark-antiquark pairs as shuffle sums over cyclically ordered primitive one-loop amplitudes. The other large part is focused on the local subtraction of divergences off the one-loop integrands of primitive one-loop amplitudes. A method for local UV renormalization has thereby been developed, which uses local UV counterterms and efficient recursive routines. Together with suitable virtual soft and collinear subtraction terms, the subtraction method is extended to the virtual contributions in the calculations of NLO observables, which enables the fully numerical evaluation of the one-loop integrals in the virtual contributions. The method has been successfully applied to the calculation of jet rates in electron-positron annihilation to NLO accuracy in the large-N{sub c} limit.
Numerical precision calculations for LHC physics
Reuschle, Christian Andreas
2013-01-01
In this thesis I present aspects of QCD calculations, which are related to the fully numerical evaluation of next-to-leading order (NLO) QCD amplitudes, especially of the one-loop contributions, and the efficient computation of associated collider observables. Two interrelated topics have thereby been of concern to the thesis at hand, which give rise to two major parts. One large part is focused on the general group-theoretical behavior of one-loop QCD amplitudes, with respect to the underlying SU(N c ) theory, in order to correctly and efficiently handle the color degrees of freedom in QCD one-loop amplitudes. To this end a new method is introduced that can be used in order to express color-ordered partial one-loop amplitudes with multiple quark-antiquark pairs as shuffle sums over cyclically ordered primitive one-loop amplitudes. The other large part is focused on the local subtraction of divergences off the one-loop integrands of primitive one-loop amplitudes. A method for local UV renormalization has thereby been developed, which uses local UV counterterms and efficient recursive routines. Together with suitable virtual soft and collinear subtraction terms, the subtraction method is extended to the virtual contributions in the calculations of NLO observables, which enables the fully numerical evaluation of the one-loop integrals in the virtual contributions. The method has been successfully applied to the calculation of jet rates in electron-positron annihilation to NLO accuracy in the large-N c limit.
Numerical calculation of two-phase flows
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.)
Multiloop integral system test (MIST)
Gloudemans, J.R.
1989-07-01
The multiloop integral system test (MIST) was part of a multiphase program started in 1983 to address small-break loss-of-coolant accidents (SBLOCAs) specific to Babcock and Wilcox-designed plants. MIST was sponsored by the US Nuclear Regulatory Commission, the Babcock and Wilcox Owners Group, the Electric Power Research Institute, and Babcock and Wilcox. The unique features of the Babcock and Wilcox design, specifically the hot leg U-bends and steam generators, prevented the use of existing integral system data or existing integral system facilities to address the thermal-hydraulic SBLOCA questions. MIST and two other supporting facilities were specifically designed and constructed for this program, and an existing facility -- the once-through integral system (OTIS) -- was also used. Data from MIST and the other facilities will be used to benchmark the adequacy of system codes, such as RELAP5 and TRAC, for predicting abnormal plant transients. The individual tests are described in detail in Volumes 2 through 8 and Volume 11, and are summarized in Volume 1. Inter-group comparisons are addressed in this document, Volume 9. These comparisons are grouped as follows: mapping versus SBLOCA transients, SBLOCA, pump effects, and the effects of noncondensible gases. Appendix A provides an index and description of the microfiched plots for each test, which are enclosed with the corresponding Volumes 2 through 8. 147 figs., 5 tabs
The diamond rule for multi-loop Feynman diagrams
Ruijl, B.; Ueda, T.; Vermaseren, J.A.M.
2015-01-01
An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed
Numerical calculation of the Fresnel transform.
Kelly, Damien P
2014-04-01
In this paper, we address the problem of calculating Fresnel diffraction integrals using a finite number of uniformly spaced samples. General and simple sampling rules of thumb are derived that allow the user to calculate the distribution for any propagation distance. It is shown how these rules can be extended to fast-Fourier-transform-based algorithms to increase calculation efficiency. A comparison with other theoretical approaches is made.
Numerical calculation of backfilling of scour holes
Sumer, B. Mutlu; Baykal, Cüneyt; Fuhrman, David R.
2014-01-01
A fully-coupled hydrodynamic and morphologic CFD model is presented for simulating backfilling processes around structures. The hydrodynamic model is based on Reynolds-averaged Navier-Stokes equations, coupled with two-equation k-ω turbulence closure. The sediment transport model consists of sepa...... of structures: piles, and pipelines. Initial scour holes are generated by the same model. The numerical results appear to be in accord with the existing experimental information....
Numerical challenges of short range wake field calculations
Lau, Thomas; Gjonaj, Erion; Weiland, Thomas [Technische Universitaet Darmstadt (Germany). Institut fuer Theorie Elektromagnetischer Felder (TEMF)
2011-07-01
For present and future accelerator projects with ultra short bunches the accurate and reliable calculation of short range wake fields is an important issue. However, the numerical calculation of short range wake fields is a numerical challenging task. The presentation gives an overview over the numerical challenges and techniques for short range wake field calculations. Finally, some simulation results obtained by the program PBCI developed at the TU Darmstadt are presented.
Nodal methods in numerical reactor calculations
Hennart, J.P.; Valle, E. del
2004-01-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Nodal methods in numerical reactor calculations
Hennart, J P [UNAM, IIMAS, A.P. 20-726, 01000 Mexico D.F. (Mexico); Valle, E del [National Polytechnic Institute, School of Physics and Mathematics, Department of Nuclear Engineering, Mexico, D.F. (Mexico)
2004-07-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Worldline Green functions for multiloop diagrams
Schmidt, M.G.; Heidelberg Univ.; Schubert, C.
1994-03-01
We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop graph, and for a loop with an arbitrary number of propagator insertions. For scalar and abelian gauge theories, the resulting integral representations allow to combine whole classes of Feynman diagrams into compact expressions. (orig.)
Numerical calculations in elementary quantum mechanics using Feynman path integrals
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
Transforming differential equations of multi-loop Feynman integrals into canonical form
Meyer, Christoph [Institut für Physik, Humboldt-Universität zu Berlin,12489 Berlin (Germany)
2017-04-03
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Transforming differential equations of multi-loop Feynman integrals into canonical form
Meyer, Christoph
2017-04-01
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Transforming differential equations of multi-loop Feynman integrals into canonical form
Meyer, Christoph
2017-01-01
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Numerical calculation of two phase flow in a shock tube
Rivard, W.C.; Travis, J.R.; Torrey, M.D.
1976-01-01
Numerical calculations of the dynamics of initially saturated water-steam mixtures in a shock tube demonstrate the accuracy and efficiency of a new solution technique for the transient, two-dimensional, two-fluid equations. The dependence of the calculated results on time step and cell size are investigated. The effects of boiling and condensation on the flow physics suggest the merits of basic fluid dynamic measurements for the determination and evaluation of mass exchange models
Numerical calculation of economic uncertainty by intervals and fuzzy numbers
Schjær-Jacobsen, Hans
2010-01-01
This paper emphasizes that numerically correct calculation of economic uncertainty with intervals and fuzzy numbers requires implementation of global optimization techniques in contrast to straightforward application of interval arithmetic. This is demonstrated by both a simple case from managerial...... World Academic Press, UK. All rights reserved....
Numerical Calculation of the Output Power of a MHD Generator
Adrian CARABINEANU
2014-12-01
Full Text Available Using Lazăr Dragoş’s analytic solution for the electric potential we perform some numerical calculations in order to find the characteristics of a Faraday magnetohydrodymamics (MHD power generator (total power, useful power and Joule dissipation power.
Numeric calculation of celestial bodies with spreadsheet analysis
Koch, Alexander
2016-04-01
The motion of the planets and moons in our solar system can easily be calculated for any time by the Kepler laws of planetary motion. The Kepler laws are a special case of the gravitational law of Newton, especially if you consider more than two celestial bodies. Therefore it is more basic to calculate the motion by using the gravitational law. But the problem is, that by gravitational law it is not possible to calculate the state of motion with only one step of calculation. The motion has to be numerical calculated for many time intervalls. For this reason, spreadsheet analysis is helpful for students. Skills in programmes like Excel, Calc or Gnumeric are important in professional life and can easily be learnt by students. These programmes can help to calculate the complex motions with many intervalls. The more intervalls are used, the more exact are the calculated orbits. The sutdents will first get a quick course in Excel. After that they calculate with instructions the 2-D-coordinates of the orbits of Moon and Mars. Step by step the students are coding the formulae for calculating physical parameters like coordinates, force, acceleration and velocity. The project is limited to 4 weeks or 8 lessons. So the calcualtion will only include the calculation of one body around the central mass like Earth or Sun. The three-body problem can only be shortly discussed at the end of the project.
A systematic and efficient method to compute multi-loop master integrals
Xiao Liu
2018-04-01
Full Text Available We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems with arbitrary kinematic configurations. Numerical tests show that our method can not only achieve results with high precision, but also be much faster than the only existing systematic method sector decomposition. As a by product, we find a new strategy to compute scalar one-loop integrals without reducing them to master integrals.
Newsom, J. R.; Mukhopadhyay, V.
1983-01-01
A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables is used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two output drone flight control system.
A systematic and efficient method to compute multi-loop master integrals
Liu, Xiao; Ma, Yan-Qing; Wang, Chen-Yu
2018-04-01
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems with arbitrary kinematic configurations. Numerical tests show that our method can not only achieve results with high precision, but also be much faster than the only existing systematic method sector decomposition. As a by product, we find a new strategy to compute scalar one-loop integrals without reducing them to master integrals.
MATH: A Scientific Tool for Numerical Methods Calculation and Visualization
Henrich Glaser-Opitz
2016-02-01
Full Text Available MATH is an easy to use application for various numerical methods calculations with graphical user interface and integrated plotting tool written in Qt with extensive use of Qwt library for plotting options and use of Gsl and MuParser libraries as a numerical and parser helping libraries. It can be found at http://sourceforge.net/projects/nummath. MATH is a convenient tool for use in education process because of its capability of showing every important step in solution process to better understand how it is done. MATH also enables fast comparison of similar method speed and precision.
Elements of calculation of reactivity by numerical processing
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
Biased calculations: Numeric anchors influence answers to math equations
Andrew R. Smith
2011-02-01
Full Text Available People must often perform calculations in order to produce a numeric estimate (e.g., a grocery-store shopper estimating the total price of his or her shopping cart contents. The current studies were designed to test whether estimates based on calculations are influenced by comparisons with irrelevant anchors. Previous research has demonstrated that estimates across a wide range of contexts assimilate toward anchors, but none has examined estimates based on calculations. In two studies, we had participants compare the answers to math problems with anchors. In both studies, participants' estimates assimilated toward the anchor values. This effect was moderated by time limit such that the anchoring effects were larger when the participants' ability to engage in calculations was limited by a restrictive time limit.
Current system of the solar wind: results of numerical calculation
Pisanko, Yu.V.
1985-01-01
Results of numerical calculations of surface current in the interplanetary current layer and steady volume current in the solar wind for heliocentric distances (1-10)Rsub(s) (Rsub(s) is the Sun radius) are given. The strength of current dependence on spatial coordinates is considered. Stationary nondissipative magnetohydrodynamic corona expansion (SNMCE) in the reference system rotating with the Sun is studied. Calculations show that three-dimensional current system of nonaxial-symmetric and nonsymmetric relatively to helioequator plane of SNMCE is more complicated than the zonal ring current around the Sun, which is the only component of the current system in spatial symmetric case
Advanced Dynamics Analytical and Numerical Calculations with MATLAB
Marghitu, Dan B
2012-01-01
Advanced Dynamics: Analytical and Numerical Calculations with MATLAB provides a thorough, rigorous presentation of kinematics and dynamics while using MATLAB as an integrated tool to solve problems. Topics presented are explained thoroughly and directly, allowing fundamental principles to emerge through applications from areas such as multibody systems, robotics, spacecraft and design of complex mechanical devices. This book differs from others in that it uses symbolic MATLAB for both theory and applications. Special attention is given to solutions that are solved analytically and numerically using MATLAB. The illustrations and figures generated with MATLAB reinforce visual learning while an abundance of examples offer additional support. This book also: Provides solutions analytically and numerically using MATLAB Illustrations and graphs generated with MATLAB reinforce visual learning for students as they study Covers modern technical advancements in areas like multibody systems, robotics, spacecraft and des...
Numerical kinematic transformation calculations for a parallel link manipulator
Killough, S.M.
1993-01-01
Parallel link manipulators are often considered for particular robotic applications because of the unique advantages they provide. Unfortunately, they have significant disadvantages with respect to calculating the kinematic transformations because of the high-order equations that must be solved. Presented is a manipulator design that exploits the mechanical advantages of parallel links yet also has a corresponding numerical kinematic solution that can be solved in real time on common microcomputers
Numerical shoves and countershoves in electron transport calculations
Filippone, W.L.
1986-01-01
The justification for applying the relatively complex (compared to S/sub n/) streaming ray (SR) algorithm to electron transport problems is its potential for doing rapid and accurate calculations. Because of the Lagrangian treatment of the cell-uncollided electrons, the only significant sources of error are the numerical treatment of the scattering kernel and the spatial differencing scheme used for the cell-collided electrons. Considerable progress has been made in reducing the former source of error. If one is willing to pay the price, the latter source of error can be reduced to any desired level by refining the mesh size or by using high-order differencing schemes. Here the method of numerical shoves and countershoves is introduced, which reduces spatial differencing errors using relatively little additional computational effort
Numerical methods for calculating thermal residual stresses and hydrogen diffusion
Leblond, J.B.; Devaux, J.; Dubois, D.
1983-01-01
Thermal residual stresses and hydrogen concentrations are two major factors intervening in cracking phenomena. These parameters were numerically calculated by a computer programme (TITUS) using the FEM, during the deposition of a stainless clad on a low-alloy plate. The calculation was performed with a 2-dimensional option in four successive steps: thermal transient calculation, metallurgical transient calculation (determination of the metallurgical phase proportions), elastic-plastic transient (plain strain conditions), hydrogen diffusion transient. Temperature and phase dependence of hydrogen diffusion coefficient and solubility constant. The following results were obtained: thermal calculations are very consistent with experiments at higher temperatures (due to the introduction of fusion and solidification latent heats); the consistency is not as good (by 70 degrees) for lower temperatures (below 650 degrees C); this was attributed to the non-introduction of gamma-alpha transformation latent heat. The metallurgical phase calculation indicates that the heat affected zone is almost entirely transformed into bainite after cooling down (the martensite proportion does not exceed 5%). The elastic-plastic calculations indicate that the stresses in the heat affected zone are compressive or slightly tensile; on the other hand, higher tensile stresses develop on the boundary of the heat affected zone. The transformation plasticity has a definite influence on the final stress level. The return of hydrogen to the clad during the bainitic transformation is but an incomplete phenomenon and the hydrogen concentration in the heat affected zone after cooling down to room temperature is therefore sufficient to cause cold cracking (if no heat treatment is applied). Heat treatments are efficient in lowering the hydrogen concentration. These results enable us to draw preliminary conclusions on practical means to avoid cracking. (orig.)
Numerical calculation of hadron masses in lattice quantum chromodynamics
Montvay, I.
1985-07-01
Recent numerical Monte Carlo simulations of the hadron spectrum are reviewed. After a general introduction, different ways of calculating the hadron masses in the ''quenched approximation'' (i.e. neglecting virtual quark loops) are described and the latest results are summarized. The pseudofermion method and the iterative hopping expansion method for the introduction of dynamical quarks is discussed, and the first results about the hadron spectrum including the effect of virtual quark loops are reviewed. A separate section is devoted to the discussion of the questions related to scaling with dynamical quarks. (orig./HSI)
Application of a numerical transport correction in diffusion calculations
Tomatis, Daniele; Dall'Osso, Aldo
2011-01-01
Full core calculations by ordinary transport methods can demand considerable computational time, hardly acceptable in the industrial work frame. However, the trend of next generation nuclear cores goes toward more heterogeneous systems, where transport phenomena of neutrons become very important. On the other hand, using diffusion solvers is more practical allowing faster calculations, but a specific formulation of the diffusion coefficient is requested to reproduce the scalar flux with reliable physical accuracy. In this paper, the Ronen method is used to evaluate numerically the diffusion coefficient in the slab reactor. The new diffusion solution is driven toward the solution of the integral neutron transport equation by non linear iterations. Better estimates of currents are computed and diffusion coefficients are corrected at node interfaces, still assuming Fick's law. This method enables obtaining closer results to the transport solution by a common solver in multigroup diffusion. (author)
Numerical Calculation of the Flow in a Centrifugal Compressor Volute
Seong, Seon Mo; Kang, Shin Hyoung; Cho, Kyung Seok; Kim, Woo June
2007-01-01
Flows in the centrifugal compressor volute with circular cross section are numerically investigated. The computational domain contained inlet passage, impeller, radial and axial diffuser, and volute. The volute grid for the calculation utilized a multi-block arrangement to form a butterfly grid and flow calculations are performed using commercial CFD software, CFX-TASCflow. The centrifugal compressor of this study has the inlet passage like steps and axial diffuser after radial diffuser because of the shape of the motor cooling fins and installation constraints. Due to this feature the swirling flow pattern is different from the other investigations. The loss in through the inlet passage was considerable and the flow inside volute is very complex and three dimensional with strong vortex and recirculation through volute tongue
Numerical Calculation of Interaction Between Plane Jet and Subsonic Flow
V. O. Moskalenko
2016-01-01
Full Text Available The paper makes numerical calculation of interaction between plane jet and subsonic flow. Its aim is to determine the jet trajectory, velocity profiles, distribution of pressure coefficient on the plate surface at different jet angles, namely ωj=45°; 90°; 105° and at low blowing strengths ( ≤1.5 as well as a to make comparison with the experimental data of other authors.To simulate a two-dimensional jet in the subsonic flow the software package “CAD SolidWorks Flow Simulation” has been used. Initially, the test task was solved with its calculation results compared with experimental ones [6.8] in order to improve the convergence; the size of the computational domain and a computational grid within the k-ε turbulence model were selected. As a result of the calculation, were identified and analysed the pressure values, jet trajectories, and velocity profiles. In the graphs the solid lines show calculation results, and dots represent experimental data.From the calculation results it is seen that, with increasing intensity of the reduced mass flow ¯q in the above range, the change of the jet pressure coefficient p¯ distribution behind a slotted nozzle is almost linear and significant. Before the nozzle, with increasing ¯q the pressure coefficient increases slightly.Analysis of results has shown that blowing of jets with ωj>90ω, provides a greater perturbation of the subsonic flow. Thus, the jet penetrates into the flow deeper, forms a dead region of the greater length, and more significantly redistributes the pressure coefficient on the surface of the plate.The calculation results are in good compliance with the experimental data both for the jet axis and for the pressure coefficient distribution on the plate surface. The research results can be used in the designing the jet control of aircrafts.
Experimental verification of numerical calculations of railway passenger seats
Ligaj, B.; Wirwicki, M.; Karolewska, K.; Jasińska, A.
2018-04-01
The construction of railway seats is based on industry regulations and the requirements of end users, i.e. passengers. The two main documents in this context are the UIC 566 (3rd Edition, dated 7 January 1994) and the EN 12663-1: 2010+A1:2014. The study was to carry out static load tests of passenger seat frames. The paper presents the construction of the test bench and the results of experimental and numerical studies of passenger seat rail frames. The test bench consists of a frame, a transverse beam, two electric cylinders with a force value of 6 kN, and a strain gauge amplifier. It has a modular structure that allows for its expansion depending on the structure of the seats. Comparing experimental results with numerical results for points A and B allowed to determine the existing differences. It follows from it that higher stress values are obtained by numerical calculations in the range of 0.2 MPa to 35.9 MPa.
Investigation of reflood models by coupling REFLA-1D and multi-loop system model
Sugimoto, Jun; Murao, Yoshio
1983-09-01
A system analysis code REFLA-1DS was developed by coupling reflood analysis code REFLA-1D and a multi-loop primary system model. The reflood models in the code were investigated for the development of the integral system analysis code. The REFLA-1D, which was developed with the small scale reflood experiment at JAERI, consists of one-dimensional core model and a primary system model with a constant loop resistance. The multi-loop primary system model was developed with the Cylindrical Core Test Facility of JAERI's large scale reflood tests. The components modeled in the code are the upper plenum, the steam generator, the coolant pump, the ECC injection port, the downcomer and the broken cold leg nozzle. The coupling between the two models in REFLA-1DS is accomplished by applying the equivalent flow resistance calculated with the multiloop model to the REFLA-1D. The characteristics of the code is its simplicity of the system model and the solution method which enables the fast running and the easy reflood analysis for the further model development. A fairly good agreement was obtained with the results of the Cylindrical Core Test Facility for the calculated water levels in the downcomer, the core and the upper plenum. A qualitatively good agreement was obtained concerning the parametric effects of the system pressure, the ECC flow rate and the initial clad temperature. Needs for further code improvements of the models, however, were pointed out. These include the problem concerning the generation rate of the steam and water droplets in the core in an early period, the effect of the flow oscillation on the core cooling, the heat release from the downcomer wall, and the stable system calculation. (author)
Determination of hydrogen cluster velocities and comparison with numerical calculations
Täschner, A.; Köhler, E.; Ortjohann, H.-W.; Khoukaz, A.
2013-01-01
The use of powerful hydrogen cluster jet targets in storage ring experiments led to the need of precise data on the mean cluster velocity as function of the stagnation temperature and pressure for the determination of the volume density of the target beams. For this purpose a large data set of hydrogen cluster velocity distributions and mean velocities was measured at a high density hydrogen cluster jet target using a trumpet shaped nozzle. The measurements have been performed at pressures above and below the critical pressure and for a broad range of temperatures relevant for target operation, e.g., at storage ring experiments. The used experimental method is described which allows for the velocity measurement of single clusters using a time-of-flight technique. Since this method is rather time-consuming and these measurements are typically interfering negatively with storage ring experiments, a method for a precise calculation of these mean velocities was needed. For this, the determined mean cluster velocities are compared with model calculations based on an isentropic one-dimensional van der Waals gas. Based on the obtained data and the presented numerical calculations, a new method has been developed which allows to predict the mean cluster velocities with an accuracy of about 5%. For this two cut-off parameters defining positions inside the nozzle are introduced, which can be determined for a given nozzle by only two velocity measurements
Numerical calculation of beam coupling impedances in synchrotron accelerators
Haenichen, Lukas
2016-01-01
Beams of charged particles are of interest in various fields of research including particle and nuclear physics, material and medical science and many more. In synchrotron accelerators the accelerating section is passed periodically. A closed loop trajectory is enforced, by increasing the frequency of the accelerating electric field and the magnitude of the dipolar magnetic guide field synchronously. A synchrotron therefore consists of a circular assembly of various beamline elements which serve the purposes of accelerating and guiding the particle beam. For the flawless operation of such a machine it has to be assured that the particles perform a controlled motion along predefined trajectories. Amongst others, the fulfillment of the corresponding stability criteria is in close conjuction with the so-called beam coupling impedances which are an important figure of merit for collective effects in synchrotron accelerators. This work focuses on analytical and numerical methods for the calculation of beam coupling impedances. One of the primary objectives is to gain a better understanding of the electrodynamics related to charged particle beams, furthermore to recapitulate the mathematical description of charged particle beams in both time and frequency domain and finally establish the links between actual physics and numerical modeling. Analytical methods are usually restricted to symmetrical geometry and may solely serve for the approximate determination of the field distribution in real geometries or to validate certain numerical methods. More accurate prognosis is only possible with three-dimensional simulation models. Numerical simulation techniques have been established in the second half of the last century accompanying the evolution of many particle accelerators. Classical time domain codes were the prevailing simulation tools where the actual process of the particle motion sequence is reproduced. For the present case of a heavy ion synchrotron accelerator
Numerical calculation of beam coupling impedances in synchrotron accelerators
Haenichen, Lukas
2016-07-01
Beams of charged particles are of interest in various fields of research including particle and nuclear physics, material and medical science and many more. In synchrotron accelerators the accelerating section is passed periodically. A closed loop trajectory is enforced, by increasing the frequency of the accelerating electric field and the magnitude of the dipolar magnetic guide field synchronously. A synchrotron therefore consists of a circular assembly of various beamline elements which serve the purposes of accelerating and guiding the particle beam. For the flawless operation of such a machine it has to be assured that the particles perform a controlled motion along predefined trajectories. Amongst others, the fulfillment of the corresponding stability criteria is in close conjuction with the so-called beam coupling impedances which are an important figure of merit for collective effects in synchrotron accelerators. This work focuses on analytical and numerical methods for the calculation of beam coupling impedances. One of the primary objectives is to gain a better understanding of the electrodynamics related to charged particle beams, furthermore to recapitulate the mathematical description of charged particle beams in both time and frequency domain and finally establish the links between actual physics and numerical modeling. Analytical methods are usually restricted to symmetrical geometry and may solely serve for the approximate determination of the field distribution in real geometries or to validate certain numerical methods. More accurate prognosis is only possible with three-dimensional simulation models. Numerical simulation techniques have been established in the second half of the last century accompanying the evolution of many particle accelerators. Classical time domain codes were the prevailing simulation tools where the actual process of the particle motion sequence is reproduced. For the present case of a heavy ion synchrotron accelerator
Multiloop world-line Green functions from string theory
Roland, K.; Sato, H.T.
1996-01-01
We show how the multiloop bosonic Green function of closed string theory reduces to the world-line Green function as defined by Schmidt and Schubert in the limit where the string world-sheet degenerates into a Φ 3 particle diagram. To obtain this correspondence we have to make an appropriate choice of the local coordinates defined on the degenerate string world sheet. We also present a set of simple rules that specify, in the explicit setting of the Schottky parametrization, which is the corner of moduli space corresponding to a given multiloop Φ 3 diagram. (orig.)
Multiloop divergences in the closed bosonic string theory
Gava, E.; Iengo, R.; Jayaraman, T.; Ramachandran, R.
1985-12-01
We discuss the structure of the divergences in the multiloop vacuum diagrams for the closed bosonic strings in the framework of the Polyakov covariant formalism. We find, by an explicit computation, that all the divergences in the theory may be interpreted as due to tadpole diagrams in which the dilation goes into the vacuum. (author)
Numerical calculation of particle collection efficiency in an ...
Theoretical and numerical research has been previously done on ESPs to predict the efficiency ... Lagrangian simulations of particle transport in wire–plate ESP were .... The collection efficiency can be defined as the ratio of the number of ...
Numerical calculation of elastohydrodynamic lubrication methods and programs
Huang, Ping
2015-01-01
The book not only offers scientists and engineers a clear inter-disciplinary introduction and orientation to all major EHL problems and their solutions but, most importantly, it also provides numerical programs on specific application in engineering. A one-stop reference providing equations and their solutions to all major elastohydrodynamic lubrication (EHL) problems, plus numerical programs on specific applications in engineering offers engineers and scientists a clear inter-disciplinary introduction and a concise program for practical engineering applications to most important EHL problems
Numerical method for two-phase flow discontinuity propagation calculation
Toumi, I.; Raymond, P.
1989-01-01
In this paper, we present a class of numerical shock-capturing schemes for hyperbolic systems of conservation laws modelling two-phase flow. First, we solve the Riemann problem for a two-phase flow with unequal velocities. Then, we construct two approximate Riemann solvers: an one intermediate-state Riemann solver and a generalized Roe's approximate Riemann solver. We give some numerical results for one-dimensional shock-tube problems and for a standard two-phase flow heat addition problem involving two-phase flow instabilities
Numerical calculation of hemolysis levels in peripheral hemodialysis cannulas
De Wachter, D; Verdonck, P
Hemolysis in extracorporeal life support systems presents an underestimated problem. In this article, we investigate the hemolytic potential of peripheral hemodialysis cannulas numerically. An axisymmetrical finite element model of 3 cannula sizes was built (13G, 14G, and 16G) that was refined
Numerical fluid flow and heat transfer calculations on multiprocessor systems
Oehman, G.A.; Malen, T.E.; Kuusela, P.
1989-01-01
The first part of the report presents the basic principles of parallel processing, and factors influencing tbe efficiency of practical applications are discussed. In a multiprocessor computer, different parts of the program code are executed in parallel, i.e. simultaneous with respect to time, on different processors, and thus it becomes possible to decrease the overall computation time by a factor, which in the ideal case is equal to the number of processors. The application study starts from the numerical solution of the twodimesional Laplace equation, which describes the steady heat conduction in a solid plate and advances through the solution of the three dimensional Laplace equation to the case of study laminar fluid flow in a twodimensional box at Reynolds numbers up to 20. Hereby the stream function-vorticity method is first applied and the SIMPLER method. The conventional (sequential) numerical algoritms for these fluid flow and heat transfer problems are found not to be ideally suited for conversion to parallel computation, but sped-up ratios considerably above 50 % of the theoretical maximum are regularly achieved in the runs. The numerical procedures we coded in the OCCAM-2 language and the test runs were performed at who Akademi on the imperimental HATHI-computers containing 16 T4l4 and 100 INMOS T800 transputers respectively.
Numerical fluid flow and heat transfer calculations on multiprocessor systems
Oehman, G.A.; Malen, T.E.; Kuusela, P.
1989-12-31
The first part of the report presents the basic principles of parallel processing, and factors influencing tbe efficiency of practical applications are discussed. In a multiprocessor computer, different parts of the program code are executed in parallel, i.e. simultaneous with respect to time, on different processors, and thus it becomes possible to decrease the overall computation time by a factor, which in the ideal case is equal to the number of processors. The application study starts from the numerical solution of the twodimesional Laplace equation, which describes the steady heat conduction in a solid plate and advances through the solution of the three dimensional Laplace equation to the case of study laminar fluid flow in a twodimensional box at Reynolds numbers up to 20. Hereby the stream function-vorticity method is first applied and the SIMPLER method. The conventional (sequential) numerical algoritms for these fluid flow and heat transfer problems are found not to be ideally suited for conversion to parallel computation, but sped-up ratios considerably above 50 % of the theoretical maximum are regularly achieved in the runs. The numerical procedures we coded in the OCCAM-2 language and the test runs were performed at who Akademi on the imperimental HATHI-computers containing 16 T4l4 and 100 INMOS T800 transputers respectively.
Sada, Koichi; Michioka, Takenobu; Ichikawa, Yoichi
2002-01-01
Because effluent gas is sometimes released from low positions, viz., near the ground surface and around buildings, the effects caused by buildings within the site area are not negligible for gas diffusion predictions. For these reasons, the effects caused by buildings for gas diffusion are considered under the terrain following calculation coordinate system in this report. Numerical calculation meshes on the ground surface are treated as the building with the adaptation of wall function techniques of turbulent quantities in the flow calculations using a turbulence closure model. The reflection conditions of released particles on building surfaces are taken into consideration in the diffusion calculation using the Lagrangian particle model. Obtained flow and diffusion calculation results are compared with those of wind tunnel experiments around the building. It was apparent that features observed in a wind tunnel, viz., the formation of cavity regions behind the building and the gas diffusion to the ground surface behind the building, are also obtained by numerical calculation. (author)
Velocity field calculation for non-orthogonal numerical grids
Flach, G. P. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
2015-03-01
Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porous-medium numerical simulations. Such grids are referred to in this study as non-orthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Non-orthogonal grids are routinely encountered at the Savannah River Site in porous-medium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation, and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porous-medium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces. For an orthogonal grid, the normal flux at a cell face is a component of the Darcy velocity vector in the coordinate system, and the pore velocity for particle tracking is attained by dividing by water content. For a non-orthogonal grid, the flux normal to a cell face that lies outside a coordinate plane is not a true component of velocity with respect to the coordinate system. Nonetheless, normal fluxes are often taken as Darcy velocity components, either naively or with accepted approximation. To enable accurate particle tracking or otherwise present an accurate depiction of the velocity field for a non
Numerical calculation of transient field effects in quenching superconducting magnets
Schwerg, Nikolai; Russenschuck, Stephan
2009-01-01
The maximum obtainable magnetic induction of accelerator magnets, relying on normal conducting cables and iron poles, is limited to around 2 T because of ohmic losses and iron saturation. Using superconducting cables, and employing permeable materials merely to reduce the fringe field, this limit can be exceeded and fields of more than 10 T can be obtained. A quench denotes the sudden transition from the superconducting to the normal conducting state. The drastic increase in electrical resistivity causes ohmic heating. The dissipated heat yields a temperature rise in the coil and causes the quench to propagate. The resulting high voltages and excessive temperatures can result in an irreversible damage of the magnet - to the extend of a cable melt-down. The quench behavior of a magnet depends on numerous factors, e.g. the magnet design, the applied magnet protection measures, the external electrical network, electrical and thermal material properties, and induced eddy current losses. The analysis and optimizat...
Numerical groundwater flow calculations at the Finnsjoen site
Lindbom, B.; Boghammar, A.; Lindberg, H.; Bjelkaas, J.
1991-02-01
The Swedish Nuclear Fuel and Waste Management Company (SKB) has initiated a research project called SKB 91, which is related to performance assessment of repositories for high level waste from nuclear power plants. Specifically the Finnsjoen site is of concern. As part of this research project, the report describes groundwater flow calculations at the Finnsjoen site, located in northern Uppland, approximately 150 km north of Stockholm. The calculations have been performed with the finite element method applying the porous media approach. The project comprises three steps, the first of which is concerned with the presence of salt below a hydraulically significant structure. This step was modelled in two dimensions in a semi-generic fashion, while the two following steps comprised three-dimensional modelling of the site at a semi-regional and a local scale. The semi-regional model covered approximately 43 square km while the area of the local model was roughly 6.6 square km. The semi-regional model included well expressed regional fracture zones that were explicitly modelled in deterministic manner. The modelling was performed with the finite element code NAMMU, used together with the program-package HYPAC. The latter was used for pre- and postprocessing purposes. The modelling was performed with 8-noded brick elements for the three-dimensional calculations, and the two-dimensional model involved the use of 8-noded rectangular elements. The present report is a revised version of a report previously published as a working report. The difference between the present report and the previous one, is that the present report describes the conclusions more site-specifically, the presentation of a number of the cases tackled has been pruned down, some editorial effort has been put into having the volume of the report reduced, and finally the summary has been edited and cut down. (authors)
Numerical calculation of radiation pattern of plasma channel antenna
Xia Xinren; Yin Chengyou
2010-01-01
The idea of plasma channel antenna (PCA) for high power microwave weapon is presented in this paper. The radiation pattern of PCA is calculated. The directivity functions of general antenna are derived. The near electromagnetic model of PCA is created based on physical circumstances. The electromagnetic fields of PCA and surrounding air in cylindrical coordinate are given. The dispersion equation of PCA is deduced by applying the boundary conditions of electromagnetic fields. The surface wave vector of PCA is achieved. The variations of radiation characteristic with plasma density, antenna length and antenna radius are emphatically discussed. The controllability of PCA's radiation patterns is confirmed. (authors)
Numerical calculation of ion polarization in the NICA collider
Kovalenko, A. D.; Butenko, A. V.; Kekelidze, V. D.; Mikhaylov, V. A.; Kondratenko, M. A.; Kondratenko, A. M.; Filatov, Yu N.
2016-02-01
The NICA Collider with two solenoid Siberian snakes is “transparent” to the spin. The collider transparent to the spin provides a unique capability to control any polarization direction of protons and deuterons using additional weak solenoids without affecting orbital parameters of the beam. The spin tune induced by the control solenoids must significantly exceed the strength of the zero-integer spin resonance, which contains a coherent part associated with errors in the collider's magnetic structure and an incoherent part associated with the beam emittances. We present calculations of the coherent part of the resonance strength in the NICA collider for proton and deuteron beams.
Numerical calculation of ion polarization in the NICA collider
Kovalenko, A D; Butenko, A V; Kekelidze, V D; Mikhaylov, V A; Filatov, Yu N; Kondratenko, M A; Kondratenko, A M
2016-01-01
The NICA Collider with two solenoid Siberian snakes is “transparent” to the spin. The collider transparent to the spin provides a unique capability to control any polarization direction of protons and deuterons using additional weak solenoids without affecting orbital parameters of the beam. The spin tune induced by the control solenoids must significantly exceed the strength of the zero-integer spin resonance, which contains a coherent part associated with errors in the collider's magnetic structure and an incoherent part associated with the beam emittances. We present calculations of the coherent part of the resonance strength in the NICA collider for proton and deuteron beams. (paper)
fp shell spectroscopy: numerical calculations and theoretical aspects
Pasquini, E.A.
1976-01-01
The fp shell spectroscopy is reviewed and the fsup(n) model is introduced. It is shown that the two-body Hamiltonian monopolar terms play a very important part in the behavior of these spectra, and that realistic interactions do not reproduce them. The detailed study of the following nuclei was undertaken: 47 Ca, 48 Ca, 49 Ca, 56 Ni, 48 Sc, 50 Sc, 50 Ti, 46 Ti, 50 Cr, 47 V and 49 Cr. It is shown that very precise values of the few parameters defining the monopolar contributions could be extracted from the comparison between calculations and experimental data. The study of the binding energies of all the nuclei from 40 Ca to 56 Ni shows that it is necessary to introduce three-body forces. The results also reveal the effect of nondiagonal multipoles which are well reproduced by realistic interactions. A better understanding of the electromagnetic behavior of the fsup(n) nuclei of their conjugaison properties and of the relation between 42 Sc and 48 Sc was obtained. Several calculations of two-body transfer amplitudes were proposed [fr
NUMERICAL CALCULATIONS IN GEOMECHANICS APPLICABLE TO LINEAR STRUCTURES
Vlasov Aleksandr Nikolaevich
2012-10-01
Full Text Available The article covers the problem of applicability of finite-element and engineering methods to the development of a model of interaction between pipeline structures and the environment in the complex conditions with a view to the simulation and projection of exogenous geological processes, trustworthy assessment of their impacts on the pipeline, and the testing of varied calculation methodologies. Pipelining in the areas that have a severe continental climate and permafrost soils is accompanied by cryogenic and exogenous processes and developments. It may also involve the development of karst and/or thermokarst. The adverse effect of the natural environment is intensified by the anthropogenic impact produced onto the natural state of the area, causing destruction of forests and other vegetation, changing the ratio of soils in the course of the site planning, changing the conditions that impact the surface and underground waters, and causing the thawing of the bedding in the course of the energy carrier pumping, etc. The aforementioned consequences are not covered by effective regulatory documents. The latter constitute general and incomplete recommendations in this respect. The appropriate mathematical description of physical processes in complex heterogeneous environments is a separate task to be addressed. The failure to consider the above consequences has repeatedly caused both minor damages (denudation of the pipeline, insulation stripping and substantial accidents; the rectification of their consequences was utterly expensive. Pipelining produces a thermal impact on the environment; it may alter the mechanical properties of soils and de-frost the clay. The stress of the pipeline is one of the principal factors that determines its strength and safety. The pipeline stress exposure caused by loads and impacts (self-weight, internal pressure, etc. may be calculated in advance, and the accuracy of these calculations is sufficient for practical
Numerical calculations of effective elastic properties of two cellular structures
Tuncer, Enis
2005-01-01
Young's moduli of regular two-dimensional truss-like and eye-shaped structures are simulated using the finite element method. The structures are idealizations of soft polymeric materials used in ferro-electret applications. In the simulations, the length scales of the smallest representative units are varied, which changes the dimensions of the cell walls in the structures. A power-law expression with a quadratic as the exponent term is proposed for the effective Young's moduli of the systems as a function of the solid volume fraction. The data are divided into three regions with respect to the volume fraction: low, intermediate and high. The parameters of the proposed power-law expression in each region are later represented as a function of the structural parameters, the unit-cell dimensions. The expression presented can be used to predict a structure/property relationship in materials with similar cellular structures. The contribution of the cell-wall thickness to the elastic properties becomes significant at concentrations >0.15. The cell-wall thickness is the most significant factor in predicting the effective Young's modulus of regular cellular structures at high volume fractions of solid. At lower concentrations of solid, the eye-shaped structure yields a lower Young's modulus than a truss-like structure with similar anisotropy. Comparison of the numerical results with those of experimental data for poly(propylene) show good agreement regarding the influence of cell-wall thickness on elastic properties of thin cellular films
Numerical calculation of two-phase turbulent jets
Saif, A.A.
1995-05-01
Two-phase turbulent round jets were numerically simulated using a multidimensional two-phase CFD code based on the two-fluid model. The turbulence phenomena were treated with the standard k-{epsilon} model. It was modified to take into account the additional dissipation of turbulent kinetic energy by the dispersed phase. Within the context of the two-fluid model it is more appropriate and physically justified to treat the diffusion by an interfacial force in the momentum equation. In this work, the diffusion force and the additional dissipation effect by the dispersed phase were modeled starting from the classical turbulent energy spectrum analysis. A cut-off frequency was proposed to decrease the dissipation effect by the dispersed phase when large size particles are introduced in the flow. The cut-off frequency combined with the bubble-induced turbulence effect allows for an increase in turbulence for large particles. Additional care was taken in choosing the right kind of experimental data from the literature so that a good separate effect test was possible for their models. The models predicted the experimental data very closely and they were general enough to predict extreme limit cases: water-bubble and air-droplet jets.
Numerical calculation of air velocity and temperature in ice rinks
Bellache, O.; Galanis, N. [Sherbrooke Univ., PQ (Canada); Ouzzane, M.; Sunye, R. [Natural Resources Canada, Varennes, PQ (Canada). CANMET Energy Diversification Laboratory
2002-07-01
A computational fluid dynamic (CFD) model was developed to predict the energy consumption at an ice rink. Ice rinks in Canada consume approximately 3500 GWh of electricity annually and generate about 300,000 tons of gases contributing to the greenhouse effect. This newly developed model also considers ice quality and comfort conditions in the arena. The typical 2D configuration includes refrigeration loads as well as heat transfer coefficients between the air and the ice. The effects of heat losses through the ice rink envelope are also determined. A comparison of prediction results from 4 different formulations confirms that there are important differences in air velocities near the walls and in the temperature gradient near the ice. The turbulent mixed convection model gives the best estimate of the refrigeration load. It was determined that a good ventilation should circulate air throughout the building to avoid stagnant areas. Air velocities must be low near the stands where the temperature should be around 20 degrees C. Air temperature near the ice should be low to preserve ice quality and to reduce the refrigeration load. The complexity of this geometry has been taken into account in a numerical simulation of the hydrodynamic and thermal fields in the ice rink. 9 refs., 2 tabs., 5 figs.
Numerical calculation of transient field effects in quenching superconducting magnets
Schwerg, Juljan Nikolai
2010-01-01
The maximum obtainable magnetic induction of accelerator magnets, relying on normal conducting cables and iron poles, is limited to around 2 T because of ohmic losses and iron saturation. Using superconducting cables, and employing permeable materials merely to reduce the fringe field, this limit can be exceeded and fields of more than 10 T can be obtained. A quench denotes the sudden transition from the superconducting to the normal conducting state. The drastic increase in electrical resistivity causes ohmic heating. The dissipated heat yields a temperature rise in the coil and causes the quench to propagate. The resulting high voltages and excessive temperatures can result in an irreversible damage of the magnet - to the extend of a cable melt-down. The quench behavior of a magnet depends on numerous factors, e.g. the magnet design, the applied magnet protection measures, the external electrical network, electrical and thermal material properties, and induced eddy current losses. The analysis and optimization of the quench behavior is an integral part of the construction of any superconducting magnet. The dissertation is divided in three complementary parts, i.e. the thesis, the detailed treatment and the appendix. In the thesis the quench process in superconducting accelerator magnets is studied. At first, we give an overview over features of accelerator magnets and physical phenomena occurring during a quench. For all relevant effects numerical models are introduced and adapted. The different models are weakly coupled in the quench algorithm and solved by means of an adaptive time-stepping method. This allows to resolve the variation of material properties as well as time constants. The quench model is validated by means of measurement data from magnets of the Large Hadron Collider. In a second step, we show results of protection studies for future accelerator magnets. The thesis ends with a summary of the results and a critical outlook on aspects which could
Numerical calculation of transient field effects in quenching superconducting magnets
Schwerg, Juljan Nikolai
2010-07-01
The maximum obtainable magnetic induction of accelerator magnets, relying on normal conducting cables and iron poles, is limited to around 2 T because of ohmic losses and iron saturation. Using superconducting cables, and employing permeable materials merely to reduce the fringe field, this limit can be exceeded and fields of more than 10 T can be obtained. A quench denotes the sudden transition from the superconducting to the normal conducting state. The drastic increase in electrical resistivity causes ohmic heating. The dissipated heat yields a temperature rise in the coil and causes the quench to propagate. The resulting high voltages and excessive temperatures can result in an irreversible damage of the magnet - to the extend of a cable melt-down. The quench behavior of a magnet depends on numerous factors, e.g. the magnet design, the applied magnet protection measures, the external electrical network, electrical and thermal material properties, and induced eddy current losses. The analysis and optimization of the quench behavior is an integral part of the construction of any superconducting magnet. The dissertation is divided in three complementary parts, i.e. the thesis, the detailed treatment and the appendix. In the thesis the quench process in superconducting accelerator magnets is studied. At first, we give an overview over features of accelerator magnets and physical phenomena occurring during a quench. For all relevant effects numerical models are introduced and adapted. The different models are weakly coupled in the quench algorithm and solved by means of an adaptive time-stepping method. This allows to resolve the variation of material properties as well as time constants. The quench model is validated by means of measurement data from magnets of the Large Hadron Collider. In a second step, we show results of protection studies for future accelerator magnets. The thesis ends with a summary of the results and a critical outlook on aspects which could
El-Osery, I.A.
1981-01-01
The purpose of this paper is to discuss the theories, techniques and computer codes that are frequently used in numerical reactor criticality and burnup calculations. It is a part of an integrated nuclear reactor calculation scheme conducted by the Reactors Department, Inshas Nuclear Research Centre. The crude part in numerical reactor criticality and burnup calculations includes the determination of neutron flux distribution which can be obtained in principle as a solution of Boltzmann transport equation. Numerical methods used for solving transport equations are discussed. Emphasis are made on numerical techniques based on multigroup diffusion theory. These numerical techniques include nodal, modal, and finite difference ones. The most commonly known computer codes utilizing these techniques are reviewed. Some of the main computer codes that have been already developed at the Reactors Department and related to numerical reactor criticality and burnup calculations have been presented
Kallosh, R.; Morosov, A.
1988-01-01
We analyse the structure of insertions arising in multiloop calculations in the first-quantized version of the Green-Schwarz formalism. We show that at least four constant zero modes of grassmannian Θ-fields related to space-time supersymmetry are not removed by insertions. The occurrence of these zero modes straightforwardly leads to non-renormalization theorems, which imply that all 0-, 1-, 2-, 3-point functions vanish. (orig.)
A strong shock tube problem calculated by different numerical schemes
Lee, Wen Ho; Clancy, Sean P.
1996-05-01
Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 109 and density ratio of 103 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods.
A strong shock tube problem calculated by different numerical schemes
Lee, W.H.; Clancy, S.P.
1996-01-01
Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 10 9 and density ratio of 10 3 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods. copyright 1996 American Institute of Physics
Fast numerical calculations of ion-atom collisions
Reading, J.F.; Ford, A.L.; Becker, R.L.
1979-01-01
When an ion impinges on an atom, the cross sections for electronic transitions can be described in the independent electron model by functions of single electron amplitudes. A single centered expansion of the time-dependent wave function of an electron about the heavier nucleus, with charge Z/sub N/, is shown to be moderately successful in explaining the dependence of K-shell hole production on the charge, Z/sub p/, of the projectile. However, capture of electrons by the projectile is important for a complete understanding and can be incorporated, in principle, in the single-center approach by evaluation of a transition matrix element involving a final state on the projectile. This is not an easy theoretical problem even in an asymmetric (Z/sub p/ much less than Z/sub N/) collision, because long times are involved which aggravate the inadequacies of a coupled-state calculation where the continuum is replaced by a discrete set of pseudostates. Nevertheless a method was devised which allows convergence in the truncated expansion of Hilbert states. Comparisons are made to experiment. Future developments are discussed
Numerical Simulation of Shale Gas Production with Thermodynamic Calculations Incorporated
Urozayev, Dias
2015-06-01
In today’s energy sector, it has been observed a revolutionary increase in shale gas recovery induced by reservoir fracking. So-called unconventional reservoirs became profitable after introducing a well stimulation technique. Some of the analysts expect that shale gas is going to expand worldwide energy supply. However, there is still a lack of an efficient as well as accurate modeling techniques, which can provide a good recovery and production estimates. Gas transports in shale reservoir is a complex process, consisting of slippage effect, gas diffusion along the wall, viscous flow due to the pressure gradient. Conventional industrial simulators are unable to model the flow as the flow doesn’t follow Darcy’s formulation. It is significant to build a unified model considering all given mechanisms for shale reservoir production study and analyze the importance of each mechanism in varied conditions. In this work, a unified mathematical model is proposed for shale gas reservoirs. The proposed model was build based on the dual porosity continuum media model; mass conservation equations for both matrix and fracture systems were build using the dusty gas model. In the matrix, gas desorption, Knudsen diffusion and viscous flow were taken into account. The model was also developed by implementing thermodynamic calculations to correct for the gas compressibility, or to obtain accurate treatment of the multicomponent gas. Previously, the model was built on the idealization of the gas, considering every molecule identical without any interaction. Moreover, the compositional variety of shale gas requires to consider impurities in the gas due to very high variety. Peng-Robinson equation of state was used to com- pute and correct for the gas density to pressure relation by solving the cubic equation to improve the model. The results show that considering the compressibility of the gas will noticeably increase gas production under given reservoir conditions and slow down
Ability of aphasic individuals to perform numerical processing and calculation tasks
Gabriela De Luccia
2014-03-01
Full Text Available Objective To compare performance on EC301 battery calculation task between aphasic subjects and normal controls of the same sex, age, and education. Method Thirty-two aphasic patients who had suffered a single left hemisphere stroke were evaluated. Forty-four healthy volunteers were also selected. All subjects underwent a comprehensive arithmetic battery to assess their numerical and calculation skills. Performances on numerical processing and calculation tasks were then analyzed. Results Aphasic individuals showed changes in their ability to perform numerical processing and calculation tasks that were not observed in the healthy population. Conclusion Compared with healthy subjects of the same age and education level, individuals with aphasia had difficulty performing various tasks that involved numerical processing and calculation.
McMullan, Miriam; Jones, Ray; Lea, Susan
2010-04-01
This paper is a report of a correlational study of the relations of age, status, experience and drug calculation ability to numerical ability of nursing students and Registered Nurses. Competent numerical and drug calculation skills are essential for nurses as mistakes can put patients' lives at risk. A cross-sectional study was carried out in 2006 in one United Kingdom university. Validated numerical and drug calculation tests were given to 229 second year nursing students and 44 Registered Nurses attending a non-medical prescribing programme. The numeracy test was failed by 55% of students and 45% of Registered Nurses, while 92% of students and 89% of nurses failed the drug calculation test. Independent of status or experience, older participants (> or = 35 years) were statistically significantly more able to perform numerical calculations. There was no statistically significant difference between nursing students and Registered Nurses in their overall drug calculation ability, but nurses were statistically significantly more able than students to perform basic numerical calculations and calculations for solids, oral liquids and injections. Both nursing students and Registered Nurses were statistically significantly more able to perform calculations for solids, liquid oral and injections than calculations for drug percentages, drip and infusion rates. To prevent deskilling, Registered Nurses should continue to practise and refresh all the different types of drug calculations as often as possible with regular (self)-testing of their ability. Time should be set aside in curricula for nursing students to learn how to perform basic numerical and drug calculations. This learning should be reinforced through regular practice and assessment.
Numerical method for three dimensional steady-state two-phase flow calculations
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
Comparison of results of experimental research with numerical calculations of a model one-sided seal
Joachimiak Damian
2015-06-01
Full Text Available Paper presents the results of experimental and numerical research of a model segment of a labyrinth seal for a different wear level. The analysis covers the extent of leakage and distribution of static pressure in the seal chambers and the planes upstream and downstream of the segment. The measurement data have been compared with the results of numerical calculations obtained using commercial software. Based on the flow conditions occurring in the area subjected to calculations, the size of the mesh defined by parameter y+ has been analyzed and the selection of the turbulence model has been described. The numerical calculations were based on the measurable thermodynamic parameters in the seal segments of steam turbines. The work contains a comparison of the mass flow and distribution of static pressure in the seal chambers obtained during the measurement and calculated numerically in a model segment of the seal of different level of wear.
Numerical calculation of the cross section by the solution of the wave equation
Drewko, J.
1982-01-01
A numerical method of solving of the wave equation is described for chosen vibrational eigenfunctions. A prepared program calculates the total cross sections for the resonant vibrational excitation for diatomic molecules on the basis of introduced molecular data. (author)
Taghizadeh, Alireza; Mørk, Jesper; Chung, Il-Sug
2014-01-01
Four different numerical methods for calculating the quality factor and resonance wavelength of a nano or micro photonic cavity are compared. Good agreement was found for a wide range of quality factors. Advantages and limitations of the different methods are discussed.......Four different numerical methods for calculating the quality factor and resonance wavelength of a nano or micro photonic cavity are compared. Good agreement was found for a wide range of quality factors. Advantages and limitations of the different methods are discussed....
Reliability analysis and component functional allocations for the ESF multi-loop controller design
Hur, Seop; Kim, D.H.; Choi, J.K.; Park, J.C.; Seong, S.H.; Lee, D.Y.
2006-01-01
This paper deals with the reliability analysis and component functional allocations to ensure the enhanced system reliability and availability. In the Engineered Safety Features, functionally dependent components are controlled by a multi-loop controller. The system reliability of the Engineered Safety Features-Component Control System, especially, the multi-loop controller which is changed comparing to the conventional controllers is an important factor for the Probability Safety Assessment in the nuclear field. To evaluate the multi-loop controller's failure rate of the k-out-of-m redundant system, the binomial process is used. In addition, the component functional allocation is performed to tolerate a single multi-loop controller failure without the loss of vital operation within the constraints of the piping and component configuration, and ensure that mechanically redundant components remain functional. (author)
Numerical calculation of velocity distribution near a vertical flat plate immersed in bubble flow
Matsuura, Akihiro; Nakamura, Hajime; Horihata, Hideyuki; Hiraoka, Setsuro; Aragaki, Tsutomu; Yamada, Ikuho; Isoda, Shinji.
1992-01-01
Liquid and gas velocity distributions for bubble flow near a vertical flat plate were calculated numerically by using the SIMPLER method, where the flow was assumed to be laminar, two-dimensional, and at steady state. The two-fluid flow model was used in the numerical analysis. To calculate the drag force on a small bubble, Stokes' law for a rigid sphere is applicable. The dimensionless velocity distributions which were arranged with characteristic boundary layer thickness and maximum liquid velocity were adjusted with a single line and their forms were similar to that for single-phase wall-jet flow. The average wall shear stress derived from the velocity gradient at the plate wall was strongly affected by bubble diameter but not by inlet liquid velocity. The present dimensionless velocity distributions obtained numerically agreed well with previous experimental results, and the proposed numerical algorithm was validated. (author)
Advanced numerical methods for three dimensional two-phase flow calculations
Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
Advanced numerical methods for three dimensional two-phase flow calculations
Toumi, I.; Caruge, D.
1997-01-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe's method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations
Miller, Mark
2005-01-01
I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical parameter estimation in modern interferometric gravitational wave detectors. Using a post-Newtonian point particle model for the premerger phase of the binary inspiral, I calculate the maximum allowable errors for the mass and relative velocity and positions of the binary during numerical simulations of the binary inspiral. These maximum allowable errors are compared to the errors of state-of-the-art numerical simulations of multiple-orbit binary neutron star calculations in full general relativity, and are found to be smaller by several orders of magnitude. A post-Newtonian model for the error of these numerical simulations suggests that adaptive mesh refinement coupled with second-order accurate finite difference codes will not be able to robustly obtain the accuracy required for reliable gravitational wave extraction on Terabyte-scale computers. I conclude that higher-order methods (higher-order finite difference methods and/or spectral methods) combined with adaptive mesh refinement and/or multipatch technology will be needed for robustly accurate gravitational wave extraction from numerical relativity calculations of binary coalescence scenarios
A numerical approach to calculate the induced voltage in the case of conduced perturbations
Andretzko, J.P.; Hedjiedj, A.; Babouri, A.; Guendouz, L.; Nadi, M. [Nancy-1 Univ. Henri Poincare, Lab. d' Instrumentation Electronique de Nancy, Faculte des Sciences, 54 - Vandoeuvre les Nancy (France)
2006-07-01
This paper presents a method of numerical simulation that makes it possible to calculate the induced tension to the terminals of the cardiac pacemaker subjected to conduced disturbances. The physical model used for simulation is an experimental test bed which makes it possible to study the behaviour of pacemaker, in vitro, subjected to electromagnetic disturbances in low frequencies range (50 hz - 500 khz). The test bed in which the pacemaker is implanted is described in this article. The process of calculation uses the admittance method adapted to the case of conducted disturbances. Results obtained by numerical simulation are close to experimental values. (authors)
A numerical approach to calculate the induced voltage in the case of conduced perturbations
Andretzko, J.P.; Hedjiedj, A.; Babouri, A.; Guendouz, L.; Nadi, M.
2006-01-01
This paper presents a method of numerical simulation that makes it possible to calculate the induced tension to the terminals of the cardiac pacemaker subjected to conduced disturbances. The physical model used for simulation is an experimental test bed which makes it possible to study the behaviour of pacemaker, in vitro, subjected to electromagnetic disturbances in low frequencies range (50 hz - 500 khz). The test bed in which the pacemaker is implanted is described in this article. The process of calculation uses the admittance method adapted to the case of conducted disturbances. Results obtained by numerical simulation are close to experimental values. (authors)
Á. Vas
2013-06-01
Full Text Available The prediction of weather generally means the solution of differential equations on the base of the measured initial conditions where the data of close and distant neighboring points are used for the calculations. It requires the maintenance of expensive weather stations and supercomputers. However, if weather stations are not only capable of measuring but can also communicate with each other, then these smart sensors can also be applied to run forecasting calculations. This applies the highest possible level of parallelization without the collection of measured data into one place. Furthermore, if more nodes are involved, the result becomes more accurate, but the computing power required from one node does not increase. Our Distributed Sensor Network for meteorological sensing and numerical weather Prediction Calculations (DSN-PC can be applied in several different areas where sensing and numerical calculations, even the solution of differential equations, are needed.
Advanced numerical methods for three dimensional two-phase flow calculations in PWR
Toumi, I.; Gallo, D.; Royer, E.
1997-01-01
This paper is devoted to new numerical methods developed for three dimensional two-phase flow calculations. These methods are finite volume numerical methods. They are based on an extension of Roe's approximate Riemann solver to define convective fluxes versus mean cell quantities. To go forward in time, a linearized conservative implicit integrating step is used, together with a Newton iterative method. We also present here some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. This kind of numerical method, which is widely used for fluid dynamic calculations, is proved to be very efficient for the numerical solution to two-phase flow problems. This numerical method has been implemented for the three dimensional thermal-hydraulic code FLICA-4 which is mainly dedicated to core thermal-hydraulic transient and steady-state analysis. Hereafter, we will also find some results obtained for the EPR reactor running in a steady-state at 60% of nominal power with 3 pumps out of 4, and a thermal-hydraulic core analysis for a 1300 MW PWR at low flow steam-line-break conditions. (author)
Numerically induced pressure excursions in two-phase-flow calculations. Final report
Mahaffy, J.H.; Liles, D.R.
1983-01-01
Pressure spikes that cannot be traced to any physical origin sometimes are observed when standard Eulerian finite-difference methods are used to calculate two-phase-flow transients. This problem occurs with varying frequency in nuclear reactor safety codes such as RELAP, RETRAN, COBRA, and TRAC. These spikes usually result from numerical water packing or from interactions between spatial discretization and heat transfer
A numerical calculation method of environmental impacts for the deep sea mining industry - a review.
Ma, Wenbin; van Rhee, Cees; Schott, Dingena
2018-03-01
Since the gradual decrease of mineral resources on-land, deep sea mining (DSM) is becoming an urgent and important emerging activity in the world. However, until now there has been no commercial scale DSM project in progress. Together with the reasons of technological feasibility and economic profitability, the environmental impact is one of the major parameters hindering its industrialization. Most of the DSM environmental impact research focuses on only one particular aspect ignoring that all the DSM environmental impacts are related to each other. The objective of this work is to propose a framework for the numerical calculation methods of the integrated DSM environmental impacts through a literature review. This paper covers three parts: (i) definition and importance description of different DSM environmental impacts; (ii) description of the existing numerical calculation methods for different environmental impacts; (iii) selection of a numerical calculation method based on the selected criteria. The research conducted in this paper provides a clear numerical calculation framework for DSM environmental impact and could be helpful to speed up the industrialization process of the DSM industry.
High-speed atomic force microscope imaging: Adaptive multiloop mode
Ren, Juan; Zou, Qingze; Li, Bo; Lin, Zhiqun
2014-07-01
In this paper, an imaging mode (called the adaptive multiloop mode) of atomic force microscope (AFM) is proposed to substantially increase the speed of tapping mode (TM) imaging while preserving the advantages of TM imaging over contact mode (CM) imaging. Due to its superior image quality and less sample disturbances over CM imaging, particularly for soft materials such as polymers, TM imaging is currently the most widely used imaging technique. The speed of TM imaging, however, is substantially (over an order of magnitude) lower than that of CM imaging, becoming the major bottleneck of this technique. Increasing the speed of TM imaging is challenging as a stable probe tapping on the sample surface must be maintained to preserve the image quality, whereas the probe tapping is rather sensitive to the sample topography variation. As a result, the increase of imaging speed can quickly lead to loss of the probe-sample contact and/or annihilation of the probe tapping, resulting in image distortion and/or sample deformation. The proposed adaptive multiloop mode (AMLM) imaging overcomes these limitations of TM imaging through the following three efforts integrated together: First, it is proposed to account for the variation of the TM deflection when quantifying the sample topography; second, an inner-outer feedback control loop to regulate the TM deflection is added on top of the tapping-feedback control loop to improve the sample topography tracking; and, third, an online iterative feedforward controller is augmented to the whole control system to further enhance the topography tracking, where the next-line sample topography is predicted and utilized to reduce the tracking error. The added feedback regulation of the TM deflection ensures the probe-sample interaction force remains near the minimum for maintaining a stable probe-sample interaction. The proposed AMLM imaging is tested and demonstrated by imaging a poly(tert-butyl acrylate) sample in experiments. The
On a method of numerical calculation of nonlinear radial pulsations of stars
Kosovichev, A.G.
1984-01-01
Some features of using the finite difference method for numerical investigation of nonradial pulsations of stars were considered. The mathematical model of these pulsations is described by time-dependent gasdynaMic equations with gravity. A one-dimentional (spherically-symmetric) case is considered. It was obtained a two-parametric family of ultimate conservative difference schemes where the diffepence analogy of the main conservative laws as well as the additional relations for the balance to individual kinds of energy are performed. Such difference schemes provide more exact calculation of nonlinear flows with shocks as compared with the other difference schemes with the same order of approximation. The methods of numerical solution of implicit (absolute stable) difference schemes for a given family were considered. The coupled equations are solved through iterative Newton method Using martrix and separate successive eliminations. Numerical method can be used for calculation of large amplitude radial pulsations of stars
Shigemaru, Daichi; Tsukamoto, Hiroshi
2010-06-01
Whirling motion of a pump impeller was calculated for the centrifugal blood pump with Conical Spiral Groove Bearings to get a criterion for the instability of impeller whirling motion. The motion of the centrifugal blood pump impeller was calculated based on a spring damping model, and unsteady flow in the pump was computed using the commercial CFD package ANSYS CFX. Also the whirling motion of rotating impeller was measured using two displacement sensors fixed to the blood pump casing. The numerical calculations were done for the blood pump impeller with conical spiral groove bearings, and impeller whirling motion was evaluated.
Danilov, G.S.
1994-01-01
It is shown that matrices of periods characterizing complex (1|1) supermanifolds of genus n > 1 depend on a spinor structure. This dependence manifests itself in terms proportional to odd moduli. Properties of matrices of periods exert a strong influence on the holomorphic structure of multiloop amplitudes in superstring theory. The supersymmetric analog of the Belavin-Knizhnik theorem is obtained by taking into account the above dependence on odd moduli. Superconformal versions of the Schottky group are used to study matrices of periods. This is essentially the only parametrization in which matrices of periods can be expressed explicitly in terms of even and odd moduli. Superconformal Schottky groups suitable for describing all spinor structures, including the structures for which superfields have branch points, are constructed. A method for calculating vacuum correlation functions of superfields for the above spinor structures is proposed. 18 refs
Multiloop atom interferometer measurements of chameleon dark energy in microgravity
Chiow, Sheng-wey; Yu, Nan
2018-02-01
Chameleon field is one of the promising candidates of dark energy scalar fields. As in all viable candidate field theories, a screening mechanism is implemented to be consistent with all existing tests of general relativity. The screening effect in the chameleon theory manifests its influence limited only to the thin outer layer of a bulk object, thus producing extra forces orders of magnitude weaker than that of the gravitational force of the bulk. For pointlike particles such as atoms, the depth of screening is larger than the size of the particle, such that the screening mechanism is ineffective and the chameleon force is fully expressed on the atomic test particles. Extra force measurements using atom interferometry are thus much more sensitive than bulk mass based measurements, and indeed have placed the most stringent constraints on the parameters characterizing chameleon field. In this paper, we present a conceptual measurement approach for chameleon force detection using atom interferometry in microgravity, in which multiloop atom interferometers exploit specially designed periodic modulation of chameleon fields. We show that major systematics of the dark energy force measurements, i.e., effects of gravitational forces and their gradients, can be suppressed below all hypothetical chameleon signals in the parameter space of interest.
Multiloop Integral System Test (MIST): MIST Facility Functional Specification
Habib, T.F.; Koksal, C.G.; Moskal, T.E.; Rush, G.C.; Gloudemans, J.R.
1991-04-01
The Multiloop Integral System Test (MIST) is part of a multiphase program started in 1983 to address small-break loss-of-coolant accidents (SBLOCAs) specific to Babcock and Wilcox designed plants. MIST is sponsored by the US Nuclear Regulatory Commission, the Babcock ampersand Wilcox Owners Group, the Electric Power Research Institute, and Babcock and Wilcox. The unique features of the Babcock and Wilcox design, specifically the hot leg U-bends and steam generators, prevented the use of existing integral system data or existing integral facilities to address the thermal-hydraulic SBLOCA questions. MIST was specifically designed and constructed for this program, and an existing facility -- the Once Through Integral System (OTIS) -- was also used. Data from MIST and OTIS are used to benchmark the adequacy of system codes, such as RELAP5 and TRAC, for predicting abnormal plant transients. The MIST Functional Specification documents as-built design features, dimensions, instrumentation, and test approach. It also presents the scaling basis for the facility and serves to define the scope of work for the facility design and construction. 13 refs., 112 figs., 38 tabs
T.I.G. Welding of stainless steel. Numerical modelling for temperatures calculation in the Haz
Martinez-Conesa, E. J.; Estrems-Amestoy, M.; Miguel-Eguia, V.; Garrido-Hernandez, A.; Guillen-Martinez, J. A.
2010-01-01
In this work, a numerical method for calculating the temperature field into the heat affected zone for butt welded joints is presented. The method has been developed for sheet welding and takes into account a bidimensional heat flow. It has built a computer program by MS-Excel books and Visual Basic for Applications (VBA). The model has been applied to the TIG process of AISI 304 stainless steel 2mm thickness sheet. The welding process has been considered without input materials. The numerical method may be used to help the designers to predict the temperature distribution in welded joints. (Author) 12 refs.
Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification
Blottner, F.G.; Lopez, A.R.
1998-10-01
This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.
Wang, Yi
2016-07-21
Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.
Numerical Calculation of the Swirling Flow in a Centrifugal Compressor Volute
Seong, Seon Mo; Kang, Shin Hyoung; Cho, Kyung Seok; Kim, Woo June
2007-01-01
Flows in the centrifugal compressor volute with circular cross section are numerically investigated. The computational grid for the calculation utilized a multi-block arrangement to form a butterfly grid and flow calculations are performed using commercial CFD software, CFX-TASCflow. The centrifugal compressor of this study has axial diffuser after radial diffuser because of the shape of inlet duct and installation constraints. Due to this feature the swirling flow pattern is different from the other investigations. The flow inside volute is very complex and three dimensional with strong vortex and recirculation through volute tongue. The calculation results show circumferential variations of the swirl and through flow velocity and pressure distribution. The mechanism deciding flow structure is explained by considering the force balance in volute cross section. And static pressure recovery and total pressure loss are estimated from the calculated results and compared with Japikse model
An Efficient numerical method to calculate the conductivity tensor for disordered topological matter
Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.
2015-03-01
We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.
Numerical calculation of flashing from long pipes using a two-field model
Rivard, W.C.; Torrey, M.D.
1976-05-01
A two-field model for two-phase flows, in which the vapor and liquid phases have different densities, velocities, and temperatures, has been used to calculate the flashing of water from long pipes. The IMF (Implicit Multifield) technique is used to numerically solve the transient equations that govern the dynamics of each phase. The flow physics is described with finite rate phase transitions, interfacial friction, heat transfer, pipe wall friction, and appropriate state equations. The results of the calculations are compared with measured histories of pressure, temperature, and void fraction. A parameter study indicates the relative sensitivity of the results to the various physical models that are used
Numerical calculation of flashing from long pipes using a two-field model
Rivard, W.C.; Torrey, M.D.
1975-11-01
A two-field model for two-phase flows, in which the vapor and liquid phases have different densities, velocities, and temperatures, has been used to calculate the flashing of water from long pipes. The IMF (Implicit Multifield) technique is used to numerically solve the transient equations that govern the dynamics of each phase. The flow physics is described with finite rate phase transitions, interfacial friction, heat transfer, pipe wall friction, and appropriate state equations. The results of the calculations are compared with measured histories of pressure, temperature, and void fraction. A parameter study indicates the relative sensitivity of the results to the various physical models that are used
Mesoscale modelling in China: Risø DTU numerical wind atlas calculation for NE China (Dongbei)
Badger, Jake; Larsén, Xiaoli Guo; Hahmann, Andrea N.
of the wind resource for Dongbei south of 50oN. The results of the numerical wind atlas show a wind resource over the region of interest modulated mainly by topographic features. These are principally elevated terrain features, giving high resources on exposed ridges and lower resources adjacent to the low......This document reports on the methods and findings of project “A01 Mesoscale Modelling”, part of the CMA component of the Wind Energy Development (WED) programme, focusing mainly on the methods and work undertaken by Risø DTU. The KAMM/WAsP methodology for numerical wind atlas calculation....... The major new aspects of the project were the large number of KAMM/WAsP sensitivity studies, comparison with WRF, and the CMA’s numerical wind atlas method (WERAS). Additionally, the reliability of the input data for the methodology, and the wave-number spectra properties of the output data were...
Planning design of Ukrainian mines by the means of numerical calculations
Ruppel, Ulrich; Scior, Carsten [DMT GmbH und Co. KG (DMT), Essen (Germany). Rock Mechanic Dept.
2008-08-21
Using a mine in the Ukraine as an example it is shown how the DMT performs rock mechanical and support planning or roadways in hard coal mines worldwide. Therefore it is necessary to analyse existing measurements and operating experience within a few days as well as organising further surveys on site on short notice. Based on these results the numerical models are calibrated. Using the numerical simulation technology it is possible for DMT to quantify and analyse the rock mechanical impact of different support systems within a short time. Finally the results of the numerical calculations are set in comparison in a rating matrix. Besides making a decision on implementing new roadway and support systems with the objective to use the roadways up to the second longwall panel, the rating matrix is also used for analysing the optimization potentials of existing support systems. This allows the recommendations to immediate improvement of the strata control in the miner's roadways. (orig.)
Golombeck, M A; Dössel, O; Raiser, J
2003-09-01
Numerical field calculations and experimental investigations were performed to examine the heating of the surface of human skin during the application of a new electrode design for the patient return electrode. The new electrode is characterised by an equipotential ring around the central electrode pads. A multi-layer thigh model was used, to which the patient return electrode and the active electrode were connected. The simulation geometry and the dielectric tissue parameters were set according to the frequency of the current. The temperature rise at the skin surface due to the flow of current was evaluated using a two-step numerical solving procedure. The results were compared with experimental thermographical measurements that yielded a mean value of maximum temperature increase of 3.4 degrees C and a maximum of 4.5 degrees C in one test case. The calculated heating patterns agreed closely with the experimental results. However, the calculated mean value in ten different numerical models of the maximum temperature increase of 12.5 K (using a thermodynamic solver) exceeded the experimental value owing to neglect of heat transport by blood flow and also because of the injection of a higher test current, as in the clinical tests. The implementation of a simple worst-case formula that could significantly simplify the numerical process led to a substantial overestimation of the mean value of the maximum skin temperature of 22.4 K and showed only restricted applicability. The application of numerical methods confirmed the experimental assertions and led to a general understanding of the observed heating effects and hotspots. Furthermore, it was possible to demonstrate the beneficial effects of the new electrode design with an equipotential ring. These include a balanced heating pattern and the absence of hotspots.
Application of optimization numerical methods in calculation of the two-particle nuclear reactions
Titarenko, N.N.
1987-01-01
An optimization packet of PEAK-OPT applied programs intended for solution of problems of absolute minimization of functions of many variables in calculations of cross sections of binary nuclear reactions is described. The main algorithms of computerized numerical solution of systems of nonlinear equations for the least square method are presented. Principles for plotting and functioning the optimization software as well as results of its practical application are given
Akhmetov Vadim
2017-01-01
Full Text Available Swirling flow with particle deposition effects at the lateral surface is numerically investigated. The flow field calculation results have been obtained as the solutions of the Navier-Stokes equations. Various flow regimes with the formation of axial recirculation zones are presented. The convection-diffusion model is used for the determination of the flow particle concentration and the formation of typical sedimentation zones.
Kuhn, Jörg-Tobias; Ise, Elena; Raddatz, Julia; Schwenk, Christin; Dobel, Christian
2016-09-01
Deficits in basic numerical skills, calculation, and working memory have been found in children with developmental dyscalculia (DD) as well as children with attention-deficit/hyperactivity disorder (ADHD). This paper investigates cognitive profiles of children with DD and/or ADHD symptoms (AS) in a double dissociation design to obtain a better understanding of the comorbidity of DD and ADHD. Children with DD-only (N = 33), AS-only (N = 16), comorbid DD+AS (N = 20), and typically developing controls (TD, N = 40) were assessed on measures of basic numerical processing, calculation, working memory, processing speed, and neurocognitive measures of attention. Children with DD (DD, DD+AS) showed deficits in all basic numerical skills, calculation, working memory, and sustained attention. Children with AS (AS, DD+AS) displayed more selective difficulties in dot enumeration, subtraction, verbal working memory, and processing speed. Also, they generally performed more poorly in neurocognitive measures of attention, especially alertness. Children with DD+AS mostly showed an additive combination of the deficits associated with DD-only and A_Sonly, except for subtraction tasks, in which they were less impaired than expected. DD and AS appear to be related to largely distinct patterns of cognitive deficits, which are present in combination in children with DD+AS.
Time domain numerical calculations of the short electron bunch wakefields in resistive structures
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
Barrera Figueroa, Salvador; Rasmussen, Knud; Jacobsen, Finn
2009-01-01
to this problem is to measure the velocity distribution of the membrane by means of a non-contact method, such as laser vibrometry. The measured velocity distribution can be used together with a numerical formulation such as the boundary element method for estimating the microphone response and other parameters......, e.g., the acoustic center. In this work, such a hybrid method is presented and examined. The velocity distributions of a number of condenser microphones have been determined using a laser vibrometer, and these measured velocity distributions have been used for estimating microphone responses......Typically, numerical calculations of the pressure, free-field, and random-incidence response of a condenser microphone are carried out on the basis of an assumed displacement distribution of the diaphragm of the microphone; the conventional assumption is that the displacement follows a Bessel...
Calculation of residual stresses by means of a 3D numerical weld simulation
Nicak, Tomas; Huemmer, Matthias
2008-01-01
The numerical weld simulation has developed very fast in recent years. The problem complexity has increased from simple 2D models to full 3D models, which can describe the entire welding process more realistically. As recent research projects indicate, a quantitative assessment of the residual stresses by means of a 3D analysis is possible. The structure integrity can be assessed based on the weld simulation results superimposed with the operating load. Moreover, to support the qualification of welded components parametric studies for optimization of the residual stress distribution in the weld region can be performed. In this paper a full 3D numerical weld simulation for a man-hole drainage nozzle in a steam generator will be presented. The residual stresses are calculated by means of an uncoupled transient thermal and mechanical FE analysis. The paper will present a robust procedure allowing reasonable predictions of the residual stresses for complex structures in industrial practice. (authors)
Multi-loop correlators for rational theories of 2D gravity from the generalized Kontsevich models
Kristjansen, C.
1994-01-01
functions of the susceptibilities and the eigenvalues of the external field. We furthermore use the moment technique to derive a closed expression for the genus zero multi-loop correlators for $(3,3m-1)$ and $(3,3m-2)$ rational matter fields coupled to gravity. We comment on the relation between the two-matrix...
Explicit solutions of the multi-loop integral recurrence relations and its application
Baikov, P.A.
1997-01-01
Approaches to construct explicit solutions of the recurrence relations for multi-loop integrals are suggested. The resulting formulas demonstrate a high efficiency, at least for the 3-loop vacuum integral case. They also produce a new type of recurrence relations over the space-time dimension. (orig.)
Calculation of infrared radiation in the atmosphere by a numerical method
Nunes, G.S.S.; Viswanadham, Y.
1981-01-01
A numerical method is described for the calculations of the atmospheric infrared flux and radiative cooling rate in the atmosphere. It is suitable for use at all levels below lower stratosphere. The square root pressure correction factor is incorporated in the computation of the corrected optical depth. The water vapour flux emissivity data of Staley and Jurica are used in the model. The versatility of the computing scheme sugests that this method is adequate to evaluate infrared flux and flux divergence in the problems involving a large amount of atmospheric data. (Author) [pt
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
Wampler, William R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Myers, Samuel M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Modine, Normand A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-09-01
The energy-dependent probability density of tunneled carrier states for arbitrarily specified longitudinal potential-energy profiles in planar bipolar devices is numerically computed using the scattering method. Results agree accurately with a previous treatment based on solution of the localized eigenvalue problem, where computation times are much greater. These developments enable quantitative treatment of tunneling-assisted recombination in irradiated heterojunction bipolar transistors, where band offsets may enhance the tunneling effect by orders of magnitude. The calculations also reveal the density of non-tunneled carrier states in spatially varying potentials, and thereby test the common approximation of uniform- bulk values for such densities.
A contribution to the numerical calculation of static electromagnetic fields in unbounded domains
Krawczyk, F.
1990-11-01
The numerical calculation of static electromagnetic fields for arbitrarily shaped three-dimensional structures, especially in unbounded domains, is very memory and cpu-time consuming. In this thesis several schemes that reduce memory and cpu-time consumption have been developed or introduced. The memory needed can be reduced by a special simulation of boundaries towards open space and by the use of a scalar potential for the field description. Known disadvantages of the use of such a potential are avoided by an improved formulation of the used algorithms. The cpu-time for the calculations can be reduced remarkably in many cases by using a multigrid solution scheme including a defect-correction. A computer code has been written that uses these algorithms. With the help of this program it has been demonstrated that using these algorithms, distinct improvements in terms of computer memory, cpu-time consumption and accuracy can be achieved. (orig.) [de
Theory and numerical calculation of the acoustic field exerted by eddy-current forces
Kawashima, K.
1976-01-01
The equations for calculating the acoustic field produced within a nonmagnetic metal by interaction of eddy currents with a static magnetic field were obtained on the assumptions (1) an ultrasonic wave is generated by the electromagentic force through classical and macroscopic phenomena; (2) the electric, magnetic, and elastic properties of the metal are linear, isotropic, and homogeneous throughout the metal, which occupies semi-infinite space; (3) the whole system is axially symmetric; and (4) eddy currents and elastic waves show a steady-state sinusoidal variation. The acoustic field produced by a specific electromagnetic ultrasonic transducer with axial symmetry was calculated numerically, and the results showed a well-defined ultrasonic wave beam, which was narrower than had been expected from the size of the transducer. (auth)
Numerical calculation of spin echo amplitude in pulsed NMR: effects of quadrupole interaction
Sobral, R.R.
1986-01-01
The spin echo obtained by nuclear magnetic resonance, in systems which atomic nuclei interact with magnetic fields and electric field gradients, present oscillations in function of the time interval between two excitations pulses. Using the density matrix formalism, the amplitudes of these echo is calculated, analytically. In this work, echo amplitudes obtained under different excitation conditions for nuclei of different nuclear spin values are calculated. The numerical results are compared with disposable analytical solutions. Applications of this method to the case of electric field gradient without axial symmetry were studied. Within the used approximation limits, an expression for attnuation of oscillatory behaviour of echo amplitude in function of the time interval between experimentally observed pulses was obtained. (M.C.K.) [pt
Comparison of turbulence models for numerical calculation of airflow in an annex 20 room
Voigt, Lars P. K.
2000-01-01
The report deals with 2-D numerical calculation of room airflow in an isothermal annex 20 room. The report documents the ability of the flow solver EllipSys2D to give results in good agreement with measurements for the specified test case. The flow solver is a finite volume code solving the Reyno.......Applying theory for a two-dimensional wall jet, measurements are compared with calculated values of the turbulent kinetic energy....... the Reynolds Averaged Navier Stokes equations.Five two-equation turbulence models were tested. These are the standard k-epsilon model, the low-Reynolds number k-epison model by Launder & Sharma, the k-omega model by Wilcox, the k-omega baseline (BSL) model by Menter and the k-omega Shear Stress Transport (SST...
Numerical procedure for the calculation of nonsteady spherical shock fronts with radiation
Winkler, K.H.
The basis of the numerical method is an implicit difference scheme with time backward differences to a freely moving coordinate system. The coordinate system itself is determined simultaneously with the iterative solution of the physical equations as a function of the physical variables. Shock fronts, even nonsteady ones, are calculated as discontinuities according to the Rankine--Hugoniot equations. The radiation field is obtained from the two-dimensional, static, spherically symmetric transport equation in conjunction with the time-dependent one-dimensional moment equations. No artificial viscosity of any type is ever used. The applicability of the method developed is demonstrated by an example involving the calculation of protostar collapse. 11 figures
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs
Zinn-Justin, Jean; Jentschura, Ulrich D.
2004-01-01
In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton contributions to the partition function, using the formalism introduced in the first part of the treatise [Ann. Phys. (N. Y.) (previous issue) (2004)]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker-Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is non-zero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited
Solving recurrence relations for multi-loop Feynman integrals
Smirnov, Vladimir A.; Steinhauser, Matthias
2003-01-01
We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, i.e., the problem of expressing any Feynman integral from this class as a linear combination of master integrals. We show how the parametric representation invented by Baikov [Phys. Lett. B 385 (1996) 404, Nucl. Instrum. Methods A 389 (1997) 347] can be used to characterize the master integrals and to construct an algorithm for evaluating the corresponding coefficient functions. To illustrate this procedure we use simple one-loop examples as well as the class of diagrams appearing in the calculation of the two-loop heavy quark potential
An approach to first principles electronic structure calculation by symbolic-numeric computation
Akihito Kikuchi
2013-04-01
Full Text Available There is a wide variety of electronic structure calculation cooperating with symbolic computation. The main purpose of the latter is to play an auxiliary role (but not without importance to the former. In the field of quantum physics [1-9], researchers sometimes have to handle complicated mathematical expressions, whose derivation seems almost beyond human power. Thus one resorts to the intensive use of computers, namely, symbolic computation [10-16]. Examples of this can be seen in various topics: atomic energy levels, molecular dynamics, molecular energy and spectra, collision and scattering, lattice spin models and so on [16]. How to obtain molecular integrals analytically or how to manipulate complex formulas in many body interactions, is one such problem. In the former, when one uses special atomic basis for a specific purpose, to express the integrals by the combination of already known analytic functions, may sometimes be very difficult. In the latter, one must rearrange a number of creation and annihilation operators in a suitable order and calculate the analytical expectation value. It is usual that a quantitative and massive computation follows a symbolic one; for the convenience of the numerical computation, it is necessary to reduce a complicated analytic expression into a tractable and computable form. This is the main motive for the introduction of the symbolic computation as a forerunner of the numerical one and their collaboration has won considerable successes. The present work should be classified as one such trial. Meanwhile, the use of symbolic computation in the present work is not limited to indirect and auxiliary part to the numerical computation. The present work can be applicable to a direct and quantitative estimation of the electronic structure, skipping conventional computational methods.
S. G. Tikhomirov
2015-01-01
Full Text Available In the article discussed the mathematical formulation and numerical algorithm for solving the problem of calculating the temperature field in the process vulcanizing of the product, whose the thermal characteristics are depended on the temperature. As a mathematical model considered the system of differential equations of heat conduction, taking into account the change in the coefficients of thermal conductivity and heat density in multilayer product of the temperature. The system of equations is solved for a given initial distribution of temperature and for a given (time-dependent temperatures on the border of the product to the press-mold and to the diaphragm. On the border of the contacts of adjacent layers are given the condition of continuity of temperature and heat flux. Change of the thermal conductivity from the time is approximated by linear functions. The activation energy of the vulcanization process is determined on the basis of experimental data obtained in the control test samples using a reometer. Considering the function representing the corresponding integrals of the thermal conductivity, the original system of differential equations is transformed to an equivalent system of differential equations convenient for constructing numerical algorithms for solving the problem. The resulting system of partial differential equations derived using the method of finite-difference approximation is replaced by a system of algebraic equations. Solution of the system of algebraic equations is carried out under the scheme explicit difference approximation. In the article calculated the temperature field for the tire at given initial and boundary conditions. Stability and accuracy of the numerical algorithm for solving the problem is demonstrated by the calculations performed with different sampling step along the time and space coordinates. Assessment of the degree of completion of the process is carried out by calculated equivalent time for
Merker, L.; Costi, T. A.
2012-08-01
We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat Cimp to be calculated accurately from local static correlation functions; specifically via Cimp=(∂Eionic)/(∂T)+(1)/(2)(∂Ehyb)/(∂T), where Eionic and Ehyb are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to Cimp. For the nondegenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high-temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two-state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The approach could also be of interest within other impurity solvers, for example, within quantum Monte Carlo techniques.
Numerical Exact Ab Initio Four-Nucleon Scattering Calculations: from Dream to Reality
Fonseca, A. C.; Deltuva, A.
2017-03-01
In the present manuscript we review the work of the last ten years on the pursuit to obtain numerical exact solutions of the four-nucleon scattering problem using the most advanced force models that fit two nucleon data up to pion production threshold with a χ ^2 per data point approximately one, together with the Coulomb interaction between protons; three- and four-nucleon forces are also included in the framework of a meson exchange potential model where NN couples to NΔ. Failure to describe the world data on four-nucleon scattering observables in the framework of a non relativistic scattering approach falls necessarily on the force models one uses. Four-nucleon observables pose very clear challenges, particular in the low energy region where there are a number of resonances whose position and width needs to be dynamically generated by the nucleon-nucleon (NN) interactions one uses. In addition, our calculations constitute the most advance piece of work where observables for all four-nucleon reactions involving isospin I=0, I=0 coupled to I=1 and isospin I=1 initial states are calculated at energies both below and above breakup threshold. We also present a very extensive comparison between calculated results and data for cross sections and spin observables. Therefore the present work reveals both the shortcomings and successes of some of the present NN force models in describing four-nucleon data and serve as a benchmark for future developments.
Kalin, J.; Petkovsek, B.; Montarnal, Ph.; Genty, A.; Deville, E.; Krivic, J.; Ratej, J.
2011-01-01
In the past years the Slovenian Performance Analysis/Safety Assessment team has performed many generic studies for the future Slovenian low and intermediate level waste repository, most recently a Special Safety Analysis for the Krsko site. The modelling approach was to split the problem into three parts: near-field (detailed model of the repository), far-field (i.e., geosphere) and biosphere. In the Special Safety Analysis the code used to perform the near-field calculations was Hydrus2D. Recently the team has begun a cooperation with the French Commisariat al'Energie Atomique/Saclay (CEA/Saclay) and, as a part of this cooperation, began investigations into using the Alliances numerical platform for near-field calculations in order to compare the overall approach and calculated results. The article presents the comparison between these two codes for a silo-type repository that was considered in the Special Safety Analysis. The physical layout and characteristics of the repository are presented and a hydraulic and transport model of the repository is developed and implemented in Alliances. Some analysis of sensitivity to mesh fineness and to simulation timestep has been preformed and is also presented. The compared quantity is the output flux of radionuclides on the boundary of the model. Finally the results from Hydrus2D and Alliances are compared and the differences and similarities are commented.
Kalin, J., E-mail: jan.kalin@zag.s [Slovenian National Building and Civil Engineering Institute, Dimiceva 12, SI-1000 Ljubljana (Slovenia); Petkovsek, B., E-mail: borut.petkovsek@zag.s [Slovenian National Building and Civil Engineering Institute, Dimiceva 12, SI-1000 Ljubljana (Slovenia); Montarnal, Ph., E-mail: philippe.montarnal@cea.f [CEA/Saclay, DM2S/SFME/LSET, Gif-sur-Yvette, 91191 cedex (France); Genty, A., E-mail: alain.genty@cea.f [CEA/Saclay, DM2S/SFME/LSET, Gif-sur-Yvette, 91191 cedex (France); Deville, E., E-mail: estelle.deville@cea.f [CEA/Saclay, DM2S/SFME/LSET, Gif-sur-Yvette, 91191 cedex (France); Krivic, J., E-mail: jure.krivic@geo-zs.s [Geological Survey of Slovenia, Dimiceva 14, SI-1000 Ljubljana (Slovenia); Ratej, J., E-mail: joze.ratej@geo-zs.s [Geological Survey of Slovenia, Dimiceva 14, SI-1000 Ljubljana (Slovenia)
2011-04-15
In the past years the Slovenian Performance Analysis/Safety Assessment team has performed many generic studies for the future Slovenian low and intermediate level waste repository, most recently a Special Safety Analysis for the Krsko site. The modelling approach was to split the problem into three parts: near-field (detailed model of the repository), far-field (i.e., geosphere) and biosphere. In the Special Safety Analysis the code used to perform the near-field calculations was Hydrus2D. Recently the team has begun a cooperation with the French Commisariat al'Energie Atomique/Saclay (CEA/Saclay) and, as a part of this cooperation, began investigations into using the Alliances numerical platform for near-field calculations in order to compare the overall approach and calculated results. The article presents the comparison between these two codes for a silo-type repository that was considered in the Special Safety Analysis. The physical layout and characteristics of the repository are presented and a hydraulic and transport model of the repository is developed and implemented in Alliances. Some analysis of sensitivity to mesh fineness and to simulation timestep has been preformed and is also presented. The compared quantity is the output flux of radionuclides on the boundary of the model. Finally the results from Hydrus2D and Alliances are compared and the differences and similarities are commented.
Numerical Calculation and Measurement of Nonlinear Acoustic Fields in Ultrasound Diagnosis
Kawagishi, Tetsuya; Saito, Shigemi; Mine, Yoshitaka
2002-05-01
In order to develop a tool for designing on the ultrasonic probe and its peripheral devices for tissue-harmonic-imaging systems, a study is carried out to compare the calculation and observation results of nonlinear acoustic fields for a diagnostic ultrasound system. The pulsed ultrasound with a center frequency of 2.5 MHz is emanated from a weakly focusing sector probe with a 6.5 mm aperture radius and a 50 mm focal length into an agar phantom with an attenuation coefficient of about 0.6 dB/cm/MHz or 1.2 dB/cm/MHz. The nonlinear acoustic field is measured using a needle-type hydrophone. The calculation is based on the Khokhlov-Zabolotskaya-Kuznetsov(KZK) equation which is modified so that the frequency dependence of the attenuation coefficient is the same as that in biological tissue. This equation is numerically solved with the implicit backward method employing the iterative method. The measured and calculated amplitude spectra show good agreement with each other.
A numerical calculation method for flow discretisation in complex geometry with body-fitted grids
Jin, X.
2001-04-01
A numerical calculation method basing on body fitted grids is developed in this work for computational fluid dynamics in complex geometry. The method solves the conservation equations in a general nonorthogonal coordinate system which matches the curvilinear boundary. The nonorthogonal, patched grid is generated by a grid generator which solves algebraic equations. By means of an interface its geometrical data can be used by this method. The conservation equations are transformed from the Cartesian system to a general curvilinear system keeping the physical Cartesian velocity components as dependent variables. Using a staggered arrangement of variables, the three Cartesian velocity components are defined on every cell surface. Thus the coupling between pressure and velocity is ensured, and numerical oscillations are avoided. The contravariant velocity for calculating mass flux on one cell surface is resulting from dependent Cartesian velocity components. After the discretisation and linear interpolation, a three dimensional 19-point pressure equation is found. Using the explicit treatment for cross-derivative terms, it reduces to the usual 7-point equation. Under the same data and process structure, this method is compatible with the code FLUTAN using Cartesian coordinates. In order to verify this method, several laminar flows are simulated in orthogonal grids at tilted space directions and in nonorthogonal grids with variations of cell angles. The simulated flow types are considered like various duct flows, transient heat conduction, natural convection in a chimney and natural convection in cavities. Their results achieve very good agreement with analytical solutions or empirical data. Convergence for highly nonorthogonal grids is obtained. After the successful validation of this method, it is applied for a reactor safety case. A transient natural convection flow for an optional sump cooling concept SUCO is simulated. The numerical result is comparable with the
How to integrate divergent integrals: a pure numerical approach to complex loop calculations
Caravaglios, F.
2000-01-01
Loop calculations involve the evaluation of divergent integrals. Usually [G. 't Hooft, M. Veltman, Nucl. Phys. B 44 (1972) 189] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers the Laurent expansion in powers of ε=n-4. In this paper we discuss a method to extract directly all coefficients of this expansion by means of concrete and well defined integrals in a five-dimensional space. We by-pass the formal and symbolic procedure of analytic continuation; instead we can numerically compute the integrals to extract directly both the coefficient of the pole 1/ε and the finite part
Brainerd, J.J.; Petrosian, V.
1987-01-01
Calculations are performed numerically and analytically of synchrotron spectra for thermal and power-law electron distributions using the single-particle synchrotron power spectrum derived from quantum electrodynamics. It is found that the photon energy at which quantum effects appear is proportional to temperature and independent of field strength for thermal spectra; quantum effects introduce an exponential roll-off away from the classical spectra. For power law spectra, the photon energy at which quantum effects appear is inversely proportional to the magnetic field strength; quantum effects produce a steeper power law than is found classically. The results are compared with spectra derived from the classical power spectrum with an energy cutoff ensuring conservation of energy. It is found that an energy cutoff is generally an inadequate approximation of quantum effects for low photon energies and for thermal spectra, but gives reasonable results for high-energy emission from power-law electron distributions. 17 references
Halama, Arthur; Kamerdzhiev, Vsevolod; Boehme, Christian; Srinivasan, Sudharsan [Forschungszentrum Juelich, IKP-4 (Germany)
2016-07-01
The institute of Nuclear Physics 4(IKP-4) of the Research Center Juelich (FZJ) is in charge of building and commissioning the High Energy Storage Ring (HESR) within the international Facility for Antiproton and Ion Research (FAIR) at Darmstadt. Simulations and numerical calculations were performed to characterize the initial beam position pickup design. Capacitive couplings of the electrodes and the behavior of the electrical equivalent circuit were investigated. This made room for changes to the design and performance increase. A prototype of the BPM pickup was constructed and tested on a dedicated test bench. Preliminary results will be presented. In order to gain higher signal levels and higher sensitivity, another suggested design was characterized as well and put into comparison.
Pogosyan, T A
1983-01-01
The article is dedicated to the solution of systems of differential equations which describe the transfer processes in an electric power system (EES) by implicit methods of numerical integration. The distinguishing feature of the implicit methods (Euler's reverse method and the trapeze method) is their absolute stability and, consequently, the relatively small accumulation of errors in each step of integration. Therefore, they are found to be very convenient for solving problems of electric power engineering, when the transfer processes are described by a rigid system of differential equations. The rigidity is associated with the range of values of the time constants considered. The advantage of the implicit methods over explicit are shown in a specific example (calculation of the dynamic stability of the simplest electric power system), along with the field of use of the implicit methods and the expedience of their use in power engineering problems.
Numerical Calculation of Coherent Synchrotron Radiation Effects Using TraFiC4
Kabel, Andreas C.
2000-01-01
Coherent synchrotron radiation (CSR) occurs when short bunches travel on strongly bent trajectories. Its effects on high-quality beams can be severe and are well understood qualitatively. For quantitative results, however, one has to rely on numerical methods. There exist several simulation codes utilizing different approaches. The authors describe in some detail the code TraFiC 4 developed at DESY for design and analysis purposes, which approaches the problem from first principles and solves the equations of motion either perturbatively or self-consistently. They present some calculational results and comparison with experimental data. Also, they give examples of how the code can be used to design beamlines with minimal emittance growth due to CSR
Havu, V.; Blum, V.; Havu, P.; Scheffler, M.
2009-01-01
We consider the problem of developing O(N) scaling grid-based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algorithms, and specifically the creation of localized grid batches. The choice of the grid partitioning scheme plays an important role in the performance and memory consumption of the grid-based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches.
Tornow, Sabine [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg, 86135 Augsburg (Germany); Tong, Ning-Hua [Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, 76128 Karlsruhe (Germany); Bulla, Ralf [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg, 86135 Augsburg (Germany)
2006-07-05
We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.
Tornow, Sabine; Tong, Ning-Hua; Bulla, Ralf
2006-07-05
We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.
Kruis, Nathanael J. F.
Heat transfer from building foundations varies significantly in all three spatial dimensions and has important dynamic effects at all timescales, from one hour to several years. With the additional consideration of moisture transport, ground freezing, evapotranspiration, and other physical phenomena, the estimation of foundation heat transfer becomes increasingly sophisticated and computationally intensive to the point where accuracy must be compromised for reasonable computation time. The tools currently available to calculate foundation heat transfer are often either too limited in their capabilities to draw meaningful conclusions or too sophisticated to use in common practices. This work presents Kiva, a new foundation heat transfer computational framework. Kiva provides a flexible environment for testing different numerical schemes, initialization methods, spatial and temporal discretizations, and geometric approximations. Comparisons within this framework provide insight into the balance of computation speed and accuracy relative to highly detailed reference solutions. The accuracy and computational performance of six finite difference numerical schemes are verified against established IEA BESTEST test cases for slab-on-grade heat conduction. Of the schemes tested, the Alternating Direction Implicit (ADI) scheme demonstrates the best balance between accuracy, performance, and numerical stability. Kiva features four approaches of initializing soil temperatures for an annual simulation. A new accelerated initialization approach is shown to significantly reduce the required years of presimulation. Methods of approximating three-dimensional heat transfer within a representative two-dimensional context further improve computational performance. A new approximation called the boundary layer adjustment method is shown to improve accuracy over other established methods with a negligible increase in computation time. This method accounts for the reduced heat transfer
Franck, D; de Carlan, L; Pierrat, N; Broggio, D; Lamart, S
2007-01-01
Although great efforts have been made to improve the physical phantoms used to calibrate in vivo measurement systems, these phantoms represent a single average counting geometry and usually contain a uniform distribution of the radionuclide over the tissue substitute. As a matter of fact, significant corrections must be made to phantom-based calibration factors in order to obtain absolute calibration efficiencies applicable to a given individual. The importance of these corrections is particularly crucial when considering in vivo measurements of low energy photons emitted by radionuclides deposited in the lung such as actinides. Thus, it was desirable to develop a method for calibrating in vivo measurement systems that is more sensitive to these types of variability. Previous works have demonstrated the possibility of such a calibration using the Monte Carlo technique. Our research programme extended such investigations to the reconstruction of numerical anthropomorphic phantoms based on personal physiological data obtained by computed tomography. New procedures based on a new graphical user interface (GUI) for development of computational phantoms for Monte Carlo calculations and data analysis are being developed to take advantage of recent progress in image-processing codes. This paper presents the principal features of this new GUI. Results of calculations and comparison with experimental data are also presented and discussed in this work.
Comparison of different approaches to the numerical calculation of the LMJ focal
Bourgeade A.
2013-11-01
Full Text Available The beam smoothing in the focal plane of high power lasers is of particular importance to laser-plasma interaction studies in order to minimize plasma parametric and hydrodynamic instabilities on the target. Here we investigate the focal spot structure in different geometrical configurations where standard paraxial hypotheses are no longer verified. We present numerical studies in the cases of single flat top square beam, LMJ quadruplet and complete ring of quads with large azimuth angle. Different calculations are made with Fresnel diffraction propagation model in the paraxial approximation and full vector Maxwell's equations. The first model is based on Fourier transform from near to far field method. The second model uses first spherical wave decomposition in plane waves with Fourier transform and propagates them to the focal spot. These two different approaches are compared with Miró [1] modeling results using paraxial or Feit and Fleck options. The methods presented here are generic for focal spot calculations. They can be used for other complex geometric configurations and various smoothing techniques. The results will be used as boundary conditions in plasma interaction computations.
Numerical calculation on infrared characteristics of the special vehicle exhaust system
Feng, Yun-song; Li, Xiao-xia; Jin, Wei
2017-10-01
For mastery of infrared radiation characteristics and flow field of the special vehicle exhaust system, first, a physical model of the special vehicle exhaust system is established with the Gambit, and the mathematical model of flow field is determined. Secondly, software Fluent6.3 is used to simulated the 3-D exterior flow field of the special vehicle exhaust system, and the datum of flow field, such as temperature, pressure and density, are obtained. Thirdly, based on the plume temperature, the special vehicle exhaust space is divided. The exhaust is equivalent to a gray-body. A calculating model of the vehicle exhaust infrared radiation is established, and the exhaust infrared radiation characteristics are calculated by the software MATLAB, then the spatial distribution curves are drawn. Finally, the numerical results are analyzing, and the basic laws of the special vehicle exhaust infrared radiation are explored. The results show that with the increase of the engine speed, the temperature of the exhaust pipe wall of the special vehicle increases, and the temperature and pressure of the exhaust gas flow field increase, which leads to the enhancement of the infrared radiation intensity
Niedermayer, U., E-mail: u.niedermayer@gsi.de [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder, Schlossgartenstrasse 8, 64289 Darmstadt (Germany); Boine-Frankenheim, O. [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder, Schlossgartenstrasse 8, 64289 Darmstadt (Germany)
2012-09-21
The resistive wall impedance is one of the main sources for beam instabilities in synchrotrons and storage rings. The fast ramped SIS18 synchrotron at GSI and the projected SIS100 synchrotron for FAIR both employ thin (0.3 mm) stainless steel beam pipes in order to reduce eddy current effects. The lowest betatron sidebands are at about 100 kHz, which demands accurate impedance predictions in the low frequency (LF) range where the beam pipe and possibly also the structures behind the pipe are the dominating impedance sources. The longitudinal and transverse resistive wall impedances of a circular multi-layer pipe are calculated analytically using the field matching technique. We compare the impedances obtained from a radial wave model, which corresponds to the setup used in bench measurements, with the axial wave model, which corresponds to an actual beam moving with relativistic velocity. For thin beam pipes the induced wall current and the corresponding shielding properties of the pipe are important. In both models the wall current is obtained analytically. The characteristic frequencies for the onset of the wall current are calculated from equivalent lumped element circuits corresponding to the radial model. For more complex structures, like the SIS100 beam pipe, we use a numerical method, in which the impedance is obtained from the total power loss. The method is validated by the analytic expressions for circular beam pipes.
Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring
Berkovits, Nathan
2004-01-01
A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and to construct a suitable b ghost. A super-Poincare covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N 4 terms in the effective action receive no perturbative contributions above one loop. (author)
Precision multiloop (PM Design with space closing circles for lingual orthodontics
Mugdha P Mankar
2016-01-01
Full Text Available The proficiency of ancient orthodontics has been benefitted colossally and is being continually promoted over the present, by use of multiple loop wires designed for correction of dentoalveolar malocclusions. The presented discussion provides an insight into a simple, frictionless biomechanical concept of anterior space closure in lingual orthodontics by means of precision multiloop design with incorporated space closing circles. A multiple loop wire design has been demonstrated where the entire interbracket distance is used as loop area.
Precision multiloop (PM Design) with space closing circles for lingual orthodontics
Mugdha P Mankar; Achint Chachada; Harish Atram; Avanti Kulkarni
2016-01-01
The proficiency of ancient orthodontics has been benefitted colossally and is being continually promoted over the present, by use of multiple loop wires designed for correction of dentoalveolar malocclusions. The presented discussion provides an insight into a simple, frictionless biomechanical concept of anterior space closure in lingual orthodontics by means of precision multiloop design with incorporated space closing circles. A multiple loop wire design has been demonstrated where the ent...
Matthes, W.K.
1998-01-01
The 'adjoint transport equation in its integro-differential form' is derived for the radiation damage produced by atoms injected into solids. We reduce it to the one-dimensional form and prepare it for a numerical solution by: --discretizing the continuous variables energy, space and direction, --replacing the partial differential quotients by finite differences and --evaluating the collision integral by a double sum. By a proper manipulation of this double sum the adjoint transport equation turns into a (very large) set of linear equations with tridiagonal matrix which can be solved by a special (simple and fast) algorithm. The solution of this set of linear equations contains complete information on a specified damage type (e.g. the energy deposited in a volume V) in terms of the function D(i,E,c,x) which gives the damage produced by all particles generated in a cascade initiated by a particle of type i starting at x with energy E in direction c. It is essential to remark that one calculation gives the damage function D for the complete ranges of the variables {i,E,c and x} (for numerical reasons of course on grid-points in the {E,c,x}-space). This is most useful to applications where a general source-distribution S(i,E,c,x) of particles is given by the experimental setup (e.g. beam-window and and target in proton accelerator work. The beam-protons along their path through the window--or target material generate recoil atoms by elastic collisions or nuclear reactions. These recoil atoms form the particle source S). The total damage produced then is eventually given by: D = (Σ)i ∫ ∫ ∫ S(i, E, c, x)*D(i, E, c, x)*dE*dc*dx A Fortran-77 program running on a PC-486 was written for the overall procedure and applied to some problems
Jian-hua Li
2016-04-01
Full Text Available In coastal areas with complicated flow movement, deposition and scour readily occur in submarine excavation projects. In this study, a small-scale model, with a high resolution in the vertical direction, was used to simulate the tidal current around a submarine excavation project. The finite volume method was used to solve Navier-Stokes equations and the Reynolds stress transport equation, and the entire process of the tidal current was simulated with unstructured meshes, generated in the irregular shape area, and structured meshes, generated in other water areas. The meshes near the bottom and free surface were densified with a minimum layer thickness of 0.05 m. The volume of fluid method was used to track the free surface, the volume fraction of cells on the upstream boundary was obtained from the volume fraction of adjacent cells, and that on the downstream boundary was determined by the water level process. The numerical results agree with the observed data, and some conclusions can be drawn: after the foundation trench excavation, the flow velocity decreases quite a bit through the foundation trench, with reverse flow occurring on the lee slope in the foundation trench; the swirling flow impedes inflow, leading to the occurrence of dammed water above the foundation trench; the turbulent motion is stronger during ebbing than in other tidal stages, the range with the maximum value of turbulent viscosity, occurring on the south side of the foundation trench at maximum ebbing, is greater than those in other tidal stages in a tidal cycle, and the maximum value of Reynolds shear stress occurs on the south side of the foundation trench at maximum ebbing in a tidal cycle. The numerical calculation method shows a strong performance in simulation of the hydrodynamic characteristics of tidal currents in the foundation trench, providing a basis for submarine engineering construction in coastal areas.
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.
Jiang, Chao; Qiao, Mingzhong; Zhu, Peng
2017-12-01
A permanent magnet synchronous motor with radial magnetic circuit and built-in permanent magnet is designed for the electric vehicle. Finite element numerical calculation and experimental measurement are adopted to obtain the direct axis and quadrature axis inductance parameters of the motor which are vital important for the motor control. The calculation method is simple, the measuring principle is clear, the results of numerical calculation and experimental measurement are mutual confirmation. A quick and effective method is provided to obtain the direct axis and quadrature axis inductance parameters of the motor, and then improve the design of motor or adjust the control parameters of the motor controller.
Real-space, mean-field algorithm to numerically calculate long-range interactions
Cadilhe, A.; Costa, B. V.
2016-02-01
Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.
Mukhopadhyay, V.; Newsom, J. R.
1982-01-01
A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.
Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser
Cui, H.; Wang, H.; Chen, S.
2015-04-01
In the present study, the energy depreciation rule of spray heat exchanger, which is attached to a main fan diffuser, is analyzed based on the second law of thermodynamics. Firstly, the exergy equations of the exchanger are deduced. The equations are numerically calculated by the fourth-order Runge-Kutta method, and the exergy destruction is quantitatively effected by the exchanger structure parameters, working fluid (polluted air, i.e., PA; sprayed water, i.e., SW) initial state parameters and the ambient reference parameters. The results are showed: (1) heat transfer is given priority to latent transfer at the bottom of the exchanger, and heat transfer of convection and is equivalent to that of condensation in the upper. (2) With the decrease of initial temperature of SW droplet, the decrease of PA velocity or the ambient reference temperature, and with the increase of a SW droplet size or initial PA temperature, exergy destruction both increase. (3) The exergy efficiency of the exchanger is 72.1 %. An approach to analyze the energy potential of the exchanger may be provided for engineering designs.
Faix-Gantier, A.
2001-12-01
This thesis concerns the study of flame propagation in a turbulent flow of lean hydrogen-air mixtures. The aim is to precise the characteristics of propagation as well as combustion and turbulence models able to take into account the peculiarities of these mixtures. This research work is related to the prevention of fire hazards associated with accidental release of hydrogen within the reactor of a nuclear power plant. In a first part, the scales (the flame velocity and thickness) associated with the laminar flame propagation in hydrogen-air mixtures are studied. A specific attention is devoted to the intrinsic instability properties of such flames. Then, the turbulence scales potentially present within a reactor are estimated in order to allow for the determination of the regimes of combustion that might be present within the reactor and among which the flamelet regime appears to be conceivable. In a second part, starting with the analysis of the propagation properties of a mean reaction zone calculated with a flamelet model, we show that, with an adequate tuning of the parameter appearing in the mean reaction rate expression, it is possible to predict numerically the turbulent flame speeds available with the literature. (author)
Mixed layer depth calculation in deep convection regions in ocean numerical models
Courtois, Peggy; Hu, Xianmin; Pennelly, Clark; Spence, Paul; Myers, Paul G.
2017-12-01
Mixed Layer Depths (MLDs) diagnosed by conventional numerical models are generally based on a density difference with the surface (e.g., 0.01 kg.m-3). However, the temperature-salinity compensation and the lack of vertical resolution contribute to over-estimated MLD, especially in regions of deep convection. In the present work, we examined the diagnostic MLD, associated with the deep convection of the Labrador Sea Water (LSW), calculated with a simple density difference criterion. The over-estimated MLD led us to develop a new tool, based on an observational approach, to recalculate MLD from model output. We used an eddy-permitting, 1/12° regional configuration of the Nucleus for European Modelling of the Ocean (NEMO) to test and discuss our newly defined MLD. We compared our new MLD with that from observations, and we showed a major improvement with our new algorithm. To show the new MLD is not dependent on a single model and its horizontal resolution, we extended our analysis to include 1/4° eddy-permitting simulations, and simulations using the Modular Ocean Model (MOM) model.
VALIDATION OF NUMERICAL METHODS TO CALCULATE BYPASS FLOW IN A PRISMATIC GAS-COOLED REACTOR CORE
NAM-IL TAK
2013-11-01
Full Text Available For thermo-fluid and safety analyses of a High Temperature Gas-cooled Reactor (HTGR, intensive efforts are in progress in the developments of the GAMMA+ code of Korea Atomic Energy Research Institute (KAERI and the AGREE code of the University of Michigan (U of M. One of the important requirements for GAMMA+ and AGREE is an accurate modeling capability of a bypass flow in a prismatic core. Recently, a series of air experiments were performed at Seoul National University (SNU in order to understand bypass flow behavior and generate an experimental database for the validation of computer codes. The main objective of the present work is to validate the GAMMA+ and AGREE codes using the experimental data published by SNU. The numerical results of the two codes were compared with the measured data. A good agreement was found between the calculations and the measurement. It was concluded that GAMMA+ and AGREE can reliably simulate the bypass flow behavior in a prismatic core.
Amirkhizi, Alireza V; Nemat-Nasser, Sia
2008-01-01
Through the use of conductive straight wires or coils the electromagnetic properties of a composite material can be modified. The asymmetric geometry of the coils creates an overall chiral response. The polarization vectors rotate as an electromagnetic wave travels through such a medium. To calculate the chirality of a medium prior to its manufacturing, we developed a method to extract all four electromagnetic material parameter tensors for a general uniaxial bianisotropic composite based on the numerical simulation of the electromagnetic fields. Our method uses appropriate line and surface field averages in a single unit cell of the periodic structure of the composite material. These overall field quantities have physical meaning only when the microscopic variation of the electromagnetic fields in the scale of the unit cell is not important, that is when the wavelength of interest is significantly larger than the maximum linear dimension of the unit cell. The overall constitutive relations of the periodic structure can then be obtained from the relations among the average quantities
Systematic implementation of implicit regularization for multi-loop Feynman Diagrams
Cherchiglia, Adriano Lana; Sampaio, Marcos; Nemes, Maria Carolina
2011-01-01
Full text: Implicit Regularization (IR) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. The essence of the method is to write the divergences in terms of loop integrals in one internal momentum which do not need to be explicitly evaluated. Moreover it acts in the physical dimension of the theory and gauge invariance is controlled by regularization dependent surface terms which when set to zero define a constrained version of IR (CIR) and deliver gauge invariant amplitudes automatically. Therefore it is in principle applicable to all physical relevant quantum field theories, supersymmetric gauge theories included. A non trivial question is whether we can generalize this program to arbitrary loop order in consonance with locality, unitarity and Lorentz invariance, especially when overlapping divergences occur. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IR program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multi-loop amplitude in a well defined set of basic divergent integrals in one internal momentum. We present several examples (from 1-loop to n-loops) using scalar φ 6 3 theory in order to help the reader understand and visualize the essence of the IR program. The choice of a scalar theory does not reduce the generality of the method presented since all other physical theories can be treated within the same strategy after space time and internal algebra are performed. Another result of this contribution is to show that if the surface terms are not set to zero they will contaminate the renormalization group coefficients. Thus, we are forced to adopt CIR which is equivalent to demand momentum routing invariance
Mesri, Mokhtaria
2015-01-01
Highlights: • Rare measuring networks in the developing world due to technical and fiscal reasons. • Insufficient attention is paid regarding to tools for solar energy systems design. • The new interface offers solutions to the insisting need for innovative decisions. • Comprehensive comparative studies are conducted using experimental measurements. • Results are with attractive margins of error in accordance with experimental data. - Abstract: The present paper is basically devoted to the estimation of solar radiation in order to provide data on the situation of solar applications in a given site; it also aims at contributing to the performance improvement of solar energy systems. I aim to show and evaluate the performance of the most appropriate models used to recover solar components at ground level, via confronting meteorological techniques to selected semi empirical methods. I have adopted an innovative approach to testing the theory through numerical simulation by providing a friendly user ergonomic Graphic User Interface ‘GUI’, carefully designed and that principally makes use of a large range of models for the calculation of solar components. In this article I may consider three numerical models namely: Lacis and Hansen, Atwater and Ball and Lui and Jordon, which are used here to elucidate the performance of such methods facing meteorological models such as those of Angstrom, Garg and Coppolino. I debate the advantages of these latest methods, and I argue that they are of big importance because the main variable that is used is sunshine duration. Some of them involve the water content in the atmosphere, a particularly important parameter which strongly absorbs solar radiation in the infrared region. They are also perfectly suited for locations where solar irradiance is not being measured by all hydrometeorological stations, and where only meteorological data are collected. I want to complete this paper by demonstrating the efficiency of the
A calculation method for RF couplers design based on numerical simulation by microwave studio
Wang Rong; Pei Yuanji; Jin Kai
2006-01-01
A numerical simulation method for coupler design is proposed. It is based on the matching procedure for the 2π/3 structure given by Dr. R.L. Kyhl. Microwave Studio EigenMode Solver is used for such numerical simulation. the simulation for a coupler has been finished with this method and the simulation data are compared with experimental measurements. The results show that this numerical simulation method is feasible for coupler design. (authors)
Mikulović Jovan Č.
2014-01-01
Full Text Available A methodology for calculation of overvoltages in transformer windings, based on a numerical method of inverse Laplace transform, is presented. Mathematical model of transformer windings is described by partial differential equations corresponding to distributed parameters electrical circuits. The procedure of calculating overvoltages is applied to windings having either isolated neutral point, or grounded neutral point, or neutral point grounded through impedance. A comparative analysis of the calculation results obtained by the proposed numerical method and by analytical method of calculation of overvoltages in transformer windings is presented. The results computed by the proposed method and measured voltage distributions, when a voltage surge is applied to a three-phase 30 kVA power transformer, are compared. [Projekat Ministartsva nauke Republike Srbije, br. TR-33037 i br. TR-33020
Liu, Fang, E-mail: fliu@lsec.cc.ac.cn [School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Lin, Lin, E-mail: linlin@math.berkeley.edu [Department of Mathematics, University of California, Berkeley, CA 94720 (United States); Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Vigil-Fowler, Derek, E-mail: vigil@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Lischner, Johannes, E-mail: jlischner597@gmail.com [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kemper, Alexander F., E-mail: afkemper@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sharifzadeh, Sahar, E-mail: ssharifz@bu.edu [Department of Electrical and Computer Engineering and Division of Materials Science and Engineering, Boston University, Boston, MA 02215 (United States); Jornada, Felipe H. da, E-mail: jornada@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Deslippe, Jack, E-mail: jdeslippe@lbl.gov [NERSC, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Yang, Chao, E-mail: cyang@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); and others
2015-04-01
We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.
Groshev, A.I.; Slobodchuk, V.I.
1986-01-01
The results of numerical calculation of the conjugated problem of convective heat transfer under unsteady conditions are presented. The equations describing heat transfer take into account longitudinal heat diffusion in liquid and in a wall. The formulae for calculating local heat flows at the wall-liquid surface in the case of an arbitrary law of temperature variation at the outer wall surface along the channel length are proposed for steady-state heat transfer conditions
Component Functional Allocations of the ESF Multi-loop Controller for the KNICS ESF-CCS Design
Hur, Seop; Choi, Jong Kyun; Kim, Dong Hoon; Kim, Ho; Kim, Seong Tae
2006-01-01
The safety related components in nuclear power plants are traditionally controlled by single-loop controllers. Traditional single-loop controller systems utilize dedicated processors for each component but that components independence is compromised through a sharing of power supplies, auxiliary logic modules and auxiliary I/O cards. In the new design of the ESF-CCS, the multi-loop controllers with data networks are widely used. Since components are assigned to ESF-CCS functional groups in a manner consistent with their process relationship, the effects of the failures are predictable and manageable. Therefore, the key issues for the design of multi-loop controller is to allocate the components to the each multi-loop controller through plant and function analysis and grouping. This paper deals with an ESF component functional allocation which is performed through allocation criteria and a fault analysis
Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes
Huang, Shifeng; Fang, Xiongjun; Jing, Jiliang
2018-06-01
Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle-Horowitz-Strominger (GHS) dilaton spacetime and Gibbons-Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.
Pilot dynamics for instrument approach tasks: Full panel multiloop and flight director operations
Weir, D. H.; Mcruer, D. T.
1972-01-01
Measurements and interpretations of single and mutiloop pilot response properties during simulated instrument approach are presented. Pilot subjects flew Category 2-like ILS approaches in a fixed base DC-8 simulaton. A conventional instrument panel and controls were used, with simulated vertical gust and glide slope beam bend forcing functions. Reduced and interpreted pilot describing functions and remmant are given for pitch attitude, flight director, and multiloop (longitudinal) control tasks. The response data are correlated with simultaneously recorded eye scanning statistics, previously reported in NASA CR-1535. The resulting combined response and scanning data and their interpretations provide a basis for validating and extending the theory of manual control displays.
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.
K. Majidi
2000-01-01
Full Text Available The flow field in volute and circular casings interacting with a centrifugal impeller is obtained by numerical analysis. In the present study, effects of the volute and circular casings on the flow pattern have been investigated by successively combining a volute casing and a circular casing with a single centrifugal impeller. The numerical calculations are carried out with a multiple frame of reference to predict the flow field inside the entire impeller and casings. The impeller flow field is solved in a rotating frame and the flow field in the casings in a stationary frame. The static pressure and velocity in the casing and impeller, and the static pressures and secondary velocity vectors at several cross-sectional planes of the casings are calculated. The calculations show that the curvature of the casings creates pressure gradients that cause vortices at cross-sectional planes of the casings.
Numerical Calculation of Distribution of Induced Carge Density on Planar Confined Surfaces
Bolotov, V.; Druzhchenko, R.; Karazin, V.; Lominadze, J.; Kharadze, F.
2007-01-01
The calculation method of distribution of induced charge density on planar surfaces, including fractal structures of Sierpinski carpet type, is propesed. The calculation scheme is based on the fact that simply connected conducting surface of arbitrary geometry is an equipotential surface. (author)
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 numerical calculation of Rényi entropy for a sphere
Kim, Nakwoo, E-mail: nkim@khu.ac.kr
2014-06-02
We numerically compute the Rényi entropy for four-dimensional free scalar field theory with a spherical entangling surface. As is well known, the Rényi entropy as a function of the boundary area exhibits linear dependence in the leading order. The coefficient of the subleading logarithmic term from our numerical data, as a function of the Rényi order q, agrees nicely with the general prediction of conformal field theory computation. The motivation of this work is also partly to see how the efficiency of numerical computation changes as a function of q. For q<1 the summation over eigenvalues of reduced density matrix takes longer since the series converges more slowly than for q=1. For q>1 the convergence is faster, but the relative error becomes large as a general trend.
Liang, Peipeng; Jia, Xiuqin; Taatgen, Niels A; Borst, Jelmer P; Li, Kuncheng
2016-01-01
Numerical inductive reasoning refers to the process of identifying and extrapolating the rule involved in numeric materials. It is associated with calculation, and shares the common activation of the fronto-parietal regions with calculation, which suggests that numerical inductive reasoning may
Rusanov, A V; Yershov, S V [Institute of Mechanical Engineering Problems of National Academy of Sciences of Ukraine Kharkov (Ukraine)
1998-12-31
The numerical method is suggested for the calculation of the 3D periodically unsteady viscous cascade flow evoked by the aerodynamics interaction of blade rows. Such flow is described by the thin-layer Reynolds-averaged unsteady Navier-Stokes equations. The turbulent effects are simulated with the modified Baldwin-Lomax turbulence model. The problem statement allows to consider an unsteady flow through either a single turbo-machine stage or a multi stage turbomachine. The sliding mesh techniques and the time-space non-oscillatory square interpolation are used in axial spacings to calculate the flow in a computational domain that contains the reciprocally moving elements. The gasdynamical equations are integrated numerically with the implicit quasi-monotonous Godunov`s type ENO scheme of the second or third order of accuracy. The suggested numerical method is incorporated in the FlowER code developed by authors for calculations of the 3D viscous compressible flows through multi stage turbomachines. The numerical results are presented for unsteady turbine stage throughflows. The method suggested is shown to simulate qualitatively properly the main unsteady cascade effects in particular the periodically blade loadings, the propagation of stator wakes through rotor blade passage and the unsteady temperature flowfields for stages with cooled stator blades. (author) 21 refs.
Rusanov, A.V.; Yershov, S.V. [Institute of Mechanical Engineering Problems of National Academy of Sciences of Ukraine Kharkov (Ukraine)
1997-12-31
The numerical method is suggested for the calculation of the 3D periodically unsteady viscous cascade flow evoked by the aerodynamics interaction of blade rows. Such flow is described by the thin-layer Reynolds-averaged unsteady Navier-Stokes equations. The turbulent effects are simulated with the modified Baldwin-Lomax turbulence model. The problem statement allows to consider an unsteady flow through either a single turbo-machine stage or a multi stage turbomachine. The sliding mesh techniques and the time-space non-oscillatory square interpolation are used in axial spacings to calculate the flow in a computational domain that contains the reciprocally moving elements. The gasdynamical equations are integrated numerically with the implicit quasi-monotonous Godunov`s type ENO scheme of the second or third order of accuracy. The suggested numerical method is incorporated in the FlowER code developed by authors for calculations of the 3D viscous compressible flows through multi stage turbomachines. The numerical results are presented for unsteady turbine stage throughflows. The method suggested is shown to simulate qualitatively properly the main unsteady cascade effects in particular the periodically blade loadings, the propagation of stator wakes through rotor blade passage and the unsteady temperature flowfields for stages with cooled stator blades. (author) 21 refs.
Multiloop calculations in p-adic string theory and Bruhat-Tits trees. 1
Zabrodin, A.V.; Mironov, A.D.; Chekhov, L.O.
1989-01-01
The open p-adic string world sheet as a coset space F=T/Γ, where T is the Bruhat-Tits three for the p-adic linear group GL(2.Q p ) and Γ is contained it PGL(2.Q p ) is some Schottky group is treated. The boundary of this world sheet corresponds to p-adic Mumford curve of finite genus. The string dynamics is governed by the local gaussian action on the coset space F. The tachyon amplitudes expressed in terms of p-adic Θ-functions are proposed for the Mumford curve of arbitrary genus and compared them with the corresponding usual archimedian amplitudes. 25 refs.; 5 figs
Multiloop calculations in p-adic string theory and Bruhat-Tits trees.2
Zabrodin, A.V.; Mironov, A.D.; Chekhov, L.O.
1989-01-01
The open p-adic string world sheet as a coset space F=T/Γ, where T is the Bruhat-Tits tree for the p-adic linear group GL(2.Q p ) is some Schottky group is treated. The boundary of this world sheet corresponds to p-adic Mumford curve of finite genus. The string dynamics is governed by the local Gaussian action on the coset space F. The tachyon amplitudes expressed in terms of p-adic Θ-functions are proposed for the Mumford curve of arbitrary genus and compared with the corresponding usual archimedian amplitudes. 41 refs.; 14 figs
Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation
Gonzalez, Ivan; Schmidt, Ivan
2007-01-01
We present an improved form of the integration technique known as NDIM (negative dimensional integration method), which is a powerful tool in the analytical evaluation of Feynman diagrams. Using this technique we study a φ 3 +φ 4 theory in D=4-2ε dimensions, considering generic topologies of L loops and E independent external momenta, and where the propagator powers are arbitrary. The method transforms the Schwinger parametric integral associated to the diagram into a multiple series expansion, whose main characteristic is that the argument contains several Kronecker deltas which appear naturally in the application of the method, and which we call diagram presolution. The optimization we present here consists in a procedure that minimizes the series multiplicity, through appropriate factorizations in the multinomials that appear in the parametric integral, and which maximizes the number of Kronecker deltas that are generated in the process. The solutions are presented in terms of generalized hypergeometric functions, obtained once the Kronecker deltas have been used in the series. Although the technique is general, we apply it to cases in which there are 2 or 3 different energy scales (masses or kinematic variables associated to the external momenta), obtaining solutions in terms of a finite sum of generalized hypergeometric series 1 and 2 variables respectively, each of them expressible as ratios between the different energy scales that characterize the topology. The main result is a method capable of solving Feynman integrals, expressing the solutions as hypergeometric series of multiplicity (n-1), where n is the number of energy scales present in the diagram
Numerical calculation of acoustic radiation from band-vibrating structures via FEM/FAQP method
GAO Honglin
2017-08-01
Full Text Available The Finite Element Method (FEM combined with the Frequency Averaged Quadratic Pressure method (FAQP are used to calculate the acoustic radiation of structures excited in the frequency band. The surface particle velocity of stiffened cylindrical shells under frequency band excitation is calculated using finite element software, the normal vibration velocity is converted from the surface particle velocity to calculate the average energy source (frequency averaged across intensity, frequency averaged across pressure and frequency averaged across velocity, and the FAQP method is used to calculate the average sound pressure level within the bandwidth. The average sound pressure levels are then compared with the bandwidth using finite element and boundary element software, and the results show that FEM combined with FAQP is more suitable for high frequencies and can be used to calculate the average sound pressure level in the 1/3 octave band with good stability, presenting an alternative to applying frequency-by-frequency calculation and the average frequency process. The FEM/FAQP method can be used as a prediction method for calculating acoustic radiation while taking the randomness of vibration at medium and high frequencies into consideration.
Closed expressions for specific massive multiloop self-energy integrals
Berends, F.A.; Boehm, M.; Buza, M.; Scharf, R.
1994-01-01
In this paper the class of N loop massive scalar self-energy diagrams with N + 1 propagators is studied in an arbitrary number of dimensions. As it is known these integrals cannot be expressed in terms of polylogarithms. Here it is shown, however, that they can be described by generalized hypergeometric functions of several variables, namely Laricella functions. These results represent previous small and large momentum expansions in closed form. Numerical comparisons for the finite part in four dimensions with a two-dimensional integral representation show good agreement. (orig.)
Herrmann, H.J.
1989-01-01
Electrical conductivity diffusion or phonons, have an anomalous behaviour on percolation clusters at the percolation threshold due to the fractality of these clusters. The results that have been found numerically for this anomalous behaviour are reviewed. A special purpose computer built for this purpose is described and the evaluation of the data from this machine is discussed
MULTI-LOOP CONTROL DESIGN IN MULTIVARIABLE (2X2 CONTINUOUS STIRRED TANK REACTOR
Abdul Wahid
2015-06-01
Full Text Available With this study, the design and tuning of multi-loop for multivariable (2x2 CSTR will be made in order to achieve optimum CSTR control performance. This study used Bequette model reactor and MATLAB software and is expected to be able to cope with disturbances in the reactor so that the reactor system is able to stabilize quickly despite the distractions. In this study, the design will be made using multi-loop approach, along with PI controller as the next step. Then, BLT and auto-tune tuning method will be used in PI controller and given disturbances to both of tuning method. The controller performances are then compared. Results of the study are then analyzed for discussions and conclusions. Results from this study have shown that in terms of disturbance rejection, BLT is better than auto-tune based on comparison between both of controller performances. For IAE for the case of temperature, BLT is 30% better than auto-tune, but it is almost the same for the case of concentration. For settling time for the case of concentration, BLT is 30% better than auto-tune, and for the case of temperature, BLT is 18% better than auto-tune. For rise time for the case of concentration and temperature, BLT is 30% better than auto-tune.
Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.
2018-01-01
Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.
Note on the numerical calculation of the Fermi-Dirac integrals
Graef, H.; Pabst, M.
1977-11-01
Expansions of the Fermi-Dirac integrals Fsub(α)(x) are developed, suitable for numerical computation. Only integrals of integer- or half-integer order are treated and expansion coefficients are tabulated for F 1 (x),....,F 9 (x); Fsub(-1/2)(x),...,Fsub(7/2)(x). Maximal relative errors vary with the function and interval considered, but are less than 3 x 10 -6 . (orig.) [de
Tian Yong; Zhang Longqiang; Yang Zhen; Yu Bin
2014-01-01
In order to ensure a long-term reliable operation of the DCS cabinet's 220 V AC power cable, it was needed to confirm whether the conductor temperature rise of power cable meet the requirement of the cable specification. Based on the actual data in site and the theory of numerical heat transfer, conservative model was established, and the conductor temperature was calculated. The calculation results show that the cable arrangement on the cable tray will not lead to the conductor temperature rise of power cable over than the required temperature in technical specification. (authors)
Numerical calculation models of the elastoplastic response of a structure under seismic action
Edjtemai, Nima.
1982-06-01
Two digital calculation models developed in this work have made it possible to analyze the exact dynamic behaviour of ductile structures with one or several degrees of liberty, during earthquakes. With the first model, response spectra were built in the linear and non-linear fields for different absorption and ductility values and two types of seismic accelerograms. The comparative study of these spectra made it possible to check the validity of certain hypotheses suggested for the construction of elastoplastic spectra from corresponding linear spectra. A simplified method of non-linear seismic calculation based on the modal analysis and the spectra of elastoplastic response was then applied to structures with a varying number of degrees of liberty. The results obtained in this manner were compared with those provided by an exact calculation provided by the second digital model developed by us [fr
Numerical calculation of wall-to-bed heat transfer coefficients in gas-fluidized beds
Kuipers, J.A.M.; Prins, W.; van Swaaij, W.P.M.
1992-01-01
A computer model for a hot gas-fluidized bed has been developed. The theoretical description is based on a two-fluid model (TFM) approach in which both phases are considered to be continuous and fully interpenetrating. Local wall-to-bed heat-transfer coefficients have been calculated by the
Corsi, F.
1985-01-01
In connection with the design of nuclear reactors components operating at elevated temperature, design criteria need a level of realism in the prediction of inelastic structural behaviour. This concept leads to the necessity of developing non linear computer programmes, and, as a consequence, to the problems of verification and qualification of these tools. Benchmark calculations allow to carry out these two actions, involving at the same time an increased level of confidence in complex phenomena analysis and in inelastic design calculations. With the financial and programmatic support of the Commission of the European Communities (CEE) a programme of elasto-plastic benchmark calculations relevant to the design of structural components for LMFBR has been undertaken by those Member States which are developing a fast reactor project. Four principal progressive aims were initially pointed out that brought to the decision to subdivide the Benchmark effort in a calculations series of four sequential steps: step 1 to 4. The present document tries to summarize Step 1 of the Benchmark exercise, to derive some conclusions on Step 1 by comparison of the results obtained with the various codes and to point out some concluding comments on the first action. It is to point out that even if the work was designed to test the capabilities of the computer codes, another aim was to increase the skill of the users concerned
Numerical Calculation of the Phase Space Density for the Strong-Strong Beam-Beam Interaction
Sobol, A.; Ellison, J.A.
2003-01-01
We developed a parallel code to calculate the evolution of the 4D phase space density of two colliding beams, which are coupled via the collective strong-strong beam-beam interaction, in the absence of diffusion and damping, using the Perron-Frobenius (PF) operator technique
Comparison of numerical models for calculating dispersion from accidental releases of pollutants
Pepper, D W [Savannah River Lab., Aiken, SC; Cooper, R E; Baker, A J
1982-01-01
A modular, data-based system approach has been developed to facilitate computational simulation of multi-dimensional pollutant dispersion in atmospheric, steam, estuary, and groundwater applications. This system is used to assess effects of accidental releases of pollutants to the environment. Model sophistication ranges from simple statistical to complex three-dimensional numerical methods. The system used specifies desired degree of model sophistication from a terminal. The model used depends on the particular type of problem being solved, and on a basis of merit related to computer cost. The results of prediction for several model problems are presented.
Babailov, S. P., E-mail: babajlov@niic.nsc.ru [A. V. Nikolaevs Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences, Novosibirsk (Russian Federation); National Research Tomsk Polytechnic University, Lenin Avenue 30, Tomsk 634050 (Russian Federation); Purtov, P. A. [Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Insitutskaya 3, 630090 Novosibirsk (Russian Federation); Fomin, E. S. [Institute of Cytology and Genetics of the Siberian Branch of the Russian Academy of Sciences, Av. Lavrentyev 10, 630090 Novosibirsk (Russian Federation)
2016-08-07
An expression has been derived for the time dependence of the NMR line shape for systems with multi-site chemical exchange in the absence of spin-spin coupling, in a zero saturation limit. The dynamics of variation of the NMR line shape with time is considered in detail for the case of two-site chemical exchange. Mathematical programs have been designed for numerical simulation of the NMR spectra of chemical exchange systems. The analytical expressions obtained are useful for NMR line shape simulations for systems with photoinduced chemical exchange.
Numerical weld modeling - a method for calculating weld-induced residual stresses
Fricke, S.; Keim, E.; Schmidt, J.
2001-01-01
In the past, weld-induced residual stresses caused damage to numerous (power) plant parts, components and systems (Erve, M., Wesseling, U., Kilian, R., Hardt, R., Bruemmer, G., Maier, V., Ilg, U., 1994. Cracking in Stabilized Austenitic Stainless Steel Piping of German Boiling Water Reactors - Characteristic Features and Root Causes. 20. MPA-Seminar 1994, vol. 2, paper 29, pp.29.1-29.21). In the case of BWR nuclear power plants, this damage can be caused by the mechanism of intergranular stress corrosion cracking in austenitic piping or the core shroud in the reactor pressure vessel and is triggered chiefly by weld-induced residual stresses. One solution of this problem that has been used in the past involves experimental measurements of residual stresses in conjunction with weld optimization testing. However, the experimental analysis of all relevant parameters is an extremely tedious process. Numerical simulation using the finite element method (FEM) not only supplements this method but, in view of modern computer capacities, is also an equally valid alternative in its own right. This paper will demonstrate that the technique developed for numerical simulation of the welding process has not only been properly verified and validated on austenitic pipe welds, but that it also permits making selective statements on improvements to the welding process. For instance, numerical simulation can provide information on the starting point of welding for every weld bead, the effect of interpass cooling as far as a possible sensitization of the heat affected zone (HAZ) is concerned, the effect of gap width on the resultant weld residual stresses, or the effect of the 'last pass heat sink welding' (welding of the final passes while simultaneously cooling the inner surface with water) producing compressive stresses in the root area of a circumferential weld in an austenitic pipe. The computer program FERESA (finite element residual stress analysis) was based on a commercially
Static Q anti Q force from instanton gas and numerical lattice calculations
Ilgenfrits, E.M.; Mueller-Preussker, M.
1982-01-01
Lattice Monte Carlo calculation predictions for the static strength between quarks are compared with the results obtained in the framework of instanton gas model and a typical instanton size is determined. Yang-Mills theory data for different ratios of Wilson loops in case of SU(3) for the string tension are presented. The instanton corrections to perturbation strength turn to be essential to reach an agreement with obtained by lattice calculations data inside the small-distance region up to approximately 0.3 fm. Arguments in favour of the statement that data difference in this region from the phenomenologically known value is connected with the notion of infinitely heavy quarks but not with neglect of virtual quark loops are presented
Numerical Calculation of Effect of Elastic Deformation on Aerodynamic Characteristics of a Rocket
Abbas, Laith K.; Chen, Dongyang; Rui, Xiaoting
2014-01-01
The application and workflow of Computational Fluid Dynamics (CFD)/Computational Structure Dynamics (CSD) on solving the static aeroelastic problem of a slender rocket are introduced. To predict static aeroelastic behavior accurately, two-way coupling and inertia relief methods are used to calculate the static deformations and aerodynamic characteristics of the deformed rocket. The aerodynamic coefficients of rigid rocket are computed firstly and compared with the experimental data, which ver...
Expansion and compression shock wave calculation in pipes with the C.V.M. numerical method
Raymond, P.; Caumette, P.; Le Coq, G.; Libmann, M.
1983-03-01
The Control Variables Method for fluid transients computations has been used to compute expansion and compression shock waves propagations. In this paper, first analytical solutions for shock wave and rarefaction wave propagation are detailed. Then after a rapid description of the C.V.M. technique and its stability and monotonicity properties, we will present some results about standard shock tube problem, reflection of shock wave, finally a comparison between experimental results obtained on the ELF facility and calculations is given
Plotnikov Aleksandr Aleksandrovich
Full Text Available Glass unit consists of glasses hermetically-united together. The cavity of an insulating glass unit contains a fixed volume of air (gas. In the process of production regular air with atmospheric pressure and temperature is sealed inside a glass unit. During operation the atmospheric pressure is constantly changing, but the pressure inside remains constant (at a constant temperature. A change of temperature or of the external air pressure results in a pressure difference and therefore in a load on the glass panes. The action may exceed the usual load considerably. This pressure effects the glasses of the unit, deforms them, lowers the thermotechnical properties of glass units and can lead to their destruction. The action of the inside pressure can be seen all around as convex and concaved glasses, which destroys the architectural look of buildings. It is obvious that it is incorrect to calculate thin glass plates on such a load only by classical methods of strength of materials theory. In this case we need a special calculation method. The effects of a change in temperature, altitude or meteorological pressure are easily covered by the definition of an isochore pressure. This is necessary, to determine the change of pressure due to the temperature induced gas expansion in the cavity of the insulating glass according to the ideal gas law. After the integration of the analytical plate solution and the ideal gas law, the final pressure states can easily be calculated by coupling the change of volume and the change of pressure.
Shelef, Eitan; Hilley, George E.
2013-12-01
Flow routing across real or modeled topography determines the modeled discharge and wetness index and thus plays a central role in predicting surface lowering rate, runoff generation, likelihood of slope failure, and transition from hillslope to channel forming processes. In this contribution, we compare commonly used flow-routing rules as well as a new routing rule, to commonly used benchmarks. We also compare results for different routing rules using Airborne Laser Swath Mapping (ALSM) topography to explore the impact of different flow-routing schemes on inferring the generation of saturation overland flow and the transition between hillslope to channel forming processes, as well as on location of saturation overland flow. Finally, we examined the impact of flow-routing and slope-calculation rules on modeled topography produced by Geomorphic Transport Law (GTL)-based simulations. We found that different rules produce substantive differences in the structure of the modeled topography and flow patterns over ALSM data. Our results highlight the impact of flow-routing and slope-calculation rules on modeled topography, as well as on calculated geomorphic metrics across real landscapes. As such, studies that use a variety of routing rules to analyze and simulate topography are necessary to determine those aspects that most strongly depend on a chosen routing rule.
Escudier, M.P.; Smith, S. [Department of Engineering, Mechanical Engineering, University of Liverpool, Brownlow Hill, Liverpool L69 3GH (United Kingdom); Oliveira, P.J. [Departamento de Engenharia Electromecanica, Universidade da Beira Interior, Rua Marques D' Avila e Boloma, 6200 Covilha (Portugal); Pinho, F.T. [Centro de Estudos de Fenomenos de Transporte, DEMEGI, Faculdade de Engenharia, Universidade do Porto, Rua Roberto Frias, 4200-465 Porto (Portugal)
2002-07-01
Experimental data are reported for fully developed laminar flow of a shear-thinning liquid through both a concentric and an 80% eccentric annulus with and without centrebody rotation. The working fluid was an aqueous solution of 0.1% xanthan gum and 0.1% carboxymethylcellulose for which the flow curve is well represented by the Cross model. Comparisons are reported between numerical calculations and the flow data, as well as with other laminar annular-flow data for a variety of shear-thinning liquids previously reported in the literature. In general, the calculations are in good quantitative agreement with the experimental data, even in situations where viscoelastic effects, neglected in the calculations, would be expected to play a role. (orig.)
Preliminary analysis of four numerical models for calculating the mesoscale transport of Kr-85
Pepper, D W; Cooper, R E [Du Pont de Nemours (E.I.) and Co., Aiken, SC (USA). Savannah River Lab.
1983-01-01
A performance study of four numerical algorithms for multi-dimensional advection-diffusion prediction on mesoscale grids has been made. Dispersion from point and distributed sources and a simulation of a continuous source are compared with analytical solutions to assess relative accuracy. Model predictions are then compared with actual measurements of Kr-85 emitted from the Savannah River Plant (SRP). The particle-in-cell and method of moments algorithms exhibit superior accuracy in modeling single source releases. For modeling distributed sources, algorithms based on the pseudospectral and finite element interpolation concepts exhibit comparable accuracy. The method of moments is felt to be the best overall performer, although all the models appear to be relatively close in accuracy.
Design and Numerical Calculation of Variable Test Section for Small Supersonic Wind Tunnel
Václav DVOŘÁK
2010-12-01
Full Text Available The paper is concerned with numerical modelling of transition in a separated boundary layer. The model of laminar/turbulent transition is based on the combination of empirical terms determining position of the transition and averaged Navier – Stokes equations closed by the k – ω SST turbulence model. The model of transition is applied in computation of 2D flow past NACA63A421 airfoil. Computation is performed using the commercial code ANSYS Fluent 6.3.26, in which the transition method is implemented as a User-Defined-Function. Computed distributions of Cp along the airfoil are verified by comparison with experimental data, which were obtained by measurements in a closed circuit wind tunnel at the constant Reynolds number and several angles of attack. Comparisons prove applicability of the implemented transitional model.
Numerical calculation for flow field of servo-tube guided hydraulic control rod driving system
He Keyu; Han Weishi
2010-01-01
A new-style hydraulic control rod driving mechanism was put forward by using servo-tube control elements for the design of control rod driving mechanism. The results of numerical simulation by CFD program Fluent for flow field of hydraulic driving cylinder indicate that the bigger the outer diameter of servo-tube, the smaller the resistance coefficient of variable throttle orifice. The zero position gap of variable throttle orifice could be determined on 0.2 mm in the design. The pressure difference between the upper and nether surfaces of piston was mainly created by the throttle function of fixed throttle orifice. It can be effectively controlled by changing the gap of variable throttle orifice. And the lift force of driving cylinder is able to meet the requirement on the design load. (authors)
Sumi, Tomonari; Okumoto, Atsushi; Goto, Hitoshi; Sekino, Hideo
2017-10-01
A two-step subdiffusion behavior of lateral movement of transmembrane proteins in plasma membranes has been observed by using single-molecule experiments. A nested double-compartment model where large compartments are divided into several smaller ones has been proposed in order to explain this observation. These compartments are considered to be delimited by membrane-skeleton "fences" and membrane-protein "pickets" bound to the fences. We perform numerical simulations of a master equation using a simple two-dimensional lattice model to investigate the heterogeneous diffusion dynamics behavior of transmembrane proteins within plasma membranes. We show that the experimentally observed two-step subdiffusion process can be described using fence and picket models combined with decreased local diffusivity of transmembrane proteins in the vicinity of the pickets. This allows us to explain the two-step subdiffusion behavior without explicitly introducing nested double compartments.
Kinetic calculations for miniature neutron source reactor using analytical and numerical techniques
Ampomah-Amoako, E.
2008-06-01
The analytical methods, step change in reactivity and ramp change in reactivity as well as numerical methods, fixed point iteration and Runge Kutta-gill were used to simulate the initial build up of neutrons in a miniature neutron source reactor with and without temperature feedback effect. The methods were modified to include photo neutron concentration. PARET 7.3 was used to simulate the transients behaviour of Ghana Research Reactor-1. The PARET code was capable of simulating the transients for 2.1 mk and 4 mk insertions of reactivity with peak powers of 49.87 kW and 92.34 kW, respectively. PARET code however failed to simulate 6.71 mk of reactivity which was predicted by Akaho et al through TEMPFED. (au)
Numerical tables of anomalous scattering factors calculated by the Cromer and Liberman's method
Sasaki, Satoshi.
1989-02-01
Anomalous scattering factors f' and f'' have been calculated for the atoms Li through Bi, plus U, using the relativistic treatment described by Cromer and Liberman. The final f' value does not include the Jensen's correction term on the magnetic scattering. The tables are presented with the f' and f'' values (i) at 0.01 A intervals in the wavelength range from 0.1 to 2.89 A and (ii) at 0.0001 A intervals in the neighborhood of the K, L 1 , L 2 , and L 3 absorption edges. (author)
Ion cyclotron emission calculations using a 2D full wave numerical code
Batchelor, D.B.; Jaeger, E.F.; Colestock, P.L.
1987-01-01
Measurement of radiation in the HF band due to cyclotron emission by energetic ions produced by fusion reactions or neutral beam injection promises to be a useful diagnostic on large devices which are entering the reactor regime of operation. A number of complications make the modelling and interpretation of such measurements difficult using conventional geometrical optics methods. In particular the long wavelength and lack of high directivity of antennas in this frequency regime make observation of a single path across the plasma into a viewing dump impractical. Pickup antennas effectively see the whole plasma and wall reflection effects are important. We have modified our 2D full wave ICRH code 2 to calculate wave fields due to a distribution of energetic ions in tokamak geometry. The radiation is modeled as due to an ensemble of localized source currents distributed in space. The spatial structure of the coherent wave field is then calculated including cyclotron harmonic damping as compared to the usual procedure of incoherently summing powers of individual radiators. This method has the advantage that phase information from localized radiating currents is globally retained so the directivity of the pickup antennas is correctly represented. Also standing waves and wall reflections are automatically included
A numerical method to calculate flow-induced vibrations in a turbulent flow
Sadaoka, Noriyuki; Umegaki, Kikuo
1993-01-01
An unsteady fluid force on structures in a turbulent flow can cause their vibration. The phenomenon is the most important among various flow-induced vibrations and it is an important subject in design nuclear plant components such as heat exchangers. A new approach to simulate flow-induced vibrations is introduced. A fully coupled analysis of fluid-structure interaction has been realized in a turbulent flow field by integrating the following calculational steps: (a) solving turbulent flow by a direct simulation method where the ALE (arbitrary Lagrangian Eulerian) type approximation is adopted to take account of structure displacements; (b) estimating fluid force on structures by integrating fluid pressure and shear stress; (c) calculating dynamic response of structures and determining the amount of displacement; (d) regenerate curvilinear grids for new geometry using the boundary-fitted coordinate transformation method. Forced vibration of a circular cylinder in a cross flow were successfully simulated and the synchronization phenomena between Karman-vortices and cylinder vibrations were clearly seen
Zhou, Dan; Niu, Jiqiang
2017-01-01
Trains with different numbers of cars running in the open air were simulated using the delayed detached-eddy simulation (DDES). The numbers of cars included in the simulation are 3, 4, 5 and 8. The aim of this study was to investigate how train length influences the boundary layer, the wake flow, the surface pressure, the aerodynamic drag and the friction drag. To certify the accuracy of the mesh and methods, the drag coefficients from numerical simulation of trains with 3 cars were compared with those from the wind tunnel test, and agreement was obtained. The results show that the boundary layer is thicker and the wake vortices are less symmetric as the train length increases. As a result, train length greatly affects pressure. The upper surface pressure of the tail car reduced by 2.9%, the side surface pressure of the tail car reduced by 8.3% and the underneath surface pressure of the tail car reduced by 19.7% in trains that included 3 cars to those including 8 cars. In addition, train length also has a significant effect on the friction drag coefficient and the drag coefficient. The friction drag coefficient of each car in a configuration decreases along the length of the train. In a comparison between trains consisting of 3 cars to those consisting of 8 cars, the friction drag coefficient of the tail car reduced by 8.6% and the drag coefficient of the tail car reduced by 3.7%. PMID:29261758
Numerical calculations of heat engineering parameters of a solar greenhouse dryer
Akhatov, Zh.S.; Khalimov, A.S.
2015-01-01
The results of numerical simulation to determine the optimum volume of a thermal storage water heater in a solar greenhouse dryer are presented. A CAD (computer-aided design) model is created for the given installation by simulating the heat transfer processes with the aid of the Solid Works Flow Simulation software. The given CAD model consists of a concrete foundation and a steel frame in which translucent coatings made from two-layer polycarbonate sheets 6 mm in thickness with an air gap between the two layers are attached. The north wall is made of bricks with size and thickness of 2 x 4 m"2 and 0.4 m, respectively. The front surface has an angle of inclination 39.53 degree with respect to the horizontal surface for the maximum incidence of solar radiation to its surface. All the geometrical dimensions of the solar greenhouse dryer were selected on the basis of the allocated platform for the solar drying installation 3 x 4 m"2 in size. It is shown that the optimum volume of the heat storage tank for the present installation is 500 L. (authors)
Numerical Calculation of Transient Thermal Characteristics in Gas-Insulated Transmission Lines
Hongtao Li
2013-11-01
Full Text Available For further knowledge of the thermal characteristics in gas-insulated transmission lines (GILs installed above ground, a finite-element model coupling fluid field and thermal field is established, in which the corresponding assumptions and boundary conditions are given. Â Transient temperature rise processes of the GIL under the conditions of variable ambient temperature, wind velocity and solar radiation are respectively investigated. Equivalent surface convective heat transfer coefficient and heat flux boundary conditions are updated in the analysis process. Unlike the traditional finite element methods (FEM, the variability of the thermal properties with temperature is considered. The calculation results are validated by the tests results reported in the literature. The conclusion provides method and theory basis for the knowledge of transient temperature rise characteristics of GILs in open environment.
Lindbom, B.; Boghammar, A.
1992-04-01
The present report describes the modelling efforts of the groundwater flow situation at the Finnsjoen site in northern Uppland, approximately 140 km north of Stockholm. The study forms part of the SKB 91 performance assessment project, and aims at describing the model sensitivity to changes in the prevailing regional gradient, as well as the local, with regard to both direction and magnitude. Particular emphasis has been put into the evaluation of travel times and travel paths form a potential repository, and also on flux values at repository level. The analyses were based on the finite element technique and made use of the NAMMU-code for stationary calculations in three dimensions. The fracture zones within the modelled area were modelled implicitly with an averaging technique. (au)
Hathout, A.M.; Hassan, F.; Elsady, Z.
2009-01-01
One of the familiar pollutants is the black cloud. The black cloud is a term written to describe the arrival of an enormous cloud of gas that enters the solar system and threatens to destroy most of the life on earth by blocking the sun radiation, [7]. Close to the burning area, black clouds appear indicating strong absorption. While, further down wind they may look white, indicating weaker or no absorption. In previous study, it can be pointed out that the electromagnetic waves are an effective factor in the existence of the black cloud, [2]. The detection of the cloud was described using mathematical equations. In this paper, the effect of the ionosphere on the concentration of pollutants is investigated. Also, the behavior of the environmental pollutants in the occurrence of electric and magnetic fields is calculated and discussed.
Numerical calculation of high frequency fast wave current drive in a reactor grade tokamak
Ushigusa, Kenkichi; Hamamatsu, Kiyotaka
1988-02-01
A fast wave current drive with a high frequency is estimated for a reactor grade tokamak by the ray tracing and the quasi-linear Fokker-Planck calculations with an assumption of single path absorption. The fast wave can drive RF current with the drive efficiency of η CD = n-bar e (10 19 m -3 )I RC (A)R(m)/P RF (W) ∼ 3.0 when the wave frequency is selected to be f/f ci > 7. A sharp wave spectrum and a ph|| >/υ Te ∼ 3.0 are required to obtain a good efficiency. A center peaked RF current profile can be formed with an appropriate wave spectrum even in the high temperature plasma. (author)
Mierau, Anna; Weiland, Thomas [Technische Universitaet Darmstadt (DE). Institut fuer Theorie Elektromagnetischer Felder (TEMF); Schnizer, Pierre; Fischer, Egbert [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Akishin, Pavel [JINR, Dubna (Russian Federation)
2010-07-01
The heavy ion synchrotron SIS100, the core component of the Facility of Antiproton and Ion Research will accelerate high current ion beams of up to U{sup 27+}. For operating such a machine the static and transient magnetic field quality must be fully understood. This is also necessary to keep the beam losses well below acceptable limits and to prepare a sound strategy for high resolution magnetic measurements and data analysis. Challenging preconditions to perform such work are to find a proper description for the non. Cartesian symmetry of the magnets, most important for curved dipoles with elliptical apertures. We describe the parameterisation methods using elliptic and toroidal multipoles and summarise comparing the calculated to the measured field quality.
V. I. Milykh
2016-12-01
Full Text Available Purpose. The work is dedicated to the presentation of the principle of construction and implementation of an automated synthesis system of the turbo-generator (TG electromagnetic system in the case of its modernization. This is done on the example of changing the number of the stator core slots. Methodology. The basis of the synthesis is a TG basic construction. Its structure includes the mathematical and physical-geometrical models, as well as the calculation model for the FEMM software environment, providing the numerical calculations of the magnetic fields and electromagnetic parameters of TG. The mathematical model links the changing and basic dimensions and parameters of the electromagnetic system, provided that the TG power parameters are ensured. The physical-geometrical model is the geometric mapping of the electromagnetic system with the specified physical properties of its elements. This model converts the TG electromagnetic system in a calculation model for the FEMM program. Results. Testing of the created synthesis system is carried out on the example of the 340 MW TG. The geometric, electromagnetic and power parameters of its basic construction and its new variants at the different numbers of the stator slots are compared. The harmonic analysis of the temporal function of the stator winding EMF is also made for the variants being compared. Originality. The mathematical model, relating the new and base parameters of TG at the changing of the number of the stator slots is created. A Lua script, providing the numerical-field calculations of the TG electromagnetic parameters in the FEMM software environment is worked out. Construction of the constructive and calculation models, the numerical-field calculations and delivery of results are performed by a computer automatically, that ensures high efficiency of the TG design process. Practical value. The considered version of the TG modernization on the example of changing the number of the
Johnson, M. T.
2010-02-01
The transfer velocity determines the rate of exchange of a gas across the air-water interface for a given deviation from Henry's law equilibrium between the two phases. In the thin film model of gas exchange, which is commonly used for calculating gas exchange rates from measured concentrations of trace gases in the atmosphere and ocean/freshwaters, the overall transfer is controlled by diffusion-mediated films on either side of the air-water interface. Calculating the total transfer velocity (i.e. including the influence from both molecular layers) requires the Henry's law constant and the Schmidt number of the gas in question, the latter being the ratio of the viscosity of the medium and the molecular diffusivity of the gas in the medium. All of these properties are both temperature and (on the water side) salinity dependent and extensive calculation is required to estimate these properties where not otherwise available. The aim of this work is to standardize the application of the thin film approach to flux calculation from measured and modelled data, to improve comparability, and to provide a numerical framework into which future parameter improvements can be integrated. A detailed numerical scheme is presented for the calculation of the gas and liquid phase transfer velocities (ka and kw respectively) and the total transfer velocity, K. The scheme requires only basic physical chemistry data for any gas of interest and calculates K over the full range of temperatures, salinities and wind-speeds observed in and over the ocean. Improved relationships for the wind-speed dependence of ka and for the salinity-dependence of the gas solubility (Henry's law) are derived. Comparison with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general but significant improvements under certain conditions. The scheme is provided as a downloadable program in the supplementary material, along with input files containing molecular
Numerically Exact Calculation of Rovibrational Levels of Cl^-H_2O
Wang, Xiao-Gang; Carrington, Tucker
2014-06-01
Large amplitude vibrations of Van der Waals clusters are important because they reveal large regions of a potential energy surface (PES). To calculate spectra of Van der Waals clusters it is common to use an adiabatic approximation. When coupling between intra- and inter-molecular coordinates is important non-adiabatic coupling cannot be neglected and it is therefore critical to develop and test theoretical methods that couple both types of coordinates. We have developed new product basis and contracted basis Lanczos methods for Van der Waals complexes and tested them by computing rovibrational energy levels of Cl^-H_2O. The new product basis is made of functions of the inter-monomer distance, Wigner functions that depend on Euler angles specifying the orientation of H_2O with respect to a frame attached to the inter-monomer Jacobi vector, basis functions for H_2O vibration, and Wigner functions that depend on Euler angles specifying the orientation of the inter-monomer Jacobi vector with respect to a space-fixed frame. An advantage of this product basis is that it can be used to make an efficient contracted basis by replacing the vibrational basis functions for the monomer with monomer vibrational wavefunctions. Due to weak coupling between intra- and inter-molecular coordinates, only a few tens of monomer vibrational wavefunctions are necessary. The validity of the two new methods is established by comparing energy levels with benchmark rovibrational levels obtained with polyspherical coordinates and spherical harmonic type basis functions. For all bases, product structure is exploited to calculate eigenvalues with the Lanczos algorithm. For Cl^-H_2O, we are able, for the first time, to compute accurate splittings due to tunnelling between the two equivalent C_s minima. We use the PES of Rheinecker and Bowman (RB). Our results are in good agreement with experiment for the five fundamental bands observed. J. Rheinecker and J. M. Bowman, J. Chem. Phys. 124 131102
MULTILOOP PI CONTROLLER FOR ACHIEVING SIMULTANEOUS TIME AND FREQUENCY DOMAIN SPECIFICATIONS
M. SENTHILKUMAR
2015-08-01
Full Text Available Most of the controllers in control system are designed to satisfy either time domain or frequency domain specifications. This work presents the computation of a multiloop PI controller for achieving time and frequency domain specifications simultaneously. The desired time and frequency domain measures are to be specified initially to the design. To obtain the desired value of the performance measures the graphical relationship between the PI controller and the performance criteria is given. Thus by using graphical method a set of PI controller parameters to meet the desired performance measures are obtained in an effective and simpler way. The coupled tank has become a classic design of control engineering for multivariable process. The proposed control strategy has been implemented in the same coupled tank process and validated through simulation studies.
Multiloop soliton and multibreather solutions of the short pulse model equation
Matsuno, Yoshimasa
2007-01-01
We develop a systematic procedure for constructing the multisoliton solutions of the short pulse (SP) model equation which describes the propagation of ultra-short pulses in nonlinear medica. We first introduce a novel hodograph transformation to convert the SP equation into the sine-Gordon (sG) equation. With the soliton solutions of the sG equation, the system of linear partial differential equations governing the inverse mapping can be integrated analytically to obtain the soliton solutions of the SP equation in the form of the parametric representation. By specifying the soliton parameters, we obtain the multiloop and multibreather solutions. We investigate the asymptotic behavior of both solutions and confirm their solitonic feature. The nonsingular breather solutions may play an important role in studying the propagation of ultra-short pulses in an optical fibre. (author)
Numerical Calculation of Effect of Elastic Deformation on Aerodynamic Characteristics of a Rocket
Laith K. Abbas
2014-01-01
Full Text Available The application and workflow of Computational Fluid Dynamics (CFD/Computational Structure Dynamics (CSD on solving the static aeroelastic problem of a slender rocket are introduced. To predict static aeroelastic behavior accurately, two-way coupling and inertia relief methods are used to calculate the static deformations and aerodynamic characteristics of the deformed rocket. The aerodynamic coefficients of rigid rocket are computed firstly and compared with the experimental data, which verified the accuracy of CFD output. The results of the analysis for elastic rocket in the nonspinning and spinning states are compared with the rigid ones. The results highlight that the rocket deformation aspects are decided by the normal force distribution along the rocket length. Rocket deformation becomes larger with increasing the flight angle of attack. Drag and lift force coefficients decrease and pitching moment coefficients increase due to rocket deformations, center of pressure location forwards, and stability of the rockets decreases. Accordingly, the flight trajectory may be affected by the change of these aerodynamic coefficients and stability.
Akhtulov, A. L.
2018-01-01
The questions of construction and practical application of the automation system for the design of components and aggregates for the construction of transport vehicles are considered, taking into account their dynamic characteristics. Based on the results of the studies, a unified method for determining the reactions of bonds of a complex spatial structure is proposed. The technique, based on the method of substructures, allows us to determine the values of the transfer functions taking into account the reactions of the bonds. After the carried out researches it is necessary to note, that such approach gives the most satisfactory results and can be used for calculations of complex mechanical systems of machines and units of different purposes. The directions of increasing the degree of validity of technical decisions are shown, especially in the early stages of design, when the cost of errors is high, with careful thorough working out of all the elements of the design, which is really feasible only on the basis of automation of design and technological work.
Correa, M. A.; Bohn, F.
2018-05-01
We perform a theoretical and experimental investigation of the magnetic properties and magnetization dynamics of a ferromagnetic magnetostrictive multilayer grown onto a flexible substrate and submitted to external stress. We calculate the magnetic behavior and magnetoimpedance effect for a trilayered system from an approach that considers a magnetic permeability model for planar geometry and a magnetic free energy density which takes into account induced uniaxial and magnetoelastic anisotropy contributions. We verify remarkable modifications of the magnetic anisotropy with external stress, as well as we show that the dynamic magnetic response is strongly affected by these changes. We discuss the magnetic features that lead to modifications of the frequency limits where distinct mechanisms are responsible by the magnetoimpedance variations, enabling us to manipulate the resonance fields. To test the robustness of the approach, we directly compare theoretical results with experimental data. Thus, we provide experimental evidence to confirm the validity of the theoretical approach, as well as to manipulate the resonance fields to tune the MI response according to real applications in devices.
Alireza Khoshfetrat
2018-05-01
Full Text Available Under transient flow condition, the behavior of water conveyance system varies according to their characteristics. In the present study, the pressure was measured using a fast and sensitive pressure gauge in Bukan and Piranshahr water conveyance system. The pressure simulation was conducted using Bentley Hammer software. The friction head loss was calculated by different methods. The results showed that Unsteady Vitkovsky method had minimum error comparing with other methods. Wave velocity increase had direct effect on maximum pressures while velocity decrease affected minimum pressures. In a shorter water conveyance system, the reduction of wave velocity had direct effect on maximum pressure. Destruction to the long conveyance system was more probable and maximum and minimum pressures occurred during the first period. Shorter conveyance system had more pressure fluctuations and the minimum pressure did not occur in the first period. Coincidence of periods happened at the beginning and continued untill the end of data recording in the longer conveyance system. However, as time passed by, such coincidence did not occure in shorter conveyance system.
Ergün, A Sanlı
2011-10-01
Focused ultrasound therapy relies on acoustic power absorption by tissue. The stronger the absorption the higher the temperature increase is. However, strong acoustic absorption also means faster attenuation and limited penetration depth. Hence, there is a trade-off between heat generation efficacy and penetration depth. In this paper, we formulated the acoustic power absorption as a function of frequency and attenuation coefficient, and defined two figures of merit to measure the power absorption: spatial peak of the acoustic power absorption density, and the acoustic power absorbed within the focal area. Then, we derived "rule of thumb" expressions for the optimum frequencies that maximized these figures of merit given the target depth and homogeneous tissue type. We also formulated a method to calculate the optimum frequency for inhomogeneous tissue given the tissue composition for situations where the tissue structure can be assumed to be made of parallel layers of homogeneous tissue. We checked the validity of the rules using linear acoustic field simulations. For a one-dimensional array of 4cm acoustic aperture, and for a two-dimensional array of 4×4cm(2) acoustic aperture, we found that the power absorbed within the focal area is maximized at 0.86MHz, and 0.79MHz, respectively, when the target depth is 4cm in muscle tissue. The rules on the other hand predicted the optimum frequencies for acoustic power absorption as 0.9MHz and 0.86MHz, respectively for the 1D and 2D array case, which are within 6% and 9% of the field simulation results. Because radiation force generated by an acoustic wave in a lossy propagation medium is approximately proportional to the acoustic power absorption, these rules can be used to maximize acoustic radiation force generated in tissue as well. Copyright © 2011 Elsevier B.V. All rights reserved.
Sebelin, E.
1997-01-01
Full-wave calculations based on trial functions are carried out for solving the lower hybrid current drive problem in tokamaks. A variational method is developed and provides an efficient system to describe in a global manner both the propagation and the absorption of the electromagnetic waves in plasmas. The calculation is fully carried out in the case of circular and concentric flux surfaces. The existence and uniqueness of the solution of the wave propagation equation is mathematically proved. The first realistic simulations are performed for the high aspect ratio tokamak TRIAM-1M. It is checked that the main features of the lower-hybrid wave dynamics are well described numerically. (A.C.)
An approach to 3D magnetic field calculation using numerical and differential algebra methods
Caspi, S.; Helm, M.; Laslett, L.J.; Brady, V.O.
1992-01-01
Motivated by the need for new means for specification and determination of 3D fields that are produced by electromagnetic lens elements in the region interior to coil windings and seeking to obtain techniques that will be convenient for accurate conductor placement and dynamical study of particle motion, we have conveniently gene the representation of a 2D magnetic field to 3D. We have shown that the 3 dimensioal magnetic field components of a multipole magnet in the curl-fire divergence-fire region near the axis r=0 can be derived from one dimensional functions A n (z) and their derivatives (part 1). In the region interior to coil windings of accelerator magnets the three spatial components of magnet fields can be expressed in terms of ''harmonic components'' proportional to functions sin (nθ) or cos (nθ) of the azimuthal angle. The r,z dependence of any such component can then be expressed in terms of powers of r times functions A n (z) and their derivatives. For twodimensional configurations B z of course is identically zero, the derivatives of A n (z) vanish, and the harmonic components of the transverse field then acquire a simple proportionality B r,n ∝ r n-1 sin (nθ),B θ,n ∝ r n-1 cos (nθ), whereas in a 3-D configuration the more complex nature of the field gives rise to additional so-called ''psuedomultipole'' components as judged by additional powers of r required in the development of the field. Computation of the 3-D magnetic field arising at a sequence of field points, as a direct result of a specified current configuration or coil geometry, can be calculated explicitly through use of the Biot-Savart law and from such data the coefficients can then be derived for a general development of the type indicated above. We indicate, discuss, and illustrate two means by which this development may be performed
Ruslan, Siti Zaharah Mohd; Jaffar, Maheran Mohd
2017-05-01
Islamic banking in Malaysia offers variety of products based on Islamic principles. One of the concepts is a diminishing musyarakah. The concept of diminishing musyarakah helps Muslims to avoid transaction which are based on riba. The diminishing musyarakah can be defined as an agreement between capital provider and entrepreneurs that enable entrepreneurs to buy equity in instalments where profits and losses are shared based on agreed ratio. The objective of this paper is to determine the internal rate of return (IRR) for a diminishing musyarakah model by applying a numerical method. There are several numerical methods in calculating the IRR such as by using an interpolation method and a trial and error method by using Microsoft Office Excel. In this paper we use a bisection method and secant method as an alternative way in calculating the IRR. It was found that the diminishing musyarakah model can be adapted in managing the performance of joint venture investments. Therefore, this paper will encourage more companies to use the concept of joint venture in managing their investments performance.
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs
M. T. Johnson
2010-10-01
Full Text Available The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest. Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone, such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases, but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.
Johnson, M. T.
2010-10-01
The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest). Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone), such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases), but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility) are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.
Liang, Peipeng; Jia, Xiuqin; Taatgen, Niels A; Borst, Jelmer P; Li, Kuncheng
2016-05-19
Numerical inductive reasoning refers to the process of identifying and extrapolating the rule involved in numeric materials. It is associated with calculation, and shares the common activation of the fronto-parietal regions with calculation, which suggests that numerical inductive reasoning may correspond to a general calculation process. However, compared with calculation, rule identification is critical and unique to reasoning. Previous studies have established the central role of the fronto-parietal network for relational integration during rule identification in numerical inductive reasoning. The current question of interest is whether numerical inductive reasoning exclusively corresponds to calculation or operates beyond calculation, and whether it is possible to distinguish between them based on the activity pattern in the fronto-parietal network. To directly address this issue, three types of problems were created: numerical inductive reasoning, calculation, and perceptual judgment. Our results showed that the fronto-parietal network was more active in numerical inductive reasoning which requires more exchanges between intermediate representations and long-term declarative knowledge during rule identification. These results survived even after controlling for the covariates of response time and error rate. A computational cognitive model was developed using the cognitive architecture ACT-R to account for the behavioral results and brain activity in the fronto-parietal network.
Caffo, Michele; Czyż, Henryk; Gunia, Michał; Remiddi, Ettore
2009-03-01
We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations. Program summaryProgram title: BOKASUN Catalogue identifier: AECG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9404 No. of bytes in distributed program, including test data, etc.: 104 123 Distribution format: tar.gz Programming language: FORTRAN77 Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUX Operating system: LINUX RAM: 120 kbytes Classification: 4.4 Nature of problem: Any integral arising in the evaluation of the two-loop sunrise Feynman diagram can be expressed in terms of a given set of Master Integrals, which should be calculated numerically. The program provides a fast and precise evaluation method of the Master Integrals for arbitrary (but not vanishing) masses and arbitrary value of the external momentum. Solution method: The integrals depend on three internal masses and the external momentum squared p. The method is a combination of an accelerated expansion in 1/p in its (pretty large!) region of fast convergence and of a Runge-Kutta numerical solution of a system of linear differential equations. Running time: To obtain 4 Master Integrals on PC with 2 GHz processor it takes 3 μs for series expansion with pre-calculated coefficients, 80 μs for series expansion without pre-calculated coefficients, from a few seconds up to a few minutes for Runge-Kutta method (depending
Bosevski, T.; Strugar, P.
1966-10-01
In determining the criticality parameters of a two-zone reactor with flat central zone one encounters a numerical problem requiring the solution of a system of two non-linear equations. To solve them the Newton method, which proved convenient, was used n this work. By comparing our results with those reported one obtains about 5% smaller values of both the radius of the flat zone and of the radial buckling of the outer zone. This discrepancy probably results from some approximations used in solving the same system of equations used in solving the same system of equations where the procedure form was applied, whereas the calculation time is by one order of magnitude smaller
Saghinadze, Ivane; Pkhakadze, Manana
2016-04-01
(The article was published with support of the Sh. Rustaveli National Science Foundation) The serious environmental problems started in Poti after transfer of the main flow of the river Rioni to the north. As a result the flooding of the city stopped, but the reduction of water consumption in the city channel, caused a decrease of the sediments carried away by the river, what leads to coastal erosion. The coast changes are connected with the movement of the waves and currents in the coastal part of the sea. In the paper, the three-dimensional mathematical model of sediment transport and coastal zone lithodynamics is developed. The finite element formulations for the problems of wave modes, coastal currents, sediment transport and evolution of the coastal zone of the sea, are given. The numerical algorithms, implemented in the form of software. Programs are allowing to bring the solutions of the tasks to numerical results. The numerical modeling was developed in three stages. In the first stage the topography of the coast and the initial geometry of the structures are considered as an input parameters. Then, coastal wave field is calculated for the conditions prescribed in the initial wave. In the second stage, the calculated wave field is used to estimate the spatial distribution of the radiation stresses near-bottom orbital velocity. In the third stage the coastal wave fields and flow fields are used in the sub-models of sediment transport and changes in the topography of the coast. In the numerical solution of basic equations of motion of the waves, coastal currents and changes in sea bottom topography we use: finite element, finite difference methods and the method of upper relaxation, Crank-Nicolson scheme. As an example, we are giving the results of research of the wave regime in the coastal area of the city of Poti (700X600m) adjacent to the port of Poti. The bottom profile, in this area is rather complicated. During the calculations of the average rise of
Yu Mingrui; Han Weishi; Wang Ge
2014-01-01
Servo-piston hydraulic control rod driving mechanism is a new type built-in driving mechanism which is suitable for integrated reactor and it can be moved continuously. The numerical calculation and analysis of the internal three-dimensional flow field inside the driving mechanism were carried out by the computational fluid dynamics software FLUENT. The result shows that the unique pressure mutation area of flow field inside the driving mechanism is at the place of the servo variable throttle orifice. The differential pressure of the piston can be effectively controlled by changing the gap of variable throttle orifice. When the gap changes within 0.5 mm, the differential pressure can be greatly changed, and then the driving mechanism motion state would be changed too. When the working pressure is 0.1 MPa, the hoisting capacity of the driving mechanism can meet the design requirements, and the flow rate is small. (authors)
Numerical Calculation of the Peaking Factor of a Water-Cooled W/Cu Monoblock for a Divertor
Han, Le; Chang, Haiping; Zhang, Jingyang; Xu, Tiejun
2015-09-01
In order to accurately predict the incident critical heat flux (ICHF, the heat flux at the heated surface when CHF occurs) of a water-cooled W/Cu monoblock for a divertor, the exact knowledge of its peaking factors (fp) under one-sided heating conditions with different design parameters is a key issue. In this paper, the heat conduction in the solid domain of a water-cooled W/Cu monoblock is calculated numerically by assuming the local heat transfer coefficients (HTC) of the cooling wall to be functions of the local wall temperature, so as to obtain fp. The reliability of the calculation method is validated by an experimental example result, with the maximum error of 2.1% only. The effects of geometric and flow parameters on the fp of a water-cooled W/Cu monoblock are investigated. Within the scope of this study, it is shown that the fp increases with increasing dimensionless W/Cu monoblock width and armour thickness (the shortest distance between the heated surface and Cu layer), and the maximum increases are 43.8% and 22.4% respectively. The dimensionless W/Cu monoblock height and Cu thickness have little effect on fp. The increase of Reynolds number and Jakob number causes the increase of fp, and the maximum increases are 6.8% and 9.6% respectively. Based on the calculated results, an empirical correlation on peaking factor is obtained via regression. These results provide a valuable reference for the thermal-hydraulic design of water-cooled divertors. supported by National Magnetic Confinement Fusion Science Program of China (No. 2010GB104005) and Funding of Jiangsu Innovation Program for Graduate Education, China (CXLX12_0170), the Fundamental Research Funds for the Central Universities of China
Kondo, Koichi; Yoshida, Kenji; Okawa, Tomio; Kataoka, Isao
2004-01-01
Experiment and numerical calculation were carried out for upward, turbulent bubbly two-phase flow in a vertical pipe with an axisymmetric sudden expansion, which is one of the typical multi-dimensional channel geometries. The void fraction, the liquid velocity and turbulent intensity along the flow direction below and the above the sudden expansion point were measured for various turbulent flow conditions by using a point-electrode resistivity probe and a hot-film anemometry probe. They showed quite complicated behaviors depending upon flow rates of gas and liquid phases and bubble size. In particular, the geometry of sudden expansion affected on the bubble behaviors in multi-dimensional two-phase flow, such as the bubble-stagnation, the bubble-deformation, the enhancement and suppression effects due to the two-phase turbulence etc. Through the measurements, fundamental parameters of the two-phase flow were clarified for the sudden expansion channel. Moreover, a three-dimensional one-way bubble tracking simulation of a single bubble behavior in turbulent flow field along the downstream of the sudden expansion was also demonstrated where equation of motion of bubble was solved by assuming appropriate constitutive models and turbulence model. Based on the trajectories of large number of bubbles, the void fraction distribution was predicted in this calculation. It concretely revealed that the lift force and the two-phase turbulence model were the most important parameters in determining the multi-dimensional void fraction distribution and the calculation should be considered by using the measured experimental data. (author)
Numerical Calculation of the Peaking Factor of a Water-Cooled W/Cu Monoblock for a Divertor
Han Le; Chang Haiping; Zhang Jingyang; Xu Tiejun
2015-01-01
In order to accurately predict the incident critical heat flux (ICHF, the heat flux at the heated surface when CHF occurs) of a water-cooled W/Cu monoblock for a divertor, the exact knowledge of its peaking factors (f p ) under one-sided heating conditions with different design parameters is a key issue. In this paper, the heat conduction in the solid domain of a water-cooled W/Cu monoblock is calculated numerically by assuming the local heat transfer coefficients (HTC) of the cooling wall to be functions of the local wall temperature, so as to obtain f p . The reliability of the calculation method is validated by an experimental example result, with the maximum error of 2.1% only. The effects of geometric and flow parameters on the f p of a water-cooled W/Cu monoblock are investigated. Within the scope of this study, it is shown that the f p increases with increasing dimensionless W/Cu monoblock width and armour thickness (the shortest distance between the heated surface and Cu layer), and the maximum increases are 43.8% and 22.4% respectively. The dimensionless W/Cu monoblock height and Cu thickness have little effect on f p . The increase of Reynolds number and Jakob number causes the increase of f p , and the maximum increases are 6.8% and 9.6% respectively. Based on the calculated results, an empirical correlation on peaking factor is obtained via regression. These results provide a valuable reference for the thermal-hydraulic design of water-cooled divertors. (paper)
Multi-loop PWR modeling and hardware-in-the-loop testing using ACSL
Thomas, V.M.; Heibel, M.D.; Catullo, W.J.
1989-01-01
Westinghouse has developed an Advanced Digital Feedwater Control System (ADFCS) which is aimed at reducing feedwater related reactor trips through improved control performance for pressurized water reactor (PWR) power plants. To support control system setpoint studies and functional design efforts for the ADFCS, an ACSL based model of the nuclear steam supply system (NSSS) of a Westinghouse (PWR) was generated. Use of this plant model has been extended from system design to system testing through integration of the model into a Hardware-in-Loop test environment for the ADFCS. This integration includes appropriate interfacing between a Gould SEL 32/87 computer, upon which the plant model executes in real time, and the Westinghouse Distributed Processing family (WDPF) test hardware. A development program has been undertaken to expand the existing ACSL model to include capability to explicitly model multiple plant loops, steam generators, and corresponding feedwater systems. Furthermore, the program expands the ADFCS Hardware-in-Loop testing to include the multi-loop plant model. This paper provides an overview of the testing approach utilized for the ADFCS with focus on the role of Hardware-in-Loop testing. Background on the plant model, methodology and test environment is also provided. Finally, an overview is presented of the program to expand the model and associated Hardware-in-Loop test environment to handle multiple loops
Pluzhnikov Vladimir
2017-01-01
Full Text Available The author’s research is dedicated to the enhancement of the level of the enterprise economic safety. This task involves developing the concept of an integrated system for early prevention of dangers and threats of business activity, substantiation of procedures for regulating the activities of the enterprise in accordance with the changing external and internal factors. Multiloop diagnostics model is proposed to identify causal relations of management dysfunction. It allows you to receive an adequate assessment of the basic parameters of activity of the enterprise and accurately identify its status. Researching problems of economic safety of the enterprise such diagnostic methods as economic and logical analysis, statistical monitoring and strategic management were applied. There was made a conclusion that a qualitative assessment is a key tool of the level assessment of the enterprise economic safety, its control, and monitoring. It allows you to get reliable information about the real possibilities of the enterprise at different stages of development, to monitor and evaluate the level of economic security, find effective solutions to transition to a higher level of economic safety of the enterprise.
Multiloop integral system test (MIST): Final report, Inter-group comparisons
Gloudemans, J.R.
1989-07-01
The multiloop integral system test (MIST) was part of a multiphase program started in 1983 to address small-break loss-of-coolant accidents (SBLOCAs) specific to Babcock and Wilcox-designed plants. MIST was sponsored by the US Nuclear Regulatory Commission, the Babcock and Wilcox Owners Group, the Electric Power Research Institute, and Babcock and Wilcox. The unique features of the Babcock and Wilcox design, specifically the hot leg U-bends and steam generators, prevented the use of existing integral system data or existing integral system facilities to address the thermal-hydraulic SBLOCA questions. MIST and two other supporting facilities were specifically designed and constructed for this program, and an existing facility -- the once-through integral system (OTIS) -- was also used. Data from MIST and the other facilities will be used to benchmark the adequacy of system codes, such as RELAP5 and TRAC, for predicting abnormal plant transients. The individual tests are described in detail in Volumes 2 through 8 and Volume 11, and are summarized in Volume 1. Inter-group comparisons are addressed in this document, Volume 9. These comparisons are grouped as follows: mapping versus SBLOCA transients, SBLOCA, pump effects, and the effects of noncondensible gases. Appendix A provides an index and description of the microfiched plots for each test, which are enclosed with the corresponding Volumes 2 through 8. 147 figs., 5 tabs.
Low-noise sub-harmonic injection locked multiloop ring oscillator
Weilin, Xu; Di, Wu; Xueming, Wei; Baolin, Wei; Jihai, Duan; Fadi, Gui
2016-09-01
A three-stage differential voltage-controlled ring oscillator is presented for wide-tuning and low-phase noise requirement of clock and data recovery circuit in ultra wideband (UWB) wireless body area network. To improve the performance of phase noise of delay cell with coarse and fine frequency tuning, injection locked technology together with pseudo differential architecture are adopted. In addition, a multiloop is employed for frequency boosting. Two RVCOs, the standard RVCO without the IL block and the proposed IL RVCO, were fabricated in SMIC 0.18 μm 1P6M Salicide CMOS process. The proposed IL RVCO exhibits a measured phase noise of -112.37 dBc/Hz at 1 MHz offset from the center frequency of 1 GHz, while dissipating a current of 8 mA excluding the buffer from a 1.8-V supply voltage. It shows a 16.07 dB phase noise improvement at 1 MHz offset compared to the standard topology. Project supported by the National Natural Science Foundation of China (No. 61264001), the Guangxi Natural Science Foundation (Nos. 2013GXNSFAA019333, 2015GXNSFAA139301, 2014GXNSFAA118386), the Graduate Education Innovation Program of GUET (No. GDYCSZ201457), the Project of Guangxi Education Department (No. LD14066B) and the High-Level-Innovation Team and Outstanding Scholar Project of Guangxi Higher Education Institutes.
Yang, Tzuhsiung; Berry, John F
2018-06-04
The computation of nuclear second derivatives of energy, or the nuclear Hessian, is an essential routine in quantum chemical investigations of ground and transition states, thermodynamic calculations, and molecular vibrations. Analytic nuclear Hessian computations require the resolution of costly coupled-perturbed self-consistent field (CP-SCF) equations, while numerical differentiation of analytic first derivatives has an unfavorable 6 N ( N = number of atoms) prefactor. Herein, we present a new method in which grid computing is used to accelerate and/or enable the evaluation of the nuclear Hessian via numerical differentiation: NUMFREQ@Grid. Nuclear Hessians were successfully evaluated by NUMFREQ@Grid at the DFT level as well as using RIJCOSX-ZORA-MP2 or RIJCOSX-ZORA-B2PLYP for a set of linear polyacenes with systematically increasing size. For the larger members of this group, NUMFREQ@Grid was found to outperform the wall clock time of analytic Hessian evaluation; at the MP2 or B2LYP levels, these Hessians cannot even be evaluated analytically. We also evaluated a 156-atom catalytically relevant open-shell transition metal complex and found that NUMFREQ@Grid is faster (7.7 times shorter wall clock time) and less demanding (4.4 times less memory requirement) than an analytic Hessian. Capitalizing on the capabilities of parallel grid computing, NUMFREQ@Grid can outperform analytic methods in terms of wall time, memory requirements, and treatable system size. The NUMFREQ@Grid method presented herein demonstrates how grid computing can be used to facilitate embarrassingly parallel computational procedures and is a pioneer for future implementations.
Kolahdooz, M.; Abotalebi, A.; Sheikh Aleslam, F.
2011-01-01
The goal of this article is calculation of the electric field at the end of loaded path in solid-state track detectors. For the calculation, Laplace-Equation has been solved numerically. By solving the equation, upon considering a specific potential at the boundary of the region, in addition to calculating the electric field at the end of path, the parameters which are affecting the electric field have also been investigated.
Jian Cheng
2016-03-01
Full Text Available Rapid growth and ultra-precision machining of large-size KDP (KH2PO4 crystals with high laser damage resistance are tough challenges in the development of large laser systems. It is of high interest and practical significance to have theoretical models for scientists and manufacturers to determine the laser-induced damage threshold (LIDT of actually prepared KDP optics. Here, we numerically and experimentally investigate the laser-induced damage on KDP crystals in ultra-short pulse laser regime. On basis of the rate equation for free electron generation, a model dedicated to predicting the LIDT is developed by considering the synergistic effect of photoionization, impact ionization and decay of electrons. Laser damage tests are performed to measure the single-pulse LIDT with several testing protocols. The testing results combined with previously reported experimental data agree well with those calculated by the model. By taking the light intensification into consideration, the model is successfully applied to quantitatively evaluate the effect of surface flaws inevitably introduced in the preparation processes on the laser damage resistance of KDP crystals. This work can not only contribute to further understanding of the laser damage mechanisms of optical materials, but also provide available models for evaluating the laser damage resistance of exquisitely prepared optical components used in high power laser systems.
Bernstein, W.; Hildebrand, V.; Ullrich, B.; Szilagyi, J.
2000-07-01
Power plant reliability depends to a large extent on steam generator operation. Investigations were therefore carried out for early detection of combustion chamber soiling at different operating conditions. Apart from CFD numerical simulations of the gaseous phase and particle tracks, both in the original and coupled with thermochemical calculations, emphasis was given to validations with measured values in the original plant, in combustion chamber models, and in experimental facilities. Three different fuels with different composition and behaviour were investigated, i.e. oil shales, mixed coal, and coal pretreated with sorption agents. Apart from the influence of the temperature and reaction conditions (oxygen concentration) in the vicinity of the particle, also different times of residue were investigated. [German] Die Betriebssicherheit von Kraftanlagen wird massgeblich von der Arbeitsweise der Dampferzeuger bestimmt. Ziel dieses Forschungskomplexes ist es, fruehzeitig Aussagen zum Ansatzverhalten im Feuerraum bei verschiedenen Betriebsbedingungen zu treffen. Neben der numerischen Simulation der Gasphase und der Partikelbahnen mit CFD-Codes im Original und der Kopplung mit thermochemischen Berechnungen stehen vor allem Validierungen mit Messwerten am Original, an Feuerraummodellen und Versuchsanlagen im Vordergrund der Arbeiten. Die hier vorgestellten Untersuchungen erfolgten an drei unterschiedlichen Brennstoffen, die sich sowohl in der Zusammensetzung als auch im Einsatz stark voneinander unterscheiden. Dies sind: Oelschiefer, Mischkohle und vorbehandelte Kohle mit Sorbent. Dabei werden neben den Einfluessen der Temperatur und der Reaktionsbedingung (Sauerstoffgehalt) in der Umgebung des Partikels auch verschiedene Verweilzeiten untersucht. (orig./AKF)
Chien-Chun Kuo
2009-09-01
Full Text Available This case report describes the treatment of a 17-year-old girl with an anterior open- bite and Class III malocclusion, who had a history of thumb-sucking habit in childhood. The multiloop edgewise archwire technique was used on the mandibular arch to facilitate uprighting of the mandibular posterior teeth, change the cant of occlusal plane, close the anterior open-bite, and correct the Class III malocclusion. At the end of treatment, Class I occlusion and correction of the anterior open-bite had been achieved. An examination 8 years 8 months after treatment revealed long-term stability of the treatment results.
Liu, Yuanrong; Chen, Weimin; Zhong, Jing
2017-01-01
The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard...... sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were...... obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples....
Multi-loop control of UPS inverter with a plug-in odd-harmonic repetitive controller.
Razi, Reza; Karbasforooshan, Mohammad-Sadegh; Monfared, Mohammad
2017-03-01
This paper proposes an improved multi-loop control scheme for the single-phase uninterruptible power supply (UPS) inverter by using a plug-in odd-harmonic repetitive controller to regulate the output voltage. In the suggested control method, the output voltage and the filter capacitor current are used as the outer and inner loop feedback signals, respectively and the instantaneous value of the reference voltage feedforwarded to the output of the controller. Instead of conventional linear (proportional-integral/-resonant) and conventional repetitive controllers, a plug-in odd-harmonic repetitive controller is employed in the outer loop to regulate the output voltage, which occupies less memory space and offers faster tracking performance compared to the conventional one. Also, a simple proportional controller is used in the inner loop for active damping of possible resonances and improving the transient performance. The feedforward of the converter reference voltage enhances the robust performance of the system and simplifies the system modelling and the controller design. A step-by-step design procedure is presented for the proposed controller, which guarantees stability of the system under worst-case scenarios. Simulation and experimental results validate the excellent steady-state and transient performance of the proposed control scheme and provide the exact comparison of the proposed method with the conventional multi-loop control method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Sogukpinar, Haci; Bozkurt, Ismail
2018-02-01
Aerodynamic performance of the airfoil plays the most important role to obtain economically maximum efficiency from a wind turbine. Therefore airfoil should have an ideal aerodynamic shape. In this study, aerodynamic simulation of S809 airfoil is conducted and obtained result compared with previously made NASA experimental result and NREL theoretical data. At first, Lift coefficient, lift to drag ratio and pressure coefficient around S809 airfoil are calculated with SST turbulence model, and are compared with experimental and other theoretical data to correlate simulation correctness of the computational approaches. And result indicates good correlation with both experimental and theoretical data. This calculation point out that as the increasing relative velocity, lift to drag ratio increases. Lift to drag ratio attain maximum at the angle around 6 degree and after that starts to decrease again. Comparison shows that CFD code used in this calculation can predict aerodynamic properties of airfoil.
Medema, W.J.; Wals, A.E.J.; Adamowski, J.
2014-01-01
Managing social-ecological systems and human well being in a sustainable way requires knowledge of these systems in their full complexity. Multi-loop social learning is recognized as a crucial element to sustainable decision-making for land and water resources management involving a process of
Nogueira, A.C.R.
1981-10-01
The numerical calculation of the main variables of the laminar, incompressible, axissimmetric, steady flow around a circunferential square obstacle placed at the wall of a circular pipe, is done. The velocity profiles, the separating length and the shape of the separating streamline are compared with experimental available data and a good agreement is achieved. (E.G.) [pt
Zhang, Y. C.; Zhang, J. Z. H.; Kouri, D. J.; Haug, K.; Schwenke, D. W.
1988-01-01
Numerically exact, fully three-dimensional quantum mechanicl reactive scattering calculations are reported for the H2Br system. Both the exchange (H + H-prime Br to H-prime + HBr) and abstraction (H + HBR to H2 + Br) reaction channels are included in the calculations. The present results are the first completely converged three-dimensional quantum calculations for a system involving a highly exoergic reaction channel (the abstraction process). It is found that the production of vibrationally hot H2 in the abstraction reaction, and hence the extent of population inversion in the products, is a sensitive function of initial HBr rotational state and collision energy.
Numerical calculation of the tensor of diffusion in the nuclear reactor cells by Monte-Carlo method
Gorodkov, S.S.; Kalugin, M.A.
2009-01-01
New algorithm based on the sequential application of the RMS path method has been proposed for the diffusion constants calculation. The offered algorithm conforms to the diffusion constants calculation in arbitrary segments of nuclear reactors without detail description of geometry, dependence of cross-sections from energy or neutron scattering anisotropy by kernel medium. The proposed algorithm is used for the diffusion constants calculation in uranium-graphite reactor sells
Salveter, G.
2000-07-01
In this thesis, the results of experimental research work on global bearing behaviour with respect to the existing theoretical basis are systematically analysed for the evaluation and interpretation of measuring results. Among other things, the geometry of the pipeline route, the compactness of the backfilling material and the temperature dependence are considered. The mutual influence of friction and bedding resistances in the region of bends could not yet be determined for a local analysis by existing numerical models. This requires the determination of the induced stress distribution on the pipe perimeter due to lateral displacement of the pipe. The influence is therefore described by a numerical consideration of relative displacements between the pipe and the surrounding soil. Ultimately, relative displacements are verified on the basis of our own complementary results from experimental research carried out in a laboratory for soil mechanics with specially designed test equipment. The global analysis of bearing loads and displacements is done with a numerical model, in which the plastic jacked pipe is idealized as a beam, and the effect of the soil is idealized by spring elements with non-linear force displacement characteristics. An existing numerical model is extended with regard to the new findings and while taking vertical displacements into account. It is used for numerical simulations of selected tests on the global bearing behaviour of underground district heating pipelines which were carried out as part of the research cooperation project. Apart from a good correspondence between calculated results and test results this also provides a plausible description of interrelations. At the same time, however, it also makes itclear that further research is necessary. This thesis provides a contribution to the validation of recent methods for the calculated modelling of the interaction between a district heating pipeline and the subsoil on the basis of
Price, Gavin R; Wilkey, Eric D; Yeo, Darren J
2017-05-01
A growing body of research suggests that the processing of nonsymbolic (e.g. sets of dots) and symbolic (e.g. Arabic digits) numerical magnitudes serves as a foundation for the development of math competence. Performance on magnitude comparison tasks is thought to reflect the precision of a shared cognitive representation, as evidence by the presence of a numerical ratio effect for both formats. However, little is known regarding how visuo-perceptual processes are related to the numerical ratio effect, whether they are shared across numerical formats, and whether they relate to math competence independently of performance outcomes. The present study investigates these questions in a sample of typically developing adults. Our results reveal a pattern of associations between eye-movement measures, but not their ratio effects, across formats. This suggests that ratio-specific visuo-perceptual processing during magnitude processing is different across nonsymbolic and symbolic formats. Furthermore, eye movements are related to math performance only during symbolic comparison, supporting a growing body of literature suggesting symbolic number processing is more strongly related to math outcomes than nonsymbolic magnitude processing. Finally, eye-movement patterns, specifically fixation dwell time, continue to be negatively related to math performance after controlling for task performance (i.e. error rate and reaction time) and domain general cognitive abilities (IQ), suggesting that fluent visual processing of Arabic digits plays a unique and important role in linking symbolic number processing to formal math abilities. Copyright © 2017 Elsevier B.V. All rights reserved.
Caffo, Michele; Czyz, Henryk; Gunia, Michal; Remiddi, Ettore
2008-01-01
We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations.
Lepechinsky, D; Parlange, F [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1964-07-01
Dispersion curves including the effect of collisions have been calculated with a 7090 IBM computer for several types of laboratory hydrogen plasmas; Te = Ti = 1 eV; Te = 1 eV, Ti = 0,1 eV; Te = 10 eV, Ti = 2 eV; Te = 50 eV, Ti 10 eV, with neutral gas pressures of 10{sup -1}, 10{sup -3} and 10{sup -4} mmHg and electron densities of 10{sup 10}, 10{sup 13} and eventually 10{sup 15} el/cc. The corresponding collision frequencies with neutrals and between electrons and ions have been derived using appropriate relationships The dispersion equations used correspond to the macroscopic treatment. The real and imaginary parts of the wave number K are presented as a function of real values of the frequency {omega}, for electrostatic and electromagnetic waves and for e.m. waves propagating parallel to a permanent magnetic field of 500 gauss and 12.5 Kgauss. (authors) [French] Des courbes de dispersion tenant compte de l'effet des collisions ont ete calculees a l'aide d'un ordinateur IBM 7090 pour differents types de plasmas d'hydrogene se presentant au laboratoire; les temperatures electroniques et ioniques envisagees ont ete les suivantes: Te = Ti = 1 Ev; Te = 1 eV, Ti 0,1 eV; Te = 10 eV, Ti = 2 eV; Te = 50 eV, Ti = 10 eV; les pressions de neutres - de 10{sup -1}, 10{sup -3} et 10{sup -4} mmHg; les densites electroniques - de 10{sup 10}, 10{sup 13} et eventuellement de 10{sup 15} el/cc. Les frequences de collision avec les neutres et entre electrons et ions ont ete evaluees en fonction de ces donnees. Les equations, de dispersion utilisees correspondant au traitement macroscopique. On presente les valeurs des parties reelle et imaginaire du nombre d'ondes K en fonction de valeurs reelles de la frequence {omega} pour les ondes electrostatiques et electromagnetiques et pour les ondes e.m. se propageant parallelement a un champ magnetique permanent de 500 gauss et de 12,5 kgauss. (auteurs)
Nakamura, Kazuo; Hiraki, Naoji; Toi, Kazuo; Itoh, Satoshi
1984-10-01
The energy spectra of charge-exchanged neutrals are observed in the TRIAM-1 tokamak by vertical scanning of the neutral energy analyzer. The ''apparent'' ion temperature obtained directly from the energy spectrum observed in the peripheral region is much higher than that predicted by neoclassical transport theory. The ''actual'' ion temperature profile is derived numerically from the energy spectra observed at various positions taking into account the wall-reflection effect of neutrals and the impermeability of the plasma. As a result, the ''actual'' ion temperature profile is found to agree well with that predicted by neoclassical transport theory.
Nakamura, Kazuo; Hiraki, Naoji; Toi, Kazuo; Itoh, Satoshi
1984-01-01
The energy spectra of charge-exchanged neutrals are observed in the TRIAM-1 tokamak by vertical scanning of the neutral energy analyzer. The ''apparent'' ion temperature obtained directly from the energy spectrum observed in the peripheral region is much higher than that predicted by neoclassical transport theory. The ''actual'' ion temperature profile is derived numerically from the energy spectra observed at various positions taking into account the wall-reflection effect of neutrals and the impermeability of the plasma. As a result, the ''actual'' ion temperature profile is found to agree well with that predicted by neoclassical transport theory. (author)
Matthiä, Daniel; Berger, Thomas
2017-08-01
Galactic cosmic radiation and secondary particles produced in the interaction with the atmosphere lead to a complex radiation field on the Martian surface. A workshop ("1st Mars Space Radiation Modeling Workshop") organized by the MSL-RAD science team was held in June 2016 in Boulder with the goal to compare models capable to predict this radiation field with each other and measurements from the RAD instrument onboard the curiosity rover taken between November 15, 2015 and January 15, 2016. In this work the results of PLANETOCOSMICS/GEANT4 contributed to the workshop are presented. Calculated secondary particle spectra on the Martian surface are investigated and the radiation field's directionality of the different particles in dependence on the energy is discussed. Omnidirectional particle fluxes are used in combination with fluence to dose conversion factors to calculate absorbed dose rates and dose equivalent rates in a slab of tissue. Copyright © 2017. Published by Elsevier Ltd.
Rosales, Carlos; Lim, Kian Meng
2005-06-01
This paper presents detailed numerical calculations of the dielectrophoretic force in traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that a small number of multipolar terms need to be considered in order to obtain accurate results for spheres, even in the proximity of the electrodes, and that the full MST calculation is only required in the study of non-spherical particles.
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs
Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland
2014-01-01
with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and the main domain only, thus avoiding the need to solve a backward wave propagation problem inside the CFS-UPML, which is known to be highly......In recent years, the application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint elastic wave propagation problems. An important challenge is to design...... convolution formulation of the complex-frequency-shifted unsplit-field perfectly matched layer (CFS-UPML) derived in previous work more flexible by providing a new treatment to analytically remove singular parameters in the formulation. We also extend this new formulation to 3-D. Furthermore, we derive...
A. V. Pavlov
Full Text Available This study compares the OV1-10 satellite measurements of the integral airglow intensities at 630 nm in the SAR arc regions observed in the northern and southern hemisphere as a conjugate phenomenon, with the model results obtained using the time-dependent one-dimensional mathematical model of the Earth ionosphere and plasmasphere (the IZMIRAN model during the geomagnetic storm of the period 15–17 February 1967. The major enhancements to the IZMIRAN model developed in this study are the inclusion of He^{+} ions (three major ions: O^{+}, H^{+}, and He^{+}, and three ion temperatures, the updated photochemistry and energy balance equations for ions and electrons, the diffusion of NO^{+} and O_{2}^{+} ions and O(^{1}D and the revised electron cooling rates arising from their collisions with unexcited N_{2}, O_{2} molecules and N_{2} molecules at the first vibrational level. The updated model includes the option to use the models of the Boltzmann or non-Boltzmann distributions of vibrationally excited molecular nitrogen. Deviations from the Boltzmann distribution for the first five vibrational levels of N_{2} were calculated. The calculated distribution is highly non-Boltzmann at vibrational levels v > 2 and leads to a decrease in the calculated electron density and integral intensity at 630 nm in the northern and southern hemispheres in comparison with the electron density and integral intensity calculated using the Boltzmann vibrational distribution of N_{2}. It is found that the intensity at 630 nm is very sensitive to the oxygen number densities. Good agreement between the modelled and measured intensities is obtained provided that at all altitudes of the southern hemisphere a reduction of about factor 1.35 in MSIS-86 atomic oxygen densities is included in the IZMIRAN model with the non-Boltzmann vibrational distribution of N_{2}
Matsuura, Koji
2014-06-01
Recent studies suggest that the microenvironment and embryo density used during embryo culture considerably affect development to the blastocyst stage. High embryo density allows for autocrine secretions to diffuse to neighbouring embryos during group culture, with a positive effect on further development. A variation of group culture is the well-of-the-well (WOW) culture system, allowing for individual identification of embryos cultured in small holes in a microdroplet. Bovine blastocyst development is higher in the WOW culture system than in conventional group culture. To compare the concentration of chemical factors between conventional and WOW culture, a model was constructed to calculate the concentration of secreted factors based on Fick's second law of diffusion using spreadsheet software. Furthermore, model was used to determine the concentration of growth factors and waste materials adjacent to the embryo periphery. The results of these calculations suggest that the highest difference in the concentration of secreted small molecules and macromolecules was at the most two- to threefold, with the concentrations reduced more and diffusion kinetics facilitated to a greater extent in the WOW culture system. The average ratio of the concentration of secreted macromolecules (10nm diameter) around the embryos was also compared between systems with well widths of 0.1 and 0.3mm. The concentration of secreted materials surrounding embryos increased in a narrow tapered well. The findings suggest that the WOW culture system is better than conventional group culture because of the increased final concentration of autocrine factors and higher diffusion kinetics of waste materials.
V. V. Lobzin
Full Text Available This study compares the Isis II satellite measurements of the electron density and temperature, the integral airglow intensity and volume emission rate at 630 nm in the SAR arc region, observed at dusk on 4 August, 1972, in the Southern Hemisphere, during the main phase of the geomagnetic storm. The model results were obtained using the time dependent one-dimensional mathematical model of the Earth's ionosphere and plasmasphere (the IZMIRAN model. The major enhancement to the IZMIRAN model developed in this study to explain the two component 630 nm emission observed is the analytical yield spectrum approach to calculate the fluxes of precipitating electrons and the additional production rates of N^{+}_{2}, O^{+}_{2}, O^{+}(^{4}S, O^{+}(^{2}D, O^{–}(^{2}P, and O^{+}(^{2}P ions, and O(^{1}D in the SAR arc regions in the Northern and Southern Hemispheres. In order to bring the measured and modelled electron temperatures into agreement, the additional heating electron rate of 1.05 eV cm^{–3} s^{–1} was added in the energy balance equation of electrons at altitudes above 5000 km during the main phase of the geomagnetic storm. This additional heating electron rate determines the thermally excited 630 nm emission observed. The IZMIRAN model calculates a 630 nm integral intensity above 350 km of 4.1 kR and a total 630 nm integral intensity of 8.1 kR, values which are slightly lower compared to the observed 4.7 kR and 10.6 kR. We conclude that the 630 nm emission observed can be explained considering both the soft energy electron excited component and the thermally excited component. It is found that the inclusion of N_{2}(v > 0 and O_{2}(v > 0 in the calculations of the O^{+}(^{4}S loss rate improves the agreement between the calculated N
V. V. Lobzin
1999-11-01
Full Text Available This study compares the Isis II satellite measurements of the electron density and temperature, the integral airglow intensity and volume emission rate at 630 nm in the SAR arc region, observed at dusk on 4 August, 1972, in the Southern Hemisphere, during the main phase of the geomagnetic storm. The model results were obtained using the time dependent one-dimensional mathematical model of the Earth's ionosphere and plasmasphere (the IZMIRAN model. The major enhancement to the IZMIRAN model developed in this study to explain the two component 630 nm emission observed is the analytical yield spectrum approach to calculate the fluxes of precipitating electrons and the additional production rates of N+2, O+2, O+(4S, O+(2D, O–(2P, and O+(2P ions, and O(1D in the SAR arc regions in the Northern and Southern Hemispheres. In order to bring the measured and modelled electron temperatures into agreement, the additional heating electron rate of 1.05 eV cm–3 s–1 was added in the energy balance equation of electrons at altitudes above 5000 km during the main phase of the geomagnetic storm. This additional heating electron rate determines the thermally excited 630 nm emission observed. The IZMIRAN model calculates a 630 nm integral intensity above 350 km of 4.1 kR and a total 630 nm integral intensity of 8.1 kR, values which are slightly lower compared to the observed 4.7 kR and 10.6 kR. We conclude that the 630 nm emission observed can be explained considering both the soft energy electron excited component and the thermally excited component. It is found that the inclusion of N2(v > 0 and O2(v > 0 in the calculations of the O+(4S loss rate improves the agreement between the calculated Ne and the data on 4 August, 1972. The N2(v > 0 and O2(v > 0 effects are enough to explain the electron density depression in the SAR arc F-region and above F2 peak altitude. Our calculations show that the increase in the O++N2 rate factor due to the vibrationally
Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2010-10-15
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)
Chuan Wang
2013-01-01
Full Text Available In order to improve the efficiency of stainless steel stamping multistage pump, quadratic regression orthogonal test, hydraulic design, and computational fluid dynamics (CFD are used to analyze the effect of pump geometric parameters. Sixteen impellers are designed based on the quadratic regression orthogonal test, which have three factors including impeller outlet slope, impeller blade outlet stagger angle, and impeller blade outlet width. Through quadratic regression equation, the function relationship between efficiency values and three factors is established. The optimal combination of geometric parameters is found through the analysis of the regression equation. To further study the influence of blade thickness on the performance of multistage pump, numerical simulations of multistage pump with different blade thicknesses are carried out. The influence law of blade thickness on pump performance is built from the external characteristics and internal flow field. In conclusion, with the increase of blade thickness, the best efficiency point of the pump shifts to the small flow rate direction, and the vortex regions inside the pump at rated flow gradually increase, which is the main reason that pump efficiency decreases along with the increase of the blade thickness at rated flow.
Pavlovic, R.N.
1981-01-01
Nowadays, our rivers are polluted to an ever increasing degree by industrial and domestic discharges of waste heat and sewage. An important task of environmental protection is to predict the consequences of such pollutions in order to be able to plan and perform protective measures. For the solution of this problem a reliable mathematical model is very helpful. In the present paper a depth-averaged model is developed consisting of a two-dimensional elliptical model component for the direct near-field of a discharge and a two-dimensional parabolic separate model for the calculation of longer river distances further downstream. This model is exhaustively tested by application to a number of laboratory flows and real discharges to rivers. (orig./RW) [de
Han, Song; Zhang, Wei; Zhang, Jie
2017-09-01
A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.
Boughrara Kamel
2009-01-01
Full Text Available This paper deals with the analytical and numerical analysis of the flux density distribution in the slotted air gap of permanent magnet motors with surface mounted tangentially magnetized permanent magnets. Two methods for magnetostatic field calculations are developed. The first one is an analytical method in which the effect of stator slots is taken into account by modulating the magnetic field distribution by the complex relative air gap permeance. The second one is a numerical method using 2-D finite element analysis with consideration of Dirichlet and anti-periodicity (periodicity boundary conditions and Lagrange Multipliers for simulation of movement. The results obtained by the analytical method are compared to the results of finite-element analysis.
Dumortier, Laurent [Luleaa Univ. of Technology (Sweden)
2001-01-01
Validation of numerical predictions of the flow field in a powder fired industry boiler by flow visualisation in a water model has been studied. The bark powder fired boiler at AssiDomaen Kraftliner in Piteaa has been used as a case study. A literature study covering modelling of combusting flows by water models and different flow visualisation techniques has been carried out. The main conclusion as regards the use of water models is that only qualitative information can be expected. As far as turbulent flow is assured in the model as well as the real furnace, the same Reynolds number is not required. Geometrical similarity is important but modelling of burner jets requires adaptation of the jet diameters in the model. Guidelines for this are available and are presented in the report. The review of visualisation techniques shows that a number of methods have been used successfully for validation of flow field predictions. The conclusion is that the Particle Image Velocimetry and Particle Tracking Velocimetry methods could be very suitable for validation purposes provided that optical access is possible. The numerical predictions include flow fields in a 1130 scale model of the AssiDomaen furnace with water flow as well as flow and temperature fields in the actual furnace. Two burner arrangements were considered both for the model and the actual furnace, namely the present configuration with four front burners and a proposed modification where an additional burner is positioned at a side wall below the other burners. There are many similarities between the predicted flow fields in the model and the full scale furnace but there are also some differences, in particular in the region above the burners and the effects of the low region re-circulation on the lower burner jets. The experiments with the water model have only included the arrangement with four front burners. There were problems determining the velocities in the jets and the comparisons with predictions are
Maiz, F., E-mail: fethimaiz@gmail.com [University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413 (Saudi Arabia)
2015-04-15
A novel method to calculate the quantum transmission, resonance and eigenvalue energies forming the sub-bands structure of non-symmetrical, non-periodical semiconducting heterostructure potential has been proposed in this paper. The method can be applied on a multilayer system with varying thickness of the layer and effective mass of electrons and holes. Assuming an approximated effective mass and using Bastard's boundary conditions, Schrödinger equation at each media is solved and then using a confirmed recurrence method, the transmission and reflection coefficients and the energy quantification condition are expressed. They are simple combination of coupled equations. Schrödinger's equation solutions are Airy functions or plane waves, depending on the electrical potential energy slope. To illustrate the feasibility of the proposed method, the N barriers – (N−1) wells structure for N=3, 5, 8, 9, 17 and 35 are studied. All results show very good agreements with previously published results obtained from applying different methods on similar systems.
Alvarez Cardona, C.M.; Rodriguez Gual, M.; Hernandez Valle, S.
2001-01-01
The calculation of neutron fluxes and fluence into reactor pressure vessel is a regulatory requirement in the stages of the design, operation and plan lifetime extension. The reactor vessel is considered a unique and non-substitutable part of the NPP that undergoes degradation. The main source of the aging comes from the fast neutron damage induced in the steel crystalline lattice. Due to the proximity of the core edge to the vessel inner surface; the vessel steel is exposed to high fast neutron fluence. The effect of this irradiation on the mechanical properties becomes more acute because of the impurities measured in the Russian steel alloys. In the present paper, a PC version of the Monte Carlo 3-D HEXANN-EVALU system is used for the estimation of the WWER reactor pressure vessel irradiation. It was selected on the basis of its flexible options that on the other hand need to be quantified in connection with the desired magnitudes. The parameters that control the random walk of neutrons as well as the efficiency increasing options included in the code are studied in order to identify their impact in the final results for fluxes and fluence in the reactor pressure vessel. As a result an optimal set of parameters is suggested. (authors)
Johannesson, Björn; Hosokawa, Yoshifumi; Yamada, Kazuo
2009-01-01
A method to analyse and calculate concentration profiles of different types of ions in the pore solution of porous materials such as concrete subjected to external wetting and drying is described. The equations in use have a solid theoretical meaning and are derived from a porous media technique......, which is a special branch of the more general mixture theory. The effect of chemical action is ignored making the presented model suitable to be implemented into codes dealing solely with chemical equilibrium. The coupled set of equations for diffusion of ionic species, the internal electrical potential...... of the model should be judged from the assumptions made when developing the balance laws and the constitutive equations and the assumptions made in obtaining a working numerical calculation scheme....
Levy, Lionel L., Jr.; Yoshikawa, Kenneth K.
1959-01-01
A method based on linearized and slender-body theories, which is easily adapted to electronic-machine computing equipment, is developed for calculating the zero-lift wave drag of single- and multiple-component configurations from a knowledge of the second derivative of the area distribution of a series of equivalent bodies of revolution. The accuracy and computational time required of the method to calculate zero-lift wave drag is evaluated relative to another numerical method which employs the Tchebichef form of harmonic analysis of the area distribution of a series of equivalent bodies of revolution. The results of the evaluation indicate that the total zero-lift wave drag of a multiple-component configuration can generally be calculated most accurately as the sum of the zero-lift wave drag of each component alone plus the zero-lift interference wave drag between all pairs of components. The accuracy and computational time required of both methods to calculate total zero-lift wave drag at supersonic Mach numbers is comparable for airplane-type configurations. For systems of bodies of revolution both methods yield similar results with comparable accuracy; however, the present method only requires up to 60 percent of the computing time required of the harmonic-analysis method for two bodies of revolution and less time for a larger number of bodies.
Furumura, T [Hokkaido Univ. of Education, Sapporo (Japan); Koketsu, K [The University of Tokyo, Tokyo (Japan). Earthquake Research Institute
1996-10-01
Hyogo-ken Nanbu earthquake with a focus in the Akashi straits has given huge earthquake damages in and around Awaji Island and Kobe City in 1995. It is clear that the basement structure, which is steeply deepened at Kobe City from Rokko Mountains towards the coast, and the focus under this related closely to the local generation of strong ground motion. Generation process of the strong ground motion was discussed using 2D and 3D numerical simulation methods. The 3D pseudospectral method was used for the calculation. Space of 51.2km{times}25.6km{times}25.6km was selected for the calculation. This space was discretized with the lattice interval of 200m. Consequently, it was found that the basement structure with a steeply deepened basement, soft and weak geological structure thickly deposited on the basement, and earthquake faults running under the boundary of base rock and sediments related greatly to the generation of strong ground motion. Numerical simulation can be expected to predict the strong ground motion by shallow earthquakes. 9 refs., 7 figs.
Wang Jinhua; Huang Yifan; Wu Bin
2013-01-01
The spent fuel of 10 MW High Temperature Gas Cooled Reactor (HTR-10) could be stored in the shielded tank, and the tank is stored in the concrete shielded canister in spent fuel storage room, the residual heat of the spent fuel could be removed by the air. The ability of residual heat removal is analyzed in the paper, and the temperature field is numerically calculated through FEA program ANSYS, the analysis and the calculation are used to validate the safety of the spent fuel and the tank, the ultimate temperature of the spent fuel and the tank should below the safety limit. The calculation shows that the maximum temperature locates in the middle of the fuel pebble bed in the spent fuel tank, and the temperature decreases gradually with radial distance, the temperature in the tank body is evenly distributed, and the temperature in the concrete shielded canister decreases gradually with radial distance. It is feasible to remove the residual heat of the spent fuel storage tank by natural ventilation, in natural ventilation condition, the temperature of the spent fuel and the tank is lower than the temperature limit, which provides theoretical evidence for the choice of the residual heat removal method. (authors)
Morita, Y; Iwawaki, T; Fujisawa, T; Tani, T [Science University of Tokyo, Tokyo (Japan)
1997-11-25
In order to investigate characteristics of photovoltaic (PV)/thermal hybrid collectors (PV/T{sub s}) operating under varying conditions, energy equilibrium equations have been developed for numerical calculation, and the calculated results were compared with the observed ones. The calculated characteristics are close to the observed ones, both for photoelectric conversion and heat collecting characteristics, demonstrating validity of these energy equations. It is found, by comparing characteristics of PV/T{sub A} (covered with glass) with those of PV/T{sub B} (not covered with glass), that these characteristics are greatly affected by glass cover. Maximum overall excergy levels attained are 13.29% with PV/T{sub A} and 11.48% with PV/T{sub B} under the conditions of solar radiation intensity H: 800W/m{sup 2}, ambient temperature: 20degC and wind velocity: 0.5m/s, where flow rates of heat medium are 2.0times10{sup -3} and 4.0times10{sup -3}kg/s, respectively. Thus, the PV/T{sub A} system has a higher maximum excergy efficiency than the PV/T{sub B} system. The PV/T{sub A} gives water of higher temperature, demonstrating that covering the system with glass increases maximum excergy efficiency and optimum temperature. 6 refs., 5 figs., 2 tabs.
Rye, Henrik; Reed, Mark; Frost, Tone Karin; Smit, Mathijs G D; Durgut, Ismail; Johansen, Øistein; Ditlevsen, May Kristin
2008-04-01
Drilling discharges are complex mixtures of chemical components and particles which might lead to toxic and nontoxic stress in the environment. In order to be able to evaluate the potential environmental consequences of such discharges in the water column and in sediments, a numerical model was developed. The model includes water column stratification, ocean currents and turbulence, natural burial, bioturbation, and biodegradation of organic matter in the sediment. Accounting for these processes, the fate of the discharge is modeled for the water column, including near-field mixing and plume motion, far-field mixing, and transport. The fate of the discharge is also modeled for the sediment, including sea floor deposition, and mixing due to bioturbation. Formulas are provided for the calculation of suspended matter and chemical concentrations in the water column, and burial, change in grain size, oxygen depletion, and chemical concentrations in the sediment. The model is fully 3-dimensional and time dependent. It uses a Lagrangian approach for the water column based on moving particles that represent the properties of the release and an Eulerian approach for the sediment based on calculation of the properties of matter in a grid. The model will be used to calculate the environmental risk, both in the water column and in sediments, from drilling discharges. It can serve as a tool to define risk mitigating measures, and as such it provides guidance towards the "zero harm" goal.
F. Álvarez-Velarde
2012-01-01
Full Text Available A fast numerical method for the calculation in a zero-dimensional approach of the equilibrium isotopic composition of an iteratively used transmutation system in an advanced fuel cycle, based on the Banach fixed point theorem, is described in this paper. The method divides the fuel cycle in successive stages: fuel fabrication, storage, irradiation inside the transmutation system, cooling, reprocessing, and incorporation of the external material into the new fresh fuel. The change of the fuel isotopic composition, represented by an isotope vector, is described in a matrix formulation. The resulting matrix equations are solved using direct methods with arbitrary precision arithmetic. The method has been successfully applied to a double-strata fuel cycle with light water reactors and accelerator-driven subcritical systems. After comparison to the results of the EVOLCODE 2.0 burn-up code, the observed differences are about a few percents in the mass estimations of the main actinides.
Kubota, Tomohiro; Samukawa, Seiji; Watanabe, Naoki; Ohtsuka, Shingo; Iwasaki, Takuya; Ono, Kohei; Iriye, Yasuroh
2014-01-01
The charge transfer process between chlorine particles (ions or neutrals) and a graphite surface on collision was investigated by using a highly stable numerical simulator based on time-dependent density functional theory to understand the generation mechanism of a high-efficiency neutral beam developed by Samukawa et al (2001 Japan. J. Appl. Phys. 40 L779). A straightforward calculation was achieved by adopting a large enough unit cell. The dependence of the neutralization efficiency on the incident energy of the particle was investigated, and the trend of the experimental result was reproduced. It was also found that doping the electrons and holes into graphite could change the charge transfer process and neutralization probability. This result suggests that it is possible to develop a neutral beam source that has high neutralization efficiency for both positive and negative ions. (paper)
Yu, Jen-Shiang K; Hwang, Jenn-Kang; Tang, Chuan Yi; Yu, Chin-Hui
2004-01-01
A number of recently released numerical libraries including Automatically Tuned Linear Algebra Subroutines (ATLAS) library, Intel Math Kernel Library (MKL), GOTO numerical library, and AMD Core Math Library (ACML) for AMD Opteron processors, are linked against the executables of the Gaussian 98 electronic structure calculation package, which is compiled by updated versions of Fortran compilers such as Intel Fortran compiler (ifc/efc) 7.1 and PGI Fortran compiler (pgf77/pgf90) 5.0. The ifc 7.1 delivers about 3% of improvement on 32-bit machines compared to the former version 6.0. Performance improved from pgf77 3.3 to 5.0 is also around 3% when utilizing the original unmodified optimization options of the compiler enclosed in the software. Nevertheless, if extensive compiler tuning options are used, the speed can be further accelerated to about 25%. The performances of these fully optimized numerical libraries are similar. The double-precision floating-point (FP) instruction sets (SSE2) are also functional on AMD Opteron processors operated in 32-bit compilation, and Intel Fortran compiler has performed better optimization. Hardware-level tuning is able to improve memory bandwidth by adjusting the DRAM timing, and the efficiency in the CL2 mode is further accelerated by 2.6% compared to that of the CL2.5 mode. The FP throughput is measured by simultaneous execution of two identical copies of each of the test jobs. Resultant performance impact suggests that IA64 and AMD64 architectures are able to fulfill significantly higher throughput than the IA32, which is consistent with the SpecFPrate2000 benchmarks.
Yoriyaz, Hélio; Moralles, Maurício; Siqueira, Paulo de Tarso Dalledone; Guimarães, Carla da Costa; Cintra, Felipe Belonsi; dos Santos, Adimir
2009-11-01
Radiopharmaceutical applications in nuclear medicine require a detailed dosimetry estimate of the radiation energy delivered to the human tissues. Over the past years, several publications addressed the problem of internal dose estimate in volumes of several sizes considering photon and electron sources. Most of them used Monte Carlo radiation transport codes. Despite the widespread use of these codes due to the variety of resources and potentials they offered to carry out dose calculations, several aspects like physical models, cross sections, and numerical approximations used in the simulations still remain an object of study. Accurate dose estimate depends on the correct selection of a set of simulation options that should be carefully chosen. This article presents an analysis of several simulation options provided by two of the most used codes worldwide: MCNP and GEANT4. For this purpose, comparisons of absorbed fraction estimates obtained with different physical models, cross sections, and numerical approximations are presented for spheres of several sizes and composed as five different biological tissues. Considerable discrepancies have been found in some cases not only between the different codes but also between different cross sections and algorithms in the same code. Maximum differences found between the two codes are 5.0% and 10%, respectively, for photons and electrons. Even for simple problems as spheres and uniform radiation sources, the set of parameters chosen by any Monte Carlo code significantly affects the final results of a simulation, demonstrating the importance of the correct choice of parameters in the simulation.
M. Małysza
2011-07-01
Full Text Available Owing to high plastic deformability while maintaining stress values constant and relatively low, ordered cellular structures arecharacterised by excellent properties and the ability to dissipate the impact energy. Due to the low weight, structures of this type can beused, among others, for different parts of motor vehicles. For tests, a trapezoidal ordered cellular structure of 50.8 x 50.8 x 25.4 (mmoverall dimensions was selected. It was made as an investment casting from AlSi9Mg eutectic alloy by the method of Rapid Prototyping(RP. During FEM computations using an Abaqus programme, it was assumed that the material is isotropic and exhibits the features of anelastic – plastic body, introducing to calculations the, listed in a table, values of the stress-strain curve obtained in tensile tests performedon a MTS testing machine (10T. The computations used Johnson - Cook model, which is usually sufficiently accurate when modelling thephenomena of penetration of an element by an object of high initial velocity. The performed numerical calculations allowed identification
Analysis of the two-fluid model and the drift-flux model for numerical calculation of two-phase flow
Munkejord, Svend Tollak
2006-05-11
This thesis analyses models for two-phase flows and methods for the numerical resolution of these models. It is therefore one contribution to the development of reliable design tools for multiphase applications. Such tools are needed and expected by engineers in a range of fields, including in the oil and gas industry. The approximate Riemann solver of Roe has been studied. Roe schemes for three different two-phase flow models have been implemented in the framework of a standard numerical algorithm for the solution of hyperbolic conservation laws. The schemes have been analysed by calculation of benchmark tests from the literature, and by comparison with each other. A Roe scheme for the four-equation one-pressure two-fluid model has been implemented, and a second-order extension based on wave decomposition and flux-difference splitting was shown to work well and to give improved results compared to the first-order scheme. The convergence properties of the scheme were tested on smooth and discontinuous solutions. A Roe scheme has been proposed for a five-equation two-pressure two-fluid model with pressure relaxation. The use of analogous numerical methods for the five-equation and four-equation models allowed for a direct comparison of a method with and without pressure relaxation. Numerical experiments demonstrated that the two approaches converged to the same results, but that the five-equation pressure-relaxation method was significantly more dissipative, particularly for contact discontinuities. Furthermore, even though the five-equation model with instantaneous pressure relaxation has real eigenvalues, the calculations showed that it produced oscillations for cases where the four-equation model had complex eigenvalues. A Roe scheme has been constructed for the drift-flux model with general closure laws. For the case of the Zuber-Findlay slip law describing bubbly flows, the Roe matrix is completely analytical. Hence the present Roe scheme is more efficient than
Jin, X.
2001-04-01
A numerical calculation method basing on body fitted grids is developed in this work for computational fluid dynamics in complex geometry. The method solves the conservation equations in a general nonorthogonal coordinate system which matches the curvilinear boundary. The nonorthogonal, patched grid is generated by a grid generator which solves algebraic equations. By means of an interface its geometrical data can be used by this method. The conservation equations are transformed from the Cartesian system to a general curvilinear system keeping the physical Cartesian velocity components as dependent variables. Using a staggered arrangement of variables, the three Cartesian velocity components are defined on every cell surface. Thus the coupling between pressure and velocity is ensured, and numerical oscillations are avoided. The contravariant velocity for calculating mass flux on one cell surface is resulting from dependent Cartesian velocity components. After the discretisation and linear interpolation, a three dimensional 19-point pressure equation is found. Using the explicit treatment for cross-derivative terms, it reduces to the usual 7-point equation. Under the same data and process structure, this method is compatible with the code FLUTAN using Cartesian coordinates. In order to verify this method, several laminar flows are simulated in orthogonal grids at tilted space directions and in nonorthogonal grids with variations of cell angles. The simulated flow types are considered like various duct flows, transient heat conduction, natural convection in a chimney and natural convection in cavities. Their results achieve very good agreement with analytical solutions or empirical data. Convergence for highly nonorthogonal grids is obtained. After the successful validation of this method, it is applied for a reactor safety case. A transient natural convection flow for an optional sump cooling concept SUCO is simulated. The numerical result is comparable with the
Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes
Bern, Z.; Carrasco, J.J.M.; Dixon, L.J.; Johansson, H.; Roiban, R.
2012-02-15
We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N{sub c}{sup 2} single-trace divergence in N = 4 super-Yang-Mills theory.
Cheng, Jian [Center for Precision Engineering, School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001 (China); Department of Physics, The Ohio State University, 191 W. Woodruff Ave, Columbus, OH 43210 (United States); Chen, Mingjun, E-mail: chenmj@hit.edu.cn, E-mail: chowdhury.24@osu.edu; Wang, Jinghe; Xiao, Yong [Center for Precision Engineering, School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001 (China); Kafka, Kyle; Austin, Drake; Chowdhury, Enam, E-mail: chenmj@hit.edu.cn, E-mail: chowdhury.24@osu.edu [Department of Physics, The Ohio State University, 191 W. Woodruff Ave, Columbus, OH 43210 (United States)
2016-03-15
Rapid growth and ultra-precision machining of large-size KDP (KH{sub 2}PO{sub 4}) crystals with high laser damage resistance are tough challenges in the development of large laser systems. It is of high interest and practical significance to have theoretical models for scientists and manufacturers to determine the laser-induced damage threshold (LIDT) of actually prepared KDP optics. Here, we numerically and experimentally investigate the laser-induced damage on KDP crystals in ultra-short pulse laser regime. On basis of the rate equation for free electron generation, a model dedicated to predicting the LIDT is developed by considering the synergistic effect of photoionization, impact ionization and decay of electrons. Laser damage tests are performed to measure the single-pulse LIDT with several testing protocols. The testing results combined with previously reported experimental data agree well with those calculated by the model. By taking the light intensification into consideration, the model is successfully applied to quantitatively evaluate the effect of surface flaws inevitably introduced in the preparation processes on the laser damage resistance of KDP crystals. This work can not only contribute to further understanding of the laser damage mechanisms of optical materials, but also provide available models for evaluating the laser damage resistance of exquisitely prepared optical components used in high power laser systems.
Matrix model calculations beyond the spherical limit
Ambjoern, J.; Chekhov, L.; Kristjansen, C.F.; Makeenko, Yu.
1993-01-01
We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We develop a version which gives directly the result in the double scaling limit and present explicit results up to genus four. Using the latter version we prove that the hermitian and the complex matrix model are equivalent in the double scaling limit and that in this limit they are both equivalent to the Kontsevich model. We discuss how our results away from the double scaling limit are related to the structure of moduli space. (orig.)
Reynolds, J. M.; Lopez-Bruna, D.
2009-10-12
In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs.
Multi-loop positivity of the planar N=4 SYM six-point amplitude
Dixon, Lance J. [SLAC National Accelerator Laboratory,Stanford University, Stanford, CA 94309 (United States); Hippel, Matt von [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada); McLeod, Andrew J. [SLAC National Accelerator Laboratory,Stanford University, Stanford, CA 94309 (United States); Trnka, Jaroslav [Center for Quantum Mathematics and Physics (QMAP),Department of Physics, University of California, Davis, CA 95616 (United States)
2017-02-22
We study the six-point NMHV ratio function in planar N=4 SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a “radial” direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.
Ozer Sozdinler, C.; Arikawa, T.; Necmioglu, O.; Ozel, N. M.
2016-12-01
The Aegean and its surroundings form the most active part of the Africa-Eurasia collision zone responsible for the high level of seismicity in this region. It constitutes more than 60% of the expected seismicity in Europe up to Mw=8.2 (Moratto et al., 2007; Papazachos, 1990). Shaw and Jackson (2010) argued that the existing system of Hellenic Arc subduction-zone is capable of allowing very large but rare earthquakes on splay faults, such as the one occurred in 365, together with the contribution of small earthquakes. Based on an extensive earthquake generated tsunami scenario database, Necmioğlu and Özel (2015) showed that maximum wave heights in the Eastern Mediterranean for shallow earthquakes defined is >3 m in locations in, around and orthogonal to the Hellenic Arc. Considering the seismicity and the tsunami potential in Eastern Mediterranean, the investigation and monitoring of earthquake and tsunami hazard, and the preparation of mitigation strategies and national resilience plans would become inevitable in Turkey. Gocek town, as one of the Tsunami Forecast Points having a unique geography with many small bays and islands and a very popular touristic destination especially for yachtsmen, is selected in this study for the tsunami modeling by using high resolution bathymetric and topographic data with less than 4m grid size. The tsunami analyses are performed by the numerical codes NAMIDANCE (NAMIDANCE,2011) for 2D modeling and STOC-CADMAS (Arikawa,2014) for 3D modeling for the calculations of tsunami hydrodynamic parameters. Froude numbers, as one of the most important indicators for tsunami damage (Ozer, 2012) and the directions of current velocities inside marinas are solved by NAMIDANCE while STOC-CADMAS determines the tsunami pressure and force exerted onto the sea and land structures with 3D and non-hydrostatic approaches. The results are then used to determine the tsunami inundation and structural resilience and establish the tsunami preparedness and
Guangtao Zhang
2017-05-01
Full Text Available Inter-turn short circuit of field windings (ISCFW may cause the field current of a generator to increase, output reactive power to decrease, and unit vibration to intensify, seriously affecting its safe and stable operation. Full integration of mechanical and electrical characteristics can improve the sensitivity of online monitoring, and detect the early embryonic period fault of small turns. This paper studies the calculations and variations of unbalanced magnetic pull (UMP, of which the excitation source of rotor vibration is the basis and key to online fault monitoring. In grid load operation, ISCFW are first calculated with the multi-loop method, so as to obtain the numerical solutions of the stator and the rotor currents during the fault. Next, the air-gap magnetic field of the ISCFW is analyzed according to the actual composition modes of the motor loops in the fault, so as to obtain the analytic expressions of the air-gap magnetic motive force (MMF and magnetic density. The UMP of the rotor is obtained by solving the integral of the Maxwell stress. The correctness of the electric quantity calculation is verified by the ISCFW experiment, conducted in a one pair-pole non-salient pole model machine. On this basis, comparing the simulation analysis with the calculation results of the model in this paper not only verifies the accuracy of the electromagnetic force calculation, but also proves that the latter has the advantages of a short time consumption and high efficiency. Finally, the influencing factors and variation law of UMP are analyzed by means of an analytic model. This develops a base for the online monitoring of ISCFW with the integration of mechanical and electrical information.
Marañón-Vásquez, Guido Artemio; Soldevilla Galarza, Luciano Carlos; Tolentino Solis, Freddy Antonio; Wilson, Cliff; Romano, Fábio Lourenço
2017-09-01
Occasionally, orthodontists will be challenged to treat malocclusions and skeletal disharmonies, which by their complexity one might think that the only treatment alternative is the surgical-orthodontic approach. A male patient, aged 17 years old, was diagnosed with a skeletal Class III malocclusion, anterior open bite and negative overjet. An unpleasant profile was the patient's 'chief complaint' showing interest in facial aesthetics improvement. Nevertheless, the patient and his parents strongly preferred a non-surgical treatment approach. He was treated with a multiloop edgewise archwire to facilitate uprighting and distal en-masse movement of lower teeth, correct the Class III open bite malocclusion, change the inclination of the occlusal plane and obtain the consequent morphological-functional adaptation of the mandible. The Class III malocclusion was corrected and satisfactory changes in the patient's profile were obtained. Active treatment was completed in 2 years, and facial result remained stable at 2 years 6 months after debonding.
Shanming Wang
2015-01-01
Full Text Available Now electric machines integrate with power electronics to form inseparable systems in lots of applications for high performance. For such systems, two kinds of nonlinearities, the magnetic nonlinearity of iron core and the circuit nonlinearity caused by power electronics devices, coexist at the same time, which makes simulation time-consuming. In this paper, the multiloop model combined with FE model of AC-DC synchronous generators, as one example of electric machine with power electronics system, is set up. FE method is applied for magnetic nonlinearity and variable-step variable-topology simulation method is applied for circuit nonlinearity. In order to improve the simulation speed, the incomplete Cholesky conjugate gradient (ICCG method is used to solve the state equation. However, when power electronics device switches off, the convergence difficulty occurs. So a straightforward approach to achieve convergence of simulation is proposed. At last, the simulation results are compared with the experiments.
Masuyama, Y.; Fukasawa, T. [Kanazawa Institute of Technology, Ishikawa (Japan); Kitazaki, T. [DMW Corp., Tokyo (Japan)
1997-06-01
Sailing forces are measured with a 10.3m long full-scale sailing boat, equipped with a sail force dynamometer, CCD camera for sail shape measurement and an instrument for detecting sailing conditions of the hull, in order to obtain highly reliable performance data of a sailing yacht. The vortex lattice method is used for step-by-step numerical calculations, and the results are compared with the observed ones. The test results clearly show performance changing with slight changes in relative wind directions and sail shapes, which are not clearly obtained by the traditional wind tunnel tests. The calculated results, although deviating from the observed ones to some extent, well represent trends of performance changing with wind directions and sail shapes. In particular, changed performance caused by slight changes in draft at the main sail is clearly demonstrated. The numerical calculation is considered to be useful for searching for sail trim conditions. 17 refs., 18 figs., 1 tab.
Rye, H.; Reed, M.; Frost, T.K.; Smit, M.G.D.; Durgut, S.
2008-01-01
Drilling discharges are complex mixtures of chemical components and particles which might lead to toxic and nontoxic stress in the environment. In order to be able to evaluate the potential environmental consequences of such discharges in the water column and in sediments, a numerical model was
Martinez-Conesa, E. J.; Estrems-Amestoy, M.; Miguel-Eguia, V.; Garrido-Hernandez, A.; Guillen-Martinez, J. A.
2010-07-01
In this work, a numerical method for calculating the temperature field into the heat affected zone for butt welded joints is presented. The method has been developed for sheet welding and takes into account a bidimensional heat flow. It has built a computer program by MS-Excel books and Visual Basic for Applications (VBA). The model has been applied to the TIG process of AISI 304 stainless steel 2mm thickness sheet. The welding process has been considered without input materials. The numerical method may be used to help the designers to predict the temperature distribution in welded joints. (Author) 12 refs.
Shin, Chang Hwan; Seo, Kyong Won; Chun, Tae Hyun; Kim, Kang Seog
2005-03-01
Code coupling activities have so far focused on coupling the neutronics modules with the CFD module. An interface module for the CFD-ACE/DeCART coupling was established as an alternative to the original STAR-CD/DeCART interface. The interface module for DeCART/CFD-ACE was validated by single-pin model. The optimized CFD mesh was decided through the calculation of multi-pin model. It was important to consider turbulent mixing of subchannels for calculation of fuel temperature. For the parallel calculation, the optimized decompose process was necessary to reduce the calculation costs and setting of the iteration and convergence criterion for each code was important, too
Shin, Chang Hwan; Seo, Kyong Won; Chun, Tae Hyun; Kim, Kang Seog
2005-03-15
Code coupling activities have so far focused on coupling the neutronics modules with the CFD module. An interface module for the CFD-ACE/DeCART coupling was established as an alternative to the original STAR-CD/DeCART interface. The interface module for DeCART/CFD-ACE was validated by single-pin model. The optimized CFD mesh was decided through the calculation of multi-pin model. It was important to consider turbulent mixing of subchannels for calculation of fuel temperature. For the parallel calculation, the optimized decompose process was necessary to reduce the calculation costs and setting of the iteration and convergence criterion for each code was important, too.
Komarov, I. I.; Rostova, D. M.; Vegera, A. N.
2017-11-01
This paper presents the results of study on determination of degree and nature of influence of operating conditions of burner units and flare geometric parameters on the heat transfer in a combustion chamber of the fire-tube boilers. Change in values of the outlet gas temperature, the radiant and convective specific heat flow rate with appropriate modification of an expansion angle and a flare length was determined using Ansys CFX software package. Difference between values of total heat flow and bulk temperature of gases at the flue tube outlet calculated using the known methods for thermal calculation and defined during the mathematical simulation was determined. Shortcomings of used calculation methods based on the results of a study conducted were identified and areas for their improvement were outlined.
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
Zhang, Han-Wei; Zheng, Yong; Du, Lan; Pan, Guan-Song
The tidal variation in Earth rotation rate is a periodical response to solar-lunar tide generating potential (TGP). Some theoretical formulae are given here based on Doodson development of TGP including the variations in Earth rotation rate, LOD and UT1. Finally the zonal tidal effect on the variation in the fluid core Earth rotation rate is calculated according to the formula deduced by Xi Qinwen (1995). The calculation shows that the results in this paper are well consistent with the ones in IERS (96), which indicates the correctness of the theoretical formula we deduced. It is also shown that the effects from the high frequency parts are relatively small, within the observing precision so far; relatively large effects due to the lower parts, which should be able to be seperated from the observed data, are actually difficult to make because of the influence from some non-tidal factors as well as short time span data.
Reynolds, J. M.; Lopez-Bruna, D.
2009-12-11
This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs.
Martin, A.; Alvarez, D.; Cases, F.; Stelletta, S.
1997-06-01
This report explains the last results about the mixing in the 900 MW PWR vessels. The accurate fluid flow transient, induced by the RCP starting-up, is represented. In a first time, we present the Thermalhydraulic Finite Element Code N3S used for the 3D numerical computations. After that, results obtained for one reactor operation case are given. This case is dealing with the transient mixing of a clear plug in the vessel when one primary pump starts-up. A comparison made between two injection modes; a steady state fluid flow conditions or the accurate RCP transient fluid flow conditions. The results giving the local minimum of concentration and the time response of the mean concentration at the core inlet are compared. The results show the real importance of the unsteadiness characteristics of the fluid flow transport of the clear water plug. (author)
Malet, J., E-mail: jeanne.malet@irsn.fr [Institut de Radioprotection et de Surete Nucleaire (IRSN), PSN-RES, SCA, BP 68, 91192 Gif-sur-Yvette (France); Porcheron, E.; Dumay, F.; Vendel, J. [Institut de Radioprotection et de Surete Nucleaire (IRSN), PSN-RES, SCA, BP 68, 91192 Gif-sur-Yvette (France)
2012-12-15
Highlights: Black-Right-Pointing-Pointer Steam condensation on walls has been investigated in the TOSQAN vessel. Black-Right-Pointing-Pointer Experiments on 7 different tests have been performed. Black-Right-Pointing-Pointer Different steam injections and wall temperatures are used. Black-Right-Pointing-Pointer Simulations are performed in 2D using the TONUS code. Black-Right-Pointing-Pointer Code-experiments comparisons at many different locations show a good agreement. - Abstract: During the course of a severe Pressurized Water Reactor accident, pressurization of the containment occurs and hydrogen can be produced by the reactor core oxidation and distributed in the containment according to convection flows and wall condensation. Filmwise wall condensation in the presence of non-condensable gases is a subject of many interests and extensive studies have been performed in the past. Some empirical correlations have demonstrated their limit for extrapolation under different thermal-hydraulic conditions and at different geometries/scales. The French Institute for Radiological Protection and Nuclear Safety (IRSN) has developed a numerical tool and an experimental facility in order to investigate free convection flows in the presence of condensation. The objective of this paper is to present numerical results obtained on different wall condensation tests in 7 m{sup 3} volume vessel (TOSQAN facility), and to compare them with the experimental ones. Over eight tests are considered here, and code-experiment comparison is performed on many different locations, giving an extensive insight of the code assessment for air-steam mixture flows involving wall condensation in the presence of non-condensable gases.
Thierry Woignier
2015-06-01
Full Text Available Pest control technology was introduced into the tropics without considering the specificity of their ecosystems and the risk of pollution was underestimated. Some volcanic soils (andosols contain nanoclay (allophane with a unique structure and porous properties compared to crystalline clays. Andosols are characterized by large pore volume and pore size distribution, a high specific surface area, and a fractal structure. These soils are more polluted than the other kinds of tropical soils but release less pollutants (chlordecone to water and plants. The literature shows that the allophane microstructure favors accumulation and sequestration of chlordecone, an organochlorine pesticide, in andosols.We used a numerical model to simulate the structure of allophane aggregates. The algorithm is based on a cluster-cluster aggregation model. From the simulated data, we derived the structural features, pore volume and tortuosity, and its transport properties, hydraulic conductivity and diffusion. We show that transport properties decrease because of the presence of allophane. We propose that low hydraulic conductivity and diffusion are important parameters to explain the high concentrations and trapping of pollutants in andosols.
Berger, E.; Till, E.; Brenne, T.; Heath, A.; Hochholdinger, B.; Kassem-Manthey, K.; Kessler, L.; Koch, N.; Kortmann, G.; Kroeff, A.; Otto, T.; Verhoeven, H.; Steinbeck, G.; Vu, T.-C.; Wiegand, K.
2005-01-01
To increase the accuracy of finite element simulations in daily practice the local German and Austrian Deep Drawing Research Groups of IDDRG founded a special Working Group in year 2000. The main objective of this group was the continuously ongoing study and discussion of numerical / material effects in simulation jobs and to work out possible solutions. As a first theme of this group the intensive study of small die radii and the possibility of detecting material failure in these critical forming positions was selected. The part itself is a fictional body panel outside in which the original door handle of the VW Golf A4 has been constructed, a typical position of possible material necking or rupture in the press shop. All conditions to do a successful simulation have been taken care of in advance, material data, boundary conditions, friction, FLC and others where determined for the two materials in investigation - a mild steel and a dual phase steel HXT500X. The results of the experiments have been used to design the descriptions of two different benchmark runs for the simulation. The simulations with different programs as well as with different parameters showed on one hand negligible and on the other hand parameters with strong impact on the result - thereby having a different impact on a possible material failure prediction
Mutu Costin Stelian
2016-12-01
Full Text Available Cable-stayed bridges are complex structures and for their design, the traditional calculation methods are hard, even impossible to use for a global analysis. Separate analyses for the each component of the bridge in a simplified manner can be conducted, but in this case the concurrence of the elements into the structure is not taken into account, leading to errors in estimating the structural response. For these structures, the construction method and the presence of the stays, which are elements having a nonlinear behaviour, implies to consider a nonlinear staged analysis including the second order effects in order to transmit form one stage to the other the stress-strain state.
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.
Alejandro Acevedo-Malavé
2016-09-01
Full Text Available In this study, the finite volume method is employed to simulate the coalescence collision between water drops immersed in a continuous phase (n-heptane. For that purpose, it is chosen a range of values for the velocity of collisions for the finite volume calculations may yield different possible outcomes of the collision process. It can be seen for head-on collisions that when the velocity of collision is 0.2 m/s and 3.5 m/s, the little drop induces the formation of a hole in the bigger drop, until the surface tension forces to restore the circular form of the resulting drop. For a velocity of collision of 16.0 m/s, the little drop deforms the bigger one, and the system is converted into a thin ligament with the evolution of the dynamics. In this case, a little mass of n-heptane is trapped between the two drops, but at the end of the dynamics it drains to the continuous phase. For off-center collisions, two different values for the velocity of collisions were chosen, and the drops exhibit a lot of waves on the droplets’ surface. The streamlines are calculated for the process of coalescence of drops. These streamlines allow the understanding of the dynamics of the droplets immersed on the n-heptane phase. The effect of the interfacial tension it is showed due to the oscillations that the droplet exhibits. When the coalescence has begun, the streamlines form circular patterns at the zone of contact between the drops which explain the increment of the thickness of the bridge structure of the fluid between the two drops. At the end of the dynamics, when the velocity is of 0.2 m/s, the bigger drop reaches a circular form approximately, but when the velocity is of 3.5 m/s the drop reaches an elongated form.
Nakamura, Hiroki; Okumura, Masahiko; Machida, Masahiko
2015-01-01
The authors examined, based on first-principles calculation, the mechanism of mordenite as a species of zeolite to show high adsorption selectivity for Cs, with a focus on the pores as adsorption site. For increasing the adsorption selectivity for Cs, the following three conditions for mordenite were proposed: (1) to have many pores with a radius of about 3 Å, (2) relatively small ratio of Al and Si, and (3) uniform distribution of Al atoms around the pores to adsorb Cs. The superposition effect of the interaction obtained by embracing positive ions with all the pores was revealed to be important, which verified the importance of computational science. It was also successfully conducted to reproduce with Monte Carlo method the thermodynamic level data of ion exchange isotherms, which became engineering metrics after actual measurement. This method was able to reproduce the difference in properties shown by different zeolites, and also able to explain changes in the adsorption performance that depends on Al and Si ratio, which remained the findings from experience up to date, by utilizing the method to associate the result to microscopic factors. Based on these results, this paper discusses how far material development would be realized depending on the leadership of computational science, and what kinds of research and development would be required in the future. (A.O)
Douady, Jerome
1969-10-01
A simplified SCF Method is developed. The wave function of molecular systems and spin densities in the case of free radicals are computed from geometrical data. This method, including at the beginning a delocalization of electrons over all the molecular system, two methods which clear out bonding and anti-bonding interactions have been studied and programmed: a) overlap population analysis, b) localisation of molecular orbitals. These methods have been carried out in the case of organic compounds and free radicals. (author) [French] Mise en oeuvre d'une methode de champ self-consistant simplifie qui, a partir des donnees geometriques, permet de calculer la fonction d'onde des systemes moleculaires et les densites de spin dans le cas des radicaux libres. Cette methode introduisant au depart une delocalisation des electrons sur tout le systeme moleculaire, deux methodes permettant de rendre compte du caractere liant et antiliant de ces electrons ont ete etudiees et programmees: a) analyse des populations de recouvrement, b) localisation des orbitales moleculaires. Ces methodes ont ete appliquees a divers composes organiques radicalaires et non radicalaires. (auteur)
Cecenas F, M., E-mail: mcf@iie.org.mx [Instituto Nacional de Electricidad y Energias Limpias, Reforma 113, Col. Palmira, 62490 Cuernavaca, Morelos (Mexico)
2017-09-15
A parallel channel model with boiling and punctual neutron kinetics is used to compare the implementation of its programming in C language through a conventional scheme and through a parallel programming scheme. In both cases the subroutines written in C are practically the same, but they vary in the way of controlling the execution of the tasks that calculate the different channels. Parallel Virtual Machine is used for the parallel solution, which allows the passage of messages between tasks to control convergence and transfer the variables of interest between the tasks that run simultaneously on a platform equipped with a multi-core microprocessor. For some problems defined as a study case, such as the one presented in this paper, a computer with two cores can reduce the computation time to 54-56% of the time required by the same program in its conventional sequential version. Similarly, a processor with four cores can reduce the time to 22-33% of execution time of the conventional serial version. These results of substantially reducing the computation time are very motivating of all those applications that can be prepared to be parallelized and whose execution time is an important factor. (Author)
Xu, Gaohuan; Chen, Jianneng; Zhao, Huacheng
2018-06-01
The transmission systems of the differential velocity vane pumps (DVVP) have periodic vibrations under loads. And it is not easy to find the reason. In order to optimize the performance of the pump, the authors proposed DVVP driven by the hybrid Higher-order Fourier non-circular gears and tested it. There were also similar periodic vibrations and noises under loads. Taking into account this phenomenon, the paper proposes fluid mechanics and solid mechanics simulation methodology to analyze the coupling dynamics between fluid and transmission system and reveals the reason. The results show that the pump has the reverse drive phenomenon, which is that the blades drive the non-circular gears when the suction and discharge is alternating. The reverse drive phenomenon leads the sign of the shaft torque to be changed in positive and negative way. So the transmission system produces torsional vibrations. In order to confirm the simulation results, micro strains of the input shaft of the pump impeller are measured by the Wheatstone bridge and wireless sensor technology. The relationships between strain and torque are obtained by experimental calibration, and then the true torque of input shaft is calculated indirectly. The experimental results are consistent to the simulation results. It is proven that the periodic vibrations are mainly caused by fluid solid coupling, which leads to periodic torsional vibration of the transmission system.
Sebelin, E
1997-12-15
Full-wave calculations based on trial functions are carried out for solving the lower hybrid current drive problem in tokamaks. A variational method is developed and provides an efficient system to describe in a global manner both the propagation and the absorption of the electromagnetic waves in plasmas. The calculation is fully carried out in the case of circular and concentric flux surfaces. The existence and uniqueness of the solution of the wave propagation equation is mathematically proved. The first realistic simulations are performed for the high aspect ratio tokamak TRIAM-1M. It is checked that the main features of the lower-hybrid wave dynamics are well described numerically. (A.C.) 81 refs.
Reynolds, J. M.; Lopez-Bruna, D.
2009-12-11
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs.
Sommerfeld M.
2006-11-01
Full Text Available The present paper concerns experiments and numerical calculations of an isopropyl-alcohol spray evaporating in a co-flowing turbulent heated air flow. The measurements provided detailed inlet and boundary conditions for the numerical calculations and allowed the validation of the numerical method and models. Phase-Doppler anemometry was used in order to obtain the spatial change of the droplet size distribution and the correlation between droplet size and velocity throughout the flow field. Additionally, a reliable method based on the detection of the signal amplitudes was applied to determine the droplet mass flux. By integration of the droplet mass flux profiles, the global evaporation rates could be determined for different flow conditions. Numerical calculations of the evaporating spray were performed by the Eulerian / Lagrangian approach. The modelling of droplet evaporation is briefly reviewed prior to the description of the applied numerical models and methods. Calculations for a single phase flow showed good agreement with the experiments. Also for all of the droplet phase properties reasonable agreement with the experiments could be achieved and the global evaporation rates agreed well with the measurements. Cet article expose en détail les expériences et les calculs concernant l'évaporation d'isopropanol pulvérisé dans un flux d'air chaud turbulent. Les mesures ont fourni le détail des conditions initiales et des conditions limites pour les calculs numériques ; elles ont également permis de valider la méthode et le modèle. L'anémométrie de phase-Doppler a permis de définir la modification spatiale de la distribution des dimensions de gouttelettes ainsi que la corrélation entre dimension et vitesse des gouttelettes, dans l'ensemble du champ d'écoulement. De plus, une méthode fiable fondée sur la détection des amplitudes de signal a été appliquée afin de déterminer le débit massique des gouttelettes. L
Numerical Calculation of Overhead Power Lines Dynamics
Gogola Roman
2016-11-01
Full Text Available This paper contains results of transient analysis of airflow around the ACSR power line cross-section in unsymmetric multi-span. The forces applied to the power line are obtained from CFD simulations, where the wind induced vibration is studied. Effect of these forces to the maximal displacement of the power line and the maximal mechanical forces in the points of attachment are studied and evaluated.
108 NUMERICAL CALCULATIONS IN THE GENERAL DYNAMICAL ...
DR. AMINU
Dynamical Principles and Laws and compare to construct a corresponding theory of Gravitational. Time Dilation and compute the ratio of the ... mass mi and passive and mass mp and active mass mA of a photon of frequency ν is given by. 2 ... Conservation of mechanical Energy in gravitational fields that the instantaneous ...
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.)
Petersen, Kurt Erling
1986-01-01
Risk and reliability analysis is increasingly being used in evaluations of plant safety and plant reliability. The analysis can be performed either during the design process or during the operation time, with the purpose to improve the safety or the reliability. Due to plant complexity and safety...... and availability requirements, sophisticated tools, which are flexible and efficient, are needed. Such tools have been developed in the last 20 years and they have to be continuously refined to meet the growing requirements. Two different areas of application were analysed. In structural reliability probabilistic...... approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis of very...
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
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.
Petersen, K.E.
1986-03-01
Risk and reliability analysis is increasingly being used in evaluations of plant safety and plant reliability. The analysis can be performed either during the design process or during the operation time, with the purpose to improve the safety or the reliability. Due to plant complexity and safety and availability requirements, sophisticated tools, which are flexible and efficient, are needed. Such tools have been developed in the last 20 years and they have to be continuously refined to meet the growing requirements. Two different areas of application were analysed. In structural reliability probabilistic approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis of very complex systems. In order to increase the applicability of the programs variance reduction techniques can be applied to speed up the calculation process. Variance reduction techniques have been studied and procedures for implementation of importance sampling are suggested. (author)
McCarty, George
1982-01-01
How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the functio...
Nonrelativistic effective field theories of QED and QCD. Applications and automatic calculations
Shtabovenko, Vladyslav
2017-05-22
}υ{sup 2}, where m{sub Q} is the heavy quark mass and υ is the relative velocity of the heavy quarks in the quarkonium. The novelty of this study is the inclusion of the effects from higher order Fock states vertical stroke Q anti Qg right angle, that were incorrectly ignored in the previous investigations of the O(α{sup 0}{sub s}υ{sup 2}) relativistic corrections for e{sup +}e{sup -}→χ{sub cJ}γ. Physically, these effects describe the situation, when a heavy quark pair and a soft gluon together undergo a nonperturbative evolution into the heavy quarkonium χ{sub cJ}. In this work we explicitly compute the matching coefficients multiplying the corresponding long distance matrix elements (LDMEs) in the NRQCD-factorized production cross sections. The phenomenological importance of these contribution remains unclear, due to the lack of experimental data and large uncertainties in the estimates of the nonperturbative LDMEs. Good perspectives for the measurement of the electromagnetic χ{sub cJ} production will exist at Belle II in Japan. The last part of this thesis is dedicated to the development of software tools for automatic calculations in relativistic and nonrelativistic EFTs. First of all, we describe the recent progress in the FEYNCALC project. FEYNCALC is a MATHEMATICA package for semi-automatic symbolic QFT calculations that was originally developed by Rolf Mertig in 1991. Since 2001 the active development of the package almost halted, despite its large popularity among theorists and phenomenologists. In 2014 the author of this thesis became lead developer of the package. Apart from fixing numerous bugs, he has also improved the overall performance of FEYNCALC and added many new functions relevant for 1-loop and multi-loop calculations. In the next step, an interface called FEYNHELPERS was developed. FEYNHELPERS connects FEYNCALC to PACKAGE-X and FIRE. The former provides a library of analytic results for scalar 1-loop integrals with up to 4 legs, while the
Nonrelativistic effective field theories of QED and QCD. Applications and automatic calculations
Shtabovenko, Vladyslav
2017-01-01
velocity of the heavy quarks in the quarkonium. The novelty of this study is the inclusion of the effects from higher order Fock states vertical stroke Q anti Qg right angle, that were incorrectly ignored in the previous investigations of the O(α 0 s υ 2 ) relativistic corrections for e + e - →χ cJ γ. Physically, these effects describe the situation, when a heavy quark pair and a soft gluon together undergo a nonperturbative evolution into the heavy quarkonium χ cJ . In this work we explicitly compute the matching coefficients multiplying the corresponding long distance matrix elements (LDMEs) in the NRQCD-factorized production cross sections. The phenomenological importance of these contribution remains unclear, due to the lack of experimental data and large uncertainties in the estimates of the nonperturbative LDMEs. Good perspectives for the measurement of the electromagnetic χ cJ production will exist at Belle II in Japan. The last part of this thesis is dedicated to the development of software tools for automatic calculations in relativistic and nonrelativistic EFTs. First of all, we describe the recent progress in the FEYNCALC project. FEYNCALC is a MATHEMATICA package for semi-automatic symbolic QFT calculations that was originally developed by Rolf Mertig in 1991. Since 2001 the active development of the package almost halted, despite its large popularity among theorists and phenomenologists. In 2014 the author of this thesis became lead developer of the package. Apart from fixing numerous bugs, he has also improved the overall performance of FEYNCALC and added many new functions relevant for 1-loop and multi-loop calculations. In the next step, an interface called FEYNHELPERS was developed. FEYNHELPERS connects FEYNCALC to PACKAGE-X and FIRE. The former provides a library of analytic results for scalar 1-loop integrals with up to 4 legs, while the latter is a general-purpose tool for reduction of multi-loop scalar integrals using Integration-by-Parts (IBP
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…
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…
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...
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...
Ganguly, J.; Tirone, M.; Sorcar, N.
2013-12-01
Reliable thermodynamic databases for rock forming minerals are essential for petrological and geodynamic studies. While the available databases (1-3) represent laudable efforts, none seems to be completely satisfactory. We show inter-comparison of phase diagrams computed from different databases and also their comparisons with experimental phase diagrams in complex systems. The results show good agreement and also significant disagreements in some P-T-X regimes; resolution of these disagreements via new experimental and thermodynamic data is needed to sort out the problems and make further progress. Two of the main challenges in the development of databases (4) seem to be (a) appropriate formulation of an EoS for solids that is suitable for studies of Earth and planetary interiors and (b) relatively simple formulations of thermodynamic mixing properties of mantle minerals that perform well within the compositional space of interest. While work on EoS formulation continues, we present a semi-empirical numerical approach that creates a consistent set of material properties (α, K, Cp, Cv) up to very high P-T conditions by satisfying certain physical constraints. Adequate experimental data are not available to constrain the mixing properties of several minerals that would be valid over the compositional range of interest in the natural environments. We have, thus, pursued an alternative approach on the basis of physical and crystal-chemical data. It is found that combination of elastic mixing energy, incorporating the effect of multi-atom interactions (5, 6), and crystal-field (CF) energy of mixing provide enthalpy of mixing in binary solid solutions that are in good agreement with experimental and calorimetric data. The CF-splitting vs. composition in a solid solution involving transition metal ion may be approximated by a semi-empirical relation using mean metal-oxygen bond-distance when such data are not available from spectroscopic studies. We also discuss the
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<
Baker, John G.
2009-01-01
Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.
Henriquez, Vicente Cutanda
This thesis describes the development of a numerical model of the propagation of sound waves in fluids with viscous and thermal losses, with application to the simulation of acoustic transducers, in particular condenser microphones for measurement. The theoretical basis is presented, numerical...... manipulations are developed to satisfy the more complicated boundary conditions, and a model of a condenser microphone with a coupled membrane is developed. The model is tested against measurements of ¼ inch condenser microphones and analytical calculations. A detailed discussion of the results is given....
On numerical Bessel transformation
Sommer, B.; Zabolitzky, J.G.
1979-01-01
The authors present a computer program to calculate the three dimensional Fourier or Bessel transforms and definite integrals with Bessel functions. Numerical integration of systems containing Bessel functions occurs in many physical problems, e.g. electromagnetic form factor of nuclei, all transitions involving multipole expansions at high momenta. Filon's integration rule is extended to spherical Bessel functions. The numerical error is of the order of the Simpson error term of the function which has to be transformed. Thus one gets a stable integral even at large arguments of the transformed function. (Auth.)
National Oceanic and Atmospheric Administration, Department of Commerce — Declination is calculated using the current International Geomagnetic Reference Field (IGRF) model. Declination is calculated using the current World Magnetic Model...
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.
Jacques, Ian
1987-01-01
This book is primarily intended for undergraduates in mathematics, the physical sciences and engineering. It introduces students to most of the techniques forming the core component of courses in numerical analysis. The text is divided into eight chapters which are largely self-contained. However, with a subject as intricately woven as mathematics, there is inevitably some interdependence between them. The level of difficulty varies and, although emphasis is firmly placed on the methods themselves rather than their analysis, we have not hesitated to include theoretical material when we consider it to be sufficiently interesting. However, it should be possible to omit those parts that do seem daunting while still being able to follow the worked examples and to tackle the exercises accompanying each section. Familiarity with the basic results of analysis and linear algebra is assumed since these are normally taught in first courses on mathematical methods. For reference purposes a list of theorems used in the t...
Carou A.
2006-11-01
Full Text Available Le calcul de la résistance de vague d'une carène par éléments finis concentrés sur un ouvert borné nécessite la connaissance de la fonction de Green du problème à grande distance. Cette fonction est très difficile à calculer numériquement. On justifie dans ce travail une méthode asymptotique rapide, remplaçant avantageusement l'intégration numérique. Computing wave resistance -by finite elements concentrated on a bounded open set requires the prior knowledge of the Green function of the problem at a great distance. Computing this function is numerically very difficult. A fast asymptotic method is iustified in this article, and it can be used ta advantage as a replacemenf for numerical integration.
Superfield approach to calculation of effective potential in supersymmetric field theories
Bukhbinder, I.L.; Kuzenko, S.M.; Yarevskaya, Zh.V.
1993-01-01
Superfield method of computing effective potential in supersymmetric field theories is suggested. The one-loop effective potential of the Wess-Zumino model is found. The prescription for obtaining multi-loop corrections is described
Scholtyssek, W.
1995-01-01
In the first phase of a benchmark comparison, the CONTAIN code was used to calculate an assumed EPR accident 'medium-sized leak in the cold leg', especially for the first two days after initiation of the accident. The results for global characteristics compare well with those of FIPLOC, MELCOR and WAVCO calculations, if the same materials data are used as input. However, significant differences show up for local quantities such as flows through leakages. (orig.)
Gillard, Ph. [Centre National de la Recherche Scientifique (CNRS), 86 - Poitiers (France)
1998-04-01
Self-ignition of energetic material was investigated in order to optimize safety in the field of pyrotechnic applications. Two approaches were used; the first one is relative to Frank-Kamenetskii stationary thermal explosion theory. The second approach consists of a choice of some numerical solutions of heat conduction equations in a non-stationary state. Comparison between these results was carried out in order to find the numerical scheme which is the most compatible with Frank-Kamenetskii stationary thermal explosion theory. Numerical data were used for three explosive substances. One of them was studied by the author. In all cases, the numerical stationary state is in agreement with the Frank-Kamenetskii stationary thermal explosion theory, more or less accurately. From this comparison, it may be concluded that it is preferable, for this kind of problem, to use an implicit scheme with linearization of the heat source term. Explicit numerical methods, with or without the addition of the heat term with the Zinn and Mader scheme are revealed to be less accurate and to need a greater optimization of spatial and temporal meshing. (author) 7 refs.
Sensitivity analysis of numerical solutions for environmental fluid problems
Tanaka, Nobuatsu; Motoyama, Yasunori
2003-01-01
In this study, we present a new numerical method to quantitatively analyze the error of numerical solutions by using the sensitivity analysis. If a reference case of typical parameters is one calculated with the method, no additional calculation is required to estimate the results of the other numerical parameters such as more detailed solutions. Furthermore, we can estimate the strict solution from the sensitivity analysis results and can quantitatively evaluate the reliability of the numerical solution by calculating the numerical error. (author)
Bodvarsson, G.S.; Lippmann, M.J.
1980-01-01
The computer program CCC (conduction-convection-consolidation), developed at Lawrence Berkeley Laboratory, solves numerically the heat and mass flow equations for a fully saturated medium, and computes one-dimensional consolidation of the simulated systems. The model employs the Integrated Finite Difference Method (IFDM) in discretizing the saturated medium and formulating the governing equations. The sets of equations are solved either by an iterative solution technique (old version) or an efficient sparse solver (new version). The deformation of the medium is calculated using the one-dimensional consolidation theory of Terzaghi. In this paper, the numerical code is described, validation examples given and areas of application discussed. Several example problems involving flow through fractured media are also presented
Calculation of Spectra of Solids:
Lindgård, Per-Anker
1975-01-01
The Gilat-Raubenheimer method simplified to tetrahedron division is used to calculate the real and imaginary part of the dynamical response function for electrons. A frequency expansion for the real part is discussed. The Lindhard function is calculated as a test for numerical accuracy...
Dose calculation for electrons
Hirayama, Hideo
1995-01-01
The joint working group of ICRP/ICRU is advancing the works of reviewing the ICRP publication 51 by investigating the data related to radiation protection. In order to introduce the 1990 recommendation, it has been demanded to carry out calculation for neutrons, photons and electrons. As for electrons, EURADOS WG4 (Numerical Dosimetry) rearranged the data to be calculated at the meeting held in PTB Braunschweig in June, 1992, and the question and request were presented by Dr. J.L. Chartier, the responsible person, to the researchers who are likely to undertake electron transport Monte Carlo calculation. The author also has carried out the requested calculation as it was the good chance to do the mutual comparison among various computation codes regarding electron transport calculation. The content that the WG requested to calculate was the absorbed dose at depth d mm when parallel electron beam enters at angle α into flat plate phantoms of PMMA, water and ICRU4-element tissue, which were placed in vacuum. The calculation was carried out by the versatile electron-photon shower computation Monte Carlo code, EGS4. As the results, depth dose curves and the dependence of absorbed dose on electron energy, incident angle and material are reported. The subjects to be investigated are pointed out. (K.I.)
Ángela Anyur García Bernal
2012-11-01
Full Text Available Antecedentes: uno de los problemas más complejos del diagnósticoy tratamiento de las maloclusiones lo constituye la corrección de laclase III esquelética. Objetivo: determinar los cambios esqueléticos,dentales y faciales de la maloclusión clase III esquelética tratadacon la filosofía Edgewise Multiloop (MEAW, en pacientes queasistieron a una clínica odontológica privada entre marzo de 2009a septiembre de 2012. Métodos: se realizó un estudio descriptivoretrospectivo, donde se analizaron los registros clínicos de sietepacientes con diagnóstico de maloclusión clase III esquelética.Se evaluaron las variables edad, género, medidas cefalométricasiniciales y finales en radiografías y fotografías laterales. Resultados:los pacientes de ángulo alto fueron 60% mujeres, con edad mediade 21,8 años (DE± 7,25. El ángulo de la convejidad pasó de 10,58° a16,4°; el Indicador de Displasia Antero-Posterior (APDI disminuyóde 96,7° a 91,0°; el Plano Palatino (PP aumentó de 114,3°a 115,4° yel plano oclusal aumentó la inclinación de 17,8°a 24,7°. El promediode tiempo en el tratamiento fue de 19,4 meses. Conclusiones: lafilosofía MEAW es una alternativa terapéutica de camuflaje en eltratamiento de las maloclusiones clase III esquelética.
叶小军; 杜忠华; 胡传辉; 唐佑辉; 张跃林
2012-01-01
Penetration process of penetrator with enhanced lateral effect (PELE) into reinforced concrete(RC) target was simulated by the ANSYS/LS-DYNA 3D software. The destructive effect,dimension of the impact crater,diameter of hole,dimension of spalling pit and rebar cut were obtained. In order to verify the calculated results, the PELE penetration into and broken RC was test by gun. The results show that the test results are in agreement with the calculated results. The PELE projectile penetration damage of reinforced concrete ability, enhanced lateral effect, deformation and damage problems under high speed impact were further analyzed by experimental results.%采用ANSYS/LS-DYNA 3D软件,对横向效应增强型侵彻体(PELE)侵彻破坏钢筋混凝土靶进行数值计算,得到PELE弹对钢筋混凝土靶侵彻破坏效应及开坑直径、崩落直径、通孔直径、钢筋断裂等参数.为验证数值计算结果,利用火炮进行了试验,试验结果与计算结果吻合良好,并利用实验结果进一步分析了高速撞击条件下PELE弹侵彻破坏钢筋混凝土的能力、PELE的横向效能、弹体变形和破坏等问题.
Salgado, C A; Salgado, Carlos A.; Wiedemann, Urs Achim
2003-01-01
We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peign\\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus colli...
Li, D.
1980-01-01
Reviewed is the effect of heat flux of different system parameters on critical density in order to give an initial view on the value of several parameters. A thorough analysis of different equations is carried out to calculate burnout is steam-water flows in uniformly heated tubes, annular, and rectangular channels and rod bundles. Effect of heat flux density distribution and flux twisting on burnout and storage determination according to burnout are commended [ru
Cariou A.
2006-11-01
Full Text Available Cet article est le prolongement de deux publications dejà parues dans cette revue [I] [5]. On rappelle que le calcul de la résistance de vague d'une carène par éléments finis sur un ouvert borné nécessite la connaissance de la fonction de Green du problème à grande distance. Cette fonction est très difficile à calculer par une intégration numérique classique. Dans ce qui suit on rappelle donc les résultats et les méthodes des précédents articles et on achève la justification d'une méthode asymptotique pour le calcul de la fonction de Green. This article is the second of two already published in this journal. The wave resistance of a hull is calculated by finite elements on a bounded domain. For this, the Green function of the problem atgreat distance must be known. It is very difficult to calculate this function by a conventional numerical integration. This article reviews the results and methods of the preceding articles, and an asymptotic method for colculating the Green function ïs justified.
Disch, Mario; Wittmeier, Felix; Widdecke, Nils; Wiedemann, Jochen [Forschungsinstitut fuer Fahrzeugmotoren und Kraftfahrwesen (FKFS), Stuttgart (Germany); Reister, Heinrich; Weidmann, Ernst-Peter [Daimler AG, Sindelfingen (Germany)
2012-11-01
In the vehicle development process at Daimler, thermal protection is an important task that has to be fulfilled. In the early stages of car development numerical analysis techniques are used to ensure that all critical components stay well below given temperature limits. Especially engine mounts are in the focus of investigation due to the geometrical design and the arrangement next to hot exhaust components. For a better understanding of the complex heat transfer mechanisms taking place in this part and as a first step into transient full Vehicle Thermal Management (VTM) computation, two different transient computational analyses are performed and described in this paper. The first one is the Conjugate Heat Transfer method (CHT) in which convection, conduction and radiation phenomena are solved simultaneously. The second one is a COSIM-method in which fluid and solid structures are splitted into two different simulations and brought to interaction by exchanging data at predetermined points. The major problem in transient computation is that thermal time scales on solid and fluid structures vary over a wide range. Using CHT a fine temporal discretization is needed for fluid and solid computation causing an enormous computational effort. In the COSIM-method solid structures are computed unsteady while the corresponding fluid is treated as steady and recalculated after each exchange. Corresponding measurements at an engine mount test rig show that both transient coupling schemes fit well to unsteady experimental results. In conclusion it can be said that the COSIM-method is an effective alternative to CHT computations for transient thermal applications. Computational and modeling effort can be reduced considerably especially for larger time scales which are relevant for full VTM computations. (orig.)
Numerical modeling of slow shocks
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
Numerical Verification Of Equilibrium Chemistry
Piro, Markus; Lewis, Brent; Thompson, William T.; Simunovic, Srdjan; Besmann, Theodore M.
2010-01-01
A numerical tool is in an advanced state of development to compute the equilibrium compositions of phases and their proportions in multi-component systems of importance to the nuclear industry. The resulting software is being conceived for direct integration into large multi-physics fuel performance codes, particularly for providing boundary conditions in heat and mass transport modules. However, any numerical errors produced in equilibrium chemistry computations will be propagated in subsequent heat and mass transport calculations, thus falsely predicting nuclear fuel behaviour. The necessity for a reliable method to numerically verify chemical equilibrium computations is emphasized by the requirement to handle the very large number of elements necessary to capture the entire fission product inventory. A simple, reliable and comprehensive numerical verification method is presented which can be invoked by any equilibrium chemistry solver for quality assurance purposes.
Hart, C.F.
1981-01-01
A gauge invariant effective action which generalizes the usual background field method is applied to quantum non-Abelian gauge theories. The gauge properties of the theory as well as its equivalence to the conventional theory are presented. Solutions to the new effective field equations are found to be physical and it is shown how S-matrix elements may be computed in terms of this new effective action. Feynman rules are given and the renormalization theory is discussed using minimal subtraction and dimensional regularization. The resulting computation of counterterms is found to be simpler than that of the usual method. A complete two-loop calculation of the β function for pure Yang-Mills theory is given as a specific example of this approach
Lattice calculations in gauge theory
Rebbi, C.
1985-01-01
The lattice formulation of quantum gauge theories is discussed as a viable technique for quantitative studies of nonperturbative effects in QCD. Evidence is presented to ascertain that whole classes of lattice actions produce a universal continuum limit. Discrepancies between numerical results from Monto Carlo simulations for the pure gauge system and for the system with gauge and quark fields are discussed. Numerical calculations for QCD require very substantial computational resources. The use of powerful vector processors of special purpose machines, in extending the scope and magnitude or the calculations is considered, and one may reasonably expect that in the near future good quantitative predictions will be obtained for QCD
Numerical precision control and GRACE
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
Learning from numerical calculations of ion-atom collisions
Reading, J.F.; Ford, A.L.; Martir, M.; Becker, R.L.
1981-01-01
Violent collision of two independent many-particle systems, victims, are discussed in the atomic sphere. The asymmetric region where the charge of the projectile Z/sub p/ is less than the target nuclear charge Z/sub n/ is now well understood though interesting details still need to be worked out. Negatively charged projectiles offer a new illustration of Fadeev re-arrangement collisions. Multi-electron coherence effects illustrate the richness of the field but a symmetric (Z/sub p/ approx. Z/sub n/) collision treatment is needed. A new one and a half center expansion method promises a solution to this problem. Future areas of interest are discussed
Numerical Simulation of Shale Gas Production with Thermodynamic Calculations Incorporated
Urozayev, Dias
2015-01-01
to pressure relation by solving the cubic equation to improve the model. The results show that considering the compressibility of the gas will noticeably increase gas production under given reservoir conditions and slow down the production decline curve
Learning from numerical calculations of ion-atom collisions
Reading, J.F.; Ford, A.L.; Martir, M.
1982-01-01
Violent collisions of two independent many-particle systems, victims, are discussed in the atomic sphere. The asymmetric region where the charge of the projectile Zsub(p) is less than the target nuclear charge Zsub(N) is now well understood, though interesting details still need to be worked out. Negatively charged projectiles offer a new illustration of Fadeev re-arrangement collisions. Multi-electron coherence effects illustrate the richness of the field but a symmetric (Zsub(p) approx. equal to Zsub(N)) collision treatment is needed. A new one-and-a-half center expansion method promises a solution to this problem. Future areas of interest are discussed. (orig.)
Numerical calculation of axisymmetric non-neutral plasma equilibria
Spencer, R.L.; Rasband, S.N.; Vanfleet, R.R.
1993-01-01
Efficient techniques for computing axisymmetric non-neutral plasma equilibria are described. These equilibria may be obtained either by requiring global thermal equilibrium, by specifying the midplane radial density profile, or by specifying the radial profile of ∫n dz. Both splines and finite-differences are used, and the accuracy of the two is compared by using a new characterization of the thermal equilibrium density profile which gives a simple formula for estimating the radial and axial gradient scale lengths of thermal equilibria. It is found that for global thermal equilibrium 1% accuracy is achieved with splines if the distance between neighboring splines is about two Debye lengths while finite differences require a grid spacing of about one-half Debye length to achieve the same accuracy
Introduction to calculations of recuperators
Dollar, M.
1977-01-01
Physical principles of heat transfer between fluid under turbulent flow conditions and a wall of a duct are described. The methods of calculations of heat transfer coefficient and the theory of recuperative heat exchangers are presented. Numerical examples are given to illustrate the theory. (author)
Numerical simulation of hypersonic flight experiment vehicle
Yamamoto, Yukimitsu; Yoshioka, Minako; 山本 行光; 吉岡 美菜子
1994-01-01
Hypersonic aerodynamic characteristics of Hypersonic FLight EXperiment (HYFLEX vehicle were investigated by numerical simulations using Navier-Stokes CFD (Computational Fluid Dynamics) code of NAL. Numerical results were compared with experimental data obtained at Hypersonic Wind Tunnel at NAL. In order to investigate real flight aerodynamic characteristics. numerical calculations corresponding to the flight conditions suffering from maximum aero thermodynamic heating were also made and the d...
Gravitational radiation and 3D numerical relativity
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
Probabilistic numerics and uncertainty in computations.
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.
Numerical Optimization in Microfluidics
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....
Methods of numerical relativity
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 analysis of electromagnetic fields
Zhou Pei Bai
1993-01-01
Numerical methods for solving boundary value problems have developed rapidly. Knowledge of these methods is important both for engineers and scientists. There are many books published that deal with various approximate methods such as the finite element method, the boundary element method and so on. However, there is no textbook that includes all of these methods. This book is intended to fill this gap. The book is designed to be suitable for graduate students in engineering science, for senior undergraduate students as well as for scientists and engineers who are interested in electromagnetic fields. Objective Numerical calculation is the combination of mathematical methods and field theory. A great number of mathematical concepts, principles and techniques are discussed and many computational techniques are considered in dealing with practical problems. The purpose of this book is to provide students with a solid background in numerical analysis of the field problems. The book emphasizes the basic theories ...
On Sums of Numerical Series and Fourier Series
Pavao, H. Germano; de Oliveira, E. Capelas
2008-01-01
We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)
Kavka, P.; Jeřábek, J.; Strouhal, L.
2016-12-01
The contribution presents a numerical model SMODERP that is used for calculation and prediction of surface runoff and soil erosion from agricultural land. The physically based model includes the processes of infiltration (Phillips equation), surface runoff routing (kinematic wave based equation), surface retention, surface roughness and vegetation impact on runoff. The model is being developed at the Department of Irrigation, Drainage and Landscape Engineering, Civil Engineering Faculty, CTU in Prague. 2D version of the model was introduced in last years. The script uses ArcGIS system tools for data preparation. The physical relations are implemented through Python scripts. The main computing part is stand alone in numpy arrays. Flow direction is calculated by Steepest Descent algorithm and in multiple flow algorithm. Sheet flow is described by modified kinematic wave equation. Parameters for five different soil textures were calibrated on the set of hundred measurements performed on the laboratory and filed rainfall simulators. Spatially distributed models enable to estimate not only surface runoff but also flow in the rills. Development of the rills is based on critical shear stress and critical velocity. For modelling of the rills a specific sub model was created. This sub model uses Manning formula for flow estimation. Flow in the ditches and streams are also computed. Numerical stability of the model is controled by Courant criterion. Spatial scale is fixed. Time step is dynamic and depends on the actual discharge. The model is used in the framework of the project "Variability of Short-term Precipitation and Runoff in Small Czech Drainage Basins and its Influence on Water Resources Management". Main goal of the project is to elaborate a methodology and online utility for deriving short-term design precipitation series, which could be utilized by a broad community of scientists, state administration as well as design planners. The methodology will account for
Starck, Patricia L; Love, Karen; McPherson, Robert
2008-01-01
In recent years, the focus has been on increasing the number of registered nurse (RN) graduates. Numerous states have initiated programs to increase the number and quality of students entering nursing programs, and to expand the capacity of their programs to enroll additional qualified students. However, little attention has been focused on an equally, if not more, effective method for increasing the number of RNs produced-increasing the graduation rate of students enrolling. This article describes a project that undertook the task of compiling graduation data for 15 entry-level programs, standardizing terms and calculations for compiling the data, and producing a regional report on graduation rates of RN students overall and by type of program. Methodology is outlined in this article. This effort produced results that were surprising to program deans and directors and is expected to produce greater collaborative efforts to improve these rates both locally and statewide.
Numerical approach to one-loop integrals
Fujimoto, Junpei; Shimizu, Yoshimitsu; Kato, Kiyoshi; Oyanagi, Yoshio.
1992-01-01
Two numerical methods are proposed for the calculation of one-loop scalar integrals. In the first method, the singularity is cancelled by the symmetrization of the integrand and the integration is done by a Monte-Carlo method. In the second one, after the transform of the integrand into a standard form, the integral is reduced into a regular numerical integral. These methods provide us practical tools to evaluate one-loop Feynman diagrams with desired numerical accuracy. They are extended to the integral with numerator and the treatment of the one-loop virtual correction to the cross section is also presented. (author)
Multiloop control of a drum boiler
Alena Kozáková
2014-05-01
Full Text Available The Equivalent Subsystems Method (ESM (Kozáková et al., 2011 is methodology of decentralized controller design in the frequency domain which allows designing local controllers using any SISO frequency domain method. The paper deals with the digital ESM version where digital local PID controllers guaranteeing required performance for the full system are designed for individual equivalent subsystems using the practice-oriented Sine-wave method (Bucz et al., 2012. The proposed decentralized controller design procedure was verified on the nonlinear benchmark drum boiler simulation model (Morilla, 2012.
Kourdey, A.
2002-09-15
The determination of the sliding surface of slope (dam, slope natural..) is one of the important and complicated problems in geotechnics. The Analyze of stability by the methods of Limit Equilibrium like the method of slices are the most used methods. They are able to determine a safety factor for a geometrically defined failure surface. These methods well adapted to the homogeneous mediums, have been developed a lot but they do not integrate the basic relations of mechanics (stress-strain). The numerical methods are better adapted to mediums having more complexity (effect of water, seismicity, fracturing,..). But, they are seldom used to determine a sliding surface and a safety factor. Each family offers appreciable advantages in the analysis of slope stability. For that purpose, we have developed a method that combines the advantages of the numerical methods as well as those of Limit Equilibrium allowing obtaining a slip surface determined by the calculated constraints. This slip surface may be imposed or better optimized, thus providing a minimal safety factor. Methods of operation research are used to obtain this surface. They are search methods by level, dynamic research.. or both at the same time. We integrated these developments in an existing computer code based on the method of Finite Differences known as FLAC. The stresses are determined for a linear behavior and for nonlinear. Interfaces and graphic tools are also produced to facilitate the analysis of stability. The validity of this approach was carried out for a standard case of slope, we analyzed and compared the results with the methods of Limit Equilibrium. The parametric study shows that this approach takes account of different parameters, which influences stability. We also kept a particular place for the application on real cases presenting slopes of different nature (dams, mining slops,...). (author)
Configuration space Faddeev calculations
Payne, G.L.; Klink, W.H.; Polyzou, W.N.
1989-01-01
The detailed study of few-body systems provides one of the most effective means for studying nuclear physics at subnucleon distance scales. For few-body systems the model equations can be solved numerically with errors less than the experimental uncertainties. We have used such systems to investigate the size of relativistic effects, the role of meson-exchange currents, and the importance of quark degrees of freedom in the nucleus. Complete calculations for momentum-dependent potentials have been performed, and the properties of the three-body bound state for these potentials have been studied. Few-body calculations of the electromagnetic form factors of the deuteron and pion have been carried out using a front-form formulation of relativistic quantum mechanics. The decomposition of the operators transforming convariantly under the Poincare group into kinematical and dynamical parts has been studies. New ways for constructing interactions between particles, as well as interactions which lead to the production of particles, have been constructed in the context of a relativistic quantum mechanics. To compute scattering amplitudes in a nonperturbative way, classes of operators have been generated out of which the phase operator may be constructed. Finally, we have worked out procedures for computing Clebsch-Gordan and Racah coefficients on a computer, as well as giving procedures for dealing with the multiplicity problem
Shielding calculations for NET
Verschuur, K.A.; Hogenbirk, A.
1991-05-01
In the European Fusion Technology Programme there is only a small activity on research and development for fusion neutronics. Never-the-less, looking further than blanket design now, as ECN is getting involved in design of radiation shields for the coils and biological shields, it becomes apparent that fusion neutronics as a whole still needs substantial development. Existing exact codes for calculation of complex geometries like MCNP and DORT/TORT are put over the limits of their numerical capabilities, whilst approximate codes for complex geometries like FURNACE and MERCURE4 are put over the limits of their modelling capabilities. The main objective of this study is just to find out how far we can get with existing codes in obtaining reliable values for the radiation levels inside and outside the cryostat/shield during operation and after shut-down. Starting with a 1D torus model for preliminary parametric studies, more dimensional approximation of the torus or parts of it including the main heterogeneities should follow. Regular contacts with the NET-Team are kept, to be aware of main changes in NET design that might affect our calculation models. Work on the contract started 1 July 1990. The technical description of the contract is given. (author). 14 refs.; 4 figs.; 1 tab
Selfconsistent calculations at finite temperatures
Brack, M.; Quentin, P.
1975-01-01
Calculations have been done for the spherical nuclei 40 Ca, 208 Pb and the hypothetical superheavy nucleus with Z=114, A=298, as well as for the deformed nucleus 168 Yb. The temperature T was varied from zero up to 5 MeV. For T>3 MeV, some numerical problems arise in connection with the optimization of the basis when calculating deformed nuclei. However, at these high temperatures the occupation numbers in the continuum are sufficiently large so that the nucleus starts evaporating particles and no equilibrium state can be described. Results are obtained for excitation energies and entropies. (Auth.)
Thermohydraulic calculations of PWR primary circuits
Botelho, D.A.
1984-01-01
Some mathematical and numerical models from Retran computer codes aiming to simulate reactor transients, are presented. The equations used for calculating one-dimensional flow are integrated using mathematical methods from Flash code, with steam code to correlate the variables from thermodynamic state. The algorithm obtained was used for calculating a PWR reactor. (E.G.) [pt
Numerical simulation of fire vortex
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.
Development of Pelton turbine using numerical simulation
Patel, K; Patel, B; Yadav, M [Hydraulic Engineer, ALSTOM Hydro R and D India Ltd., GIDC Maneja, Vadodara - 390 013, Gujarat (India); Foggia, T, E-mail: patel@power.alstom.co [Hydraulic Engineer, Alstom Hydro France, Etablissement de Grenoble, 82, avenue Leon Blum BP 75, 38041 Grenoble Cedex (France)
2010-08-15
This paper describes recent research and development activities in the field of Pelton turbine design. Flow inside Pelton turbine is most complex due to multiphase (mixture of air and water) and free surface in nature. Numerical calculation is useful to understand flow physics as well as effect of geometry on flow. The optimized design is obtained using in-house special optimization loop. Either single phase or two phase unsteady numerical calculation could be performed. Numerical results are used to visualize the flow pattern in the water passage and to predict performance of Pelton turbine at full load as well as at part load. Model tests are conducted to determine performance of turbine and it shows good agreement with numerically predicted performance.
Development of Pelton turbine using numerical simulation
Patel, K.; Patel, B.; Yadav, M.; Foggia, T.
2010-08-01
This paper describes recent research and development activities in the field of Pelton turbine design. Flow inside Pelton turbine is most complex due to multiphase (mixture of air and water) and free surface in nature. Numerical calculation is useful to understand flow physics as well as effect of geometry on flow. The optimized design is obtained using in-house special optimization loop. Either single phase or two phase unsteady numerical calculation could be performed. Numerical results are used to visualize the flow pattern in the water passage and to predict performance of Pelton turbine at full load as well as at part load. Model tests are conducted to determine performance of turbine and it shows good agreement with numerically predicted performance.
Development of Pelton turbine using numerical simulation
Patel, K; Patel, B; Yadav, M; Foggia, T
2010-01-01
This paper describes recent research and development activities in the field of Pelton turbine design. Flow inside Pelton turbine is most complex due to multiphase (mixture of air and water) and free surface in nature. Numerical calculation is useful to understand flow physics as well as effect of geometry on flow. The optimized design is obtained using in-house special optimization loop. Either single phase or two phase unsteady numerical calculation could be performed. Numerical results are used to visualize the flow pattern in the water passage and to predict performance of Pelton turbine at full load as well as at part load. Model tests are conducted to determine performance of turbine and it shows good agreement with numerically predicted performance.
Numerical methods using Matlab
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
Analyzed method for calculating the distribution of electrostatic field
Lai, W.
1981-01-01
An analyzed method for calculating the distribution of electrostatic field under any given axial gradient in tandem accelerators is described. This method possesses satisfactory accuracy compared with the results of numerical calculation
Radiation transport in numerical astrophysics
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
Time's arrow: A numerical experiment
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.
Physical and Relativistic Numerical Cosmology.
Anninos, Peter
1998-01-01
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations addressing specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark-hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.
Physical and Relativistic Numerical Cosmology
Peter Anninos
1998-01-01
Full Text Available In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations addressing specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark--hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.
Insertion device calculations with mathematica
Carr, R. [Stanford Synchrotron Radiation Lab., CA (United States); Lidia, S. [Univ. of California, Davis, CA (United States)
1995-02-01
The design of accelerator insertion devices such as wigglers and undulators has usually been aided by numerical modeling on digital computers, using code in high level languages like Fortran. In the present era, there are higher level programming environments like IDL{reg_sign}, MatLab{reg_sign}, and Mathematica{reg_sign} in which these calculations may be performed by writing much less code, and in which standard mathematical techniques are very easily used. The authors present a suite of standard insertion device modeling routines in Mathematica to illustrate the new techniques. These routines include a simple way to generate magnetic fields using blocks of CSEM materials, trajectory solutions from the Lorentz force equations for given magnetic fields, Bessel function calculations of radiation for wigglers and undulators and general radiation calculations for undulators.
Excel spreadsheet in teaching numerical methods
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.
Numerical Algorithm for Delta of Asian Option
Boxiang Zhang
2015-01-01
Full Text Available We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.
Coincidental match of numerical simulation and physics
Pierre, B.; Gudmundsson, J. S.
2010-08-01
Consequences of rapid pressure transients in pipelines range from increased fatigue to leakages and to complete ruptures of pipeline. Therefore, accurate predictions of rapid pressure transients in pipelines using numerical simulations are critical. State of the art modelling of pressure transient in general, and water hammer in particular include unsteady friction in addition to the steady frictional pressure drop, and numerical simulations rely on the method of characteristics. Comparison of rapid pressure transient calculations by the method of characteristics and a selected high resolution finite volume method highlights issues related to modelling of pressure waves and illustrates that matches between numerical simulations and physics are purely coincidental.
Calculation of Rydberg interaction potentials
Weber, Sebastian; Büchler, Hans Peter; Tresp, Christoph; Urvoy, Alban; Hofferberth, Sebastian; Menke, Henri; Firstenberg, Ofer
2017-01-01
The strong interaction between individual Rydberg atoms provides a powerful tool exploited in an ever-growing range of applications in quantum information science, quantum simulation and ultracold chemistry. One hallmark of the Rydberg interaction is that both its strength and angular dependence can be fine-tuned with great flexibility by choosing appropriate Rydberg states and applying external electric and magnetic fields. More and more experiments are probing this interaction at short atomic distances or with such high precision that perturbative calculations as well as restrictions to the leading dipole–dipole interaction term are no longer sufficient. In this tutorial, we review all relevant aspects of the full calculation of Rydberg interaction potentials. We discuss the derivation of the interaction Hamiltonian from the electrostatic multipole expansion, numerical and analytical methods for calculating the required electric multipole moments and the inclusion of electromagnetic fields with arbitrary direction. We focus specifically on symmetry arguments and selection rules, which greatly reduce the size of the Hamiltonian matrix, enabling the direct diagonalization of the Hamiltonian up to higher multipole orders on a desktop computer. Finally, we present example calculations showing the relevance of the full interaction calculation to current experiments. Our software for calculating Rydberg potentials including all features discussed in this tutorial is available as open source. (tutorial)
Relativistic few body calculations
Gross, F.
1988-01-01
A modern treatment of the nuclear few-body problem must take into account both the quark structure of baryons and mesons, which should be important at short range, and the relativistic exchange of mesons, which describes the long range, peripheral interactions. A way to model both of these aspects is described. The long range, peripheral interactions are calculated using the spectator model, a general approach in which the spectators to nucleon interactions are put on their mass-shell. Recent numerical results for a relativistic OBE model of the NN interaction, obtained by solving a relativistic equation with one-particle on mass-shell, will be presented and discussed. Two meson exchange models, one with only four mesons (π,σ,/rho/,ω) but with a 25% admixture of γ 5 coupling for the pion, and a second with six mesons (π,σ,/rho/,ω,δ,/eta/) but pure γ 5 γ/sup μ/ pion coupling, are shown to give very good quantitative fits to the NN scattering phase shifts below 400 MeV, and also a good description of the /rvec p/ 40 Ca elastic scattering observables. Applications of this model to electromagnetic interactions of the two body system, with emphasis on the determination of relativistic current operators consistent with the dynamics and the exact treatment of current conservation in the presence of phenomenological form factors, will be described. 18 refs., 8 figs
Numerical ability predicts mortgage default.
Gerardi, Kristopher; Goette, Lorenz; Meier, Stephan
2013-07-09
Unprecedented levels of US subprime mortgage defaults precipitated a severe global financial crisis in late 2008, plunging much of the industrialized world into a deep recession. However, the fundamental reasons for why US mortgages defaulted at such spectacular rates remain largely unknown. This paper presents empirical evidence showing that the ability to perform basic mathematical calculations is negatively associated with the propensity to default on one's mortgage. We measure several aspects of financial literacy and cognitive ability in a survey of subprime mortgage borrowers who took out loans in 2006 and 2007, and match them to objective, detailed administrative data on mortgage characteristics and payment histories. The relationship between numerical ability and mortgage default is robust to controlling for a broad set of sociodemographic variables, and is not driven by other aspects of cognitive ability. We find no support for the hypothesis that numerical ability impacts mortgage outcomes through the choice of the mortgage contract. Rather, our results suggest that individuals with limited numerical ability default on their mortgage due to behavior unrelated to the initial choice of their mortgage.
Numerical ability predicts mortgage default
Gerardi, Kristopher; Goette, Lorenz; Meier, Stephan
2013-01-01
Unprecedented levels of US subprime mortgage defaults precipitated a severe global financial crisis in late 2008, plunging much of the industrialized world into a deep recession. However, the fundamental reasons for why US mortgages defaulted at such spectacular rates remain largely unknown. This paper presents empirical evidence showing that the ability to perform basic mathematical calculations is negatively associated with the propensity to default on one’s mortgage. We measure several aspects of financial literacy and cognitive ability in a survey of subprime mortgage borrowers who took out loans in 2006 and 2007, and match them to objective, detailed administrative data on mortgage characteristics and payment histories. The relationship between numerical ability and mortgage default is robust to controlling for a broad set of sociodemographic variables, and is not driven by other aspects of cognitive ability. We find no support for the hypothesis that numerical ability impacts mortgage outcomes through the choice of the mortgage contract. Rather, our results suggest that individuals with limited numerical ability default on their mortgage due to behavior unrelated to the initial choice of their mortgage. PMID:23798401
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
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
National Oceanic and Atmospheric Administration, Department of Commerce — The Magnetic Field Calculator will calculate the total magnetic field, including components (declination, inclination, horizontal intensity, northerly intensity,...
Remarks on numerical semigroups
Torres, F.
1995-12-01
We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights state in [To]. (author). 25 refs
Numerical semigroups and applications
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...
Mastorakis, Nikos E
2009-01-01
Features contributions that are focused on significant aspects of current numerical methods and computational mathematics. This book carries chapters that advanced methods and various variations on known techniques that can solve difficult scientific problems efficiently.
Introductory numerical analysis
Pettofrezzo, Anthony J
2006-01-01
Written for undergraduates who require a familiarity with the principles behind numerical analysis, this classical treatment encompasses finite differences, least squares theory, and harmonic analysis. Over 70 examples and 280 exercises. 1967 edition.
Introduction to numerical analysis
Hildebrand, F B
1987-01-01
Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, other topics in lucid presentation. Includes 150 additional problems in this edition. Bibliography.
Numerical analysis of bifurcations
Guckenheimer, J.
1996-01-01
This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory. copyright 1996 American Institute of Physics
Numerical computations with GPUs
Kindratenko, Volodymyr
2014-01-01
This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and engineering computations. Each chapter is written by authors working on a specific group of methods; these leading experts provide mathematical background, parallel algorithms and implementation details leading to
The number processing and calculation system: evidence from cognitive neuropsychology.
Salguero-Alcañiz, M P; Alameda-Bailén, J R
2015-04-01
Cognitive neuropsychology focuses on the concepts of dissociation and double dissociation. The performance of number processing and calculation tasks by patients with acquired brain injury can be used to characterise the way in which the healthy cognitive system manipulates number symbols and quantities. The objective of this study is to determine the components of the numerical processing and calculation system. Participants consisted of 6 patients with acquired brain injuries in different cerebral localisations. We used Batería de evaluación del procesamiento numérico y el cálculo, a battery assessing number processing and calculation. Data was analysed using the difference in proportions test. Quantitative numerical knowledge is independent from number transcoding, qualitative numerical knowledge, and calculation. Recodification is independent from qualitative numerical knowledge and calculation. Quantitative numerical knowledge and calculation are also independent functions. The number processing and calculation system comprises at least 4 components that operate independently: quantitative numerical knowledge, number transcoding, qualitative numerical knowledge, and calculation. Therefore, each one may be damaged selectively without affecting the functioning of another. According to the main models of number processing and calculation, each component has different characteristics and cerebral localisations. Copyright © 2013 Sociedad Española de Neurología. Published by Elsevier Espana. All rights reserved.
Power and thermal efficient numerical processing
Liu, Wei; Nannarelli, Alberto
2015-01-01
Numerical processing is at the core of applications in many areas ranging from scientific and engineering calculations to financial computing. These applications are usually executed on large servers or supercomputers to exploit their high speed, high level of parallelism and high bandwidth...
COVE 2A Benchmarking calculations using NORIA
Carrigan, C.R.; Bixler, N.E.; Hopkins, P.L.; Eaton, R.R.
1991-10-01
Six steady-state and six transient benchmarking calculations have been performed, using the finite element code NORIA, to simulate one-dimensional infiltration into Yucca Mountain. These calculations were made to support the code verification (COVE 2A) activity for the Yucca Mountain Site Characterization Project. COVE 2A evaluates the usefulness of numerical codes for analyzing the hydrology of the potential Yucca Mountain site. Numerical solutions for all cases were found to be stable. As expected, the difficulties and computer-time requirements associated with obtaining solutions increased with infiltration rate. 10 refs., 128 figs., 5 tabs
Carossi, Jean-Claude
1969-02-01
A CO 2 flowrate calculator has been designed for measuring and recording the gas flow in the loops of Pegase reactor. The analog calculator applies, at every moment, Bernoulli's formula to the values that characterize the carbon dioxide flow through a nozzle. The calculator electronics is described (it includes a sampling calculator and a two-variable function generator), with its amplifiers, triggers, interpolator, multiplier, etc. Calculator operation and setting are presented
Numerical models for high beta magnetohydrodynamic flow
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
Mechanical calculation of heat exchangers
Osweiller, Francis.
1977-01-01
Many heat exchangers are still being dimensioned at the present time by means of the American TEMA code (Tubular Exchanger Manufacturers Association). The basic formula of this code often gives rise to significant tubular plate thicknesses which, apart from the cost of materials, involve significant machining. Some constructors have brought into use calculation methods that are more analytic so as to take into better consideration the mechanical phenomena which come into play in a heat exchanger. After a brief analysis of these methods it is shown, how the original TEMA formulations have changed to reach the present version and how this code has incorporated Gardner's results for treating exchangers with two fixed heads. A formal and numerical comparison is then made of the analytical and TEMA methods by attempting to highlight a code based on these methods or a computer calculation programme in relation to the TEMA code [fr
McKee, S.; Elliott, C.M.
1986-01-01
The applications of mathematics to industrial problems involves the formulation of problems which are amenable to mathematical investigation, mathematical modelling, the solution of the mathematical problem and the inter-pretation of the results. There are 12 chapters describing industrial problems where mathematics and numerical analysis can be applied. These range from the numerical assessment of the flatness of engineering surfaces and plates, the design of chain links, control problems in tidal power generation and low thrust satellite trajectory optimization to mathematical models in welding. One chapter, on the ageing of stainless steels, is indexed separately. (UK)
Numerical model of thyroid counter
Szuchta Maciej
2016-03-01
Full Text Available The aim of this study was to develop a numerical model of spectrometric thyroid counter, which is used for the measurements of internal contamination by in vivo method. The modeled detector is used for a routine internal exposure monitoring procedure in the Radiation Protection Measurements Laboratory of National Centre for Nuclear Research (NCBJ. This procedure may also be used for monitoring of occupationally exposed nuclear medicine personnel. The developed model was prepared using Monte Carlo code FLUKA 2011 ver. 2b.6 Apr-14 and FLAIR ver. 1.2-5 interface. It contains a scintillation NaI(Tl detector, the collimator and the thyroid water phantom with a reference source of iodine 131I. The geometry of the model was designed and a gamma energy spectrum of iodine 131I deposited in the detector was calculated.
Comprehensive numerical modelling of tokamaks
Cohen, R.H.; Cohen, B.I.; Dubois, P.F.
1991-01-01
We outline a plan for the development of a comprehensive numerical model of tokamaks. The model would consist of a suite of independent, communicating packages describing the various aspects of tokamak performance (core and edge transport coefficients and profiles, heating, fueling, magnetic configuration, etc.) as well as extensive diagnostics. These codes, which may run on different computers, would be flexibly linked by a user-friendly shell which would allow run-time specification of packages and generation of pre- and post-processing functions, including workstation-based visualization of output. One package in particular, the calculation of core transport coefficients via gyrokinetic particle simulation, will become practical on the scale required for comprehensive modelling only with the advent of teraFLOP computers. Incremental effort at LLNL would be focused on gyrokinetic simulation and development of the shell
Numerical studies on divertor experiments
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)
Calculating Cumulative Binomial-Distribution Probabilities
Scheuer, Ernest M.; Bowerman, Paul N.
1989-01-01
Cumulative-binomial computer program, CUMBIN, one of set of three programs, calculates cumulative binomial probability distributions for arbitrary inputs. CUMBIN, NEWTONP (NPO-17556), and CROSSER (NPO-17557), used independently of one another. Reliabilities and availabilities of k-out-of-n systems analyzed. Used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. Used for calculations of reliability and availability. Program written in C.
Thermal calculations for water cooled research reactors
Fabrega, S.
1979-01-01
The formulae and the more important numerical data necessary for thermic calculations on the core of a research reactor, cooled with low pressure water, are presented. Most of the problems met by the designer and the operator are dealt with (calculations margins, cooling after shut-down). Particular cases are considered (gas release, rough walls, asymmetric cooling slabs etc.), which are not generally envisaged in works on general thermics
Broyden's method in nuclear structure calculations
Baran, Andrzej; Bulgac, Aurel; Forbes, Michael McNeil; Hagen, Gaute; Nazarewicz, Witold; Schunck, Nicolas; Stoitsov, Mario V.
2008-01-01
Broyden's method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broyden's method a tool of choice for large-scale nuclear structure calculations
Njifenjou A.
2006-11-01
Full Text Available Le cadre de ce travail est le calcul des paramètres pétrophysiques effectifs d'un milieu poreux hétérogène pour le simulateur de réservoirs pétroliers. Après le choix d'un modèle d'écoulement dans un milieu poreux hétérogène comportant une microstructure périodique nous rappelons brièvement les grandes étapes de la méthode des échelles multiples pour l'homogénéisation de ce modèle. Cela nous conduit à la formule classique d'homogénéisation de la perméabilité absolue. Par la suite nous présentons une démarche originale permettant de passer de cette formule classique à une formule plus simple (d'un point de vue numérique s'exprimant en termes d'énergie dissipée par les forces de viscosité locales et caractérisant le milieu hétérogène périodique considéré. Nous démontrons ensuite, sous certaines hypothèses, l'égalité entre les énergies dissipées par les forces de viscosité associées respectivement à l'écoulement local et à l'écoulement macroscopique. Nous terminons par la présentation de quelques résultats numériques concernant des modèles d'écoulement diphasique incompressible. This project falls within the general framework of computing the effective petrophysical parameters characterizing a heterogeneous medium when it is considered from a macroscopic viewpoint as opposed to a description on the local scale. The concept of scale inevitably appears as soon as the concept of heterogeneity is broached. Depending on the applications planned, it is easy to define different observation scales of natural porous media. The local scale is a small in which the porous medium may be considered to be continuous, and in which the hydrodynamic equations are written for the fluid phase. At this scale, the elements making up the medium are sufficiently small porous volumes (compared to the dimensions of medium to be considered as points (in the mathematical sense, but large enough to encompass pores with
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...
Numerical Estimation in Preschoolers
Berteletti, Ilaria; Lucangeli, Daniela; Piazza, Manuela; Dehaene, Stanislas; Zorzi, Marco
2010-01-01
Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School-age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear…
Sollogoub, Pierre
2001-01-01
Numerical analyses are needed in different steps of the overall design process. Complex models or non-linear reactor core behaviour are important for qualification and/or comparison of results obtained. Adequate models and test should be defined. Fuel assembly, fuel row, and the complete core should be tested for seismic effects causing LOCA and flow-induced vibrations (FIV)
Development of numerical concepts
Sabine Peucker
2013-06-01
Full Text Available The development of numerical concepts is described from infancy to preschool age. Infants a few days old exhibit an early sensitivity for numerosities. In the course of development, nonverbal mental models allow for the exact representation of small quantities as well as changes in these quantities. Subitising, as the accurate recognition of small numerosities (without counting, plays an important role. It can be assumed that numerical concepts and procedures start with insights about small numerosities. Protoquantitative schemata comprise fundamental knowledge about quantities. One-to-one-correspondence connects elements and numbers, and, for this reason, both quantitative and numerical knowledge. If children understand that they can determine the numerosity of a collection of elements by enumerating the elements, they have acquired the concept of cardinality. Protoquantitative knowledge becomes quantitative if it can be applied to numerosities and sequential numbers. The concepts of cardinality and part-part-whole are key to numerical development. Developmentally appropriate learning and teaching should focus on cardinality and part-part-whole concepts.
Isaacson, Eugene
1994-01-01
This excellent text for advanced undergraduates and graduate students covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, and other topics. It offers a careful analysis and stresses techniques for developing new methods, plus many examples and problems. 1966 edition.
Heterogeneous Calculation of {epsilon}
Jonsson, Alf
1961-02-15
A heterogeneous method of calculating the fast fission factor given by Naudet has been applied to the Carlvik - Pershagen definition of {epsilon}. An exact calculation of the collision probabilities is included in the programme developed for the Ferranti - Mercury computer.
Heterogeneous Calculation of ε
Jonsson, Alf
1961-02-01
A heterogeneous method of calculating the fast fission factor given by Naudet has been applied to the Carlvik - Pershagen definition of ε. An exact calculation of the collision probabilities is included in the programme developed for the Ferranti - Mercury computer
Numerical Analysis of Dusty-Gas Flows
Saito, T.
2002-02-01
This paper presents the development of a numerical code for simulating unsteady dusty-gas flows including shock and rarefaction waves. The numerical results obtained for a shock tube problem are used for validating the accuracy and performance of the code. The code is then extended for simulating two-dimensional problems. Since the interactions between the gas and particle phases are calculated with the operator splitting technique, we can choose numerical schemes independently for the different phases. A semi-analytical method is developed for the dust phase, while the TVD scheme of Harten and Yee is chosen for the gas phase. Throughout this study, computations are carried out on SGI Origin2000, a parallel computer with multiple of RISC based processors. The efficient use of the parallel computer system is an important issue and the code implementation on Origin2000 is also described. Flow profiles of both the gas and solid particles behind the steady shock wave are calculated by integrating the steady conservation equations. The good agreement between the pseudo-stationary solutions and those from the current numerical code validates the numerical approach and the actual coding. The pseudo-stationary shock profiles can also be used as initial conditions of unsteady multidimensional simulations.
Application of laser speckle to randomized numerical linear algebra
Valley, George C.; Shaw, Thomas J.; Stapleton, Andrew D.; Scofield, Adam C.; Sefler, George A.; Johannson, Leif
2018-02-01
We propose and simulate integrated optical devices for accelerating numerical linear algebra (NLA) calculations. Data is modulated on chirped optical pulses and these propagate through a multimode waveguide where speckle provides the random projections needed for NLA dimensionality reduction.
Numerical determination of transmission probabilities in cylindrical geometry
Queiroz Bogado Leite, S. de.
1989-11-01
Efficient methods for numerical calculation of transmission probabilities in cylindrical geometry are presented. Relative errors of the order of 10 -5 or smaller are obtained using analytical solutions and low order quadrature integration schemes. (author) [pt
On the atomic shell structure calculation (1)
Choe Sun Chol
1986-01-01
We have considered the problem of atomic shell structure calculation using operator technique. We introduce reduced matrix elements of annihilation operators according to eg. (4). The normalized basis function is denoted as || ...>. The reduced matrix elements of the pair annihilation operators are expressed throw one-electron matrix elements. Some numerical results are represented and the problem of sign assignment is discussed. (author)
Staggering towards a calculation of weak amplitudes
Sharpe, S.R.
1988-09-01
An explanation is given of the methods required to calculate hadronic matrix elements of the weak Hamiltonians using lattice QCD with staggered fermions. New results are presented for the 1-loop perturbative mixing of the weak interaction operators. New numerical techniques designed for staggered fermions are described. A preliminary result for the kaon B parameter is presented. 24 refs., 3 figs.
Cognitive Reflection Versus Calculation in Decision Making
Aleksandr eSinayev
2015-05-01
Full Text Available Scores on the three-item Cognitive Reflection Test (CRT have been linked with dual-system theory and normative decision making (Frederick, 2005. In particular, the CRT is thought to measure monitoring of System 1 intuitions such that, if cognitive reflection is high enough, intuitive errors will be detected and the problem will be solved. However, CRT items also require numeric ability to be answered correctly and it is unclear how much numeric ability vs. cognitive reflection contributes to better decision making. In two studies, CRT responses were used to calculate Cognitive Reflection and numeric ability; a numeracy scale was also administered. Numeric ability, measured on the CRT or the numeracy scale, accounted for the CRT’s ability to predict more normative decisions (a subscale of decision-making competence, incentivized measures of impatient and risk-averse choice, and self-reported financial outcomes; Cognitive Reflection contributed no independent predictive power. Results were similar whether the two abilities were modeled (Study 1 or calculated using proportions (Studies 1 and 2. These findings demonstrate numeric ability as a robust predictor of superior decision making across multiple tasks and outcomes. They also indicate that correlations of decision performance with the CRT are insufficient evidence to implicate overriding intuitions in the decision-making biases and outcomes we examined. Numeric ability appears to be the key mechanism instead.
Cognitive reflection vs. calculation in decision making.
Sinayev, Aleksandr; Peters, Ellen
2015-01-01
Scores on the three-item Cognitive Reflection Test (CRT) have been linked with dual-system theory and normative decision making (Frederick, 2005). In particular, the CRT is thought to measure monitoring of System 1 intuitions such that, if cognitive reflection is high enough, intuitive errors will be detected and the problem will be solved. However, CRT items also require numeric ability to be answered correctly and it is unclear how much numeric ability vs. cognitive reflection contributes to better decision making. In two studies, CRT responses were used to calculate Cognitive Reflection and numeric ability; a numeracy scale was also administered. Numeric ability, measured on the CRT or the numeracy scale, accounted for the CRT's ability to predict more normative decisions (a subscale of decision-making competence, incentivized measures of impatient and risk-averse choice, and self-reported financial outcomes); Cognitive Reflection contributed no independent predictive power. Results were similar whether the two abilities were modeled (Study 1) or calculated using proportions (Studies 1 and 2). These findings demonstrate numeric ability as a robust predictor of superior decision making across multiple tasks and outcomes. They also indicate that correlations of decision performance with the CRT are insufficient evidence to implicate overriding intuitions in the decision-making biases and outcomes we examined. Numeric ability appears to be the key mechanism instead.
Hamming generalized corrector for reactivity calculation
Suescun-Diaz, Daniel; Ibarguen-Gonzalez, Maria C.; Figueroa-Jimenez, Jorge H.
2014-01-01
This work presents the Hamming method generalized corrector for numerically resolving the differential equation of delayed neutron precursor concentration from the point kinetics equations for reactivity calculation, without using the nuclear power history or the Laplace transform. A study was carried out of several correctors with their respective modifiers with different time step calculations, to offer stability and greater precision. Better results are obtained for some correctors than with other existing methods. Reactivity can be calculated with precision of the order h 5 , where h is the time step. (orig.)
Borcard, Daniel; Legendre, Pierre
2018-01-01
This new edition of Numerical Ecology with R guides readers through an applied exploration of the major methods of multivariate data analysis, as seen through the eyes of three ecologists. It provides a bridge between a textbook of numerical ecology and the implementation of this discipline in the R language. The book begins by examining some exploratory approaches. It proceeds logically with the construction of the key building blocks of most methods, i.e. association measures and matrices, and then submits example data to three families of approaches: clustering, ordination and canonical ordination. The last two chapters make use of these methods to explore important and contemporary issues in ecology: the analysis of spatial structures and of community diversity. The aims of methods thus range from descriptive to explanatory and predictive and encompass a wide variety of approaches that should provide readers with an extensive toolbox that can address a wide palette of questions arising in contemporary mul...
Numerical simulation in astrophysics
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.)
NUMERICAL AND ANALYTIC METHODS OF ESTIMATION BRIDGES’ CONSTRUCTIONS
Y. Y. Luchko
2010-03-01
Full Text Available In this article the numerical and analytical methods of calculation of the stressed-and-strained state of bridge constructions are considered. The task on increasing of reliability and accuracy of the numerical method and its solution by means of calculations in two bases are formulated. The analytical solution of the differential equation of deformation of a ferro-concrete plate under the action of local loads is also obtained.
NUMERICAL DETERMINATION OF HORIZONTAL SETTLERS PERFORMANCE
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
Hybrid undulator numerical optimization
Hairetdinov, A.H. [Kurchatov Institute, Moscow (Russian Federation); Zukov, A.A. [Solid State Physics Institute, Chernogolovka (Russian Federation)
1995-12-31
3D properties of the hybrid undulator scheme arc studied numerically using PANDIRA code. It is shown that there exist two well defined sets of undulator parameters which provide either maximum on-axis field amplitude or minimal higher harmonics amplitude of the basic undulator field. Thus the alternative between higher field amplitude or pure sinusoidal field exists. The behavior of the undulator field amplitude and harmonics structure for a large set of (undulator gap)/(undulator wavelength) values is demonstrated.
Comments on numerical simulations
Sato, T.
1984-01-01
The author comments on a couple of things about numerical simulation. One is just about the philosophical discussion that is, spontaneous or driven. The other thing is the numerical or technical one. Frankly, the author didn't want to touch on the technical matter because this should be a common sense one for those who are working at numerical simulation. But since many people take numerical simulation results at their face value, he would like to remind you of the reality hidden behind them. First, he would point out that the meaning of ''driven'' in driven reconnection is different from that defined by Schindler or Akasofu. The author's definition is closer to Axford's definition. In the spontaneous case, for some unpredicted reason an excess energy of the system is suddenly released at a certain point. However, one does not answer how such an unstable state far beyond a stable limit is realized in the magnetotail. In the driven case, there is a definite energy buildup phase starting from a stable state; namely, energy in the black box increases from a stable level subject to an external source. When the state has reached a certain position, the energy is released suddenly. The difference between driven and spontaneous is whether the cause (plasma flow) to trigger reconnection is specified or reconnection is triggered unpredictably. Another difference is that in driven reconnection the reconnection rate is dependent on the speed of the external plasma flow, but in spontaneous reconnection the rate is dependent on the internal condition such as the resistivity
Numerical simulation of plasmas
Dnestrovskii, Y.N.; Kostomarov, D.P.
1986-01-01
This book contains a modern consistent and systematic presentation of numerical computer simulation of plasmas in controlled thermonuclear fusion. The authors focus on the Soviet research in mathematical modelling of Tokamak plasmas, and present kinetic hydrodynamic and transport models with special emphasis on the more recent hybrid models. Compared with the first edition (in Russian) this book has been greatly revised and updated. (orig./WL)
Numerical analysis II essentials
REA, The Editors of; Staff of Research Education Association
1989-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Numerical Analysis II covers simultaneous linear systems and matrix methods, differential equations, Fourier transformations, partial differential equations, and Monte Carlo methods.
Handbook of numerical analysis
Ciarlet, Philippe G
Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas an
Numerical study of fluid motion in bioreactor with two mixers
Zheleva, I., E-mail: izheleva@uni-ruse.bg [Department of Heat Technology, Hydraulics and Ecology, Angel Kanchev University of Rousse, 8 Studentska str., 7017 Rousse (Bulgaria); Lecheva, A., E-mail: alecheva@uni-ruse.bg [Department of Mathematics, Angel Kanchev University of Rousse, 8 Studentska str., 7017 Rousse (Bulgaria)
2015-10-28
Numerical study of hydrodynamic laminar behavior of a viscous fluid in bioreactor with multiple mixers is provided in the present paper. The reactor is equipped with two disk impellers. The fluid motion is studied in stream function-vorticity formulation. The calculations are made by a computer program, written in MATLAB. The fluid structure is described and numerical results are graphically presented and commented.
Nagao, Yoshiharu [Japan Atomic Energy Research Inst., Oarai, Ibaraki (Japan). Oarai Research Establishment
1998-03-01
In material testing reactors like the JMTR (Japan Material Testing Reactor) of 50 MW in Japan Atomic Energy Research Institute, the neutron flux and neutron energy spectra of irradiated samples show complex distributions. It is necessary to assess the neutron flux and neutron energy spectra of an irradiation field by carrying out the nuclear calculation of the core for every operation cycle. In order to advance core calculation, in the JMTR, the application of MCNP to the assessment of core reactivity and neutron flux and spectra has been investigated. In this study, in order to reduce the time for calculation and variance, the comparison of the results of the calculations by the use of K code and fixed source and the use of Weight Window were investigated. As to the calculation method, the modeling of the total JMTR core, the conditions for calculation and the adopted variance reduction technique are explained. The results of calculation are shown. Significant difference was not observed in the results of neutron flux calculations according to the difference of the modeling of fuel region in the calculations by K code and fixed source. The method of assessing the results of neutron flux calculation is described. (K.I.)
Hybrid reduced order modeling for assembly calculations
Bang, Youngsuk; Abdel-Khalik, Hany S.; Jessee, Matthew A.; Mertyurek, Ugur
2015-01-01
Highlights: • Reducing computational cost in engineering calculations. • Reduced order modeling algorithm for multi-physics problem like assembly calculation. • Non-intrusive algorithm with random sampling. • Pattern recognition in the components with high sensitive and large variation. - Abstract: While the accuracy of assembly calculations has considerably improved due to the increase in computer power enabling more refined description of the phase space and use of more sophisticated numerical algorithms, the computational cost continues to increase which limits the full utilization of their effectiveness for routine engineering analysis. Reduced order modeling is a mathematical vehicle that scales down the dimensionality of large-scale numerical problems to enable their repeated executions on small computing environment, often available to end users. This is done by capturing the most dominant underlying relationships between the model's inputs and outputs. Previous works demonstrated the use of the reduced order modeling for a single physics code, such as a radiation transport calculation. This manuscript extends those works to coupled code systems as currently employed in assembly calculations. Numerical tests are conducted using realistic SCALE assembly models with resonance self-shielding, neutron transport, and nuclides transmutation/depletion models representing the components of the coupled code system.
Hybrid reduced order modeling for assembly calculations
Bang, Youngsuk, E-mail: ysbang00@fnctech.com [FNC Technology, Co. Ltd., Yongin-si (Korea, Republic of); Abdel-Khalik, Hany S., E-mail: abdelkhalik@purdue.edu [Purdue University, West Lafayette, IN (United States); Jessee, Matthew A., E-mail: jesseema@ornl.gov [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Mertyurek, Ugur, E-mail: mertyurek@ornl.gov [Oak Ridge National Laboratory, Oak Ridge, TN (United States)
2015-12-15
Highlights: • Reducing computational cost in engineering calculations. • Reduced order modeling algorithm for multi-physics problem like assembly calculation. • Non-intrusive algorithm with random sampling. • Pattern recognition in the components with high sensitive and large variation. - Abstract: While the accuracy of assembly calculations has considerably improved due to the increase in computer power enabling more refined description of the phase space and use of more sophisticated numerical algorithms, the computational cost continues to increase which limits the full utilization of their effectiveness for routine engineering analysis. Reduced order modeling is a mathematical vehicle that scales down the dimensionality of large-scale numerical problems to enable their repeated executions on small computing environment, often available to end users. This is done by capturing the most dominant underlying relationships between the model's inputs and outputs. Previous works demonstrated the use of the reduced order modeling for a single physics code, such as a radiation transport calculation. This manuscript extends those works to coupled code systems as currently employed in assembly calculations. Numerical tests are conducted using realistic SCALE assembly models with resonance self-shielding, neutron transport, and nuclides transmutation/depletion models representing the components of the coupled code system.
Efficient sound barrier calculations with the BEM
Juhl, Peter Møller; Cutanda Henriquez, Vicente
2018-01-01
The Boundary Element Method has been used for calculating the effect of introducing sound barriers for some decades. The method has also been used for optimizing the shape of the barrier and in some cases the effects of introducing sound absorption. However, numerical calculations are still quite...... time consuming and inconvenient to use, which is limiting their use for many practical problems. Moreover, measurements are mostly taken in one-third or full octave bands opposed to the numerical computations at specific frequencies, which then has to be conducted using a fine density in frequencies....... This paper addresses some of the challenges and possible solutions for developing BEM into a more efficient tool for sound barrier calculations....
Extraction of gravitational waves in numerical relativity.
Bishop, Nigel T; Rezzolla, Luciano
2016-01-01
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.
The numerical solution of boundary value problems over an infinite domain
Shepherd, M.; Skinner, R.
1976-01-01
A method is presented for the numerical solution of boundary value problems over infinite domains. An example that illustrates also the strength and accuracy of a numerical procedure for calculating Green's functions is described in detail
Electronics Environmental Benefits Calculator
U.S. Environmental Protection Agency — The Electronics Environmental Benefits Calculator (EEBC) was developed to assist organizations in estimating the environmental benefits of greening their purchase,...
Electrical installation calculations basic
Kitcher, Christopher
2013-01-01
All the essential calculations required for basic electrical installation workThe Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike. The book provides a step-by-step guide to the successful application of electrical installation calculations required in day-to-day electrical engineering practice. A step-by-step guide to everyday calculations used on the job An essential aid to the City & Guilds certificates at Levels 2 and 3Fo
Electrical installation calculations advanced
Kitcher, Christopher
2013-01-01
All the essential calculations required for advanced electrical installation workThe Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike. The book provides a step-by-step guide to the successful application of electrical installation calculations required in day-to-day electrical engineering practiceA step-by-step guide to everyday calculations used on the job An essential aid to the City & Guilds certificates at Levels 2 and 3For apprentices and electrical installatio
Radar Signature Calculation Facility
Federal Laboratory Consortium — FUNCTION: The calculation, analysis, and visualization of the spatially extended radar signatures of complex objects such as ships in a sea multipath environment and...
Waste Package Lifting Calculation
H. Marr
2000-01-01
The objective of this calculation is to evaluate the structural response of the waste package during the horizontal and vertical lifting operations in order to support the waste package lifting feature design. The scope of this calculation includes the evaluation of the 21 PWR UCF (pressurized water reactor uncanistered fuel) waste package, naval waste package, 5 DHLW/DOE SNF (defense high-level waste/Department of Energy spent nuclear fuel)--short waste package, and 44 BWR (boiling water reactor) UCF waste package. Procedure AP-3.12Q, Revision 0, ICN 0, calculations, is used to develop and document this calculation
Caremoli, C.; Erhard, P.
1996-01-01
Computerized simulation uses calculation codes whose validation is reliable. Reactor simulators should take greater advantage of latest computer technology impact, in particular in the field of parallel processing. Instead of creating more global simulation codes whose validation might be a problem, connecting several existing codes should be a promising solution. (D.L.). 3 figs
Numerical properties of staggered overlap fermions
de Forcrand, Philippe; Panero, Marco
2010-01-01
We report the results of a numerical study of staggered overlap fermions, following the construction of Adams which reduces the number of tastes from 4 to 2 without fine-tuning. We study the sensitivity of the operator to the topology of the gauge field, its locality and its robustness to fluctuations of the gauge field. We make a first estimate of the computing cost of a quark propagator calculation, and compare with Neuberger's overlap.
Numerical Simulation of the Kinetic Critical Nucleus
Sanada, Masaaki; Nishioka, Kazumi; Okada, Masahumi; Maksimov, Igor, L.
1997-01-01
Our main interest is to see whether the number density indicates a peak at the kinetically stable critical nucleus due to its kinetical stability. We have numerically calculated the time evolution of the number densities of clusters in the case of water vapor nucleation. We employ the condition in which the difference between the size of the thermodynamic crtitical nucleus and that of the kinetic one is appreciable. The results show that the peak does not appear in the number densities of clu...
Henderson, Michael
1997-08-01
The Numerical Analysis Objects project (NAO) is a project in the Mathematics Department of IBM's TJ Watson Research Center. While there are plenty of numerical tools available today, it is not an easy task to combine them into a custom application. NAO is directed at the dual problems of building applications from a set of tools, and creating those tools. There are several "reuse" projects, which focus on the problems of identifying and cataloging tools. NAO is directed at the specific context of scientific computing. Because the type of tools is restricted, problems such as tools with incompatible data structures for input and output, and dissimilar interfaces to tools which solve similar problems can be addressed. The approach we've taken is to define interfaces to those objects used in numerical analysis, such as geometries, functions and operators, and to start collecting (and building) a set of tools which use these interfaces. We have written a class library (a set of abstract classes and implementations) in C++ which demonstrates the approach. Besides the classes, the class library includes "stub" routines which allow the library to be used from C or Fortran, and an interface to a Visual Programming Language. The library has been used to build a simulator for petroleum reservoirs, using a set of tools for discretizing nonlinear differential equations that we have written, and includes "wrapped" versions of packages from the Netlib repository. Documentation can be found on the Web at "http://www.research.ibm.com/nao". I will describe the objects and their interfaces, and give examples ranging from mesh generation to solving differential equations.
Numerical differential protection
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 modelling of fuel sprays
Bergstroem, C.
1999-06-01
The way the fuel is introduced into the combustion chamber is one of the most important parameters for the power output and the generation of emissions in the combustion of liquid fuels. The interaction between the turbulent gas flow field and the liquid fuel droplets, the vaporisation of them and the mixing of the gaseous fuel with the ambient air that are vital parameters in the combustion process. The use of numerical calculations is an important tool to better understand these complex interacting phenomena. This thesis reports on the numerical modelling of fuel sprays in non-reacting cases using an own developed spray module. The spray module uses the stochastic parcel method to represent the spray. The module was made in such manner that it could by coupled with different gas flow solver. Results obtained from four different gas flow solvers are presented in the thesis, including the use of two different kinds of turbulence models. In the first part the spray module is coupled with a k-{eta} based 2-D cylindrical gas flow solver. A thorough sensitivity analysis was performed on the spray and gas flow solver parameters, such as grid size dependence and sensitivity to initial values of k-{eta}. The results of the spray module were also compared to results from other spray codes, e.g. the well known KIVA code. In the second part of this thesis the spray was injected into a turbulent and fully developed crossflow studied. The spray module was attached to a LES (Large Eddy Simulation) based flow solvers enabling the study of the complex structures and time dependent phenomena involved in spray in crossflows. It was found that the spray performs an oscillatory motion and that the Strouhal number in the wake was about 0.1. Different spray breakup models were evaluated by comparing with experimental results 66 refs, 56 figs
Numerical and experimental study of a hydrodynamic cavitation tube
Hu, H.; Finch, J. A.; Zhou, Z.; Xu, Z.
1998-08-01
A numerical analysis of hydrodynamics in a cavitation tube used for activating fine particle flotation is described. Using numerical procedures developed for solving the turbulent k-ɛ model with boundary fitted coordinates, the stream function, vorticity, velocity, and pressure distributions in a cavitation tube were calculated. The calculated pressure distribution was found to be in excellent agreement with experimental results. The requirement of a pressure drop below approximately 10 m water for cavitation to occur was observed experimentally and confirmed by the model. The use of the numerical procedures for cavitation tube design is discussed briefly.
Trkov, A.; Ravnik, M.; Zeleznik, N.
1992-01-01
Functional description of the programme package Cord-2 for PWR core design calculations is presented. Programme package is briefly described. Use of the package and calculational procedures for typical core design problems are treated. Comparison of main results with experimental values is presented as part of the verification process. (author) [sl
Uneconomical top calculation method
De Noord, M.; Vanm Sambeek, E.J.W.
2003-08-01
The methodology used to calculate the financial gap of renewable electricity sources and technologies is described. This methodology is used for calculating the production subsidy levels (MEP subsidies) for new renewable electricity projects in 2004 and 2005 in the Netherlands [nl
Confidence in Numerical Simulations
Hemez, Francois M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-02-23
This PowerPoint presentation offers a high-level discussion of uncertainty, confidence and credibility in scientific Modeling and Simulation (M&S). It begins by briefly evoking M&S trends in computational physics and engineering. The first thrust of the discussion is to emphasize that the role of M&S in decision-making is either to support reasoning by similarity or to “forecast,” that is, make predictions about the future or extrapolate to settings or environments that cannot be tested experimentally. The second thrust is to explain that M&S-aided decision-making is an exercise in uncertainty management. The three broad classes of uncertainty in computational physics and engineering are variability and randomness, numerical uncertainty and model-form uncertainty. The last part of the discussion addresses how scientists “think.” This thought process parallels the scientific method where by a hypothesis is formulated, often accompanied by simplifying assumptions, then, physical experiments and numerical simulations are performed to confirm or reject the hypothesis. “Confidence” derives, not just from the levels of training and experience of analysts, but also from the rigor with which these assessments are performed, documented and peer-reviewed.
Confidence in Numerical Simulations
Hemez, Francois M.
2015-01-01
This PowerPoint presentation offers a high-level discussion of uncertainty, confidence and credibility in scientific Modeling and Simulation (M&S). It begins by briefly evoking M&S trends in computational physics and engineering. The first thrust of the discussion is to emphasize that the role of M&S in decision-making is either to support reasoning by similarity or to ''forecast,'' that is, make predictions about the future or extrapolate to settings or environments that cannot be tested experimentally. The second thrust is to explain that M&S-aided decision-making is an exercise in uncertainty management. The three broad classes of uncertainty in computational physics and engineering are variability and randomness, numerical uncertainty and model-form uncertainty. The last part of the discussion addresses how scientists ''think.'' This thought process parallels the scientific method where by a hypothesis is formulated, often accompanied by simplifying assumptions, then, physical experiments and numerical simulations are performed to confirm or reject the hypothesis. ''Confidence'' derives, not just from the levels of training and experience of analysts, but also from the rigor with which these assessments are performed, documented and peer-reviewed.
How to Deal with FFT Sampling Influences on ADEV Calculations
Chang, Po-Cheng
2007-01-01
...) values while the numerical integration is used for the time and frequency (T&F) conversion. These ADEV errors occur because parts of the FFT sampling have no contributions to the ADEV calculation...
The accuracy of heavy ion optical model calculations
Kozik, T.
1980-01-01
There is investigated in detail the sources and magnitude of numerical errors in heavy ion optical model calculations. It is shown on example of 20 Ne + 24 Mg scattering at Esub(LAB)=100 MeV. (author)
Bivariational calculations for radiation transfer in an inhomogeneous participating media
El Wakil, S.A.; Machali, H.M.; Haggag, M.H.; Attia, M.T.
1986-07-01
Equations for radiation transfer are obtained for dispersive media with space dependent albedo. Bivariational bound principle is used to calculate the reflection and transmission coefficients for such media. Numerical results are given and compared. (author)
Peters, C.; Kampe, F. (Principal Investigator)
1980-01-01
The mathematical description and implementation of the statistical estimation procedure known as the Houston integrated spatial/spectral estimator (HISSE) is discussed. HISSE is based on a normal mixture model and is designed to take advantage of spectral and spatial information of LANDSAT data pixels, utilizing the initial classification and clustering information provided by the AMOEBA algorithm. The HISSE calculates parametric estimates of class proportions which reduce the error inherent in estimates derived from typical classify and count procedures common to nonparametric clustering algorithms. It also singles out spatial groupings of pixels which are most suitable for labeling classes. These calculations are designed to aid the analyst/interpreter in labeling patches with a crop class label. Finally, HISSE's initial performance on an actual LANDSAT agricultural ground truth data set is reported.
Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling
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.
Benchmark calculations of thermal reaction rates. I - Quantal scattering theory
Chatfield, David C.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
The thermal rate coefficient for the prototype reaction H + H2 yields H2 + H with zero total angular momentum is calculated by summing, averaging, and numerically integrating state-to-state reaction probabilities calculated by time-independent quantum-mechanical scattering theory. The results are very carefully converged with respect to all numerical parameters in order to provide high-precision benchmark results for confirming the accuracy of new methods and testing their efficiency.
XLOOPS - a package calculating one- and two-loop diagrams
Bruecher, L.
1997-01-01
A program package for calculating massive one- and two-loop diagrams is introduced. It consists of five parts: - a graphical user interface, - routines for generating diagrams from particle input, - procedures for calculating one-loop integrals both analytically and numerically, - routines for massive two-loop integrals, - programs for numerical integration of two-loop diagrams. Here the graphical user interface and the text interface to Maple are presented. (orig.)
Appropriateness of one-dimensional calculations for repository analysis
Eaton, R.R.
1994-01-01
This paper brings into focus the results of numerous studies that have addressed issues associated with the validity of assumptions which are used to justify reducing the dimensionality of numerical calculations of water flow through Yucca Mountain, NV. It is shown that in many cases, one-dimensional modeling is more rigorous than previously assumed
Ionization efficiency calculations for cavity thermoionization ion source
Turek, M.; Pyszniak, K.; Drozdziel, A.; Sielanko, J.; Maczka, D.; Yuskevich, Yu.V.; Vaganov, Yu.A.
2009-01-01
The numerical model of ionization in a thermoionization ion source is presented. The review of ion source ionization efficiency calculation results for various kinds of extraction field is given. The dependence of ionization efficiency on working parameters like ionizer length and extraction voltage is discussed. Numerical simulations results are compared to theoretical predictions obtained from a simplified ionization model
The appropriateness of one-dimensional Yucca Mountain hydrologic calculations
Eaton, R.R.
1993-07-01
This report brings into focus the results of numerous studies that have addressed issues associated with the validity of assumptions which are used to justify reducing the dimensionality of numerical calculations of water flow through Yucca Mountain, NV. it is shown that, in many cases, one-dimensional modeling is more rigorous than previously assumed
Govoni, Marco; Argonne National Lab., Argonne, IL; Galli, Giulia; Argonne National Lab., Argonne, IL
2015-01-01
We present GW calculations of molecules, ordered and disordered solids and interfaces, which employ an efficient contour deformation technique for frequency integration and do not require the explicit evaluation of virtual electronic states nor the inversion of dielectric matrices. We also present a parallel implementation of the algorithm, which takes advantage of separable expressions of both the single particle Green's function and the screened Coulomb interaction. The method can be used starting from density functional theory calculations performed with semilocal or hybrid functionals. The newly developed technique was applied to GW calculations of systems of unprecedented size, including water/semiconductor interfaces with thousands of electrons
Radioactive cloud dose calculations
Healy, J.W.
1984-01-01
Radiological dosage principles, as well as methods for calculating external and internal dose rates, following dispersion and deposition of radioactive materials in the atmosphere are described. Emphasis has been placed on analytical solutions that are appropriate for hand calculations. In addition, the methods for calculating dose rates from ingestion are discussed. A brief description of several computer programs are included for information on radionuclides. There has been no attempt to be comprehensive, and only a sampling of programs has been selected to illustrate the variety available
Essential numerical computer methods
Johnson, Michael L
2010-01-01
The use of computers and computational methods has become ubiquitous in biological and biomedical research. During the last 2 decades most basic algorithms have not changed, but what has is the huge increase in computer speed and ease of use, along with the corresponding orders of magnitude decrease in cost. A general perception exists that the only applications of computers and computer methods in biological and biomedical research are either basic statistical analysis or the searching of DNA sequence data bases. While these are important applications they only scratch the surface of the current and potential applications of computers and computer methods in biomedical research. The various chapters within this volume include a wide variety of applications that extend far beyond this limited perception. As part of the Reliable Lab Solutions series, Essential Numerical Computer Methods brings together chapters from volumes 210, 240, 321, 383, 384, 454, and 467 of Methods in Enzymology. These chapters provide ...
Numerical relativity beyond astrophysics
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.
Testability of numerical systems
Soulas, B.
1992-01-01
In order to face up to the growing complexity of systems, the authors undertook to define a new approach for the qualification of systems. This approach is based on the concept of Testability which, supported by system modelization, validation and verification methods and tools, would allow Integrated Qualification process, applied throughout the life-span of systems. The general principles of this approach are introduced in the general case of numerical systems; in particular, this presentation points out the difference between the specification activity and the modelization and validation activity. This approach is illustrated firstly by the study of a global system and then by case of communication protocol as the software point of view. Finally MODEL which support this approach is described. MODEL tool is a commercial tool providing modelization and validation techniques based on Petri Nets with triple extension: Predicate/Transition, Timed and Stochastic Petri Nets
Numerical relativity beyond astrophysics.
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.
Calculating Optimal Inventory Size
Ruby Perez
2010-01-01
Full Text Available The purpose of the project is to find the optimal value for the Economic Order Quantity Model and then use a lean manufacturing Kanban equation to find a numeric value that will minimize the total cost and the inventory size.