Liu, Hongxu; Jiao, Xiangmin
2016-06-01
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighted least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO.
Birth of oscillation in coupled non-oscillatory Rayleigh-Duffing oscillators
Guin, A.; Dandapathak, M.; Sarkar, S.; Sarkar, B. C.
2017-01-01
We have studied the dynamics of two bilaterally-coupled non-oscillatory Rayleigh-Duffing oscillators (RDOs). With the increase of coupling factor (CF) between RDOs, birth of periodic oscillations observed. For increased values of CF, dynamics becomes chaotic through a quasi-periodicroute but for even higher CF, synchronized stable periodic oscillations in RDOs are found. Taking direct and anti-diffusive coupling cases into consideration, we derive conditions for periodic bifurcation in parameter space analytically and verified them through numerical solution of system equations. Numerical simulation is also used to predict system states in two parameter space involving CF and linear damping parameter of RDOs. It indicates non-oscillatory, periodic, quasi-periodic and chaotic zones of system dynamics. Qualitative explanation of the simulated dynamics is given using homoclinic perturbation theory. Hardware experiment is performed on analog circuits simulating RDO model and obtained results confirm the predictions regarding birth of periodic oscillation and other features of system dynamics. Experimental results examining onset of oscillations in two under-biased bi-laterally coupled X-band Gunn oscillators (which are modelled as RDOs) is presented in support of the analysis.
Third-order modified coefficient scheme based on essentially non-oscillatory scheme
Institute of Scientific and Technical Information of China (English)
LI Ming-jun; YANG Yu-yue; SHU Shi
2008-01-01
A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory (MCENO) scheme without increasing the base points during construction of the scheme.The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially non oscillatory (ENO) scheme for its essential non-oscillation,total variation bounded (TVB),etc.The new scheme improves accuracy by one order compared to the original one.The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor (RT) instability with densities 1:3 and 1:100,and solve the Lax shock-wave tube numerically.The ratio of CPU time used to implement MCENO,the third-order ENO and fifth-order weighed ENO (WENO) schemes is 0.62:1:2.19.This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.
A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws.The key idea of HWENO is to evolve both with the solution and its derivative,which allows for using Hermite interpolation in the reconstruction phase,resulting in a more compact stencil at the expense of the additional work.The main difference between this work and the formal one is the procedure to reconstruct the derivative terms.Comparing with the original HWENO schemes of Qiu and Shu,one major advantage of new HWENOschemes is its robust in computation of problem with strong shocks.Extensive numerical experiments are performed to illustrate the capability of the method.
Christlieb, Andrew J; Tang, Qi
2013-01-01
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vecto...
Christlieb, Andrew J.; Rossmanith, James A.; Tang, Qi
2014-07-01
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vector potential satisfies is solved using a version of FD-WENO developed for Hamilton-Jacobi equations. The resulting numerical method is endowed with several important properties: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as point values on the same mesh (i.e., there is no mesh staggering); (2) both the spatial and temporal orders of accuracy are fourth-order; (3) no spatial integration or multidimensional reconstructions are needed in any step; and (4) special limiters in the magnetic vector potential update are used to control unphysical oscillations in the magnetic field. Several 2D and 3D numerical examples are presented to verify the order of accuracy on smooth test problems and to show high-resolution on test problems that involve shocks.
Hallal, Camilla Z; Marques, Nise R; Silva, Sarah R D; Dieën, Jaap V; Gonçalves, Mauro
2011-01-01
Pain and dysfunction of the shoulder complex are commonly found physiotherapy practice. These musculoskeletal abnormalities are related to instability and inadequate kinematic function, that depend on the integrity of the muscle tissues. Thus, to enhance the results of exercise therapies, and prevent and attenuate pain and dynfunction, the use of oscillatory pole has been implemented in clinical practice. The purpose of this study was to analyze the electromyographic (EMG) activity of shoulder stabilizing muscles during exercises performed with an oscillatory and a non-oscillatory pole. Twelve female volunteers, aged 20.4 years±1.9, participated in this study. EMG data were collected from upper trapezius (UT), lower trapezius (LT) and middle deltoid (MD) during three different exercises with an oscillatory and a non-oscillatory pole. The EMG signals were analyzed in the time domain through the calculation of Root Mean Square (RMS). The RMS values were normalized by the peak value obtained over all trials for each muscle. Statistical analysis was performed with repeated measures ANOVA and post-hoc of Bonferroni tests. The EMG activity of UT, LT and MD muscles were significantly higher with the oscillatory pole than the non-oscillatory pole (all pmuscles between exercises. The results of the present study indicated that the oscillatory pole does require higher activation of the shoulder muscles and therefore, may be useful in the training of the shoulder complex.
Energy Technology Data Exchange (ETDEWEB)
Khouider, Boualem [University of Victoria, Mathematics and Statistics, Victoria, B.C. (Canada); Majda, Andrew J. [New York University, Department of Mathematics and Center for Atmosphere/Ocean Sciences, NY (United States); Courant Institute, New York, NY (United States)
2005-10-01
We use the non-oscillatory balanced numerical scheme developed in Part I to track the dynamics of a dry highly nonlinear barotropic/baroclinic coupled solitary wave, as introduced by Biello and Majda (2004), and of the moisture fronts of Frierson et al. (2004) in the presence of dry gravity waves, a barotropic trade wind, and the beta effect. It is demonstrated that, for the barotropic/baroclinic solitary wave, except for a little numerical dissipation, the scheme utilized here preserves total energy despite the strong interactions and exchange of energy between the baroclinic and barotropic components of the flow. After a short transient period where the numerical solution stays close to the asymptotic predictions, the flow develops small scale eddies and ultimately becomes highly turbulent. It is found here that the interaction of a dry gravity wave with a moisture front can either result in a reflection of a fast moistening front or the pure extinction of the precipitation. The barotropic trade wind stretches the precipitation patches and increases the lifetime of the moisture fronts which decay naturally by the effects of dissipation through precipitation while the Coriolis effect makes the moving precipitation patches disappear and appear at other times and places. (orig.)
Shu, Chi-Wang
1998-01-01
This project is about the development of high order, non-oscillatory type schemes for computational fluid dynamics. Algorithm analysis, implementation, and applications are performed. Collaborations with NASA scientists have been carried out to ensure that the research is relevant to NASA objectives. The combination of ENO finite difference method with spectral method in two space dimension is considered, jointly with Cai [3]. The resulting scheme behaves nicely for the two dimensional test problems with or without shocks. Jointly with Cai and Gottlieb, we have also considered one-sided filters for spectral approximations to discontinuous functions [2]. We proved theoretically the existence of filters to recover spectral accuracy up to the discontinuity. We also constructed such filters for practical calculations.
Zia, H.; Simpson, G.
2013-12-01
The interaction between flowing surface water and sediment transport has numerous important applications in Earth science, including controls on river patterns, drainage basin evolution and morphological changes induced by extreme events such as tsunamis and dam breaks. Many of these problems can be investigated with the mathematical model of the shallow water equations coupled to conservation of sediment concentration and empirical functions for bed friction, substrate erosion and deposition. However, this system of equations is highly nonlinear, requiring fast and robust numerical methods. In this study, we investigate the solution of the shallow water equations coupled to sediment transports via the Non-oscillatory Central Differencing (NOC ) method, a second order scheme based on a predictor-corrector method. The scheme is chosen for its relative stability and robustness. The NOC scheme is especially favorable in situations where the water depth approaches zero and for steady flow conditions, both of which cause problems with more naive schemes. The model is verified by comparing computed results with documented solutions. We are currently using the model to investigate coupling between flow and sediment transport in alluvial rivers.
ON DISPERSION-CONTROLLED PRINCIPLES FOR NON-OSCILLATORY SHOCK-CAPTURING SCHEMES
Institute of Scientific and Technical Information of China (English)
JIANG Zonglin
2004-01-01
The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time. It is only during the last two decades that extensive studies on the dispersion-controlled dissipative (DCD) schemes were reported. The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations. The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do. Research progresses on the dispersioncontrolled principles are reviewed in this paper, including the exploration of the role of dispersions in numerical simulations, the development of the dispersion-controlled principles, efforts devoted to high-order dispersion-controlled dissipative schemes, the extension to both the finite volume and the finite element methods, scheme verification and solution validation, and comments on several aspects of the schemes from author's viewpoint.
2015-09-16
classified documents, enter the title classification in parentheses. 5a. CONTRACT NUMBER. Enter all contract numbers as they appear in the report, e.g...security classification regulations, e.g. U, C, S, etc. If this form contains classified information, stamp classification level on the top and bottom...a1 and a2 for the low- and high-order finite elements, spectral elements, isogeometric elements and the linear finite elements with reduced
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme(LU-SGS) is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference (WNND) scheme. The turbulence model adopts q-( low-Reynolds-number model. The frequency spectrums of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency spectrums of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.
Directory of Open Access Journals (Sweden)
M. Boumaza
2015-07-01
Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.
On the Linear Stability of the Fifth-Order WENO Discretization
Motamed, Mohammad
2010-10-03
We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.
2014-08-04
trigonometric functions of large arguments. 11. Conclusions We have shown that the solutions of a large class of second order differential equations can be...nonoscillatory phase functions . In addition, we describe numerical experiments which illustrate com- putational implications of this fact. For example, many...special functions of interest — such as the Bessel functions Jν and Yν — can be evaluated accurately using a number of operations which is Op1q in
Numerical methods for systems of conservation laws of mixed type using flux splitting
Shu, Chi-Wang
1990-01-01
The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.
Numerical simulations of a filament in a flowing soap film
Farnell, D. J. J.; David, T.; Barton, D. C.
2004-01-01
Experiments concerning the properties of soap films have recently been carried out and these systems have been proposed as experimental versions of theoretical two-dimensional liquids. A silk filament introduced into a flowing soap film, was seen to demonstrate various stable modes, and these were, namely, a mode in which the filament oscillates and one in which the filament is stationary and aligns with the flow of the liquid. The system could be forced from the oscillatory mode into the non- oscillatory mode by varying the length of the filament. In this article we use numerical and computational techniques in order to simulate the strongly coupled behaviour of the filament and the fluid. Preliminary results are presented for the specific case in which the filament is seen to oscillate continuously for the duration of our simulation. We also find that the filament oscillations are strongly suppressed when we reduce the effective length of the filament. We believe that these results are reminiscent of the different oscillatory and non-oscillatory modes observed in experiment. The numerical solutions show that, in contrast to experiment, vortices are created at the leading edge of the filament and are preferentially grown in the curvature of the filament and are eventually released from the trailing edge of the filament. In a similar manner to oscillating hydrofoils, it seems that the oscillating filaments are in a minimal energy state, extracting sufficient energy from the fluid to oscillate. In comparing numerical and experimental results it is possible that the soap film does have an effect on the fluid flow especially in the boundary layer where surface tension forces are large.
Shershnev, Anton A.; Kudryavtsev, Alexey N.; Kashkovsky, Alexander V.; Khotyanovsky, Dmitry V.
2016-10-01
The present paper describes HyCFS code, developed for numerical simulation of compressible high-speed flows on hybrid CPU/GPU (Central Processing Unit / Graphical Processing Unit) computational clusters on the basis of full unsteady Navier-Stokes equations, using modern shock capturing high-order TVD (Total Variation Diminishing) and WENO (Weighted Essentially Non-Oscillatory) schemes on general curvilinear structured grids. We discuss the specific features of hybrid architecture and details of program implementation and present the results of code verification.
Directory of Open Access Journals (Sweden)
Camilla Z. Hallal
2011-04-01
Full Text Available BACKGROUND: Pain and dysfunction of the shoulder complex are commonly found physiotherapy practice. These musculoskeletal abnormalities are related to instability and inadequate kinematic function, that depend on the integrity of the muscle tissues. Thus, to enhance the results of exercise therapies, and prevent and attenuate pain and dynfunction, the use of oscillatory pole has been implemented in clinical practice. OBJECTIVES: The purpose of this study was to analyze the electromyographic (EMG activity of shoulder stabilizing muscles during exercises performed with an oscillatory and a non-oscillatory pole. METHODS: Twelve female volunteers, aged 20.4 years±1.9, participated in this study. EMG data were collected from upper trapezius (UT, lower trapezius (LT and middle deltoid (MD during three different exercises with an oscillatory and a non-oscillatory pole. The EMG signals were analyzed in the time domain through the calculation of Root Mean Square (RMS. The RMS values were normalized by the peak value obtained over all trials for each muscle. Statistical analysis was performed with repeated measures ANOVA and post-hoc of Bonferroni tests. RESULTS: The EMG activity of UT, LT and MD muscles were significantly higher with the oscillatory pole than the non-oscillatory pole (all pCONTEXTUALIZAÇÃO: A dor e a disfunção no complexo articular do ombro é comumente encontrada na prática fisioterapêutica. Essas anormalidades musculoesqueléticas estão relacionadas à instabilidade e inadequado funcionamento cinemático, que dependem da integridade dos tecidos musculares. Assim, no sentido de prevenir e reabilitar esses sintomas, o uso da haste oscilatória vem sendo implantado para melhorar os resultados de técnicas cinesioterapêuticas. OBJETIVOS: Analisar a atividade eletromiográfica (EMG dos músculos que estabilizam a articulação do ombro durante a realização de exercícios com haste oscilatória e haste não-oscilatória. M
Development and Comparison of Numerical Fluxes for LWDG Methods
Institute of Scientific and Technical Information of China (English)
Jianxian Qiu
2008-01-01
The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax-Wendroff time discretization procedure is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure (LWDG) based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedrichs flux, Godunov flux, the Engquist-Osher flux etc. And the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these differ-ent numerical fluxes for convection terms with the objective of obtaining better perfor-mance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, ac-curacy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.
Mathematical modeling and numerical simulation of two-phase flow problems at pore scale
Directory of Open Access Journals (Sweden)
Paula Luna
2015-11-01
Full Text Available Mathematical modeling and numerical simulation of two-phase flow through porous media is a very active field of research, because of its relevancy in a wide range of physical and technological applications. Some outstanding applications concern reservoir simulation and oil and gas recovery, fields in which a great effort is being paid in the development of efficient numerical methods. The mathematical model used in this work is written as a system comprising an elliptic equation for pressure and a hyperbolic one for saturation. Our aim is to obtain the numerical solution of this model by combining finite element and finite volume techniques, with a second-order non-oscillatory reconstruction procedure to build the values of the velocities at the cell interfaces of the FV mesh from pointwise values of the pressure at the FE nodes. The numerical results are compared to those obtained using the commercial code ECLIPSE showing an appropriate behavior from a qualitative point of view. The use of this FE-FV procedure is not the usual numerical method in petroleum reservoir simulation, since the techniques most frequently used are based on finite differences, even in standard commercial tools.
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
A CLASS OF TWO-STEP TVD MACCORMACK TYPE NUMERICAL SCHEME FOR MHD EQUATIONS
Institute of Scientific and Technical Information of China (English)
FENG Xueshang; WEI Fengsi; ZHONG Dingkun
2003-01-01
In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.
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...
High order numerical simulations of the Richtmyer Meshkov instability in a relativistic fluid
Zanotti, Olindo
2014-01-01
We study the Richtmyer--Meshkov (RM) instability of a relativistic perfect fluid by means of high order numerical simulations with adaptive mesh refinement (AMR). The numerical scheme adopts a finite volume Weighted Essentially Non-Oscillatory (WENO) reconstruction to increase accuracy in space, a local space-time discontinuous Galerkin predictor method to obtain high order of accuracy in time and a high order one-step time update scheme together with a "cell-by-cell" space-time AMR strategy with time-accurate local time stepping. In this way, third order accurate (both in space and in time) numerical simulations of the RM instability are performed, spanning a wide parameter space. We present results both for the case in which a light fluid penetrates into a higher density one (Atwood number $A>0$), and for the case in which a heavy fluid penetrates into a lower density one (Atwood number $A<0$). We find that, for large Lorentz factors \\gamma_s of the incident shock wave, the relativistic RM instability is...
Digital Repository Service at National Institute of Oceanography (India)
Unnikrishnan, A; Manoj, N.T.
Various numerical models used to study the dynamics and horizontal distribution of salinity in Mandovi-Zuari estuaries, Goa, India is discussed in this chapter. Earlier, a one-dimensional network model was developed for representing the complex...
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 m
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<
1992-12-01
fisica matematica. ABSTRACT - We consider a new method for the numerical solution both of non- linear systems of equations and of cornplementauity...8217 Universith di Rama "La Sapienza- 00185 Roma, Italy Maria Cristina Recchioni Istituto Nazionale di Alta Matematica "’F. Severi" pia.ale Aldo Moro 5 00185
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.
Sozio, Gerry
2009-01-01
Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with and an approach that…
Migliore, Juan
2012-01-01
An unpublished example due to Joe Harris from 1983 (or earlier) gave two smooth space curves with the same Hilbert function, but one of the curves was arithmetically Cohen-Macaulay (ACM) and the other was not. Starting with an arbitrary homogeneous ideal in any number of variables, we give two constructions, each of which produces, in a finite number of steps, an ideal with the Hilbert function of a codimension two ACM subscheme. We call the subscheme associated to such an ideal "numerically ACM." We study the connections between these two constructions, and in particular show that they produce ideals with the same Hilbert function. We call the resulting ideal from either construction a "numerical Macaulification" of the original ideal. Specializing to the case where the ideals are unmixed of codimension two, we show that (a) every even liaison class, $\\mathcal L$, contains numerically ACM subschemes, (b) the subset, $\\mathcal M$, of numerically ACM subschemes in $\\mathcal L$ has, by itself, a Lazarsfeld-Rao ...
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.
Modarreszadeh, Seyedamirreza; Timofeev, Evgeny; Merlen, Alain; Matar, Olivier Bou; Pernod, Philippe
2017-07-01
The present paper is concerned with the numerical modeling of magneto-acoustic Wave Phase Conjugation (WPC) phenomena. Since ultrasonic waves in the WPC applications have short wavelengths relative to the traveling distances, high-order numerical methods in both space and time domains are required. The numerical scheme chosen for the current research is the Runge-Kutta Discontinuous Galerkin (RKDG) method incorporated into the Correction Procedure via Reconstruction (CPR) framework. In order to avoid non-physical oscillations near high-gradient regions, a Weighted Essentially Non-Oscillatory (WENO) limiter is used to reconstruct the solutions in the affected cells. After being assured that the numerical scheme has appropriate accuracy and performance, the WPC process is modeled in both linear and non-linear regimes. The results in the linear regime are in acceptable agreement with the analytical solution. The only significant deviation between the linear and non-linear results is at the sensor within the passive zone, where the mean pressure starts to grow gradually in the non-linear regime due to overtaking of the low-velocity pressure waves by the high-velocity ones.
Energy Technology Data Exchange (ETDEWEB)
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.
Properties-preserving high order numerical methods for a kinetic eikonal equation
Luo, Songting; Payne, Nicholas
2017-02-01
For the BGK (Bhatnagar-Gross-Krook) equation in the large scale hyperbolic limit, the density of particles can be transformed as the Hopf-Cole transformation, where the phase function converges uniformly to the viscosity solution of an effective Hamilton-Jacobi equation, referred to as the kinetic eikonal equation. In this work, we present efficient high order finite difference methods for numerically solving the kinetic eikonal equation. The methods are based on monotone schemes such as the Godunov scheme. High order weighted essentially non-oscillatory techniques and Runge-Kutta procedures are used to obtain high order accuracy in both space and time. The effective Hamiltonian is determined implicitly by a nonlinear equation given as integrals with respect to the velocity variable. Newton's method is applied to solve the nonlinear equation, where integrals with respect to the velocity variable are evaluated either by a Gauss quadrature formula or as expansions with respect to moments of the Maxwellian. The methods are designed such that several key properties such as the positivity of the viscosity solution and the positivity of the effective Hamiltonian are preserved. Numerical experiments are presented to demonstrate the effectiveness of the methods.
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...
Pudasaini, Shiva P; Wang, Yongqi; Hutter, Kolumban
2005-07-15
This paper presents a new model and discussions about the motion of avalanches from initiation to run-out over moderately curved and twisted channels of complicated topography and its numerical simulations. The model is a generalization of a well established and widely used depth-averaged avalanche model of Savage & Hutter and is published with all its details in Pudasaini & Hutter (Pudasaini & Hutter 2003 J. Fluid Mech. 495, 193-208). The intention was to be able to describe the flow of a finite mass of snow, gravel, debris or mud, down a curved and twisted corrie of nearly arbitrary cross-sectional profile. The governing equations for the distribution of the avalanche thickness and the topography-parallel depth-averaged velocity components are a set of hyperbolic partial differential equations. They are solved for different topographic configurations, from simple to complex, by applying a high-resolution non-oscillatory central differencing scheme with total variation diminishing limiter. Here we apply the model to a channel with circular cross-section and helical talweg that merges into a horizontal channel which may or may not become flat in cross-section. We show that run-out position and geometry depend strongly on the curvature and twist of the talweg and cross-sectional geometry of the channel, and how the topography is shaped close to run-out zones.
Robust numerical methods for conservation laws using a biased averaging procedure
Choi, Hwajeong
In this thesis, we introduce a new biased averaging procedure (BAP) and use it in developing high resolution schemes for conservation laws. Systems of conservation laws arise in variety of physical problems, such as the Euler equation of compressible flows, magnetohydrodynamics, multicomponent flows, the blast waves and the flow of glaciers. Many modern shock capturing schemes are based on solution reconstructions by high order polynomial interpolations, and time evolution by the solutions of Riemann problems. Due to the existence of discontinuities in the solution, the interpolating polynomial has to be carefully constructed to avoid possible oscillations near discontinuities. The BAP is a more general and simpler way to approximate higher order derivatives of given data without introducing oscillations, compared to limiters and the essentially non-oscillatory interpolations. For the solution of a system of conservation laws, we present a finite volume method which employs a flux splitting and uses componentwise reconstruction of the upwind fluxes. A high order piecewise polynomial constructed by using BAP is used to approximate the component of upwind fluxes. This scheme does not require characteristic decomposition nor Riemann solver, offering easy implementation and a relatively small computational cost. More importantly, the BAP is naturally extended for unstructured grids and it will be demonstrated through a cell-centered finite volume method, along with adaptive mesh refinement. A number of numerical experiments from various applications demonstrates the robustness and the accuracy of this approach, and show the potential of this approach for other practical applications.
A novel code for numerical 3-D MHD studies of CME expansion
Directory of Open Access Journals (Sweden)
J. Kleimann
2009-03-01
Full Text Available A recent third-order, essentially non-oscillatory central scheme to advance the equations of single-fluid magnetohydrodynamics (MHD in time has been implemented into a new numerical code. This code operates on a 3-D Cartesian, non-staggered grid, and is able to handle shock-like gradients without producing spurious oscillations.
To demonstrate the suitability of our code for the simulation of coronal mass ejections (CMEs and similar heliospheric transients, we present selected results from test cases and perform studies of the solar wind expansion during phases of minimum solar activity. We can demonstrate convergence of the system into a stable Parker-like steady state for both hydrodynamic and MHD winds. The model is subsequently applied to expansion studies of CME-like plasma bubbles, and their evolution is monitored until a stationary state similar to the initial one is achieved. In spite of the model's (current simplicity, we can confirm the CME's nearly self-similar evolution close to the Sun, thus highlighting the importance of detailed modelling especially at small heliospheric radii.
Additionally, alternative methods to implement boundary conditions at the coronal base, as well as strategies to ensure a solenoidal magnetic field, are discussed and evaluated.
Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory.
Richardson, Jeremy O; Thoss, Michael
2014-08-21
There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum golden-rule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems.
Numerical Integration with Derivatives
Institute of Scientific and Technical Information of China (English)
Hu Cheng
2006-01-01
A new formula with derivatives for numerical integration was presented. Based on this formula and the Richardson extrapolation process, a numerical integration method was established. It can converge faster than the Romberg's. With the same accuracy, the computation of the new numerical integration with derivatives is only half of that of Romberg's numerical integration.
Díaz, J I; Hidalgo, A; Tello, L
2014-10-08
We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge-Kutta total variation diminishing for time integration.
Greene, Patrick T.; Eldredge, Jeff D.; Zhong, Xiaolin; Kim, John
2016-07-01
In this paper, we present a method for performing uniformly high-order direct numerical simulations of high-speed flows over arbitrary geometries. The method was developed with the goal of simulating and studying the effects of complex isolated roughness elements on the stability of hypersonic boundary layers. The simulations are carried out on Cartesian grids with the geometries imposed by a third-order cut-stencil method. A fifth-order hybrid weighted essentially non-oscillatory scheme was implemented to capture any steep gradients in the flow created by the geometries and a third-order Runge-Kutta method is used for time advancement. A multi-zone refinement method was also utilized to provide extra resolution at locations with expected complex physics. The combination results in a globally fourth-order scheme in space and third order in time. Results confirming the method's high order of convergence are shown. Two-dimensional and three-dimensional test cases are presented and show good agreement with previous results. A simulation of Mach 3 flow over the logo of the Ubuntu Linux distribution is shown to demonstrate the method's capabilities for handling complex geometries. Results for Mach 6 wall-bounded flow over a three-dimensional cylindrical roughness element are also presented. The results demonstrate that the method is a promising tool for the study of hypersonic roughness-induced transition.
Díaz, J. I.; Hidalgo, A.; Tello, L.
2014-01-01
We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration. PMID:25294969
Universal Numeric Segmented Display
Azad, Md Abul kalam; Kamruzzaman, S M
2010-01-01
Segmentation display plays a vital role to display numerals. But in today's world matrix display is also used in displaying numerals. Because numerals has lots of curve edges which is better supported by matrix display. But as matrix display is costly and complex to implement and also needs more memory, segment display is generally used to display numerals. But as there is yet no proposed compact display architecture to display multiple language numerals at a time, this paper proposes uniform display architecture to display multiple language digits and general mathematical expressions with higher accuracy and simplicity by using a 18-segment display, which is an improvement over the 16 segment display.
Numerical methods using Matlab
Gupta, Abhishek
2015-01-01
Numerical Methods with MATLAB provides a highly-practical reference work to assist anyone working with numerical methods. A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied. Numerical methods have wide applicability across many scientific, mathematical, and engineering disciplines and are most often employed in situations where working out an exact answer to the problem by another method is impractical. Numerical Methods with MATLAB presents each topic in a concise and readable
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
Numerical Modelling of Streams
DEFF Research Database (Denmark)
Vestergaard, Kristian
In recent years there has been a sharp increase in the use of numerical water quality models. Numeric water quality modeling can be divided into three steps: Hydrodynamic modeling for the determination of stream flow and water levels. Modelling of transport and dispersion of a conservative...
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
Numerical Methods for Multilattices
Abdulle, Assyr; Shapeev, Alexander V
2011-01-01
Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices (Tadmor et al, 1999). Another existing numerical approach to modeling multilattices is homogenization. In the present paper we review the existing numerical methods for multilattices and propose another concurrent macro-to-micro method in the homogenization framework. We give a unified mathematical formulation of the new and the existing methods and show their equivalence. We then consider extensions of the proposed method to time-dependent problems and to random materials.
Smith, David Eugene; Ginsburg, Jekuthiel
Counting, naming numbers, numerals, computation, and fractions are the topics covered in this pamphlet. Number lore and interesting number properties are noted; the derivation of some arithmetic terms is briefly discussed. (DT)
Remarks on numerical semigroups
Torres, F
1995-01-01
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 in \\cited{To}.
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 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...
Numerical transducer modelling
DEFF Research Database (Denmark)
Cutanda, Vicente
1999-01-01
Numerical modelling is of importance for the design, improvement and study of acoustic transducers such as microphones and accelerometers. Techniques like the boundary element method and the finite element method are the most common supplement to the traditional empirical and analytical approaches...... errors and instabilities in the computations of numerical solutions. An investigation to deal with this narrow-gap problem has been carried out....
Status of numerical relativity
Indian Academy of Sciences (India)
Masaru Shibata
2004-10-01
I describe the current status of numerical relativity from my personal point of view. Here, I focus mainly on explaining the numerical implementations necessary for simulating general relativistic phenomena such as the merger of compact binaries and stellar collapse, emphasizing the well-developed current status of such implementations that enable simulations for several astrophysical phenomena. Some of our latest results for simulation of binary neutron star mergers are briefly presented.
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
Static Analysis Numerical Algorithms
2016-04-01
STATIC ANALYSIS OF NUMERICAL ALGORITHMS KESTREL TECHNOLOGY, LLC APRIL 2016 FINAL TECHNICAL REPORT APPROVED FOR PUBLIC RELEASE; DISTRIBUTION...3. DATES COVERED (From - To) NOV 2013 – NOV 2015 4. TITLE AND SUBTITLE STATIC ANALYSIS OF NUMERICAL ALGORITHMS 5a. CONTRACT NUMBER FA8750-14-C... algorithms , linear digital filters and integrating accumulators, modifying existing versions of Honeywell’s HiLiTE model-based development system and
Theoretical numerical analysis
Wendroff, Burton
1966-01-01
Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matri
Frontiers in Numerical Relativity
Evans, Charles R.; Finn, Lee S.; Hobill, David W.
2011-06-01
Preface; Participants; Introduction; 1. Supercomputing and numerical relativity: a look at the past, present and future David W. Hobill and Larry L. Smarr; 2. Computational relativity in two and three dimensions Stuart L. Shapiro and Saul A. Teukolsky; 3. Slowly moving maximally charged black holes Robert C. Ferrell and Douglas M. Eardley; 4. Kepler's third law in general relativity Steven Detweiler; 5. Black hole spacetimes: testing numerical relativity David H. Bernstein, David W. Hobill and Larry L. Smarr; 6. Three dimensional initial data of numerical relativity Ken-ichi Oohara and Takashi Nakamura; 7. Initial data for collisions of black holes and other gravitational miscellany James W. York, Jr.; 8. Analytic-numerical matching for gravitational waveform extraction Andrew M. Abrahams; 9. Supernovae, gravitational radiation and the quadrupole formula L. S. Finn; 10. Gravitational radiation from perturbations of stellar core collapse models Edward Seidel and Thomas Moore; 11. General relativistic implicit radiation hydrodynamics in polar sliced space-time Paul J. Schinder; 12. General relativistic radiation hydrodynamics in spherically symmetric spacetimes A. Mezzacappa and R. A. Matzner; 13. Constraint preserving transport for magnetohydrodynamics John F. Hawley and Charles R. Evans; 14. Enforcing the momentum constraints during axisymmetric spacelike simulations Charles R. Evans; 15. Experiences with an adaptive mesh refinement algorithm in numerical relativity Matthew W. Choptuik; 16. The multigrid technique Gregory B. Cook; 17. Finite element methods in numerical relativity P. J. Mann; 18. Pseudo-spectral methods applied to gravitational collapse Silvano Bonazzola and Jean-Alain Marck; 19. Methods in 3D numerical relativity Takashi Nakamura and Ken-ichi Oohara; 20. Nonaxisymmetric rotating gravitational collapse and gravitational radiation Richard F. Stark; 21. Nonaxisymmetric neutron star collisions: initial results using smooth particle hydrodynamics
Numerical Investigation of Boiling
Sagan, Michael; Tanguy, Sebastien; Colin, Catherine
2012-11-01
In this work, boiling is numerically investigated, using two phase flow direct numerical simulation based on a level set / Ghost Fluid method. Nucleate boiling implies both thermal issue and multiphase dynamics issues at different scales and at different stages of bubble growth. As a result, the different phenomena are investigated separately, considering their nature and the scale at which they occur. First, boiling of a static bubble immersed in an overheated liquid is analysed. Numerical simulations have been performed at different Jakob numbers in the case of strong density discontinuity through the interface. The results show a good agreement on bubble radius evolution between the theoretical evolution and numerical simulation. After the validation of the code for the Scriven test case, interaction of a bubble with a wall is studied. A numerical method taking into account contact angle is evaluated by comparing simulations of the spreading of a liquid droplet impacting on a plate, with experimental data. Then the heat transfer near the contact line is investigated, and simulations of nucleate boiling are performed considering different contact angles values. Finally, the relevance of including a model to take into account the evaporation of the micro layer is discussed.
DEFF Research Database (Denmark)
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...... tools and implementation techniques are described and performance tests are carried out. The equations that govern the motion of fluids with losses and the corresponding boundary conditions are reduced to a form that is tractable for the Boundary Element Method (BEM) by adopting some hypotheses...... that are allowable in this case: linear variations, absence of flow, harmonic time variation, thermodynamical equilibrium and physical dimensions much larger than the molecular mean free path. A formulation of the BEM is also developed with an improvement designed to cope with the numerical difficulty associated...
Introduction to Numerical Methods
Energy Technology Data Exchange (ETDEWEB)
Schoonover, Joseph A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-14
These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.
Parallel WENO Scheme for Three-Dimensional Steady Viscous Fluid Computation%并行WENO格式在三维定常粘性流体计算中的应用
Institute of Scientific and Technical Information of China (English)
叶钦巴图; 胡晓东; 张鉴; 陆忠华; 李新亮
2013-01-01
WENO (Weighted Essentially Non-Oscillatory) is a popular high precision scheme in CFD. In this paper, WEDO is introduced into large-scale parallel simulation. The simulation tests for ONERA-M6 Wing, DLR-F6 Body/Wing and DLR-F6 Body/Wing/Nacelle/Pylon modes are performed with the implicit WENO 3-order and WENO 5-order schemes. The number of compute nodes is ranged from 64 to 1024. The comparison of calculation with experimental results shows that the WENO schemes in massively parallel computing can effectively play its advantages of high-precision, and get good results in shock wave and vortex lfow simulation.%我们将目前计算流体力学中比较流行的高精度WENO (Weighted Essentially Non-Oscillatory)格式引入到大规模并行计算求解中，使用隐式WENO3阶格式和WENO5阶格式对ONERA-M6翼型和DLR-F6机身/机翼以及DLR-F6机身/机翼/发动仓/吊架模型进行了模拟测试。并行规模从64核到1024核。通过数值计算结果和实验结果的对比分析，得出WENO格式在大规模并行计算中能够有效的发挥其高精度的优势，对于激波捕获和涡脱离流动的模拟中能够获得较好的模拟效果。
Mehrmann, Volker; Xu, Hongguo
2000-11-01
We study classical control problems like pole assignment, stabilization, linear quadratic control and H[infinity] control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches.
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...
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.
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…
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
Hybrid undulator numerical optimization
Energy Technology Data Exchange (ETDEWEB)
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.
Numerical transducer modelling
DEFF Research Database (Denmark)
Cutanda, Vicente
1999-01-01
Numerical modelling is of importance for the design, improvement and study of acoustic transducers such as microphones and accelerometers. Techniques like the boundary element method and the finite element method are the most common supplement to the traditional empirical and analytical approaches....... However, there are several difficulties to be addressed that are derived from the size, internal structure and precision requirements that are characteristic of these devices. One of them, the presence of very close surfaces (e.g. the microphone diaphragm and back-electrode), leads to machine precision...
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
Confidence in Numerical Simulations
Energy Technology Data Exchange (ETDEWEB)
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.
Numerical Propulsion System Simulation
Naiman, Cynthia
2006-01-01
The NASA Glenn Research Center, in partnership with the aerospace industry, other government agencies, and academia, is leading the effort to develop an advanced multidisciplinary analysis environment for aerospace propulsion systems called the Numerical Propulsion System Simulation (NPSS). NPSS is a framework for performing analysis of complex systems. The initial development of NPSS focused on the analysis and design of airbreathing aircraft engines, but the resulting NPSS framework may be applied to any system, for example: aerospace, rockets, hypersonics, power and propulsion, fuel cells, ground based power, and even human system modeling. NPSS provides increased flexibility for the user, which reduces the total development time and cost. It is currently being extended to support the NASA Aeronautics Research Mission Directorate Fundamental Aeronautics Program and the Advanced Virtual Engine Test Cell (AVETeC). NPSS focuses on the integration of multiple disciplines such as aerodynamics, structure, and heat transfer with numerical zooming on component codes. Zooming is the coupling of analyses at various levels of detail. NPSS development includes capabilities to facilitate collaborative engineering. The NPSS will provide improved tools to develop custom components and to use capability for zooming to higher fidelity codes, coupling to multidiscipline codes, transmitting secure data, and distributing simulations across different platforms. These powerful capabilities extend NPSS from a zero-dimensional simulation tool to a multi-fidelity, multidiscipline system-level simulation tool for the full development life cycle.
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.
Learning numerical progressions.
Vitz, P C; Hazan, D N
1974-01-01
Learning of simple numerical progressions and compound progressions formed by combining two or three simple progressions is investigated. In two experiments, time to solution was greater for compound vs simple progressions; greater the higher the progression's solution level; and greater if the progression consisted of large vs small numbers. A set of strategies is proposed to account for progression learning based on the assumption S computes differences between integers, differences between differences, etc., in a hierarchical fashion. Two measures of progression difficulty, each a summary of the strategies, are proposed; C1 is a count of the number of differences needed to solve a progression; C2 is the same count with higher level differences given more weight. The measures accurately predict in both experiments the mean time to solve 16 different progressions with C2 being somewhat superior. The measures also predict the learning difficulty of 10 other progressions reported by Bjork (1968).
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.
Numerical Relativity Beyond Astrophysics
Garfinkle, David
2016-01-01
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.
Computing the Alexander Polynomial Numerically
DEFF Research Database (Denmark)
Hansen, Mikael Sonne
2006-01-01
Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically.......Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically....
Numerical relativity; La relatividad numerica
Energy Technology Data Exchange (ETDEWEB)
Alcubierre, M.
2015-07-01
Today the numerical relativity has developed numerical techniques and an understanding of the structure of the field equations and terms of coordinates, as well as an explosion in speed and memory capacity of supercomputers, make it possible to simulate the collision of black holes with masses and different spins in gravitational orbits. It has also allowed to study in detail the collapse and collision of stars neutrons.la numerical relativity has allowed other both numerical and theoretical studies. (Author)
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
Personalized numerical observer
Brankov, Jovan G.; Pretorius, P. Hendrik
2010-02-01
It is widely accepted that medical image quality should be assessed using task-based criteria, such as humanobserver (HO) performance in a lesion-detection (scoring) task. HO studies are time consuming and cost prohibitive to be used for image quality assessment during development of either reconstruction methods or imaging systems. Therefore, a numerical observer (NO), a HO surrogate, is highly desirable. In the past, we have proposed and successfully tested a NO based on a supervised-learning approach (namely a support vector machine) for cardiac gated SPECT image quality assessment. In the supervised-learning approach, the goal is to identify the relationship between measured image features and HO myocardium defect likelihood scores. Thus far we have treated multiple HO readers by simply averaging or pooling their respective scores. Due to observer variability, this may be suboptimal and less accurate. Therefore, in this work, we are setting our goal to predict individual observer scores independently in the hope to better capture some relevant lesion-detection mechanism of the human observers. This is even more important as there are many ways to get equivalent observer performance (measured by area under receiver operating curve), and simply predicting some joint (average or pooled) score alone is not likely to succeed.
Numerical methods used in fusion science numerical modeling
Yagi, M.
2015-04-01
The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.
Numerical software: science or alchemy
Energy Technology Data Exchange (ETDEWEB)
Gear, C.W.
1979-06-01
This is a summary of the Forsythe lecture presented at the Computer Science Conference, Dayton, Ohio, in February 1979. It examines the activity called Numerical Software, first to see what distinguishes numerical software from any other form of software and why numerical software is so much more difficult. Then it examines the scientific basis of such software and discusses that is lacking in that basis.
Introduction to precise numerical methods
Aberth, Oliver
2007-01-01
Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content for this title is now available on the Web. · Clearer, simpler descriptions and explanations ofthe various numerical methods· Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.
How to Circumvent Church Numerals
DEFF Research Database (Denmark)
Goldberg, Mayer; Torgersen, Mads
2002-01-01
In this work we consider a standard numeral system in the lambda-calculus, and the elementary arithmetic and Boolean functions and predicates defined on this numeral system, and show how to construct terms that "circumvent" or "defeat" these functions: The equality predicate is satisfied when...
Numerical simulation of dusty plasmas
Energy Technology Data Exchange (ETDEWEB)
Winske, D.
1995-09-01
The numerical simulation of physical processes in dusty plasmas is reviewed, with emphasis on recent results and unresolved issues. Three areas of research are discussed: grain charging, weak dust-plasma interactions, and strong dust-plasma interactions. For each area, we review the basic concepts that are tested by simulations, present some appropriate examples, and examine numerical issues associated with extending present work.
Numerical prediction of slamming loads
DEFF Research Database (Denmark)
Seng, Sopheak; Jensen, Jørgen J; Pedersen, Preben T
2012-01-01
. The pressure distribution as well as the total force is then determined by integration over a pseudo-three-dimensional presentation of the hull geometry.In this paper the evaluation of the slamming load is taken one step further by performing direct three-dimensional, fully non-linear numerical calculations...... in a realistic wave environment.Both the global and the local slamming loads are assessed numerically using a finite-volume formulation with the free surface captured by a volume-of-fluid technique. This numerical procedure is justified by comprehensive validation studies where numerically evaluated slamming...... pressures are compared with experimentally measured results.To obtain an insight into the three-dimensional flow effects the next step is to apply the validated numerical procedure to evaluate and compare the accuracy and performance of the traditionally used two-dimensional formulations by a comparison...
Numerical shadows: measures and densities on the numerical range
Dunkl, Charles F; Holbrook, John A; Puchała, Zbigniew; Zyczkowski, Karol \\
2010-01-01
For any operator $M$ acting on an $N$-dimensional Hilbert space $H_N$ we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of $M$. The shadow of $M$ at point $z$ is defined as the probability that the inner product $(Mu,u)$ is equal to $z$, where $u$ stands for a random complex vector from $H_N$, satisfying $||u||=1$. In the case of N=2 the numerical shadow of a non-normal operator can be interpreted as a shadow of a hollow sphere projected on a plane. A similar interpretation is provided also for higher dimensions. For a hermitian $M$ its numerical shadow forms a probability distribution on the real axis which is shown to be a one dimensional $B$-spline. In the case of a normal $M$ the numerical shadow corresponds to a shadow of a transparent solid simplex in $R^{N-1}$ onto the complex plane. Numerical shadow is found explicitly for Jordan matrices $J_N$, direct sums of matrices and in all cases where the shadow is rotation invariant. Results...
Two kinds of modified numerals
Directory of Open Access Journals (Sweden)
Rick Nouwen
2010-01-01
Full Text Available In this article, I show that there are two kinds of numeral modifiers: (Class A those that express the comparison of a certain cardinality with the value expressed by the numeral and (Class B those that express a bound on a degree property. The goal is, first of all, to provide empirical evidence for this claim and second to account for these data within a framework that treats modified numerals as degree quantifiers. doi:10.3765/sp.3.3 BibTeX info
Numerical modeling of economic uncertainty
DEFF Research Database (Denmark)
Schjær-Jacobsen, Hans
2007-01-01
Representation and modeling of economic uncertainty is addressed by different modeling methods, namely stochastic variables and probabilities, interval analysis, and fuzzy numbers, in particular triple estimates. Focusing on discounted cash flow analysis numerical results are presented, comparisons...
Program Verification of Numerical Computation
Pantelis, Garry
2014-01-01
These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that outline the definitions and rules upon which VPC is based. The initial motivation of this project was to address some practical issues of computation, especially of numerically intensive programs that are commonplace in computer models. The project evolved into a...
Numerical experiments modelling turbulent flows
Directory of Open Access Journals (Sweden)
Trefilík Jiří
2014-03-01
Full Text Available The work aims at investigation of the possibilities of modelling transonic flows mainly in external aerodynamics. New results are presented and compared with reference data and previously achieved results. For the turbulent flow simulations two modifications of the basic k – ω model are employed: SST and TNT. The numerical solution was achieved by using the MacCormack scheme on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability.
Numerical Analysis of Multiscale Computations
Engquist, Björn; Tsai, Yen-Hsi R
2012-01-01
This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2003-01-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.
Bidirectional Modulation of Numerical Magnitude.
Arshad, Qadeer; Nigmatullina, Yuliya; Nigmatullin, Ramil; Asavarut, Paladd; Goga, Usman; Khan, Sarah; Sander, Kaija; Siddiqui, Shuaib; Roberts, R E; Cohen Kadosh, Roi; Bronstein, Adolfo M; Malhotra, Paresh A
2016-05-01
Numerical cognition is critical for modern life; however, the precise neural mechanisms underpinning numerical magnitude allocation in humans remain obscure. Based upon previous reports demonstrating the close behavioral and neuro-anatomical relationship between number allocation and spatial attention, we hypothesized that these systems would be subject to similar control mechanisms, namely dynamic interhemispheric competition. We employed a physiological paradigm, combining visual and vestibular stimulation, to induce interhemispheric conflict and subsequent unihemispheric inhibition, as confirmed by transcranial direct current stimulation (tDCS). This allowed us to demonstrate the first systematic bidirectional modulation of numerical magnitude toward either higher or lower numbers, independently of either eye movements or spatial attention mediated biases. We incorporated both our findings and those from the most widely accepted theoretical framework for numerical cognition to present a novel unifying computational model that describes how numerical magnitude allocation is subject to dynamic interhemispheric competition. That is, numerical allocation is continually updated in a contextual manner based upon relative magnitude, with the right hemisphere responsible for smaller magnitudes and the left hemisphere for larger magnitudes.
Numeral Incorporation in Japanese Sign Language
Ktejik, Mish
2013-01-01
This article explores the morphological process of numeral incorporation in Japanese Sign Language. Numeral incorporation is defined and the available research on numeral incorporation in signed language is discussed. The numeral signs in Japanese Sign Language are then introduced and followed by an explanation of the numeral morphemes which are…
Extensible Numerical Library in JAVA
Institute of Scientific and Technical Information of China (English)
T.Aso; H.Okazawa; 等
2001-01-01
In this paper,we present the current status of the project for developing the numerical librayr in JAVA.We have presented how object-oriented techniques improve usage and also development of numerical libraries compared with the conventional way at previous conference,we need many functions for data analysis which is not provided within JAVA language,for example,good random number generators.special functions and so on.Our development strategy is focused on easiness of implementation and adding new features by users themselves not only by developers.In HPC filed,there are other focus efforts to develop numerical libraries in JAVA,However,their focus is on the performance of execution.not easiness of extension.Following the strategy,we have degigned and implemented more classes for random number generators and so on .
A numerical method of regenerator
Energy Technology Data Exchange (ETDEWEB)
Zhu, Shaowei [Aisin Seiki Co. Ltd., Aichi (Japan); Matsubara, Yoichi [Nihon Univ., Chiba (Japan). Inst. of Quantum Science
2004-02-01
A numerical method for regenerators is introduced in this paper. It is not only suitable for the regenerators in cryocoolers and Stirling engines, but also suitable for the stacks in acoustic engines and the pulse tubes in pulse tube refrigerators. The numerical model is one dimensional periodic unsteady flow model. The numerical method is based on the control volume concept with the implicitly solve method. The iteration acceleration method, which considers the one-dimensional periodic unsteady problem as the steady two-dimensional problem, is used for decreasing the calculation time. By this method, the regenerator in an inertance tube pulse tube refrigerator was simulated. The result is useful for understanding how the inefficiency of the regenerator changes with the inertance effect. (author)
Numerical models for differential problems
Quarteroni, Alfio
2014-01-01
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, an...
Numerical Modeling of Shoreline Undulations
DEFF Research Database (Denmark)
Kærgaard, Kasper Hauberg
The present thesis considers undulations on sandy shorelines. The aim of the study is to determine the physical mechanisms which govern the morphologic evolution of shoreline undulations, and thereby to be able to predict their shape, dimensions and evolution in time. In order to do so a numerical...... model has been developed which describes the longshore sediment transport along arbitrarily shaped shorelines. The numerical model is based on a spectral wave model, a depth integrated flow model, a wave-phase resolving sediment transport description and a one-line shoreline model. First the theoretical...... length of the shoreline undulations is determined in the linear regime using a shoreline stability analysis based on the numerical model. The analysis shows that the length of the undulations in the linear regime depends on the incoming wave conditions and on the coastal profile. For larger waves...
A numerical method of regenerator
Zhu, Shaowei; Matsubara, Yoichi
2004-02-01
A numerical method for regenerators is introduced in this paper. It is not only suitable for the regenerators in cryocoolers and Stirling engines, but also suitable for the stacks in acoustic engines and the pulse tubes in pulse tube refrigerators. The numerical model is one dimensional periodic unsteady flow model. The numerical method is based on the control volume concept with the implicitly solve method. The iteration acceleration method, which considers the one-dimensional periodic unsteady problem as the steady two-dimensional problem, is used for decreasing the calculation time. By this method, the regenerator in an inertance tube pulse tube refrigerator was simulated. The result is useful for understanding how the inefficiency of the regenerator changes with the inertance effect.
Numerical methods in multibody dynamics
Eich-Soellner, Edda
1998-01-01
Today computers play an important role in the development of complex mechanical systems, such as cars, railway vehicles or machines. Efficient simulation of these systems is only possible when based on methods that explore the strong link between numerics and computational mechanics. This book gives insight into modern techniques of numerical mathematics in the light of an interesting field of applications: multibody dynamics. The important interaction between modeling and solution techniques is demonstrated by using a simplified multibody model of a truck. Different versions of this mechanical model illustrate all key concepts in static and dynamic analysis as well as in parameter identification. The book focuses in particular on constrained mechanical systems. Their formulation in terms of differential-algebraic equations is the backbone of nearly all chapters. The book is written for students and teachers in numerical analysis and mechanical engineering as well as for engineers in industrial research labor...
Inhomogeneous Cosmology with Numerical Relativity
Macpherson, Hayley J; Price, Daniel J
2016-01-01
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble flow over a factor of ~350 change in scale factor (redshift). We simulate the growth of linear perturbations into the non-linear regime, where effects such as gravitational slip and tensor perturbations appear. We therefore show that numerical relativity is a viable tool for investigating nonlinear effects in cosmology.
Matlab programming for numerical analysis
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. Programming MATLAB for Numerical Analysis introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. You will first become
Numerical relativity and spectral methods
Grandclement, P.
2016-12-01
The term numerical relativity denotes the various techniques that aim at solving Einstein's equations using computers. Those computations can be divided into two families: temporal evolutions on the one hand and stationary or periodic solutions on the other one. After a brief presentation of those two classes of problems, I will introduce a numerical tool designed to solve Einstein's equations: the KADATH library. It is based on the the use of spectral methods that can reach high accuracy with moderate computational resources. I will present some applications about quasicircular orbits of black holes and boson star configurations.
Numerical experiments for turbulent flows
Directory of Open Access Journals (Sweden)
Příhoda Jaromír
2013-04-01
Full Text Available The aim of the work is to explore the possibilities of modelling transonic flows in the internal and external aerodynamics. Several configurations were analyzed and calculations were performed using both inviscid and viscous models of flow. Viscous turbulent flows have been simulated using either zero equation algebraic Baldwin-Lomax model and two equation k—ω model in its basic version and improved TNT variant. The numerical solution was obtained using Lax-Wendroff scheme in the MacCormack form on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability. Achieved results are compared with experimental data.
Multipole Moments of numerical spacetimes
Pappas, George
2012-01-01
In this article we present some recent results on identifying correctly the relativistic multipole moments of numerically constructed spacetimes, and the consequences that this correction has on searching for appropriate analytic spacetimes that can approximate well the previously mentioned numerical spacetimes. We also present expressions that give the quadrupole and the spin octupole as functions of the spin parameter of a neutron star for various equations of state and in a range of masses for every equation of state used. These results are relevant for describing the exterior spacetime of rotating neutron stars that are made up of matter obeying realistic equations of state.
Numeric invariants from multidimensional persistence
Energy Technology Data Exchange (ETDEWEB)
Skryzalin, Jacek [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Carlsson, Gunnar [Stanford Univ., Stanford, CA (United States)
2017-05-19
In this paper, we analyze the space of multidimensional persistence modules from the perspectives of algebraic geometry. We first build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence over one-dimensional persistence. We argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Lastly, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data.
A numerical grid generation technique
Gilding, B.H.
1988-01-01
The paper describes a technique for the generation of boundary-fitted curvilinear coordinate systems for the numerical solution of partial differential equations in two space dimensions. The technique is algebraic, has a transfinite character, and is based on the blending of shearing transformations
Numerical modeling of economic uncertainty
DEFF Research Database (Denmark)
Schjær-Jacobsen, Hans
2007-01-01
Representation and modeling of economic uncertainty is addressed by different modeling methods, namely stochastic variables and probabilities, interval analysis, and fuzzy numbers, in particular triple estimates. Focusing on discounted cash flow analysis numerical results are presented, comparisons...... are made between alternative modeling methods, and characteristics of the methods are discussed....
Numerical Modeling of Supercavitating Flows
2001-02-01
scheme was designed in accordance with the numerical stability analysis of Vada and Nakos (1993). A key result of that analysis was the demonstration...Carderock Division, Carderock, MD. Vada, T., and D.E. Nakos (1993) "Time-Marching Schemes for Ship Motion Simulations," 8 th Int’l Workshop on Water Waves
Numerical investigation of acoustic solitons
Lombard, Bruno; Richoux, Olivier
2014-01-01
Acoustic solitons can be obtained by considering the propagation of large amplitude sound waves across a set of Helmholtz resonators. The model proposed by Sugimoto and his coauthors has been validated experimentally in previous works. Here we examine some of its theoretical properties: low-frequency regime, balance of energy, stability. We propose also numerical experiments illustrating typical features of solitary waves.
Numerical Studies of Quantum Turbulence
Tsubota, Makoto; Fujimoto, Kazuya; Yui, Satoshi
2017-09-01
We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose-Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross-Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equilibrium. Hence, numerical studies have been indispensable for studying quantum turbulence. In fact, numerical studies have contributed to revealing the various problems of quantum turbulence. This article reviews the recent developments in numerical studies of quantum turbulence. We start with the motivation and the basics of quantum turbulence and invite readers to the frontier of this research. Though there are many important topics in the quantum turbulence of superfluid helium, this article focuses on inhomogeneous quantum turbulence in a channel, which has been motivated by recent visualization experiments. Atomic Bose-Einstein condensates are a modern issue in quantum turbulence, and this article reviews a variety of topics in the quantum turbulence of condensates, e.g., two-dimensional quantum turbulence, weak wave turbulence, turbulence in a spinor condensate, some of which have not been addressed in superfluid helium and paves the novel way for quantum turbulence researches. Finally, we discuss open problems.
Douglas, M R; Lukic, S; Reinbacher, R; Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene
2006-01-01
We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics, and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results.
Numerical methods for stellarator optimization
Energy Technology Data Exchange (ETDEWEB)
Morris, R.N.; Hedrick, C.L.; Hirshman, S.P.; Lyon, J.F.; Rome, J.A.
1989-01-01
A numerical optimization procedure utilizing an inverse 3-D equilibrium solver, a Mercier stability assessment, a deeply-trapped-particle loss assessment, and a nonlinear optimization package has been used to produce low aspect ratio (A = 4) stellarator designs. These designs combine good stability and improved transport with a compact configuration. 7 refs., 2 figs., 1 tab.
Numerical micromagnetism of strong inhomogeneities
Energy Technology Data Exchange (ETDEWEB)
Andreas, Christian [Peter Grünberg Institut (PGI-6), Forschungszentrum Jülich GmbH, D-52428 Jülich (Germany); Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, Strasbourg (France); Gliga, Sebastian [Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, 5232 Villigen PSI (Switzerland); Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich (Switzerland); Hertel, Riccardo, E-mail: hertel@ipcms.unistra.fr [Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, Strasbourg (France)
2014-08-01
The size of micromagnetic structures, such as domain walls or vortices, is comparable to the exchange length of the ferromagnet. Both, the exchange length of the stray field l{sub s} and the magnetocrystalline exchange length l{sub k}, are material-dependent quantities that usually lie in the nanometer range. This emphasizes the theoretical challenges associated with the mesoscopic nature of micromagnetism: the magnetic structures are much larger than the atomic lattice constant, but at the same time much smaller than the sample size. In computer simulations, the smallest exchange length serves as an estimate for the largest cell size admissible to prevent appreciable discretization errors. This general rule is not valid in special situations where the magnetization becomes particularly inhomogeneous. When such strongly inhomogeneous structures develop, micromagnetic simulations inevitably contain systematic and numerical errors. It is suggested to combine micromagnetic theory with a Heisenberg model to resolve such problems. We analyze cases where strongly inhomogeneous structures pose limits to standard micromagnetic simulations, arising from fundamental aspects as well as from numerical drawbacks. - Highlights: • We discuss the impact of strong inhomogeneities on micromagnetic simulations. • Analysis of fundamental and numerical errors in micromagnetic point singularities. • Numerical and methodological errors in exchange energy terms are quantified. • Suggestion to combine atomistic Heisenberg models with micromagnetism in such cases.
Numerical modeling of advanced materials
Meinders, T.; Perdahcioglu, E.S.; Riel, van M.; Wisselink, H.H.
2007-01-01
The finite element (FE) method is widely used to numerically simulate forming processes. The accuracy of an FE analysis strongly depends on the extent to which a material model can represent the real material behavior. The use of new materials requires complex material models which are able to descr
Numerical methods for metamaterial design
2013-01-01
This book describes a relatively new approach for the design of electromagnetic metamaterials. Numerical optimization routines are combined with electromagnetic simulations to tailor the broadband optical properties of a metamaterial to have predetermined responses at predetermined wavelengths. After a review of both the major efforts within the field of metamaterials and the field of mathematical optimization, chapters covering both gradient-based and derivative-free design methods are considered. Selected topics including surrogate-base optimization, adaptive mesh search, and genetic algorithms are shown to be effective, gradient-free optimization strategies. Additionally, new techniques for representing dielectric distributions in two dimensions, including level sets, are demonstrated as effective methods for gradient-based optimization. Each chapter begins with a rigorous review of the optimization strategy used, and is followed by numerous examples that combine the strategy with either electromag...
Numerical Solution of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory....... Among the special features of this book can be mentioned the presentation of a practical approach to reliable estimates of the global error, including warning signals if the reliability is questionable. The technique is generally applicable for estimating the discretization error in numerical...... approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...
Numerical Hydrodynamics in Special Relativity
Directory of Open Access Journals (Sweden)
Martí José Maria
2003-01-01
Full Text Available This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD. Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
Numerical Modelling of Scramjet Combustor
Directory of Open Access Journals (Sweden)
M. Deepu
2007-07-01
Full Text Available Numerical modelling of turbulent-reacting flow field of supersonic combustion ramjet(scramjet combustors are presented. The developed numerical procedure is based on the implicittreatment of chemical source terms by preconditioning and solved along with unstedy turbulentNavier-Stokes equations explicitly. Reaction is modelled using an eight-step hydrogen-airchemistry. Code is validated against a standard wall jet experimental data and is successfullyused to model the turbulent-reacting flow field resulting due to the combustion of hydrogeninjected from diamond-shaped strut and also in the wake region of wedge-shaped strut placedin the heated supersonic airstream. The analysis could demonstrate the effect of interaction ofoblique shock wave with a supersonic stream of hydrogen in its (fuel-air mixing and reactionfor strut-based scramjet combustors.
Discretized Volumes in Numerical Methods
Antal, Miklós
2007-01-01
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem is sought. We associate a group and a graph to that volume. When the group is symmetry of the boundary value problem under investigation, one can specify the structure of the solution, and find out if there are equispectral volumes of a given type. The second technique uses a complex mapping to transplant the solution from volume to volume and a correction function. Equation for the correction function is given. A simple example demonstrates the feasibility of the suggested method.
Numerical and Evolutionary Optimization Workshop
Trujillo, Leonardo; Legrand, Pierrick; Maldonado, Yazmin
2017-01-01
This volume comprises a selection of works presented at the Numerical and Evolutionary Optimization (NEO) workshop held in September 2015 in Tijuana, Mexico. The development of powerful search and optimization techniques is of great importance in today’s world that requires researchers and practitioners to tackle a growing number of challenging real-world problems. In particular, there are two well-established and widely known fields that are commonly applied in this area: (i) traditional numerical optimization techniques and (ii) comparatively recent bio-inspired heuristics. Both paradigms have their unique strengths and weaknesses, allowing them to solve some challenging problems while still failing in others. The goal of the NEO workshop series is to bring together people from these and related fields to discuss, compare and merge their complimentary perspectives in order to develop fast and reliable hybrid methods that maximize the strengths and minimize the weaknesses of the underlying paradigms. Throu...
Numerical relativity in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Zilhao, Miguel; Herdeiro, Carlos [Departamento de Fisica e Centro de Fisica do Porto, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Witek, Helvi; Cardoso, Vitor; Nerozzi, Andrea [Centro Multidisciplinar de Astrofisica - CENTRA, Departamento de Fisica, Instituto Superior Tecnico - IST, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); Sperhake, Ulrich [California Institute of Technology, Pasadena, CA 91109 (United States); Gualtieri, Leonardo, E-mail: mzilhao@fc.up.p, E-mail: helvi.witek@ist.utl.p, E-mail: vitor.cardoso@ist.utl.p, E-mail: Leonardo.Gualtieri@roma1.infn.i, E-mail: crherdei@fc.up.p, E-mail: andrea.nerozzi@ist.utl.p, E-mail: sperhake@tapir.caltech.ed [Dipartimento di Fisica, Universita di Roma ' Sapienza' and Sezione, INFN Roma1, P.A. Moro 5, 00185, Roma (Italy)
2010-05-01
We give a status report on our project targeted at performing numerical simulations of a head-on collision of non-spinning black holes in higher dimensional non-compact space-times. These simulations should help us understand black objects in higher dimensions and their stability properties. They are also relevant for the problem of black hole formation and evaporation in particle accelerators and cosmic rays. We use the symmetries of the system to reduce the problem to an effective 3+1 problem, allowing the use of existing numerical codes. As a simple application of the formalism, we present the results for the evolution of a five dimensional single black hole space-time.
Numerical Hydrodynamics in Special Relativity.
Martí, José Maria; Müller, Ewald
2003-01-01
This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
Deactivations during the numerical processing
Institute of Scientific and Technical Information of China (English)
FENG HongBo; ZHANG Ye; TANG YiYuan; JIN Jing; DONG Feng; FENG ShiGang; ZHANG WuTian
2007-01-01
Deactivation has been encountered frequently in functional brain imaging researches. However,the deactivations during the numerical processing have not been reported yet. In this study,the functional magnetic resonance imaging (fMRI) was employed to investigate the pattern of the deactivation in the brain of 15 healthy subjects during the numerical addition task. Analyses revealed significant deactivations in several brain regions,including the posterior cingulate,precuneus,anterior cingulate and prefrontal cortex. Especially,we found notable deactivation in bilateral insula. Accounting for the cognitive functions of these regions participating in a combinated way,we discuss their contributions in sustaining the brain activity during conscious resting state,and indicate that the insula is an important area of gathering auditory information from the external world.
Numerical simulation of gas explosions
Energy Technology Data Exchange (ETDEWEB)
Van den Berg, A.C.; Van Wingerden, J.M.; Verhagen, T.L.
1989-08-01
Recent developments in numerical fluid dynamics and computer technology enable detailed simulation of gas explosions. Prins Maurits Laboratory TNO of the Netherlands Organization for Applied Scientific Research developed the necessary software. This software is a useful tool to develop and evaluate explosion safe installations. One of the possible applications is the design of save offshore rigs. (f.i. to prevent Piper Alpha disasters). The two-dimensional blast model is described and an example is given. 4 figs., 6 refs.
Numerical Simulation of Protoplanetary Vortices
2003-12-01
UNCLASSIFIED Center for Turbulence Research 81 Annual Research Briefs 2003 Numerical simulation of protoplanetary vortices By H. Lin, J.A. Barranco t AND P.S...planetesimals and planets. In earlier works ( Barranco & Marcus 2000; Barranco et al. 2000; Lin et al. 2000) we have briefly described the possible physical...transport. In particular, Barranco et al. (2000) provided a general mathe- matical framework that is suitable for the asymptotic regime of the disk
Numerical and symbolic scientific computing
Langer, Ulrich
2011-01-01
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from
Physics-compatible numerical methods
Barry, Koren; Abgrall, Remi; Pavel, Bochev; Jason, Frank; Blair, Perrot
2014-01-01
International audience; Physics-compatible numerical methods are methods that aim to preserve key mathematical and physical properties of continuum physics models in their finite-dimensional algebraic representations. They include methods which preserve properties such as energy, monotonicity, maximum principles, symmetries, and involutions of the continuum models. Examples are mimetic methods for spatial discretizations, variational and geometric integrators, conservative finite-volume and f...
Numerical precision and data structures
Schenk, W.
1978-01-01
Technical proposals and recommendations for revising FORTRAN were studied and categorized. In the area of numerical precision, the proposals basically agree on a set of necessary parameters, although a wide range of nomenclature and specific function names are used. Environmental parameters identified include the following: (1) base of floating point representation, (2) largest positive real number, exponent and integer, (3) largest negative real number, exponent and integer, (4) number of significant digits, and (5) exponent bias.
Cuba: Multidimensional numerical integration library
Hahn, Thomas
2016-08-01
The Cuba library offers four independent routines for multidimensional numerical integration: Vegas, Suave, Divonne, and Cuhre. The four algorithms work by very different methods, and can integrate vector integrands and have very similar Fortran, C/C++, and Mathematica interfaces. Their invocation is very similar, making it easy to cross-check by substituting one method by another. For further safeguarding, the output is supplemented by a chi-square probability which quantifies the reliability of the error estimate.
Numerical methods for turbulent flow
Turner, James C., Jr.
1988-01-01
It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.
Dense magnetized plasma numerical simulations
Energy Technology Data Exchange (ETDEWEB)
Bilbao, L [INFIP-CONICET, and Physics Department (FCEN-UBA), Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina); Bernal, L, E-mail: bilbao@df.uba.a [Physics Department (FCEYN-UNMDP), Complejo Universitario, Funes y Pena, 7600 Mar del Plata (Argentina)
2010-06-15
The scope for developing the present numerical method was to perform parametric studies for optimization of several configurations in magnetized plasmas. Nowadays there exist several efficient numerical codes in the subject. However, the construction of one's own computational codes brings the following important advantages: (a) to get a deeper knowledge of the physical processes involved and the numerical methods used to simulate them and (b) more flexibility to adapt the code to particular situations in a more efficient way than would be possible for a closed general code. The code includes ion viscosity, thermal conduction (electrons and ions), magnetic diffusion, thermonuclear or chemical reaction, Bremsstrahlung radiation, and equation of state (from the ideal gas to the degenerate electron gas). After each calculation cycle, mesh vertices are moved arbitrarily over the fluid. The adaptive method consists of shifting mesh vertices over the fluid in order to keep a reasonable mesh structure and increase the spatial resolution where the physical solution demands. The code was a valuable tool for parametric study of different physical problems, mainly optimization of plasma focus machine, detonation and propagation of thermonuclear reactions and Kelvin-Helmholtz instabilities in the boundary layer of the terrestrial magnetopause.
Recent advances in numerical PDEs
Zuev, Julia Michelle
In this thesis, we investigate four neighboring topics, all in the general area of numerical methods for solving Partial Differential Equations (PDEs). Topic 1. Radial Basis Functions (RBF) are widely used for multi-dimensional interpolation of scattered data. This methodology offers smooth and accurate interpolants, which can be further refined, if necessary, by clustering nodes in select areas. We show, however, that local refinements with RBF (in a constant shape parameter [varepsilon] regime) may lead to the oscillatory errors associated with the Runge phenomenon (RP). RP is best known in the case of high-order polynomial interpolation, where its effects can be accurately predicted via Lebesgue constant L (which is based solely on the node distribution). We study the RP and the applicability of Lebesgue constant (as well as other error measures) in RBF interpolation. Mainly, we allow for a spatially variable shape parameter, and demonstrate how it can be used to suppress RP-like edge effects and to improve the overall stability and accuracy. Topic 2. Although not as versatile as RBFs, cubic splines are useful for interpolating grid-based data. In 2-D, we consider a patch representation via Hermite basis functions s i,j ( u, v ) = [Special characters omitted.] h mn H m ( u ) H n ( v ), as opposed to the standard bicubic representation. Stitching requirements for the rectangular non-equispaced grid yield a 2-D tridiagonal linear system AX = B, where X represents the unknown first derivatives. We discover that the standard methods for solving this NxM system do not take advantage of the spline-specific format of the matrix B. We develop an alternative approach using this specialization of the RHS, which allows us to pre-compute coefficients only once, instead of N times. MATLAB implementation of our fast 2-D cubic spline algorithm is provided. We confirm analytically and numerically that for large N ( N > 200), our method is at least 3 times faster than the
Numerical methods for multibody systems
Glowinski, Roland; Nasser, Mahmoud G.
1994-01-01
This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.
Numerical methods in mathematica environment
Tayyab, M
1999-01-01
The objective of this work is to numerically solve one group and multi-group steady state diffusion equation by transforming into finite difference form. A program has been developed for the solution of diffusion equation which requires suitably averaged cross sections as input. Output of the program includes multiplication factor and neutron flux in one dimension in slab, cylindrical, or spherical geometry. In addition this program has the capability of conducting a search on poison concentration to achieve a specified value of multiplication factor. The criticality search was also performed to determine the critical radius for a particular composition.
Smith, David Eugene
2004-01-01
The numbers that we call Arabic are so familiar throughout Europe and the Americas that it can be difficult to realize that their general acceptance in commercial transactions is a matter of only the last four centuries and they still remain unknown in parts of the world.In this volume, one of the earliest texts to trace the origin and development of our number system, two distinguished mathematicians collaborated to bring together many fragmentary narrations to produce a concise history of Hindu-Arabic numerals. Clearly and succinctly, they recount the labors of scholars who have studied the
Numerical models of complex diapirs
Podladchikov, Yu.; Talbot, C.; Poliakov, A. N. B.
1993-12-01
Numerically modelled diapirs that rise into overburdens with viscous rheology produce a large variety of shapes. This work uses the finite-element method to study the development of diapirs that rise towards a surface on which a diapir-induced topography creeps flat or disperses ("erodes") at different rates. Slow erosion leads to diapirs with "mushroom" shapes, moderate erosion rate to "wine glass" diapirs and fast erosion to "beer glass"- and "column"-shaped diapirs. The introduction of a low-viscosity layer at the top of the overburden causes diapirs to develop into structures resembling a "Napoleon hat". These spread lateral sheets.
Disruptive Innovation in Numerical Hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Waltz, Jacob I. [Los Alamos National Laboratory
2012-09-06
We propose the research and development of a high-fidelity hydrodynamic algorithm for tetrahedral meshes that will lead to a disruptive innovation in the numerical modeling of Laboratory problems. Our proposed innovation has the potential to reduce turnaround time by orders of magnitude relative to Advanced Simulation and Computing (ASC) codes; reduce simulation setup costs by millions of dollars per year; and effectively leverage Graphics Processing Unit (GPU) and future Exascale computing hardware. If successful, this work will lead to a dramatic leap forward in the Laboratory's quest for a predictive simulation capability.
Results from Numerical General Relativity
Baker, John G.
2011-01-01
For several years numerical simulations have been revealing the details of general relativity's predictions for the dynamical interactions of merging black holes. I will review what has been learned of the rich phenomenology of these mergers and the resulting gravitational wave signatures. These wave forms provide a potentially observable record of the powerful astronomical events, a central target of gravitational wave astronomy. Asymmetric radiation can produce a thrust on the system which may accelerate the single black hole resulting from the merger to high relative velocity.
Numerical methods for image registration
Modersitzki, Jan
2003-01-01
Based on the author's lecture notes and research, this well-illustrated and comprehensive text is one of the first to provide an introduction to image registration with particular emphasis on numerical methods in medical imaging. Ideal for researchers in industry and academia, it is also a suitable study guide for graduate mathematicians, computer scientists, engineers, medical physicists, and radiologists.Image registration is utilised whenever information obtained from different viewpoints needs to be combined or compared and unwanted distortion needs to be eliminated. For example, CCTV imag
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.
ON NUMERICAL TECHNIQUES IN CFD
Institute of Scientific and Technical Information of China (English)
Zhuang Fenggan
2000-01-01
Numerical techniques play an important role in CFD. Some of them are reviewed in this paper. The necessity of using high order difference scheme is demonstrated for the study of high Reynolds number viscous flow. Physical guide lines are provided for the construction of these high order schemes. To avoid unduly ad hoc treatment in the boundary region the use of compact scheme is recommended because it has a small stencil size compared with the traditional finite difference scheme. Besides preliminary Fourier analysis shows the compact scheme can also yield better space resolution which makes it more suitable to study flow with multiscales e.g. turbulence. Other approaches such as perturbation method and finite spectral method are also emphasized. Typical numerical simulations were carried out. The first deals with Euler equations to show its capabilities to capture flow discontinuity.The second deals with Navier-Stokes equations studying the evolution of a mixing layer, the pertinent structures at different times are shown. Asymmetric break down occurs and also the appearance of small vortices.
Numerical Simulations of Bouncing Jets
Bonito, Andrea; Lee, Sanghyun
2015-01-01
Bouncing jets are fascinating phenomenons occurring under certain conditions when a jet impinges on a free surface. This effect is observed when the fluid is Newtonian and the jet falls in a bath undergoing a solid motion. It occurs also for non-Newtonian fluids when the jets falls in a vessel at rest containing the same fluid. We investigate numerically the impact of the experimental setting and the rheological properties of the fluid on the onset of the bouncing phenomenon. Our investigations show that the occurrence of a thin lubricating layer of air separating the jet and the rest of the liquid is a key factor for the bouncing of the jet to happen. The numerical technique that is used consists of a projection method for the Navier-Stokes system coupled with a level set formulation for the representation of the interface. The space approximation is done with adaptive finite elements. Adaptive refinement is shown to be very important to capture the thin layer of air that is responsible for the bouncing.
Numerical Propulsion System Simulation Architecture
Naiman, Cynthia G.
2004-01-01
The Numerical Propulsion System Simulation (NPSS) is a framework for performing analysis of complex systems. Because the NPSS was developed using the object-oriented paradigm, the resulting architecture is an extensible and flexible framework that is currently being used by a diverse set of participants in government, academia, and the aerospace industry. NPSS is being used by over 15 different institutions to support rockets, hypersonics, power and propulsion, fuel cells, ground based power, and aerospace. Full system-level simulations as well as subsystems may be modeled using NPSS. The NPSS architecture enables the coupling of analyses at various levels of detail, which is called numerical zooming. The middleware used to enable zooming and distributed simulations is the Common Object Request Broker Architecture (CORBA). The NPSS Developer's Kit offers tools for the developer to generate CORBA-based components and wrap codes. The Developer's Kit enables distributed multi-fidelity and multi-discipline simulations, preserves proprietary and legacy codes, and facilitates addition of customized codes. The platforms supported are PC, Linux, HP, Sun, and SGI.
Uncertainty Quantification in Numerical Aerodynamics
Litvinenko, Alexander
2017-05-16
We consider uncertainty quantification problem in aerodynamic simulations. We identify input uncertainties, classify them, suggest an appropriate statistical model and, finally, estimate propagation of these uncertainties into the solution (pressure, velocity and density fields as well as the lift and drag coefficients). The deterministic problem under consideration is a compressible transonic Reynolds-averaged Navier-Strokes flow around an airfoil with random/uncertain data. Input uncertainties include: uncertain angle of attack, the Mach number, random perturbations in the airfoil geometry, mesh, shock location, turbulence model and parameters of this turbulence model. This problem requires efficient numerical/statistical methods since it is computationally expensive, especially for the uncertainties caused by random geometry variations which involve a large number of variables. In numerical section we compares five methods, including quasi-Monte Carlo quadrature, polynomial chaos with coefficients determined by sparse quadrature and gradient-enhanced version of Kriging, radial basis functions and point collocation polynomial chaos, in their efficiency in estimating statistics of aerodynamic performance upon random perturbation to the airfoil geometry [D.Liu et al \\'17]. For modeling we used the TAU code, developed in DLR, Germany.
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
NUMERICAL SIMULATIONS OF CAVITATING FLOWS
Institute of Scientific and Technical Information of China (English)
Wu Lei
2003-01-01
A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.
NUMERICAL SIMULATION OF INSECT FLIGHT
Institute of Scientific and Technical Information of China (English)
CHENG Mu-lin; MIAO Wen-bo; ZHONG Chang-sheng
2006-01-01
In the non-inertial coordinates attached to the model wing, the two-dimensional unsteady flow field triggered by the motion of the model wing, similar to the flapping of the insect wings, was numerically simulated. One of the advantages of our method is that it has avoided the difficulty related to the moving-boundary problem. Another advantage is that the model has three degrees of freedom and can be used to simulate arbitrary motions of a two-dimensional wing in plane only if the motion is known. Such flexibility allows us to study how insects control their flying. Our results show that there are two parameters that are possibly utilized by insects to control their flight: the phase difference between the wing translation and rotation, and the lateral amplitude of flapping along the direction perpendicular to the average flapping plane.
Moscibrodzka, M; Dolence, J; Shiokawa, H; Leung, P K
2010-01-01
We review results from general relativistic axisymmetric magnetohydrodynamic simulations of accretion in Sgr A*. We use general relativistic radiative transfer methods and to produce a broad band (from millimeter to gamma-rays) spectrum. Using a ray tracing scheme we also model images of Sgr A* and compare the size of image to the VLBI observations at 230 GHz. We perform a parameter survey and study radiative properties of the flow models for various black hole spins, ion to electron temperature ratios, and inclinations. We scale our models to reconstruct the flux and the spectral slope around 230 GHz. The combination of Monte Carlo spectral energy distribution calculations and 230 GHz image modeling constrains the parameter space of the numerical models. Our models suggest rather high black hole spin ($a_*\\approx 0.9$), electron temperatures close to the ion temperature ($T_i/T_e \\sim 3$) and high inclination angles ($i \\approx 90 \\deg$).
Automatic validation of numerical solutions
DEFF Research Database (Denmark)
Stauning, Ole
1997-01-01
This thesis is concerned with ``Automatic Validation of Numerical Solutions''. The basic theory of interval analysis and self-validating methods is introduced. The mean value enclosure is applied to discrete mappings for obtaining narrow enclosures of the iterates when applying these mappings...... is the possiblility to combine the three methods in an extremely flexible way. We examine some applications where this flexibility is very useful. A method for Taylor expanding solutions of ordinary differential equations is presented, and a method for obtaining interval enclosures of the truncation errors incurred...... with intervals as initial values. A modification of the mean value enclosure of discrete mappings is considered, namely the extended mean value enclosure which in most cases leads to even better enclosures. These methods have previously been described in connection with discretizing solutions of ordinary...
Physical and Relativistic Numerical Cosmology
Directory of Open Access Journals (Sweden)
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.
Numerical Simulation on New Perforator
Institute of Scientific and Technical Information of China (English)
姚志华; 王志军; 李德战; 付盟
2011-01-01
To study a new shaped charge of perforator, the jet formation and penetration processes in concrete targets are simulated numerically by using LS-DYNA finite element analysis software. The results show that the cylindrical liner can form jet and most materials on top of liner form the tip of jet, while the others form the tail of jet. The jet has a better continuity, and the ratio of cumulative jet length to the liner diameter can reach to 7.56. Furthermore, the ratio of bore diameter to the liner diameter is from 0. 36 and 1, and the ratio of penetration depth to the liner diameter can be up to 5.5.
Non-Standard Numeration Systems
Directory of Open Access Journals (Sweden)
P. Ambrož
2005-01-01
Full Text Available We study some properties of non-standard numeration systems with an irrational base ß >1, based on the so-called beta-expansions of real numbers [1]. We discuss two important properties of these systems, namely the Finiteness property, stating whether the set of finite expansions in a given system forms a ring, and then the problem of fractional digits arising under arithmetic operations with integers in a given system. Then we introduce another way of irrational representation of numbers, slightly different from classical beta-expansions. Here we restrict ourselves to one irrational base – the golden mean ? – and we study the Finiteness property again.
Numerical Modeling of Microelectrochemical Systems
DEFF Research Database (Denmark)
Adesokan, Bolaji James
for the reactants in the bulk electrolyte that are traveling waves. The first paper presents the mathematical model which describes an electrochemical system and simulates an electroanalytical technique called cyclic voltammetry. The model is governed by a system of advection–diffusion equations with a nonlinear...... reaction term at the boundary. We investigate the effect of flow rates, scan rates, and concentration on the cyclic voltammetry. We establish that high flow rates lead to the reduced hysteresis in the cyclic voltammetry curves and increasing scan rates lead to more pronounced current peaks. The final part...... of the paper shows that the response current in a cyclic voltammetry increases proportionally to the electrolyte concentration. In the second paper we present an experiment of an electrochemical system in a microfluidc system and compare the result to the numerical solutions. We investigate how the position...
Spectral Methods for Numerical Relativity
Grandclément, Philippe
2007-01-01
Equations arising in General Relativity are usually to complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled, partial differential, equations. Amongst the possible choices, this paper focuses on a class called spectral methods where, typically, the various functions are expanded onto sets of orthogonal polynomials or functions. A theoretical introduction on spectral expansion is first given and a particular emphasize is put on the fast convergence of the spectral approximation. We present then different approaches to solve partial differential equations, first limiting ourselves to the one-dimensional case, with one or several domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. One then turns to results obtained by various groups in the field of General Relativity by means of spectral methods. First, works which do not involve explicit t...
Numerical optimization using flow equations.
Punk, Matthias
2014-12-01
We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.
Relativistic Positioning Systems: Numerical Simulations
Puchades, Neus
2014-01-01
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true location may be found using additional information (angles or times). The zone where the Jacobian, J, of the transformation from inertial to emission coordinates vanishes is also represented and interpreted. It is shown that the uncertainties in the satellite world lines produce positioning errors, which depend on the value of |J|. The smaller this quantity the greater the expected positioning errors. Among all the available 4-tuples of satellites, the most appropriate one -for a given location- should minimize positioning errors (large enough |J| values) avoiding bifurcation. Our study is particularly important to locate objects which are far away from Earth, e.g., satellites.
Strongly correlated systems numerical methods
Mancini, Ferdinando
2013-01-01
This volume presents, for the very first time, an exhaustive collection of those modern numerical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and material science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciate consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possi...
Operator theory and numerical methods
Fujita, H; Suzuki, T
2001-01-01
In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method.
Numerical modelling of fuel sprays
Energy Technology Data Exchange (ETDEWEB)
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 Cognition without Words: Evidence from Amazonia
National Research Council Canada - National Science Library
Peter Gordon
2004-01-01
.... This addresses the classic Whorfian question about whether language can determine thought. Results of numerical tasks with varying cognitive demands show that numerical cognition is clearly affected by the lack of a counting system in the language...
RECOGNITION OF HINDI (ARABIC HANDWRITTEN NUMERALS
Directory of Open Access Journals (Sweden)
Rawan I. Zaghloul
2012-01-01
Full Text Available Recognition of handwritten numerals has been one of the most challenging topics in image processing. This is due to its contributions in the automation process in several applications. The aim of this study was to build a classifier that can easily recognize offline handwritten Arabic numerals to support those applications that are deal with Hindi (Arabic numerals. A new algorithm for Hindi (Arabic Numeral Recognition is proposed. The proposed algorithm was developed using MATLAB and tested with a large sample of handwritten numeral datasets for different writers in different ages. Pattern recognition techniques are used to identify Hindi (Arabic handwritten numerals. After testing, high recognition rates were achieved, their ranges from 95% for some numerals and up to 99% for others. The proposed algorithm used a powerful set of features which proved to be effective in the recognition of Hindi (Arabic numerals.
Numerical prediction of shoreline adjacent to breakwater
Digital Repository Service at National Institute of Oceanography (India)
Mahadevan, R.; Chandramohan, P.; Nayak, B.U.
Existing mathematical models for prediction of shoreline changes in the vicinity of a breakwater were reviewed The analytical and numerical results obtained from these models have been compared Under the numerical approach, two different implicit...
A first course in numerical analysis
Ralston, Anthony
2001-01-01
This outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents a minimum of theorems and proofs. Oriented toward computer solutions of problems, it stresses error analysis and computational efficiency, and compares different solutions to the same problem.Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms; interpolation; numerical differentiation and numerical quadrature; the numerical solution of ordinary differential equations; functional approximation by l
Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme
Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook
1995-01-01
Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.
Interagency mechanical operations group numerical systems group
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-09-01
This report consists of the minutes of the May 20-21, 1971 meeting of the Interagency Mechanical Operations Group (IMOG) Numerical Systems Group. This group looks at issues related to numerical control in the machining industry. Items discussed related to the use of CAD and CAM, EIA standards, data links, and numerical control.
On some numerical characteristics of operators
Directory of Open Access Journals (Sweden)
M. Gürdal
2015-01-01
Full Text Available We investigate some numerical characteristics of Toeplitz operators including the numerical range, maximal numerical range and maximal Berezin set. Further, we establish an inequality for the Berezin number of an arbitrary operator on the Hardy–Hilbert space of the unit disc.
Two Notes on Numerical Differentiation Formulae
Institute of Scientific and Technical Information of China (English)
ZHENG Hua-sheng
2012-01-01
Some new conclusions on asymptotic properties and inverse problems of numerical differentiation formulae have been drawn in this paper.In the first place,several asymptotic properties of intermediate points of numerical differentiation formulae are presented by using Taylor's formula.And then,based on the ideas of algebraic accuracy,several inverse problems of numerical differentiation formulae are given.
Revised numerical wrapper for PIES code
Raburn, Daniel; Reiman, Allan; Monticello, Donald
2015-11-01
A revised external numerical wrapper has been developed for the Princeton Iterative Equilibrium Solver (PIES code), which is capable of calculating 3D MHD equilibria with islands. The numerical wrapper has been demonstrated to greatly improve the rate of convergence in numerous cases corresponding to equilibria in the TFTR device where magnetic islands are present. The numerical wrapper makes use of a Jacobian-free Newton-Krylov solver along with adaptive preconditioning and a sophisticated subspace-restricted Levenberg-Marquardt backtracking algorithm. The details of the numerical wrapper and several sample results are presented.
Numerical linear algebra with applications using Matlab
Ford, William
2014-01-01
Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for
Spectral Methods for Numerical Relativity
Directory of Open Access Journals (Sweden)
Grandclément Philippe
2009-01-01
Full Text Available Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole–binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole–binary mergers.
Numerical Modeling of Nanoelectronic Devices
Klimeck, Gerhard; Oyafuso, Fabiano; Bowen, R. Chris; Boykin, Timothy
2003-01-01
Nanoelectronic Modeling 3-D (NEMO 3-D) is a computer program for numerical modeling of the electronic structure properties of a semiconductor device that is embodied in a crystal containing as many as 16 million atoms in an arbitrary configuration and that has overall dimensions of the order of tens of nanometers. The underlying mathematical model represents the quantummechanical behavior of the device resolved to the atomistic level of granularity. The system of electrons in the device is represented by a sparse Hamiltonian matrix that contains hundreds of millions of terms. NEMO 3-D solves the matrix equation on a Beowulf-class cluster computer, by use of a parallel-processing matrix vector multiplication algorithm coupled to a Lanczos and/or Rayleigh-Ritz algorithm that solves for eigenvalues. In a recent update of NEMO 3-D, a new strain treatment, parameterized for bulk material properties of GaAs and InAs, was developed for two tight-binding submodels. The utility of the NEMO 3-D was demonstrated in an atomistic analysis of the effects of disorder in alloys and, in particular, in bulk In(x)Ga(l-x)As and in In0.6Ga0.4As quantum dots.
Numerical modeling of water waves
Lin, Pengzhi
2008-01-01
Modelling large-scale wave fields and their interaction with coastal and offshore structures has become much more feasible over the last two decades with increases in computer speeds. Wave modelling can be viewed as an extension of wave theory, a mature and widely published field, applied to practical engineering through the use of computer tools. Information about the various wave models which have been developed is often widely scattered in the literature, and consequently this is one of the first books devoted to wave models and their applications. At the core of the book is an introduction to various types of wave models. For each model, the theoretical assumptions, the application range, and the advantages and limitations are elaborated. The combined use of different wave models from large-scale to local-scale is highlighted with a detailed discussion of the application and matching of boundary conditions. At the same time the book provides a grounding in hydrodynamics, wave theory, and numerical methods...
A numerical model for durotaxis.
Stefanoni, Filippo; Ventre, Maurizio; Mollica, Francesco; Netti, Paolo A
2011-07-07
Cell migration is a phenomenon that is involved in several physiological processes. In the absence of external guiding factors it shares analogies with Brownian motion. The presence of biochemical or biophysical cues, on the other hand, can influence cell migration transforming it in a biased random movement. Recent studies have shown that different cell types are able to recognise the mechanical properties of the substratum over which they move and that these properties direct the motion through a process called durotaxis. In this work a 2D mathematical model for the description of this phenomenon is presented. The model is based on the Langevin equation that has been modified to take into account the local mechanical properties of the substratum perceived by the cells. Numerical simulations of the model provide individual cell tracks, whose characteristics can be compared with experimental observations directly. The present model is solved for two important cases: an isotropic substratum, to check that random motility is recovered as a subcase, and a biphasic substratum, to investigate durotaxis. The degree of agreement is satisfactory in both cases. The model can be a useful tool for quantifying relevant parameters of cell migration as a function of the substratum mechanical properties. Copyright © 2011 Elsevier Ltd. All rights reserved.
2004-06-20
t) + 4(uWj+1,k(t)− uEj,k(t)) + uSWj+1,k(t)− uSEj,k (t) ) , (2.25) Hzj ,k+ 12 (t) = 1 12 [ g(uSWj,k+1(t)) + g(u NW j,k (t)) + 4(g(u S j,k+1(t)) + g(u...problem consists of a left–moving fast rarefaction wave (FR), followed by a tangential discontinuity ( TD ), and a right moving fast shock (FS) with Mach
Directory of Open Access Journals (Sweden)
Jyoti Prakash
2014-07-01
Full Text Available In the present paper, a sufficient condition is derived for the validity of the “principle of the exchange of stabilities” in ferromagnetic convection with magnetic field dependent viscosity, for the case of free boundaries, in porous medium in the presence of a uniform vertical magnetic field and uniform rotation about the vertical axis.
Playing Linear Numerical Board Games Promotes Low-Income Children's Numerical Development
Siegler, Robert S.; Ramani, Geetha B.
2008-01-01
The numerical knowledge of children from low-income backgrounds trails behind that of peers from middle-income backgrounds even before the children enter school. This gap may reflect differing prior experience with informal numerical activities, such as numerical board games. Experiment 1 indicated that the numerical magnitude knowledge of…
Numerical Investigation of Circumplanetary Disks
Mitchell, Tyler R.; Stewart, G. R.
2012-10-01
The regular satellites of Jupiter and Saturn are believed to have formed in circumplanetary disks that were present during the late stages of giant planet formation. At present, there is a large amount of uncertainly in both the structure of these disks and the nature of angular momentum transport within them. In circumstellar disks, magnetorotational rotational instability (MRI) is generally invoked as a mechanism to transfer angular momentum and drive accretion. It is unclear whether circumplanetary disks are sufficiently ionized for the MRI to be active. In an effort to better understand the physical nature of circumplanetary disks, we present 1+1D numerical models of Jovian and Saturnian circumplanetary disks. Our models include viscous diffusion, infall from the solar nebula and external photoevaporation. The combination of these three processes allow for steady-state, truncated disks roughly consistent with the present state of the regular satellite systems of Jupiter and Saturn (Mitchell & Stewart, 2011). Unlike recent models of tidal truncation (Martin & Lubow, 2010), our initial models showed that photoevaporation is able to truncate circumplanetary disks to a small fraction of the Hill radius. One goal of this work is to verify our previous results and confirm that truncated disks can be formed using models with more realistic viscous processes. In order to simplify the problem, our initial models employed a viscosity that was linearly dependent on radius. Our current disk models use a viscosity that is calculated locally based on the midplane temperature that is determined from detailed vertical structure calculations. These models are used to conduct an initial investigation of the viability of an active MRI as well as baroclinic instability and other instabilities that may exist.
Institute of Scientific and Technical Information of China (English)
张军; 任登凤; 谭俊杰
2009-01-01
Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-material interfaces is demonstrated. Discontinuous Galerkin finite element method is used to solve Eulerian equations. And the fifth-order weighted essentially non-oscillatory (WENO) scheme is used to solve the level set equation for capturing multi-material interfaces. The ghost fluid method is used to deal with the interfacial boundary condition. Results are obtained for two bubble interacting with a moving shock. The contours of the constant density and the pressure at different time are given. In the computational domain, three different cases are considered, i.e. two helium bubbles, a helium bubble followed by an R22 bubble in the direction of the moving shock, and an R22 bubble followed by a helium bubble. Computational results indicate that multi-material interfaces can be properly captured by the level set method. Therefore, for problems involving the flow of three different materials with two different interfaces, each interface separating two different materials can be similarly handled.%通过对激波和流体界面相互作用而诱导的大变形界面演化的数值模拟,验证了Level set 方法精确模拟多个流体界面的有效性.采用间断有限元Galerkin方法求解欧拉方程得到流场解,采用5阶WENO格式求解Level set方程追踪多流体界面,界面附近的边界条件由虚拟流体方法处理.对运动激波和两个气泡相互作用过程进行了数值模拟,得到了不同时刻的压力和密度等值线分布,并分析了计算域中两个气泡同是氦气泡,以及一个是氦气泡,一个是R22气泡情况下的计算结果.计算结果表明:利用多界面Level set方程可高质量地捕捉多个流体界面,处理3种多介质流场数值模拟问题.
Origin of the numerals, Al biruni testimony
Boucenna, Ahmed
2007-01-01
The origin of the numerals that we inherited from the arabo-Islamic civilization remained one enigma. The hypothesis of the Indian origin remained, with controversies, without serious rival. It was the dominant hypothesis since more of one century. Its partisans found to it and constructed a lot of arguments. The testimonies of the medieval authors have been interpreted to its advantage. The opposite opinions have been dismissed and ignored. An amalgam between the history of our modern numerals and the Indian mathematics history is made. Rational contradictions often passed under silence. A meticulous observation of the numerals permits to affirm that our numerals are in fact more or less modified Arabic letters. The "Ghubari" shape of the numerals shows that the symbol of a numeral corresponds to the Arabic letter whose numerical value is equal to this numeral. The numerals don't have a simple resemblance with some Arabic letters, but every number looks like the Arabic letter whose numerical value is equal t...
The Translation of Numerals and its Limits
Institute of Scientific and Technical Information of China (English)
吴贤雯
2013-01-01
Through probing into the diversity of numerals’functions in language use which gives prominence to the importance of numeral translation, this paper aims to analyze the limits of numeral translation and explain the cause for these limits. The analy-sis of the limits in numeral translation is guided by the principle of functional equivalence. It is discussed that in numeral transla-tion, the limits on different levels of culture, image, sound and form arise when the full functional equivalence can not be achieved. Furthermore, this paper finds that the differences in culture and formal structure as well as the semantic fuzziness are three reasons for the presence of limits in numeral translation. However, the author suggests that these limits in numeral transla-tion can be adjusted with the further development of research on translation methodology and the deep infiltration of different cultures.
Zdeněk Kopal: Numerical Analyst
Křížek, M.
2015-07-01
We give a brief overview of Zdeněk Kopal's life, his activities in the Czech Astronomical Society, his collaboration with Vladimír Vand, and his studies at Charles University, Cambridge, Harvard, and MIT. Then we survey Kopal's professional life. He published 26 monographs and 20 conference proceedings. We will concentrate on Kopal's extensive monograph Numerical Analysis (1955, 1961) that is widely accepted to be the first comprehensive textbook on numerical methods. It describes, for instance, methods for polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations with initial or boundary conditions, and numerical solution of integral and integro-differential equations. Special emphasis will be laid on error analysis. Kopal himself applied numerical methods to celestial mechanics, in particular to the N-body problem. He also used Fourier analysis to investigate light curves of close binaries to discover their properties. This is, in fact, a problem from mathematical analysis.
Numerical Simulations of Granular Processes
Richardson, Derek C.; Michel, Patrick; Schwartz, Stephen R.; Ballouz, Ronald-Louis; Yu, Yang; Matsumura, Soko
2014-11-01
Spacecraft images and indirect observations including thermal inertia measurements indicate most small bodies have surface regolith. Evidence of granular flow is also apparent in the images. This material motion occurs in very low gravity, therefore in a completely different gravitational environment than on the Earth. Understanding and modeling these motions can aid in the interpretation of imaged surface features that may exhibit signatures of constituent material properties. Also, upcoming sample-return missions to small bodies, and possible future manned missions, will involve interaction with the surface regolith, so it is important to develop tools to predict the surface response. We have added new capabilities to the parallelized N-body gravity tree code pkdgrav [1,2] that permit the simulation of granular dynamics, including multi-contact physics and friction forces, using the soft-sphere discrete-element method [3]. The numerical approach has been validated through comparison with laboratory experiments (e.g., [3,4]). Ongoing and recently completed projects include: impacts into granular materials using different projectile shapes [5]; possible tidal resurfacing of asteroid Apophis during its 2029 encounter [6]; the Brazil-nut effect in low gravity [7]; and avalanche modeling.Acknowledgements: DCR acknowledges NASA (grants NNX08AM39G, NNX10AQ01G, NNX12AG29G) and NSF (AST1009579). PM acknowledges the French agency CNES. SRS works on the NEOShield Project funded under the European Commission’s FP7 program agreement No. 282703. SM acknowledges support from the Center for Theory and Computation at U Maryland and the Dundee Fellowship at U Dundee. Most simulations were performed using the YORP cluster in the Dept. of Astronomy at U Maryland and on the Deepthought High-Performance Computing Cluster at U Maryland.References: [1] Richardson, D.C. et al. 2000, Icarus 143, 45; [2] Stadel, J. 2001, Ph.D. Thesis, U Washington; [3] Schwartz, S.R. et al. 2012, Gran
Numerical Methods For Chemically Reacting Flows
Leveque, R. J.; Yee, H. C.
1990-01-01
Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.
Theoretical numerical analysis a functional analysis framework
Atkinson, Kendall
2005-01-01
This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solu
An introduction to numerical methods and analysis
Epperson, James F
2013-01-01
Praise for the First Edition "". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.""-Zentralblatt MATH "". . . carefully structured with many detailed worked examples.""-The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to
Numerical simulations of rotating axisymmetric sunspots
Botha, G. J. J.; Busse, F.H.; Hurlburt, N. E.; Rucklidge, A.M.
2008-01-01
A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the nonlinear MHD equations, with density and temperature gradients simulating the upper layer of the sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotat...
Numerical simulations of rotating axisymmetric sunspots
Botha, Gert; Busse, F.H.; Hurlburt, Neal; Rucklidge, Alistair
2008-01-01
A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun’s convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rota...
EMPIRICAL-NUMERICAL ANALYSIS OF HEADCUT MIGRATION
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Headcut migration is studied by using empirical and numerical modeling approaches. Empirical formulas for the headcut migration are established using available measurement data, which consider not only the flow strength but also the properties of soil. Numerical model for the headcut migration is proposed. The influences of dynamic pressure gradient, downward flow, and bed slope on sediment entrainment are considered. The local erosion patterns and migration speeds of headcut calculated by the numerical model agree reasonably well with observed data.
OBJECTORIENTED NUMERICAL MANIFOLD METHOD
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The design and management of the objects about the numerical manifold method are studied by abstracting the finite cover system of numerical manifold method as independent data classes and the theoretical basis for the researching and expanding of numerical manifold method is also put forward. The Hammer integration of triangular area coordinates is used in the integration of the element. The calculation result shows that the program is accuracy and effective.
Doing numerical cosmology with the Cactus code
Vulcanov, D N
2002-01-01
The article presents some aspects concerning the construction of a new thorn for the Cactus code, a complete 3-dimensional machinery for numerical relativity. This thorn is completely dedicated to numerical simulations in cosmology, that means it can provide evolutions of different cosmological models, mainly based on Friedman-Robertson-Walker metric. Some numerical results are presented, testing the convergence, stability and the applicability of the code.
Theory and applications of numerical analysis
Phillips, G M
1996-01-01
This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.* a unique blend of theory and applications* two brand new chapters on eigenvalues and splines* inclusion of formal algorithms* numerous fully worked examples* a large number of problems, many with solutions
A numerical study of planar discharge motion
Directory of Open Access Journals (Sweden)
Benkhaldoun F.
2014-06-01
Full Text Available Presented paper describes a numerical study of discharge plasma motion. This non-stationary phenomenon with steep gradients and sharp peaks in unknowns is described as a coupled problem of convection-diffusion equation with source term for electron, ion densities and Poisson’s equation for electric potential. The numerical method is 2nd order of accuracy in space and time and it uses dynamical adaptation of unstructured triangular mesh. Results of numerical studies included size of computational domain, type of boundary conditions and numerical convergence test are presented.
Numerical methods in software and analysis
Rice, John R
1992-01-01
Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithm
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 modelling of elastic space tethers
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P. L.; Roberts, R. M.
2012-01-01
In this paper the importance of the ill-posedness of the classical, non-dissipative massive tether model on an orbiting tether system is studied numerically. The computations document that via the regularisation of bending resistance a more reliable numerical integrator can be produced. Furthermore......, the numerical experiments of an orbiting tether system show that bending may introduce significant forces in some regions of phase space. Finally, numerical evidence for the existence of an almost invariant slow manifold of the singularly perturbed, regularised, non-dissipative massive tether model is provided...
Numerical multilinear algebra and its applications
Institute of Scientific and Technical Information of China (English)
QI Liqun; SUN Wenyu; WANG Yiju
2007-01-01
Numerical multilinear algebra (or called tensor computation), in which instead of matrices and vectors the higher-order tensors are considered in numerical viewpoint, is a new branch of computational mathematics.Although it is an extension of numerical linear algebra, it has many essential differences from numerical linear algebra and more difficulties than it.In this paper, we present a survey on the state of the art knowledge on this topic,which is incomplete, and indicate some new trends for further research, Our survey also contains a detailed bibliography as its important part.We hope that this new area will be receiving more attention of more scholars.
Numerical Methods -- Lecture Notes 2014-2015
Hundsdorfer, W.
2014-01-01
In these notes some basic numerical methods will be described. The following topics are addressed: 1. Nonlinear Equations, 2. Linear Systems, 3. Polynomial Interpolation and Approximation, 4. Trigonometric Interpolation with DFT and FFT, 5. Numerical Integration, 6. Initial Value Problems for OD
Numerical study of one swirling flame
DEFF Research Database (Denmark)
Yang, Yang; Kær, Søren Knudsen; Yin, Chungen
This paper presents numerical study of one of Sydney swirl flames. Good agreements gained between numerical results and the experimental data. Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES) methods show different flow patterns in isothermal and reacting case. The influence...
Numerical simulation of mechatronic sensors and actuators
Kaltenbacher, Manfred
2007-01-01
Focuses on the physical modeling of mechatronic sensors and actuators and their precise numerical simulation using the Finite Element Method (FEM). This book discusses the physical modeling as well as numerical computation. It also gives a comprehensive introduction to finite elements, including their computer implementation.
Denseness of Numerical Radius Attaining Holomorphic Functions
Directory of Open Access Journals (Sweden)
Lee HanJu
2009-01-01
Full Text Available We study the density of numerical radius attaining holomorphic functions on certain Banach spaces using the Lindenstrauss method. In particular, it is shown that if a complex Banach space is locally uniformly convex, then the set of all numerical attaining elements of is dense in .
Denseness of Numerical Radius Attaining Holomorphic Functions
Directory of Open Access Journals (Sweden)
Han Ju Lee
2009-01-01
Full Text Available We study the density of numerical radius attaining holomorphic functions on certain Banach spaces using the Lindenstrauss method. In particular, it is shown that if a complex Banach space X is locally uniformly convex, then the set of all numerical attaining elements of A(BX:X is dense in A(BX:X.
Design and analysis of numerical experiments
Energy Technology Data Exchange (ETDEWEB)
Bowman, K.P.; Sacks, J.; Chang, Yuefang (Univ. of Illinois, Urbana-Champaign (United States))
1993-05-01
Calculations with numerical models are often referred to as numerical experiments, by analogy to classical laboratory experiments. Usually, many numerical experiments are carried out to determine the response of a numerical model to variations of internal or external parameters over some range of interest. If individual experiments are inexpensive to carry out, and if the number of independent parameters is small, it may be possible to search the entire parameter space of the model. This is difficult, however, if the dimension of the parameter space is even moderately large or the codes are expensive to run. In this paper methods are presented for the design and analysis of numerical experiments that are especially useful and efficient in multidimensional parameter spaces. The analysis method, which is similar to kriging in the spatial analysis literature, fits a statistical model to the output of the numerical model. As an example, the method is applied to a fully nonlinear, global, equivalent-barotropic dynamical model. The statistical model also provides estimates of the uncertainty of predicted numerical model output, which can provide guidance on where in the parameter space to conduct further experiments, if necessary. The method can provide major improvements in the efficiency with which numerical sensitivity experiments are conducted. 17 refs., 9 figs., 2 tabs.
Pure Left Neglect for Arabic Numerals
Priftis, Konstantinos; Albanese, Silvia; Meneghello, Francesca; Pitteri, Marco
2013-01-01
Arabic numerals are diffused and language-free representations of number magnitude. To be effectively processed, the digits composing Arabic numerals must be spatially arrangspan>ed along a left-to-right axis. We studied one patient (AK) to show that left neglect, after right hemisphere damage, can selectively impair the computation of the spatial…
Food for Thought: A Few Numerical Delicacies
Hong, L.; Thoo, J. B.
2004-01-01
Many students, when they take an elementary differential equations course for the first time, bring with them misconceptions from numerical methods that they had learnt in their calculus courses, most notable of which concerns the mesh width in using a numerical method. It is important that we strive to dispel any of these misconceptions as well…
Numerical Integration: One Step at a Time
Yang, Yajun; Gordon, Sheldon P.
2016-01-01
This article looks at the effects that adding a single extra subdivision has on the level of accuracy of some common numerical integration routines. Instead of automatically doubling the number of subdivisions for a numerical integration rule, we investigate what happens with a systematic method of judiciously selecting one extra subdivision for…
Numerical minimisation of Gutzwiller energy functionals
Energy Technology Data Exchange (ETDEWEB)
Buenemann, Joerg [Institut fuer Physik, BTU Cottbus, P.O. Box 101344, 03013 Cottbus (Germany); Gebhard, Florian; Schickling, Tobias [Fachbereich Physik, Philipps Universitaet, Renthof 6, 35032 Marburg (Germany); Weber, Werner [Theoretische Physik II, Technische Universitaet Dortmund, Otto-Hahn-Str. 4, 44227 Dortmund (Germany)
2012-06-15
We give a comprehensive introduction into an efficient numerical scheme for the minimisation of Gutzwiller energy functionals for multi-band Hubbard models. Our method covers all conceivable cases of Gutzwiller variational wave functions and has been used successfully in previous numerical studies. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Numeral systems in Alor-Pantar languages
Schapper, Antoinette; Klamer, Marian
2014-01-01
This chapter presents an in-depth analysis of numeral forms and systems in the Alor-Pantar (AP) languages. The AP family reflects a typologically rare combination of mono-morphemic ‘six’ with quinary forms for numerals ‘seven’ to ‘nine’, a pattern which we reconstruct to go back to proto-AP. We focu
Numeric Data Products and Services. SPEC Kit.
Cook, Michael N., Comp.; Hernandez, John J., Comp.; Nicholson, Shawn, Comp.
2001-01-01
This SPEC (Systems and Procedures Exchange Center) Kit presents the results of a survey of Association of Research Libraries (ARL) member libraries. The survey addressed the following questions about numeric data (i.e., any information resource, print or non-print, with considerable numeric content) in academic libraries: (1) What relationships…
Pure Left Neglect for Arabic Numerals
Priftis, Konstantinos; Albanese, Silvia; Meneghello, Francesca; Pitteri, Marco
2013-01-01
Arabic numerals are diffused and language-free representations of number magnitude. To be effectively processed, the digits composing Arabic numerals must be spatially arranged along a left-to-right axis. We studied one patient (AK) to show that left neglect, after right hemisphere damage, can selectively impair the computation of the spatial…
Numerical multi-loop integrals and applications
Freitas, Ayres
2016-01-01
Higher-order radiative corrections play an important role in precision studies of the electroweak and Higgs sector, as well as for the detailed understanding of large backgrounds to new physics searches. For corrections beyond the one-loop level and involving many independent mass and momentum scales, it is in general not possible to find analytic results, so that one needs to resort to numerical methods instead. This article presents an overview over a variety of numerical loop integration techniques, highlighting their range of applicability, suitability for automatization, and numerical precision and stability. In a second part of this article, the application of numerical loop integration methods in the area of electroweak precision tests is illustrated. Numerical methods were essential for obtaining full two-loop predictions for the most important precision observables within the Standard Model. The theoretical foundations for these corrections will be described in some detail, including aspects of the r...
Mathematical and Numerical Modeling in Maritime Geomechanics
Directory of Open Access Journals (Sweden)
Miguel Martín Stickle
2012-04-01
Full Text Available A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,... combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the overning equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism.
Numerical modelling approach for mine backfill
Indian Academy of Sciences (India)
MUHAMMAD ZAKA EMAD
2017-09-01
Numerical modelling is broadly used for assessing complex scenarios in underground mines, including mining sequence and blast-induced vibrations from production blasting. Sublevel stoping mining methods with delayed backfill are extensively used to exploit steeply dipping ore bodies by Canadian hard-rockmetal mines. Mine backfill is an important constituent of mining process. Numerical modelling of mine backfill material needs special attention as the numerical model must behave realistically and in accordance with the site conditions. This paper discusses a numerical modelling strategy for modelling mine backfill material. Themodelling strategy is studied using a case study mine from Canadian mining industry. In the end, results of numerical model parametric study are shown and discussed.
Numerical linear algebra theory and applications
Beilina, Larisa; Karchevskii, Mikhail
2017-01-01
This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.
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.
Modular Construction of Shape-Numeric Analyzers
Directory of Open Access Journals (Sweden)
Bor-Yuh Evan Chang
2013-09-01
Full Text Available The aim of static analysis is to infer invariants about programs that are precise enough to establish semantic properties, such as the absence of run-time errors. Broadly speaking, there are two major branches of static analysis for imperative programs. Pointer and shape analyses focus on inferring properties of pointers, dynamically-allocated memory, and recursive data structures, while numeric analyses seek to derive invariants on numeric values. Although simultaneous inference of shape-numeric invariants is often needed, this case is especially challenging and is not particularly well explored. Notably, simultaneous shape-numeric inference raises complex issues in the design of the static analyzer itself. In this paper, we study the construction of such shape-numeric, static analyzers. We set up an abstract interpretation framework that allows us to reason about simultaneous shape-numeric properties by combining shape and numeric abstractions into a modular, expressive abstract domain. Such a modular structure is highly desirable to make its formalization and implementation easier to do and get correct. To achieve this, we choose a concrete semantics that can be abstracted step-by-step, while preserving a high level of expressiveness. The structure of abstract operations (i.e., transfer, join, and comparison follows the structure of this semantics. The advantage of this construction is to divide the analyzer in modules and functors that implement abstractions of distinct features.
Elementary numerical mathematics for programmers and engineers
Stoyan, Gisbert
2016-01-01
This book covers the basics of numerical methods, while avoiding the definition-theorem-proof style and instead focusing on numerical examples and simple pseudo-codes. The book is divided into ten chapters. Starting with floating number calculations and continuing up to ordinary differential equations, including "Euler backwards". The final chapter discusses practical error estimations. Exercises (including several in MATLAB) are provided at the end of each chapter. Suitable for readers with minimal mathematical knowledge, the book not only offers an elementary introduction to numerical mathematics for programmers and engineers but also provides supporting material for students and teachers of mathematics.
Numerical Algorithm for Delta of Asian Option
Directory of Open Access Journals (Sweden)
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.
3rd International Conference on Numerical Combustion
Larrouturou, Bernard; Numerical Combustion
1989-01-01
Interest in numerical combustion is growing among applied mathematicians, physicists, chemists, engine manufacturers and many industrialists. This proceedings volume contains nine invited lectures and twenty seven contributions carefully selected by the editors. The major themes are numerical simulation of transsonic and supersonic combustion phenomena, the study of supersonic reacting mixing layers, and turbulent combustion. Emphasis is laid on hyperbolic models and on numerical simulations of hydrocarbon planes with a complete set of chemical reactions carried out in two-dimensional geometries as well as on complex reactive flow simulations.
Finger-Based Numerical Skills Link Fine Motor Skills to Numerical Development in Preschoolers.
Suggate, Sebastian; Stoeger, Heidrun; Fischer, Ursula
2017-01-01
Previous studies investigating the association between fine-motor skills (FMS) and mathematical skills have lacked specificity. In this study, we test whether an FMS link to numerical skills is due to the involvement of finger representations in early mathematics. We gave 81 pre-schoolers (mean age of 4 years, 9 months) a set of FMS measures and numerical tasks with and without a specific finger focus. Additionally, we used receptive vocabulary and chronological age as control measures. FMS linked more closely to finger-based than to nonfinger-based numerical skills even after accounting for the control variables. Moreover, the relationship between FMS and numerical skill was entirely mediated by finger-based numerical skills. We concluded that FMS are closely related to early numerical skill development through finger-based numerical counting that aids the acquisition of mathematical mental representations.
Okawa, Hirotada
2013-01-01
Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to evolve such systems, a proper understanding of the methods involved is quite important. Here we focus on the numerical solution of elliptic partial differential equations. Such equations arise when preparing initial data for numerical relativity, but also for monitoring the evolution of black holes. Because such elliptic equations play an important role in many branches of physics, we give an overview of the topic, and show how to numerically solve them with simple examples and sample codes written in C++ and Fortran90 for beginners in numerical relativity or other fields requiring numerical expertise.
Numerical approach to multi-loop integrals
Kato, K; Hamaguchi, N; Ishikawa, T; Koike, T; Kurihara, Y; Shimizu, Y; Yuasa, F
2012-01-01
For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle diagrams of arbitrary internal masses and external momenta, and can calculate integrals with general numerator function. As an example of the performance of DCM, a numerical computation of two-loop box diagrams is presented. Further discussion is given on the choice of control parameters in DCM. This method will be an indispensable tool for the higher order radiative correction when it is tested for a wider class of physical parameters and the separation of divergence is done automatically.
Numerical calculations of magnetic properties of nanostructures
Kapitan, Vitalii; Nefedev, Konstantin
2015-01-01
Magnetic force microscopy and scanning tunneling microscopy data could be used to test computer numerical models of magnetism. The elaborated numerical model of a face-centered lattice Ising spins is based on pixel distribution in the image of magnetic nanostructures obtained by using scanning microscope. Monte Carlo simulation of the magnetic structure model allowed defining the temperature dependence of magnetization; calculating magnetic hysteresis curves and distribution of magnetization on the surface of submonolayer and monolayer nanofilms of cobalt, depending on the experimental conditions. Our developed package of supercomputer parallel software destined for a numerical simulation of the magnetic-force experiments and allows obtaining the distribution of magnetization in one-dimensional arrays of nanodots and on their basis. There has been determined interpretation of magneto-force microscopy images of magnetic nanodots states. The results of supercomputer simulations and numerical calculations are in...
Mode analysis of numerical geodynamo models
Schrinner, Martin; Hoyng, Peter
2011-01-01
It has been suggested in Hoyng (2009) that dynamo action can be analysed by expansion of the magnetic field into dynamo modes and statistical evaluation of the mode coefficients. We here validate this method by analysing a numerical geodynamo model and comparing the numerically derived mean mode coefficients with the theoretical predictions. The model belongs to the class of kinematically stable dynamos with a dominating axisymmetric, antisymmetric with respect to the equator and non-periodic fundamental dynamo mode. The analysis requires a number of steps: the computation of the so-called dynamo coefficients, the derivation of the temporally and azimuthally averaged dynamo eigenmodes and the decomposition of the magnetic field of the numerical geodynamo model into the eigenmodes. For the determination of the theoretical mode excitation levels the turbulent velocity field needs to be projected on the dynamo eigenmodes. We compare the theoretically and numerically derived mean mode coefficients and find reason...
Extracting scaling laws from numerical dynamo models
Stelzer, Z
2013-01-01
Earth's magnetic field is generated by processes in the electrically conducting, liquid outer core, subsumed under the term `geodynamo'. In the last decades, great effort has been put into the numerical simulation of core dynamics following from the magnetohydrodynamic (MHD) equations. However, the numerical simulations are far from Earth's core in terms of several control parameters. Different scaling analyses found simple scaling laws for quantities like heat transport, flow velocity, magnetic field strength and magnetic dissipation time. We use an extensive dataset of 116 numerical dynamo models compiled by Christensen and co-workers to analyse these scalings from a rigorous model selection point of view. Our method of choice is leave-one-out cross-validation which rates models according to their predictive abilities. In contrast to earlier results, we find that diffusive processes are not negligible for the flow velocity and magnetic field strength in the numerical dynamos. Also the scaling of the magneti...
Numerical modelling of nearshore wave transformation
Digital Repository Service at National Institute of Oceanography (India)
Chandramohan, P.; Nayak, B.U.; SanilKumar, V.
A software has been developed for numerical refraction study based on finite amplitude wave theories. Wave attenuation due to shoaling, bottom friction, bottom percolation and viscous dissipation has also been incorporated. The software...
Value-Engineering Review for Numerical Control
Warner, J. L.
1984-01-01
Selecting parts for conversion from conventional machining to numerical control, value-engineering review performed for every part to identify potential changes to part design that result in increased production efficiency.
NUMERICAL INVESTIGATION OF FLOW OVER A WEIR
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Water flow over a weir was simulated numerically in this paper. The numerical model involved the Reynolds equation for mean flow filed with the k-ε turbulent model. To track free surface movements the VOF method with geometric reconstruction approach was employed. Three flow patterns including surface jet, surface wave and plunging jet were simulated in this paper. The free surface profile, velocity field and the distribution of shear stress on the bottom at downstream of the weir were obtained. The results of present numerical model, inviscid model and the rigid-lid assumption were compared with experimental data. It is shown that the present numerical model has great advantage to simulate the flow over a weir. The validities of the inviscid model and the rigid-lid assumption were also discussed.
Probing Strong Field Gravity Through Numerical Simulations
Choptuik, Matthew W; Pretorius, Frans
2015-01-01
This article is an overview of the contributions numerical relativity has made to our understanding of strong field gravity, to be published in the book "General Relativity and Gravitation: A Centennial Perspective", commemorating the 100th anniversary of general relativity.
Discrimination and numerical analysis of human pathogenic ...
African Journals Online (AJOL)
SERVER
2008-02-19
Feb 19, 2008 ... Numerical analysis of whole-cell protein profiles of all strains revealed 2 .... average linkage method and correlation coefficient distance. ... distance yielded a dendrogam, consisting of two basic .... Candida glabrata: review of.
Fluid dynamics theory, computation, and numerical simulation
Pozrikidis, C
2001-01-01
Fluid Dynamics Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes Two distinguishing features of the discourse are solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty Matlab codes are presented and discussed for a broad...
Verification of A Numerical Harbour Wave Model
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A numerical model for wave propagation in a harbour is verified by use of physical models. The extended time-dependent mild slope equation is employed as the governing equation, and the model is solved by use of ADI method containing the relaxation factor. Firstly, the reflection coefficient of waves in front of rubble-mound breakwaters under oblique incident waves is determined through physical model tests, and it is regarded as the basis for simulating partial reflection boundaries of the numerical model. Then model tests on refraction, diffraction and reflection of waves in a harbour are performed to measure wave height distribution. Comparative results between physical and numerical model tests show that the present numerical model can satisfactorily simulate the propagation of regular and irregular waves in a harbour with complex topography and boundary conditions.
Fluid Dynamics Theory, Computation, and Numerical Simulation
Pozrikidis, Constantine
2009-01-01
Fluid Dynamics: Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner. The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming. This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice. There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes. Two distinguishing features of the discourse are: solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty. Matlab codes are presented and discussed for ...
Coherent Structures in Numerically Simulated Plasma Turbulence
DEFF Research Database (Denmark)
Kofoed-Hansen, O.; Pécseli, H.L.; Trulsen, J.
1989-01-01
Low level electrostatic ion acoustic turbulence generated by the ion-ion beam instability was investigated numerically. The fluctuations in potential were investigated by a conditional statistical analysis revealing propagating coherent structures having the form of negative potential wells which...
Numerical Modelling of Jets and Plumes
DEFF Research Database (Denmark)
Larsen, Torben
1993-01-01
An overview on numerical models for prediction of the flow and mixing processes in turbulent jets and plumes is given. The overview is structured to follow an increasing complexity in the physical and numerical principles. The various types of models are briefly mentioned, from the one-dimensiona......An overview on numerical models for prediction of the flow and mixing processes in turbulent jets and plumes is given. The overview is structured to follow an increasing complexity in the physical and numerical principles. The various types of models are briefly mentioned, from the one......-dimensional integral method to the general 3-dimensional solution of the Navier-Stokes equations. Also the predictive capabilities of the models are discussed. The presentation takes the perspective of civil engineering and covers issues like sewage outfalls and cooling water discharges to the sea....
Some results on numerical divided difference formulas
Institute of Scientific and Technical Information of China (English)
Wang; Xinghua; Wang; Heyu; Ming-Jun; Lai
2005-01-01
The remainder estimates of numerical divided difference formula are given for the functions of lower and higher smoothness, respectively. Then several divided difference formulas with super-convergence are derived with their remainder expressions.
Benchmarking numerical models of brittle thrust wedges
Buiter, Susanne J H; Schreurs, Guido; Albertz, Markus; Gerya, Taras V.; Kaus, Boris; Landry, Walter; le Pourhiet, Laetitia; Mishin, Yury; Egholm, David L.; Cooke, Michele; Maillot, Bertrand; Thieulot, Cedric|info:eu-repo/dai/nl/270177493; Crook, Tony; May, Dave; Souloumiac, Pauline; Beaumont, Christopher
2016-01-01
We report quantitative results from three brittle thrust wedge experiments, comparing numerical results directly with each other and with corresponding analogue results. We first test whether the participating codes reproduce predictions from analytical critical taper theory. Eleven codes pass the
Parallel Worldline Numerics: Implementation and Error Analysis
Mazur, Dan
2014-01-01
We give an overview of the worldline numerics technique, and discuss the parallel CUDA implementation of a worldline numerics algorithm. In the worldline numerics technique, we wish to generate an ensemble of representative closed-loop particle trajectories, and use these to compute an approximate average value for Wilson loops. We show how this can be done with a specific emphasis on cylindrically symmetric magnetic fields. The fine-grained, massive parallelism provided by the GPU architecture results in considerable speedup in computing Wilson loop averages. Furthermore, we give a brief overview of uncertainty analysis in the worldline numerics method. There are uncertainties from discretizing each loop, and from using a statistical ensemble of representative loops. The former can be minimized so that the latter dominates. However, determining the statistical uncertainties is complicated by two subtleties. Firstly, the distributions generated by the worldline ensembles are highly non-Gaussian, and so the st...
A numerical reference model for themomechanical subduction
DEFF Research Database (Denmark)
Quinquis, Matthieu; Chemia, Zurab; Tosi, Nicola;
2010-01-01
Building an advanced numerical model of subduction requires choosing values for various geometrical parameters and material properties, among others, the initial lithosphere thicknesses, representative lithological types and their mechanical and thermal properties, rheologies, initial temperature...
Numerical methods in simulation of resistance welding
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, Paulo A.F.; Zhang, Wenqi
2015-01-01
Finite element simulation of resistance welding requires coupling betweenmechanical, thermal and electrical models. This paper presents the numerical models and theircouplings that are utilized in the computer program SORPAS. A mechanical model based onthe irreducible flow formulation is utilized...... a resistance welding point of view, the most essential coupling between the above mentioned models is the heat generation by electrical current due to Joule heating. The interaction between multiple objects is anothercritical feature of the numerical simulation of resistance welding because it influences...
Challenge in Numerical Software for Microcomputers
Energy Technology Data Exchange (ETDEWEB)
Cody, W J
1977-09-02
Microcomputers are now capable of serious numerical computation using programmed floating-point arithmetic and Basic compilers. Unless numerical software designers for these machines exploit experience gained in providing software for larger machines, history will repeat with the initial spread of treacherous software. This paper discusses good software, especially for the elementary functions, in terms of reliability and robustness. The emphasis. is on insight rather than detailed algorithms, to show why certain things are important and how they may be achieved.
The Numerical Psychology of Performance Information
DEFF Research Database (Denmark)
Olsen, Asmus Leth
2015-01-01
Performance information attaches numbers to the inputs, outputs, and outcomes of public services. Numbers are what separate performance information from other sources of information about public sector performance. In cognitive and social psychology, there are vast amounts of research...... on the profound effects of numbers on human attitudes and behavior, but these insights are largely unexplored by scholars of performance information. This article introduces the importance of numerical psychology for the study of performance information, pointing out how numerical research both challenges...
Hardware-Independent Proofs of Numerical Programs
Boldo, Sylvie; Nguyen, Thi Minh Tuyen
2010-01-01
On recent architectures, a numerical program may give different answers depending on the execution hardware and the compilation. Our goal is to formally prove properties about numerical programs that are true for multiple architectures and compilers. We propose an approach that states the rounding error of each floating-point computation whatever the environment. This approach is implemented in the Frama-C platform for static analysis of C code. Small case studies using this approach are entirely and automatically proved
Numerical simulation of "An American Haboob"
Vukovic, A; M. Vujadinovic; Pejanovic, G.; J. Andric; Kumjian, M. R.; V. Djurdjevic; M. Dacic; Prasad, A. K.; H. M. El-Askary; B. C. Paris; S. Petkovic; S. Nickovic; Sprigg, W. A.
2013-01-01
A dust storm of fearful proportions hit Phoenix in the early evening hours of 5 July 2011. This storm, an American haboob, was predicted hours in advance because numerical, land-atmosphere modeling, computing power and remote sensing of dust events have improved greatly over the past decade. High resolution numerical models are required for accurate simulation of the small-scales of the haboob process, with high velocity surface winds produced by strong convection and severe downbursts...
SPURIOUS NUMERICAL SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Hong-jiong Tian; Li-qiang Fan; Yuan-ying Zhang; Jia-xiang Xiang
2006-01-01
This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamical system in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.
Numerical tsunami modeling and the bottom relief
Kulikov, E. A.; Gusiakov, V. K.; Ivanova, A. A.; Baranov, B. V.
2016-11-01
The effect of the quality of bathymetric data on the accuracy of tsunami-wave field calculation is considered. A review of the history of the numerical tsunami modeling development is presented. Particular emphasis is made on the World Ocean bottom models. It is shown that the modern digital bathymetry maps, for example, GEBCO, do not adequately simulate the sea bottom in numerical models of wave propagation, leading to considerable errors in estimating the maximum tsunami run-ups on the coast.
Roadway Automobile Stability. A Numerical Study
Nikolov, Svetoslav; Nedev, Valentin; Bachvarov, Stefan
2008-01-01
A mathematical model of the roadway automobile motion is numerically analyzed. This model is intended to describe the roadway automobile stability. A previous paper [6] described the model in detail and the general method of qualitative analysis. In the present paper, we continue the discussion of stability by numerical simulations and the specific question we attempted to answer is: which parameter(s) of automobile geometry and quality of the roadway can serve as a reliable predictor(s) for ...
Comparing numerically exact and modelled static friction
Directory of Open Access Journals (Sweden)
Krengel Dominik
2017-01-01
Full Text Available Currently there exists no mechanically consistent “numerically exact” implementation of static and dynamic Coulomb friction for general soft particle simulations with arbitrary contact situations in two or three dimension, but only along one dimension. We outline a differential-algebraic equation approach for a “numerically exact” computation of friction in two dimensions and compare its application to the Cundall-Strack model in some test cases.
Numerical Methods for Equations and its Applications
Argyros, Ioannis K
2012-01-01
This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.
Evaluation of steel corrosion by numerical analysis
Kawahigashi, Tatsuo
2017-01-01
Recently, various non-destructive and numerical methods have been used and many cases of steel corrosion are examined. For example, methods of evaluating corrosion through various numerical methods and evaluating macrocell corrosion and micro-cell corrosion using measurements have been proposed. However, there are few reports on estimating of corrosion loss with distinguishing the macro-cell and micro-cell corrosion and with resembling an actuality phenomenon. In this study, for distinguishin...
Workflow to numerically reproduce laboratory ultrasonic datasets
Institute of Scientific and Technical Information of China (English)
A. Biryukov; N. Tisato; G. Grasselli
2014-01-01
The risks and uncertainties related to the storage of high-level radioactive waste (HLRW) can be reduced thanks to focused studies and investigations. HLRWs are going to be placed in deep geological re-positories, enveloped in an engineered bentonite barrier, whose physical conditions are subjected to change throughout the lifespan of the infrastructure. Seismic tomography can be employed to monitor its physical state and integrity. The design of the seismic monitoring system can be optimized via con-ducting and analyzing numerical simulations of wave propagation in representative repository geometry. However, the quality of the numerical results relies on their initial calibration. The main aim of this paper is to provide a workflow to calibrate numerical tools employing laboratory ultrasonic datasets. The finite difference code SOFI2D was employed to model ultrasonic waves propagating through a laboratory sample. Specifically, the input velocity model was calibrated to achieve a best match between experi-mental and numerical ultrasonic traces. Likely due to the imperfections of the contact surfaces, the resultant velocities of P- and S-wave propagation tend to be noticeably lower than those a priori assigned. Then, the calibrated model was employed to estimate the attenuation in a montmorillonite sample. The obtained low quality factors (Q) suggest that pronounced inelastic behavior of the clay has to be taken into account in geophysical modeling and analysis. Consequently, this contribution should be considered as a first step towards the creation of a numerical tool to evaluate wave propagation in nuclear waste repositories.
Numerical multi-loop integrals and applications
Freitas, A.
2016-09-01
Higher-order radiative corrections play an important role in precision studies of the electroweak and Higgs sector, as well as for the detailed understanding of large backgrounds to new physics searches. For corrections beyond the one-loop level and involving many independent mass and momentum scales, it is in general not possible to find analytic results, so that one needs to resort to numerical methods instead. This article presents an overview of a variety of numerical loop integration techniques, highlighting their range of applicability, suitability for automatization, and numerical precision and stability. In a second part of this article, the application of numerical loop integration methods in the area of electroweak precision tests is illustrated. Numerical methods were essential for obtaining full two-loop predictions for the most important precision observables within the Standard Model. The theoretical foundations for these corrections will be described in some detail, including aspects of the renormalization, resummation of leading log contributions, and the evaluation of the theory uncertainty from missing higher orders.
Numerical Characterization of Piezoceramics Using Resonance Curves
Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar
2016-01-01
Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods. PMID:28787875
Boundary acquisition for setup of numerical simulation
Energy Technology Data Exchange (ETDEWEB)
Diegert, C. [Sandia National Lab., Albuquerque, NM (United States)
1997-12-31
The author presents a work flow diagram that includes a path that begins with taking experimental measurements, and ends with obtaining insight from results produced by numerical simulation. Two examples illustrate this path: (1) Three-dimensional imaging measurement at micron scale, using X-ray tomography, provides information on the boundaries of irregularly-shaped alumina oxide particles held in an epoxy matrix. A subsequent numerical simulation predicts the electrical field concentrations that would occur in the observed particle configurations. (2) Three-dimensional imaging measurement at meter scale, again using X-ray tomography, provides information on the boundaries fossilized bone fragments in a Parasaurolophus crest recently discovered in New Mexico. A subsequent numerical simulation predicts acoustic response of the elaborate internal structure of nasal passageways defined by the fossil record. The author must both add value, and must change the format of the three-dimensional imaging measurements before the define the geometric boundary initial conditions for the automatic mesh generation, and subsequent numerical simulation. The author applies a variety of filters and statistical classification algorithms to estimate the extents of the structures relevant to the subsequent numerical simulation, and capture these extents as faceted geometries. The author will describe the particular combination of manual and automatic methods used in the above two examples.
Numerical Modeling of Ablation Heat Transfer
Ewing, Mark E.; Laker, Travis S.; Walker, David T.
2013-01-01
A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.
Numerical FEM modeling in dental implantology
Roateşi, Iulia; Roateşi, Simona
2016-06-01
This paper is devoted to a numerical approach of the stress and displacement calculation of a system made up of dental implant, ceramic crown and surrounding bone. This is the simulation of a clinical situation involving both biological - the bone tissue, and non-biological - the implant and the crown, materials. On the other hand this problem deals with quite fine technical structure details - the threads, tapers, etc with a great impact in masticatory force transmission. Modeling the contact between the implant and the bone tissue is important to a proper bone-implant interface model and implant design. The authors proposed a three-dimensional numerical model to assess the biomechanical behaviour of this complex structure in order to evaluate its stability by determining the risk zones. A comparison between this numerical analysis and clinical cases is performed and a good agreement is obtained.
Numerical Evidence for Thermally Induced Monopoles
Wirnsberger, Peter; Lightwood, Roger Adam; Šarić, Anđela; Dellago, Christoph; Frenkel, Daan
2016-01-01
Electrical charges are conserved. The same would be expected to hold for magnetic charges, yet magnetic monopoles have never been observed. It is therefore surprising that the laws of non-equilibrium thermodynamics, combined with Maxwell's equations, suggest that colloidal particles heated or cooled in certain polar or paramagnetic solvents may behave as if they carry an electrical/magnetic charge [J. Phys. Chem. B $\\textbf{120}$, 5987 (2016)]. Here we present numerical simulations that show that the field distribution around a pair of such heated/cooled colloidal particles agrees quantitatively with the theoretical predictions for a pair of oppositely charged electrical or magnetic monopoles. However, in other respects, the non-equilibrium colloids do not behave as monopoles: they cannot be moved by a homogeneous applied field. The numerical evidence for the monopole-like fields around heated/cooled colloids is crucial because the experimental and numerical determination of forces between such colloids would...
Numerical methods and modelling for engineering
Khoury, Richard
2016-01-01
This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems. Uses a “building-block” approach, starting with simpler mathemati...
Action principle for Numerical Relativity evolution systems
Bona, C; Palenzuela, C
2010-01-01
A Lagrangian density is provided, that allows to recover the Z4 evolution system from an action principle. The resulting system is then strongly hyperbolic when supplemented by gauge conditions like '1+log' or 'freezing shift', suitable for numerical evolution. The physical constraint $Z_\\mu = 0$ can be imposed just on the initial data. The corresponding Hamiltonian and canonical equations are also provided. This opens the door to analogous results for other numerical-relativity formalisms, like BSSN, that can be derived from Z4 by a symmetry-breaking procedure. The harmonic formulation can be easily recovered by a slight modification of the procedure. This provides a mechanism for deriving both the field evolution equations and the gauge conditions from the action principle, with a view on using simplectic integrators for a constraint-preserving numerical evolution.
Wave Numerical Model for Shallow Water
Institute of Scientific and Technical Information of China (English)
徐福敏; 严以新; 张长宽; 宋志尧; 茅丽华
2000-01-01
The history of forecasting wind waves by wave energy conservation equation is briefly described. Several currently used wave numerical models for shallow water based on different wave theories are discussed. Wave energy conservation models for the simulation of shallow water waves are introduced,with emphasis placed on the SWAN model, which takes use of the most advanced wave research achievements and has been applied to several theoretical and field conditions. The characteristics and applicability of the model, the finite difference numerical scheme of the action balance equation and its source terms computing methods are described in detail. The model has been verified with the propagation refraction numerical experiments for waves propagating in following and opposing currents; finally, the model is applied to the Haian Gulf area to simulate the wave height and wave period field there, and the results are compared with observed data.
Numerical simulation of the RAMAC benchmark test
Energy Technology Data Exchange (ETDEWEB)
Leblanc, J.E.; Sugihara, M.; Fujiwara, T. [Nagoya Univ. (Japan). Dept. of Aerospace Engineering; Nusca, M. [Nagoya Univ. (Japan). Dept. of Aerospace Engineering; U.S. Army Research Lab., Ballistics and Weapons Concepts Div., AMSRL-WM-BE, Aberdeen Proving Ground, MD (United States); Wang, X. [Nagoya Univ. (Japan). Dept. of Aerospace Engineering; School of Mechanical and Production Engineering, Nanyang Technological Univ. (Singapore); Seiler, F. [Nagoya Univ. (Japan). Dept. of Aerospace Engineering; French-German Research Inst. of Saint-Louis, ISL, Saint-Louis (France)
2000-11-01
Numerical simulations of the same ramac geometry and boundary conditions by different numerical and physical models highlight the variety of solutions possible and the strong effect of the chemical kinetics model on the solution. The benchmark test was defined and announced within the community of ramac researchers. Three laboratories undertook the project. The numerical simulations include Navier-Stokes and Euler simulations with various levels of physical models and equations of state. The non-reactive part of the simulation produced similar steady state results in the three simulations. The chemically reactive part of the simulation produced widely different outcomes. The original experimental data and experimental conditions are presented. A description of each computer code and the resulting flowfield is included. A comparison between codes and results is achieved. The most critical choice for the simulation was the chemical kinetics model. (orig.)
Manufacturing in space: Fluid dynamics numerical analysis
Robertson, S. J.; Nicholson, L. A.; Spradley, L. W.
1981-01-01
Natural convection in a spherical container with cooling at the center was numerically simulated using the Lockheed-developed General Interpolants Method (GIM) numerical fluid dynamic computer program. The numerical analysis was simplified by assuming axisymmetric flow in the spherical container, with the symmetry axis being a sphere diagonal parallel to the gravity vector. This axisymmetric spherical geometry was intended as an idealization of the proposed Lal/Kroes growing experiments to be performed on board Spacelab. Results were obtained for a range of Rayleigh numbers from 25 to 10,000. For a temperature difference of 10 C from the cooling sting at the center to the container surface, and a gravitional loading of 0.000001 g a computed maximum fluid velocity of about 2.4 x 0.00001 cm/sec was reached after about 250 sec. The computed velocities were found to be approximately proportional to the Rayleigh number over the range of Rayleigh numbers investigated.
Numerical methods and analysis of multiscale problems
Madureira, Alexandre L
2017-01-01
This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.
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.
Extraction of Gravitational Waves in Numerical Relativity
Bishop, Nigel T
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.
Introduction to numerical computation in Pascal
Dew, P M
1983-01-01
Our intention in this book is to cover the core material in numerical analysis normally taught to students on degree courses in computer science. The main emphasis is placed on the use of analysis and programming techniques to produce well-designed, reliable mathematical software. The treatment should be of interest also to students of mathematics, science and engineering who wish to learn how to write good programs for mathematical computations. The reader is assumed to have some acquaintance with Pascal programming. Aspects of Pascal particularly relevant to numerical computation are revised and developed in the first chapter. Although Pascal has some drawbacks for serious numerical work (for example, only one precision for real numbers), the language has major compensating advantages: it is a widely used teaching language that will be familiar to many students and it encourages the writing of clear, well structured programs. By careful use of structure and documentation, we have produced codes that we be...
Database application platform for earthquake numerical simulation
Institute of Scientific and Technical Information of China (English)
LUO Yan; ZHENG Yue-jun; CHEN Lian-wang; LU Yuan-zhong; HUANG Zhong-xian
2006-01-01
@@ Introduction In recent years, all kinds of observation networks of seismology have been established, which have been continuously producing numerous digital information. In addition, there are many study results about 3D velocity structure model and tectonic model of crust (Huang and Zhao, 2006; Huang et al, 2003; Li and Mooney, 1998),which are valuable for studying the inner structure of the earth and earthquake preparation process. It is badly needed to combine the observed data, experimental study and theoretical analyses results by the way of numerical simulation and develop a database and a corresponding application platform to be used by numerical simulation,and is also a significant way to promote earthquake prediction.
Numerical shadow and geometry of quantum states
Energy Technology Data Exchange (ETDEWEB)
Dunkl, Charles F [Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137 (United States); Gawron, Piotr; Miszczak, Jaroslaw A; Puchala, Zbigniew [Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Baltycka 5, 44-100 Gliwice (Poland); Holbrook, John A [Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Zyczkowski, Karol, E-mail: cfd5z@virginia.edu, E-mail: gawron@iitis.pl, E-mail: jholbroo@uoguelph.ca, E-mail: miszczak@iitis.pl, E-mail: z.puchala@iitis.pl, E-mail: karol@tatry.if.uj.edu.pl [Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow (Poland)
2011-08-19
The totality of normalized density matrices of dimension N forms a convex set Q{sub N} in R{sup N2-1}. Working with the flat geometry induced by the Hilbert-Schmidt distance, we consider images of orthogonal projections of Q{sub N} onto a two-plane and show that they are similar to the numerical ranges of matrices of dimension N. For a matrix A of dimension N, one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP{sup N-1}. We define generalized, mixed-state shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.
Numerical shadow and geometry of quantum states
Dunkl, Charles F; Holbrook, John A; Miszczak, Jarosław A; Puchała, Zbigniew; Życzkowski, Karol
2011-01-01
The totality of normalised density matrices of order N forms a convex set Q_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q_N onto a two-plane and show that they are similar to the numerical ranges of matrices of order N. For a matrix A of a order N one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We define generalized, mixed-states shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.
Extraction of gravitational waves in numerical relativity
Bishop, Nigel T.; Rezzolla, Luciano
2016-12-01
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.
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Numerical and approximate solutions for plume rise
Krishnamurthy, Ramesh; Gordon Hall, J.
Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).
KWIC Index for Numerical Linear Algebra
Energy Technology Data Exchange (ETDEWEB)
Carpenter, J.A.
1983-07-01
This report is a sequel to ORNL/CSD-106 in the ongoing supplements to Professor A.S. Householder's KWIC Index for Numerical Algebra. Beginning with the previous supplement, the subject has been restricted to Numerical Linear Algebra, roughly characterized by the American Mathematical Society's classification sections 15 and 65F but with little coverage of infinite matrices, matrices over fields of characteristics other than zero, operator theory, optimization and those parts of matrix theory primarily combinatorial in nature. Some consideration is given to the uses of graph theory in Numerical Linear Algebra, particularly with respect to algorithms for sparse matrix computations. The period covered by this report is roughly the calendar year 1982 as measured by the appearance of the articles in the American Mathematical Society's Contents of Mathematical Publications lagging actual appearance dates by up to nearly half a year. The review citations are limited to the Mathematical Reviews (MR).
Numerical stability in problems of linear algebra.
Babuska, I.
1972-01-01
Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.
Numerical Simulation of Underwater Explosion Loads
Institute of Scientific and Technical Information of China (English)
XIN Chunliang; XU Gengguang; LIU Kezhong
2008-01-01
Numerical simulation of TNT underwater explosion was carried out with AUTODYN software.Influences of artificial viscosity and mesh density on simulation results were discussed.Detonation waves in explosive and shock wave in water during early time of explosion are high frequency waves.Fine meshes (less than 1 mm) in explosive and water nearby,and small linear viscosity coefficients and quadratic viscosity coefficients (0.02 and 0.1 respectively,1/10 of default values) are needed in numerical simulation model.According to these rules,numerical computing pressure profiles can match well with those calculated by Zamyshlyayev empirical formula.Otherwise peak pressure would be smeared off and upstream relative errors would be cumulated downstream to make downstream peak pressure lower.
Semidefinite geometry of the numerical range
Henrion, Didier
2008-01-01
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI), an affine section of the semidefinite cone, is always dual to the numerical range of a matrix, which is therefore an affine projection of the semidefinite cone. Both primal and dual sets can also be viewed as convex hulls of explicit algebraic plane curve components. Several numerical examples illustrate this interplay between algebra, geometry and semidefinite programming duality. Finally, these techniques are used to revisit a theorem in statistics on the independence of quadratic forms in a normally distributed vector.
Semidefinite geometry of the numerical range
Henrion, Didier
2010-01-01
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI), an affine section of the semidefinite cone, is always dual to the numerical range of a matrix, which is therefore an affine projection of the semidefinite cone. Both primal and dual sets can also be viewed as convex hulls of explicit algebraic plane curve components. Several numerical examples illustrate this interplay between algebra, geometry and semidefinite programming duality. Finally, these techniques are used to revisit a theorem in statistics on the independence of quadratic forms in a normally distributed vector.
A new numerical method on unstructured grids
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A new numerical method-basic function method is proposed. This method can directly discrete differential operators on unstructured grids. By using the expansion of basic function to approach the exact function,the central and upwind schemes of derivative are constructed. By using the polynomial as basic function,applying the technique of flux splitting method and the combination of central and upwind schemes,the non-physical fluctuation near the shock wave is suppressed. The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for one-,two-and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially,combining with the adaptive remeshing technique,the satisfactory results can be obtained by these schemes.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Energy Technology Data Exchange (ETDEWEB)
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
Design and numerical simulation of novel DBRs
Institute of Scientific and Technical Information of China (English)
Wei Su (苏伟); Jingchang Zhong (钟景昌); Wenli Liu (刘文莉); Yan-Kuin Su (苏炎坤); Shoou-Jinn Chang (张守进); Hsin-Chieh Yu (龙信介); Liangwen Ji (姬梁文); Lin Li (李林); Yingjie Zhao (赵英杰)
2003-01-01
In this paper, a numerical simulation of the traditional graded distributed Bragg reflector (DBR) and a design of the novel DBR with short period superlattices (SPSs DBR) used by vertical cavity surface emitting laser (VCSEL) are reported. First, the optical characteristic matrix of the graded DBRs is derived using the theories of thin film optics. Second, its reflective spectrum is numerical simulated and it is found that the simulative results are similar with the experimental data. The difference of the cavity mode position between the experimental and simulative data is discussed. Finally, based on the simulative results of graded DBR, a novel DBR with 4.5-pair GaAs/AlAs SPSs is designed, and its reflective spectrum is numerical simulated and analyzed.
Benchmarking numerical models of brittle thrust wedges
Buiter, Susanne J. H.; Schreurs, Guido; Albertz, Markus; Gerya, Taras V.; Kaus, Boris; Landry, Walter; le Pourhiet, Laetitia; Mishin, Yury; Egholm, David L.; Cooke, Michele; Maillot, Bertrand; Thieulot, Cedric; Crook, Tony; May, Dave; Souloumiac, Pauline; Beaumont, Christopher
2016-11-01
We report quantitative results from three brittle thrust wedge experiments, comparing numerical results directly with each other and with corresponding analogue results. We first test whether the participating codes reproduce predictions from analytical critical taper theory. Eleven codes pass the stable wedge test, showing negligible internal deformation and maintaining the initial surface slope upon horizontal translation over a frictional interface. Eight codes participated in the unstable wedge test that examines the evolution of a wedge by thrust formation from a subcritical state to the critical taper geometry. The critical taper is recovered, but the models show two deformation modes characterised by either mainly forward dipping thrusts or a series of thrust pop-ups. We speculate that the two modes are caused by differences in effective basal boundary friction related to different algorithms for modelling boundary friction. The third experiment examines stacking of forward thrusts that are translated upward along a backward thrust. The results of the seven codes that run this experiment show variability in deformation style, number of thrusts, thrust dip angles and surface slope. Overall, our experiments show that numerical models run with different numerical techniques can successfully simulate laboratory brittle thrust wedge models at the cm-scale. In more detail, however, we find that it is challenging to reproduce sandbox-type setups numerically, because of frictional boundary conditions and velocity discontinuities. We recommend that future numerical-analogue comparisons use simple boundary conditions and that the numerical Earth Science community defines a plasticity test to resolve the variability in model shear zones.
Numerical methods for scientists and engineers
Antia, H M
2012-01-01
This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.
Perception of numerical methods in rarefied gasdynamics
Bird, G. A.
1989-01-01
The relationships between various numerical methods applied to problems in rarefied gasdynamics are discussed, with emphasis on conflicting viewpoints and computational requirements associated with physical simulation versus the numerical solution of the Boltzmann equation. The basic differences between the molecular dynamics and direct simulation methods are shown to affect their applicability to dense and rarefied flows. Methods for the probabilistic selection of representative collision in the direct simulation Monte Carlo method are reviewed. A method combining the most desirable features of the earlier methods is presented.
QCD and numerical analysis III. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Borici, A.; Joo, B.; Kennedy, A.; Pendleton, B. (eds.) [Edinburgh Univ. (United Kingdom). School of Physics; Frommer, A. [Bergische Univ. Wuppertal (Germany). Fachbereich C - Mathematik und Naturwissenschaften
2005-07-01
This book reports on progress in numerical methods for Lattice QCD with chiral fermions. It contains a set of pedagogical introductory articles written by experts from both the Applied Mathematics and Lattice Field Theory communities, together with detailed accounts of leading-edge algorithms for the simulation of overlap chiral fermions. Topics covered include: QCD simulations in the chiral regime; Evaluation and approximation of matrix functions; Krylov subspace methods for the iterative solution of linear systems; Eigenvalue solvers. These are complemented by a set of articles on closely related numerical and technical problems in Lattice field Theory. (orig.)
The quiet revolution of numerical weather prediction
Bauer, Peter; Thorpe, Alan; Brunet, Gilbert
2015-09-01
Advances in numerical weather prediction represent a quiet revolution because they have resulted from a steady accumulation of scientific knowledge and technological advances over many years that, with only a few exceptions, have not been associated with the aura of fundamental physics breakthroughs. Nonetheless, the impact of numerical weather prediction is among the greatest of any area of physical science. As a computational problem, global weather prediction is comparable to the simulation of the human brain and of the evolution of the early Universe, and it is performed every day at major operational centres across the world.
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Numerical Analysis of Partial Differential Equations
Lui, S H
2011-01-01
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis
Lecture notes in numerical analysis with Mathematica
Styś, Tadeusz
2014-01-01
The contents of this book include chapters on floating point computer arithmetic, natural and generalized interpolating polynomials, uniform approximation, numerical integration, polynomial splines and many more.This book is intended for undergraduate and graduate students in institutes, colleges, universities and academies who want to specialize in this field. The readers will develop a solid understanding of the concepts of numerical methods and their application. The inclusion of Lagrane and Hermite approximation by polynomials, Trapezian rule, Simpsons rule, Gauss methods and Romberg`s met
Numerical Solutions of Fractional Boussinesq Equation
Institute of Scientific and Technical Information of China (English)
WANG Qi
2007-01-01
Based upon the Adomian decomposition method,a scheme is developed to obtain numerical solutions of a fractional Boussinesq equation with initial condition,which is introduced by replacing some order time and space derivatives by fractional derivatives.The fractional derivatives are described in the Caputo sense.So the traditional Adomian decomposition method for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional differential equations.The solutions of our model equation are calculated in the form of convergent series with easily computable components.
Numerical solution of the stochastic collection equation
Simmel, Martin
2016-01-01
The Linear Discrete Method (LDM; SIMMEL 2000; SIMMEL ET AL. 2000) is used to solve the Stochastic Collection Equation (SCE) numerically. Comparisons are made to the Method of Moments (MOM; TzIVION ET AL. 1999) which is suggested as a reference for numerical solutions of the SCE. Simulations for both methods are shown for the GoLOVIN kernel (for which an analytical solution is available) and the hydrodynamic kernel after LONG (1974) as it is used by TZIVION ET AL. (1999). Different bin resolut...
Numerical analysis in electromagnetics the TLM method
Saguet, Pierre
2013-01-01
The aim of this book is to give a broad overview of the TLM (Transmission Line Matrix) method, which is one of the "time-domain numerical methods". These methods are reputed for their significant reliance on computer resources. However, they have the advantage of being highly general.The TLM method has acquired a reputation for being a powerful and effective tool by numerous teams and still benefits today from significant theoretical developments. In particular, in recent years, its ability to simulate various situations with excellent precision, including complex materials, has been
Numerical experiments in revisited brittle fracture
DEFF Research Database (Denmark)
Bourdin, Blaise; Francfort, Gilles A; Marigo, Jean-Jacques
2000-01-01
The numerical implementation of the model of brittle fracture developed in~ Francfort and Marigo (1998) is presented. Various computational methods based on variational approximations of the original functional are proposed. They are tested on several antiplanar and planar examples that are beyon...... the reach of the classical computational tools of fracture mechanics.......The numerical implementation of the model of brittle fracture developed in~ Francfort and Marigo (1998) is presented. Various computational methods based on variational approximations of the original functional are proposed. They are tested on several antiplanar and planar examples that are beyond...
Numerical study of fractional nonlinear Schrodinger equations
Klein, Christian
2014-10-08
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.
On the Hughes model and numerical aspects
Gomes, Diogo A.
2017-01-05
We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.
The Numerical Approximation of Functional Differential Equations
Venturi, Daniele
2016-01-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equations), quantum field theory (Schwinger-Dyson equations) and statistical physics (equations for generating functionals and effective action methods). However, no effective numerical method has yet been developed to compute their solution. The purpose of this manuscript is to fill this gap, and provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.
Susy Theories and QCD: Numerical Approaches
Ita, Harald
2011-01-01
We review on-shell and unitarity methods and discuss their application to precision predictions for LHC physics. Being universal and numerically robust, these methods are straight-forward to automate for next-to-leading-order computations within Standard Model and beyond. Several state-of-the-art results including studies of W/Z+3-jet and W+4-jet production have explicitly demonstrated the effectiveness of the unitarity method for describing multi-parton scattering. Here we review central ideas needed to obtain efficient numerical implementations. This includes on-shell loop-level recursions, the unitarity method, color management and further refined tricks.
Numerical Algorithms Based on Biorthogonal Wavelets
Ponenti, Pj.; Liandrat, J.
1996-01-01
Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.
Fundamentals of Numerical Modelling of Casting Processes
DEFF Research Database (Denmark)
Pryds, Nini; Thorborg, Jesper; Lipinski, Marek;
Fundamentals of Numerical Modelling of Casting Processes comprises a thorough presentation of the basic phenomena that need to be addressed in numerical simulation of casting processes. The main philosophy of the book is to present the topics in view of their physical meaning, whenever possible......, rather than relying strictly on mathematical formalism. The book, aimed both at the researcher and the practicing engineer, as well as the student, is naturally divided into four parts. Part I (Chapters 1-3) introduces the fundamentals of modelling in a 1-dimensional framework. Part II (Chapter 4...
Analysis of Numerically Generated Wake Structures
DEFF Research Database (Denmark)
Ivanell, S.; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming;
2009-01-01
Direct numerical simulations of the Navier-Stokes equations are performed to achieve a better understanding of the behaviour of wakes generated by wind turbines. The simulations are performed by combining the in-house developed computer code EllipSys3D with the actuator-line methodology. In the a......Direct numerical simulations of the Navier-Stokes equations are performed to achieve a better understanding of the behaviour of wakes generated by wind turbines. The simulations are performed by combining the in-house developed computer code EllipSys3D with the actuator-line methodology...
Theoretical and numerical method in aeroacoustics
Directory of Open Access Journals (Sweden)
Nicuşor ALEXANDRESCU
2010-06-01
Full Text Available The paper deals with the mathematical and numerical modeling of the aerodynamic noisegenerated by the fluid flow interaction with the solid structure of a rotor blade.Our analysis use Lighthill’s acoustic analogy. Lighthill idea was to express the fundamental equationsof motion into a wave equation for acoustic fluctuation with a source term on the right-hand side. Theobtained wave equation is solved numerically by the spatial discretization. The method is applied inthe case of monopole source placed in different points of blade surfaces to find this effect of noisepropagation.
Numerical and analytical methods with Matlab
Bober, William; Masory, Oren
2013-01-01
Numerical and Analytical Methods with MATLAB® presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve systems of linear equations, ODEs, roots of transcendental equations, statistical problems, optimization problems, control systems problems, and stress analysis problems. These built-in functions are essentially black boxes to students. By combining MATLAB with basic numerical and analytical techniques, the mystery of what these black boxes might contain is somewhat alleviated. This classroom-tested
Masonry constructions mechanical models and numerical applications
Lucchesi, Massimiliano; Padovani, Cristina
2008-01-01
Numerical methods for the structural analysis of masonry constructions can be of great value in assessing the safety of artistically important masonry buildings and optimizing potential operations of maintenance and strengthening in terms of their cost-effectiveness, architectural impact and static effectiveness. This monograph firstly provides a detailed description of the constitutive equation of masonry-like materials, clearly setting out its most important features. It then goes on to provide a numerical procedure to solve the equilibrium problem of masonry solids. A large portion of the w
Study of Cardiac Defibrillation Through Numerical Simulations
Bragard, J.; Marin, S.; Cherry, E. M.; Fenton, F. H.
Three-dimensional numerical simulations of the defibrillation problem are presented. In particular, in this study we use the rabbit ventricular geometry as a realistic model system for evaluating the efficacy of defibrillatory shocks. Statistical data obtained from the simulations were analyzed in term of a dose-response curve. Good quantitative agreement between our numerical results and clinically relevant values is obtained. An electric field strength of about 6.6 V/cm indicates a fifty percent probability of successful defibrillation for a 12-ms monophasic shock. Our validated model will be useful for optimizing defibrillation protocols.
Numerical integration using Wang Landau sampling
Li, Y. W.; Wüst, T.; Landau, D. P.; Lin, H. Q.
2007-09-01
We report a new application of Wang-Landau sampling to numerical integration that is straightforward to implement. It is applicable to a wide variety of integrals without restrictions and is readily generalized to higher-dimensional problems. The feasibility of the method results from a reinterpretation of the density of states in statistical physics to an appropriate measure for numerical integration. The properties of this algorithm as a new kind of Monte Carlo integration scheme are investigated with some simple integrals, and a potential application of the method is illustrated by the evaluation of integrals arising in perturbation theory of quantum many-body systems.
Introduction to 3+1 numerical relativity
Alcubierre, Miguel
2008-01-01
This book introduces the modern field of 3+1 numerical relativity. The book has been written in a way as to be as self-contained as possible, and only assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail arethe following: the initial data problem, hyperbolic reductions of the field equations, gauge conditions, the evol
Experimental and Numerical Study of Damaged Cantilever
DEFF Research Database (Denmark)
Rytter, A.; Krawczuk, M.; Kirkegaard, Poul Henning
2000-01-01
The introduction of a crack in a steel structure will cause a local change in the stiffness and damping capacity. The change in stiffness will lead to a change of some of the natural frequencies of the structure and a discontinuity in the associated mode shapes. This paper contains a presentation...... of the results from experimental and numerical tests with hollow section cantileves containing fatigue cracks. Two different finite-element (FE) models have been used to estimate the modal parameters numerically. The first FE model consists of beam elements. The second FE model consists of traditional...
Numerical orbit generators of artificial earth satellites
Kugar, H. K.; Dasilva, W. C. C.
1984-04-01
A numerical orbit integrator containing updatings and improvements relative to the previous ones that are being utilized by the Departmento de Mecanica Espacial e Controle (DMC), of INPE, besides incorporating newer modellings resulting from the skill acquired along the time is presented. Flexibility and modularity were taken into account in order to allow future extensions and modifications. Characteristics of numerical accuracy, processing quickness, memory saving as well as utilization aspects were also considered. User's handbook, whole program listing and qualitative analysis of accuracy, processing time and orbit perturbation effects were included as well.
Numerical Analysis of Partial Differential Equations
Lions, Jacques-Louis
2011-01-01
S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J.H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B.E. Hubbard: Erro
Numerical Methods for Partial Differential Equations
Guo, Ben-yu
1987-01-01
These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.
Upper Bounds on Numerical Approximation Errors
DEFF Research Database (Denmark)
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function....... The bounds apply to moregeneral problems than existing bounding methods do. For instance, since strict concavityis not required, linear models and piecewise linear approximations can bedealt with. Despite the generality, the bounds perform well in comparison with existingmethods even when applied...... to approximations of a standard (strictly concave)growth model.KEYWORDS: Numerical approximation errors, Bellman contractions, Error bounds...
When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo...
Lourenco, Stella F.; Bonny, Justin W.
2017-01-01
A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises…
Numerical Modeling of Piezoelectric Transducers Using Physical Parameters
Cappon, H.; Keesman, K.J.
2012-01-01
Design of ultrasonic equipment is frequently facilitated with numerical models. These numerical models, however, need a calibration step, because usually not all characteristics of the materials used are known. Characterization of material properties combined with numerical simulations and experimen
Numerical simulation package for speckle metrology
Kornis, Janos; Bokor, Nandor; Nemeth, Attila
1998-09-01
A computer program package for numerical simulation of speckle phenomena has been developed. It is suitable for simulating both objective and subjective speckle effects in various optical setups. Several simulation results are presented in this paper. The simulations was made in UNIX and Windows NT environment.
Benchmarking numerical models of brittle thrust wedges
Buiter, Susanne J H; Schreurs, Guido; Albertz, Markus; Gerya, Taras V.; Kaus, Boris; Landry, Walter; le Pourhiet, Laetitia; Mishin, Yury; Egholm, David L.; Cooke, Michele; Maillot, Bertrand; Thieulot, Cedric; Crook, Tony; May, Dave; Souloumiac, Pauline; Beaumont, Christopher
2016-01-01
We report quantitative results from three brittle thrust wedge experiments, comparing numerical results directly with each other and with corresponding analogue results. We first test whether the participating codes reproduce predictions from analytical critical taper theory. Eleven codes pass the s
Numerical Limit Analysis of Precast Concrete Structures
DEFF Research Database (Denmark)
Herfelt, Morten Andersen; Poulsen, Peter Noe; Hoang, Linh Cao
2016-01-01
optimisation as well as material optimisation is given and a four-storey shear wall is analysed using load optimisation. The analysis yields a capacity more than three times larger than the design load for the critical load case, and the collapse mode and stress distribution are analysed. Finally, numerical...
Numerical simulation of polariton Bose gas thermalization
Kartsev, P. F.; Kuznetsov, I. O.
2016-08-01
In this work, we present the numerical simulation of the process a Bose gas thermalization and the formation of the condensate. Our approach is based on kinetic equations and “Fermi's golden rule” in the incoherent approximation. Direct summation of terms is performed using GPGPU OpenCL parallel code using AMD Radeon HD 7970.
Experiments in orbit determination using numerical methods
Traas, C.R.
1985-01-01
The dynamics of the observed object is written as a system of integral equations. This system is solved numerically by representing the components of the force function as linear combinations of B-splines and by applying the multigrid technique. In an outer loop the orbit determination problem is
Numerical Methods through Open-Ended Projects
Cline, Kelly S.
2005-01-01
We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…
Numerical pole assignment by eigenvalue Jacobian inversion
Sevaston, George E.
1986-01-01
A numerical procedure for solving the linear pole placement problem is developed which operates by the inversion of an analytically determined eigenvalue Jacobian matrix. Attention is given to convergence characteristics and pathological situations. It is not concluded that the algorithm developed is suitable for computer-aided control system design with particular reference to the scan platform pointing control system for the Galileo spacecraft.
A brain area for visual numerals.
Shum, Jennifer; Hermes, Dora; Foster, Brett L; Dastjerdi, Mohammad; Rangarajan, Vinitha; Winawer, Jonathan; Miller, Kai J; Parvizi, Josef
2013-04-17
Is there a distinct area within the human visual system that has a preferential response to numerals, as there is for faces, words, or scenes? We addressed this question using intracranial electrophysiological recordings and observed a significantly higher response in the high-frequency broadband range (high γ, 65-150 Hz) to visually presented numerals, compared with morphologically similar (i.e., letters and false fonts) or semantically and phonologically similar stimuli (i.e., number words and non-number words). Anatomically, this preferential response was consistently localized in the inferior temporal gyrus and anterior to the temporo-occipital incisure. This region lies within or close to the fMRI signal-dropout zone produced by the nearby auditory canal and venous sinus artifacts, an observation that may account for negative findings in previous fMRI studies of preferential response to numerals. Because visual numerals are culturally dependent symbols that are only learned through education, our novel finding of anatomically localized preferential response to such symbols provides a new example of acquired category-specific responses in the human visual system.
Numerical 3-D Modelling of Overflows
DEFF Research Database (Denmark)
Larsen, Torben; Nielsen, L.; Jensen, B.;
2008-01-01
The present study uses laboratory experiments to evaluate the reliability of two types of numerical models of sewers systems: - 1-dimensional model based on the extended Saint-Venant equation including the term for curvature of the water surface (the so-called Boussinesq approximation) - 2- and 3...
Numerical methods in multidimensional radiative transfer
Meinköhn, Erik
2008-01-01
Offers an overview of the numerical modelling of radiation fields in multidimensional geometries. This book covers advances and problems in the mathematical treatment of the radiative transfer equation, a partial integro-differential equation of high dimension that describes the propagation of the radiation in various fields.
Smooth structures on Eschenburg spaces: numerical computations
Butler, Leo T
2009-01-01
This paper numerically computes the topological and smooth invariants of Eschenburg spaces with small fourth cohomology group, following Kruggel's determination of the Kreck-Stolz invariants of Eschenburg spaces that satisfy condition C. The GNU GMP arbitrary-precision library is utilised.
Quantitative Relationships Involving Additive Differences: Numerical Resilience
Ramful, Ajay; Ho, Siew Yin
2014-01-01
This case study describes the ways in which problems involving additive differences with unknown starting quantities, constrain the problem solver in articulating the inherent quantitative relationship. It gives empirical evidence to show how numerical reasoning takes over as a Grade 6 student instantiates the quantitative relation by resorting to…
Advances in numerical modelling of crash dummies
Verhoeve, R.; Kant, R.; Margerie, L.
2001-01-01
Nowadays virtual testing and prototyping are generally accepted methods in crash safety research and design studies. Validated numerical crash dummy models are necessary tools in these methods. Computer models need to be robust, accurate and CPU efficient, where the balance between accuracy and effi
Numerical Analysis of Large Diameter Butterfly Valve
Youngchul, Park; Xueguan, Song
In this paper, a butterfly valve with the diameter of 1,800 mm was studied. Three-dimensional numerical technique by using commercial code CFX were conducted to observe the flow patterns and to measure flow coefficient, hydrodynamic torque coefficient and so on, when the large butterfly valve operated with various angles and uniform incoming velocity.
Some Numerical Characteristics of Image Texture
Directory of Open Access Journals (Sweden)
O. Samarina
2012-05-01
Full Text Available Texture classification is one of the basic images processing tasks. In this paper we present some numerical characteristics to the images analysis and processing. It can be used at the solving of images classification problems, their recognition, problems of remote sounding, biomedical images analysis, geological researches.
Numerical Study of Planar GPR Antenna Measurements
DEFF Research Database (Denmark)
Meincke, Peter; Hansen, Thorkild
2004-01-01
The formulation of planar near-field measurements of GPR antennas determines the plane-wave spectra of the GPR antenna in terms of measurements obtained with a buried probe as the GPR antenna moves over a scan plane on the ground. A numerical study investigates how the formulation is affected by (1...
Numerical Solution of the Beltrami Equation
Porter, R. Michael
2008-01-01
An effective algorithm is presented for solving the Beltrami equation fzbar = mu fz in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy, working in concentric rings, is to construct a piecewise linear mu-conformal mapping and then correct the image using a known algorithm for conformal mappings. Numerical examples are provided and the computational complexity is analyzed.
Numerically Controlled Machine Tools and Worker Skills.
Keefe, Jeffrey H.
1991-01-01
Analysis of data from "Industry Wage Surveys of Machinery Manufacturers" on the skill levels of 57 machining jobs found that introduction of numerically controlled machine tools has resulted in a very small reduction in skill levels or no significant change, supporting neither the deskilling argument nor argument that skill levels…
Numerical method for solving fuzzy wave equation
Kermani, M. Afshar
2013-10-01
In this study a numerical method for solving "fuzzy partial differential equation" (FPDE) is considered. We present difference method to solve the FPDEs such as fuzzy hyperbolic equation, then see if stability of this method exist, and conditions for stability are given.
Numerical Methods for Structured Matrices and Applications
Bini, Dario A; Olshevsky, Vadim; Tyrtsyhnikov, Eugene; van Barel, Marc
2010-01-01
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications to system theory and signal processing.
Parametrical Numerical Study on Breakwater SSG Application
DEFF Research Database (Denmark)
Margheritini, Lucia; Kofoed, Jens Peter
The report presents numerical investigations on the performance of the SSG concept for different tide and wave conditions towards different levels of discretization to an optimal solution. Benefit of extra reservoir utilization and reservoir length has also been investigated. The report must be c...
Python Classes for Numerical Solution of PDE's
Mushtaq, Asif; Olaussen, Kåre
2015-01-01
We announce some Python classes for numerical solution of partial differential equations, or boundary value problems of ordinary differential equations. These classes are built on routines in \\texttt{numpy} and \\texttt{scipy.sparse.linalg} (or \\texttt{scipy.linalg} for smaller problems).
Numerical methods and optimization a consumer guide
Walter, Éric
2014-01-01
Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods and Optimization – A Consumer Guide presents methods for dealing with them. Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to · discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems; · understand the principles behind recognized algorithms used in state-of-the-art numerical software; · learn the advantag...
On the Complexity of Numerical Analysis
DEFF Research Database (Denmark)
Miltersen, Peter Bro; Kjeldgaard-Pedersen, Johan; Burgisser, Peter;
2006-01-01
We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis. We show that both hinge on the question of understanding the complexity of the following problem, which we call PosSLP: Given a division-free straight-line program producing...... of classical complexity classes) being PSPACE....
Numerically Controlled Machine Tools and Worker Skills.
Keefe, Jeffrey H.
1991-01-01
Analysis of data from "Industry Wage Surveys of Machinery Manufacturers" on the skill levels of 57 machining jobs found that introduction of numerically controlled machine tools has resulted in a very small reduction in skill levels or no significant change, supporting neither the deskilling argument nor argument that skill levels…
Advances in numerical modelling of crash dummies
Verhoeve, R.; Kant, R.; Margerie, L.
2001-01-01
Nowadays virtual testing and prototyping are generally accepted methods in crash safety research and design studies. Validated numerical crash dummy models are necessary tools in these methods. Computer models need to be robust, accurate and CPU efficient, where the balance between accuracy and effi
Numerical simulations of the solar atmosphere
Leenaarts, J.
2007-01-01
In this thesis several aspects of the solar atmosphere are investigated using numerical simulations. Simulations and observations of reversed solar granulation are compared. It is concluded that reversed granulation is a hydrodynamical process and is a consequence of convection reversal. Images are
A History of Computer Numerical Control.
Haggen, Gilbert L.
Computer numerical control (CNC) has evolved from the first significant counting method--the abacus. Babbage had perhaps the greatest impact on the development of modern day computers with his analytical engine. Hollerith's functioning machine with punched cards was used in tabulating the 1890 U.S. Census. In order for computers to become a…
Numerical simulation of the fractional Langevin equation
Directory of Open Access Journals (Sweden)
Guo Peng
2012-01-01
Full Text Available In this paper, we study the fractional Langevin equation, whose derivative is in Caputo sense. By using the derived numerical algorithm, we obtain the displacement and the mean square displacement which describe the dynamic behaviors of the fractional Langevin equation.
DEFF Research Database (Denmark)
Møhlenberg, Flemming; Christensen, Erik Damgaard
2015-01-01
. The planning and design of MUPS in MERMAID has therefore not only involved standard engineering methods, but also advanced numerical tools, that can enable a detailed understanding of the environment and the interactions between the MUP and the surrounding water environments. The intention of this report...
RECOGNITION AND VERIFICATION OF TOUCHING HANDWRITTEN NUMERALS
Zhou, J.; Kryzak, A.; Suen, C.Y.
2004-01-01
In the field of financial document processing, recognition of touching handwritten numerals has been limited by lack of good benchmarking databases and low reliability of algorithms. This paper addresses the efforts toward solving the two problems. Two databases IRIS-Bell\\\\\\'98 and TNIST are built/o
Spectral Methods in Numerical Plasma Simulation
DEFF Research Database (Denmark)
Coutsias, E.A.; Hansen, F.R.; Huld, T.;
1989-01-01
An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded...
Segmentation and Recognition of Handwritten Numeric Chains
Directory of Open Access Journals (Sweden)
Salim Ouchtati
2007-01-01
Full Text Available Automatic reading of numeric chains has been attempted in several application areas such as bank cheque processing, postal code recognition and form processing. Such applications have been very popular in handwriting recognition research, due to the possibility to reduce considerably the manual effort involved in these tasks. In this study we propose an off line system for the recognition of the handwritten numeric chains. Firstly, study was based mainly on the evaluation of neural network performances, trained with the gradient back propagation algorithm. Used parameters to form the input vector of the neural network are extracted on the binary images of the digits by several methods: distribution sequence, Barr features and centred moments of different projections and profiles. Secondly, study was extented for the reading of the handwritten numeric chains constituted of a variable number of digits. Vertical projection was used to segment the numeric chain at isolated digits and every digit (or segment was presented separately to the entry of the system achieved in the first part (recognition system of the isolated handwritten digits. The performances of the proposed system for the used database attain a recognition rate equal to 91.3%.
On the stability of numerical integration routines.
Glover, K.; Willems, J. C.
1972-01-01
Numerical integration methods for the solution of initial value problems for ordinary vector differential equations may be modelled as discrete time feedback systems. The stability criteria discovered in modern control theory are applied to these systems and criteria involving the routine, the step size and the differential equation are derived. Linear multistep, Runge-Kutta, and predictor-corrector methods are all investigated.
Numerical simulations of stellar winds: polytropic models
Keppens, R.; Goedbloed, J. P.
1999-01-01
We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We proceed stepwise from a spher
Numerical simulation of tyre/road noise
Schutte, Jan Henk
2011-01-01
In modern society, traffic noise has become an important issue for mental health. A significant contributor to this noise pollution is exterior tyre/road noise, which is caused by the interaction between tyre and road surface and. In order to reduce tyre/road noise at the source, accurate numerical
Multiaxis Computer Numerical Control Internship Report
Rouse, Sharon M.
2012-01-01
(Purpose) The purpose of this paper was to examine the issues associated with bringing new technology into the classroom, in particular, the vocational/technical classroom. (Methodology) A new Haas 5 axis vertical Computer Numerical Control machining center was purchased to update the CNC machining curriculum at a community college and the process…
Review of numerical special relativistic hydrodynamics
Odyck, D.E.A. van
2002-01-01
This paper gives an overview of numerical methods for special relativistichydrodynamics (SRHD). First, a short summary of special relativity is given. Next, the SRHD equations are introduced. The exact solution for the SRHD Riemann problem is described. This solution is used in a Godunov scheme to c
Numerical CFD Comparison of Lillgrund Employing RANS
DEFF Research Database (Denmark)
Simisiroglou, N.; Breton, S.-P.; Crasto, G.
2014-01-01
The following article will validate the results obtained using the actuator disc method in the state of the art numerical Computational Fluid Dynamic (CFD) tool WindSim using on-site measurements from the offshore wind farm Lillgrund. WindSim solves the mass, momentum and energy conservation...
Numerical methods for hyperbolic differential functional problems
Directory of Open Access Journals (Sweden)
Roman Ciarski
2008-01-01
Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
Numerical Study of Planar GPR Antenna Measurements
DEFF Research Database (Denmark)
Meincke, Peter; Hansen, Thorkild
2004-01-01
The formulation of planar near-field measurements of GPR antennas determines the plane-wave spectra of the GPR antenna in terms of measurements obtained with a buried probe as the GPR antenna moves over a scan plane on the ground. A numerical study investigates how the formulation is affected by (1...
Amorphous track models: A numerical comparison study
DEFF Research Database (Denmark)
Greilich, Steffen; Grzanka, L.; Bassler, N.;
2010-01-01
We present an open-source code library for amorphous track modelling which is suppose to faciliate the application and numerical comparability as well as serve as a frame-work for the implementation of new models. We show an example of using the library indicating the choice of submodels has a si...
Decision of numerical problems with symbolic methods
Directory of Open Access Journals (Sweden)
I. S. Kashirsky
2010-01-01
Full Text Available Modern methods for numerical decision of linear systems guarantee successful results only for good systems. Decision of bad systems (bad conditional, singular is already problem. This paper describes using symbol methods for decision of bad conditional and singular systems.
Detailed numerical simulations of laser cooling processes
Ramirez-Serrano, J.; Kohel, J.; Thompson, R.; Yu, N.
2001-01-01
We developed a detailed semiclassical numerical code of the forces applied on atoms in optical and magnetic fields to increase the understanding of the different roles that light, atomic collisions, background pressure, and number of particles play in experiments with laser cooled and trapped atoms.
Numerical Simulations of a Vibrating Elasticum
DEFF Research Database (Denmark)
Sinclair, Robert
1999-01-01
Two robust numerical algorithms for simulating the dynamics of a clamped, massless, incompressibleelasticum with a unit point mass at the free end are presented, along with some first results concerning various modes of oscillation, and further data with some relevance to the question of whether...
Numerical Study of Phase Transition in Thermoviscoelasticity
Institute of Scientific and Technical Information of China (English)
ShaoqingTANG
1997-01-01
We study the spatially periodic problem of thermoviscoelasticity with nonmonotone structure relations.By pseudo-spectral method.we demosnstrate numerically phase transitions for certain symmetric initial data.Without symmetry,the simulations show that a translation occurs for the phase boundary.
Power and thermal efficient numerical processing
DEFF Research Database (Denmark)
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...
Numerical Quadrature of Periodic Singular Integral Equations
DEFF Research Database (Denmark)
Krenk, Steen
1978-01-01
This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally...... it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....
Numerical methods in electron magnetic resonance
Energy Technology Data Exchange (ETDEWEB)
Soernes, A.R
1998-07-01
The focal point of the thesis is the development and use of numerical methods in the analysis, simulation and interpretation of Electron Magnetic Resonance experiments on free radicals in solids to uncover the structure, the dynamics and the environment of the system.
Numerical Modelling of Ground Penetrating Radar Antennas
Giannakis, Iraklis; Giannopoulos, Antonios; Pajewski, Lara
2014-05-01
Numerical methods are needed in order to solve Maxwell's equations in complicated and realistic problems. Over the years a number of numerical methods have been developed to do so. Amongst them the most popular are the finite element, finite difference implicit techniques, frequency domain solution of Helmontz equation, the method of moments, transmission line matrix method. However, the finite-difference time-domain method (FDTD) is considered to be one of the most attractive choice basically because of its simplicity, speed and accuracy. FDTD first introduced in 1966 by Kane Yee. Since then, FDTD has been established and developed to be a very rigorous and well defined numerical method for solving Maxwell's equations. The order characteristics, accuracy and limitations are rigorously and mathematically defined. This makes FDTD reliable and easy to use. Numerical modelling of Ground Penetrating Radar (GPR) is a very useful tool which can be used in order to give us insight into the scattering mechanisms and can also be used as an alternative approach to aid data interpretation. Numerical modelling has been used in a wide range of GPR applications including archeology, geophysics, forensic, landmine detection etc. In engineering, some applications of numerical modelling include the estimation of the effectiveness of GPR to detect voids in bridges, to detect metal bars in concrete, to estimate shielding effectiveness etc. The main challenges in numerical modelling of GPR for engineering applications are A) the implementation of the dielectric properties of the media (soils, concrete etc.) in a realistic way, B) the implementation of the geometry of the media (soils inhomogeneities, rough surface, vegetation, concrete features like fractures and rock fragments etc.) and C) the detailed modelling of the antenna units. The main focus of this work (which is part of the COST Action TU1208) is the accurate and realistic implementation of GPR antenna units into the FDTD
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2008-09-01
Full Text Available This article presents a comprehensive overview of numerical hydrodynamics and magnetohydrodynamics (MHD in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003, most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable
Numerical considerations in simulating the global magnetosphere
Directory of Open Access Journals (Sweden)
A. J. Ridley
2010-08-01
Full Text Available Magnetohydrodynamic (MHD models of the global magnetosphere are very good research tools for investigating the topology and dynamics of the near-Earth space environment. While these models have obvious limitations in regions that are not well described by the MHD equations, they can typically be used (or are used to investigate the majority of magnetosphere. Often, a secondary consideration is overlooked by researchers when utilizing global models – the effects of solving the MHD equations on a grid, instead of analytically. Any discretization unavoidably introduces numerical artifacts that affect the solution to various degrees. This paper investigates some of the consequences of the numerical schemes and grids that are used to solve the MHD equations in the global magnetosphere. Specifically, the University of Michigan's MHD code is used to investigate the role of grid resolution, numerical schemes, limiters, inner magnetospheric density boundary conditions, and the artificial lowering of the speed of light on the strength of the ionospheric cross polar cap potential and the build up of the ring current in the inner magnetosphere. It is concluded that even with a very good solver and the highest affordable grid resolution, the inner magnetosphere is not grid converged. Artificially reducing the speed of light reduces the numerical diffusion that helps to achieve better agreement with data. It is further concluded that many numerical effects work nonlinearly to complicate the interpretation of the physics within the magnetosphere, and so simulation results should be scrutinized very carefully before a physical interpretation of the results is made. Our conclusions are not limited to the Michigan MHD code, but apply to all MHD models due to the limitations of computational resources.
Product numerical range in a space with tensor product structure
Puchała, Zbigniew; Miszczak, Jarosław Adam; Skowronek, Łukasz; Choi, Man-Duen; Zyczkowski, Karol \\
2010-01-01
We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.
R-T instability model of magnetic fluid and its numerical simulations
Institute of Scientific and Technical Information of China (English)
郑秋云; 李明军; 舒适
2008-01-01
The Rayleigh-Taylor(R-T) instability of ferrofluid has been the subject of recent research,because of its implications on the stability of stellar.By neglecting the viscosity and rotation of magnetic fluid,and assuming that the magnetic particles are irrotational and temperature insensitive,we obtain a simplified R-T instability model of magnetic fluid.For the interface tracing,we use five-order weighted essentially non-oscillatory(WENO) scheme to spatial direction and three-order TVD R-K method to time direction on the uniform mesh,respectively.If the direction of the external magnetic field is the same as that of gravity,the velocities of the interface will be increased.But if the direction of the external magnetic field is in opposition to the direction of gravity,the velocities of the interface will be decreased.When the direction of the external magnetic field is perpendicular to the direction of gravity,the symmetry of the interface will be destroyed.Because of the action which is produced by perpendicular external magnetic field,there are other bubbles at the boudaries which parallel the direction of gravity.When we increase the magnetic susceptibility of the magnetic fluids,the effects of external magnetic fields will be more distinct for the interface tracing.
Institute of Scientific and Technical Information of China (English)
QingdongCAI
1999-01-01
A new technique in the formulation of numerical scheme for hyperbolic equation is developed.It is different from the classical FD and FE methods.We begin with the algebraic equations with some undefined parameters,and get the difference equation through Taylor-series expansion.When the parameters in the partial difference equation are defined,the equation is what the scheme will simulated.The numerical example of the viscous BUrgers equation shows the validity of the scheme.This method deals with the numerical viscosity and dispersion exactly ,giving a preliminary explanation to some problems that the CFD face now.
Numerical Simulation of the Lightning Return Stroke.
da Frota Mattos, Marcos Andre
Available from UMI in association with The British Library. Requires signed TDF. Several lightning return stroke models were developed in this work. Initially very simple models were developed, and subsequently many of the main features of the channel were added. The corona effect, the geometrical parameters, non-linear losses and the cloud losses are these features. To solve the RLC network model of the channel the numerical technique known as TLM was used. A numerical sensitivity study was made to analyse the influence of the filtering and the Gibbs effects on the results. A sensitivity study of the channel's parameters was also made. For the first time three of the main measured lightning channel quantities were calculated showing good agreement with observations. These quantities are the electromagnetic field, current waveshape at ground and the velocity of propagation. The surge impedence and the current rise-time were also calculated at all heights.
Numerical Simulation of Oil Spill in Ocean
Directory of Open Access Journals (Sweden)
Yong-Sik Cho
2012-01-01
Full Text Available The spreading of oil in an open ocean may cause serious damage to a marine environmental system. Thus, an accurate prediction of oil spill is very important to minimize coastal damage due to unexpected oil spill accident. The movement of oil may be represented with a numerical model that solves an advection-diffusion-reaction equation with a proper numerical scheme. In this study, the spilled oil dispersion model has been established in consideration of tide and tidal currents simultaneously. The velocity components in the advection-diffusion-reaction equation are obtained from the shallow-water equations. The accuracy of the model is verified by applying it to a simple but significant problem. The results produced by the model agree with corresponding analytical solutions and field-observed data. The model is then applied to predict the spreading of an oil spill in a real coastal environment.
Lattice Boltzmann Model for Numerical Relativity
Ilseven, E
2015-01-01
In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for Numerical Relativity. Our model is validated with well-established tests, showing good agreement with analytical solutions. Furthermore, we show that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improves. Finally, in order to show the potential of our approach a linear scaling law for parallelisation with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
Higher dimensional Numerical Relativity: code comparison
Witek, Helvi; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Shibata, Masaru; Sperhake, Ulrich; Zilhao, Miguel
2014-01-01
The nonlinear behavior of higher dimensional black hole spacetimes is of interest in several contexts, ranging from an understanding of cosmic censorship to black hole production in high-energy collisions. However, nonlinear numerical evolutions of higher dimensional black hole spacetimes are tremendously complex, involving different diagnostic tools and "dimensional reduction methods". In this work we compare two different successful codes to evolve Einstein's equations in higher dimensions, and show that the results of such different procedures agree to numerical precision, when applied to the collision from rest of two equal-mass black holes. We calculate the total radiated energy to be E/M=9x10^{-4} in five dimensions and E/M=8.1x10^{-4} in six dimensions.
Numerical simulation of semisolid continuous casting process
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A general mathematical model and boundary condition applicable to momentum and heat transfer in the semisolid continuous casting(SCC) process was established. Using the model, the numerical simulation of the momentum and heat transfer of molten metal was carried out in the SCC system. The obtained results fit well with the measured ones. Moreover, using the numerical simulating software, the effect of various factors on breakout and breakage was explored. The obtained results show that heat flow density of copper mold and the withdrawal beginning time are two major influencing factors. The larger the heat flow density of copper mold, or the shorter the withdrawal beginning time, the more stable the semisolid continuous casting process.
Numerical simulations of catastrophic disruption: Recent results
Benz, W.; Asphaug, E.; Ryan, E. V.
1994-01-01
Numerical simulations have been used to study high velocity two-body impacts. In this paper, a two-dimensional Largrangian finite difference hydro-code and a three-dimensional smooth particle hydro-code (SPH) are described and initial results reported. These codes can be, and have been, used to make specific predictions about particular objects in our solar system. But more significantly, they allow us to explore a broad range of collisional events. Certain parameters (size, time) can be studied only over a very restricted range within the laboratory; other parameters (initial spin, low gravity, exotic structure or composition) are difficult to study at all experimentally. The outcomes of numerical simulations lead to a more general and accurate understanding of impacts in their many forms.
Numerical Limit Analysis of Reinforced Concrete Structures
DEFF Research Database (Denmark)
Larsen, Kasper Paaske
methods provide engineers with valuable tools for limit sta- te analysis, their application becomes difficult with increased structural complexity. The main challenge is to solve the optimization problem posed by the extremum principles. This thesis is a study of how numerical methods can be used to solve...... limit state analysis problems. The work focuses on determination of the load bearing capacity of reinforced concrete structures by employing the lower bound theorem and a finite element method using equilibrium elements is developed. The recent year’s development within the field of convex optimization...... is developed for improved perfor- mance. An example is given in which an inverse T-beam is analyzed and the numerical results are compared to laboratory tests. The third and final element is a plane shell element capable of modeling membrane and plate bending behavior. The element employs a layered disk...
Numerical Simulation of Piston Ring Lubrication
DEFF Research Database (Denmark)
Felter, Christian Lotz
2006-01-01
This paper describes a numerical method that can be used to model the lubrication of piston rings. Classical lubrication theory is based on the Reynolds equation which is ap- plicable to confined geometries and open geometries where the flooding conditions are known. Lubrication of piston rings...... is extended to include also the oil film outside the piston rings. The numerical model consists of a 2D free surface code that solves the time dependent compressible Navier-Stokes equations. The equations are cast in Lagrangian form and discretized by a meshfree moving least squares method using the primitive......, however, fall outside this category of problems since the piston rings might suffer from starved running conditions. This means that the com- putational domain where Reynold equation is applicable (including a cavitation criteria) is unknown. In order to overcome this problem the computational domain...
First Numerical Simulations of Anomalous Hydrodynamics
Hongo, Masaru; Hirano, Tetsufumi
2013-01-01
Anomalous hydrodynamics is a low-energy effective theory that captures effects of quantum anomalies. We develop a numerical code of anomalous hydrodynamics and apply it to dynamics of heavy-ion collisions, where anomalous transports are expected to occur. This is the first attempt to perform fully non-linear numerical simulations of anomalous hydrodynamics. We discuss implications of the simulations for possible experimental observations of anomalous transport effects. From analyses of the charge-dependent elliptic flow parameters ($v_2^\\pm$) as a function of the net charge asymmetry $A_\\pm$, we quantitatively verify that the linear dependence of $\\Delta v_2 \\equiv v_2^- - v_2^+$ on the net charge asymmetry $A_\\pm$ cannot be regarded as a sensitive signal of anomalous transports, contrary to previous studies. We, however, find that the intercept $\\Delta v_2(A_\\pm=0)$ is sensitive to anomalous transport effects.
Numerical inductance calculations based on first principles.
Shatz, Lisa F; Christensen, Craig W
2014-01-01
A method of calculating inductances based on first principles is presented, which has the advantage over the more popular simulators in that fundamental formulas are explicitly used so that a deeper understanding of the inductance calculation is obtained with no need for explicit discretization of the inductor. It also has the advantage over the traditional method of formulas or table lookups in that it can be used for a wider range of configurations. It relies on the use of fast computers with a sophisticated mathematical computing language such as Mathematica to perform the required integration numerically so that the researcher can focus on the physics of the inductance calculation and not on the numerical integration.
A student's guide to numerical methods
Hutchinson, Ian H
2015-01-01
This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introdu...
Susy theories and QCD: numerical approaches
Ita, Harald
2011-11-01
We review on-shell and unitarity methods and discuss their application to precision predictions for Large Hadron Collider (LHC) physics. Being universal and numerically robust, these methods are straightforward to automate for next-to-leading-order computations within standard model and beyond. Several state-of-the-art results including studies of (W/Z+3)-jet and (W+4)-jet production have explicitly demonstrated the effectiveness of the unitarity method for describing multi-parton scattering. Here we review central ideas needed to obtain efficient numerical implementations. This includes on-shell loop-level recursions, the unitarity method, color management and further refined tricks. This article is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Scattering amplitudes in gauge theories’.
LISA parameter estimation using numerical merger waveforms
Energy Technology Data Exchange (ETDEWEB)
Thorpe, J I; McWilliams, S T; Kelly, B J; Fahey, R P; Arnaud, K; Baker, J G, E-mail: James.I.Thorpe@nasa.go [NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771 (United States)
2009-05-07
Recent advances in numerical relativity provide a detailed description of the waveforms of coalescing massive black hole binaries (MBHBs), expected to be the strongest detectable LISA sources. We present a preliminary study of LISA's sensitivity to MBHB parameters using a hybrid numerical/analytic waveform for equal-mass, non-spinning holes. The Synthetic LISA software package is used to simulate the instrument response, and the Fisher information matrix method is used to estimate errors in the parameters. Initial results indicate that inclusion of the merger signal can significantly improve the precision of some parameter estimates. For example, the median parameter errors for an ensemble of systems with total redshifted mass of 10{sup 6} M{sub o-dot} at a redshift of z approx 1 were found to decrease by a factor of slightly more than two for signals with merger as compared to signals truncated at the Schwarzchild ISCO.
LISA parameter estimation using numerical merger waveforms
Thorpe, J I; Kelly, B J; Fahey, R P; Arnaud, K; Baker, J G
2008-01-01
Recent advances in numerical relativity provide a detailed description of the waveforms of coalescing massive black hole binaries (MBHBs), expected to be the strongest detectable LISA sources. We present a preliminary study of LISA's sensitivity to MBHB parameters using a hybrid numerical/analytic waveform for equal-mass, non-spinning holes. The Synthetic LISA software package is used to simulate the instrument response and the Fisher information matrix method is used to estimate errors in the parameters. Initial results indicate that inclusion of the merger signal can significantly improve the precision of some parameter estimates. For example, the median parameter errors for an ensemble of systems with total redshifted mass of one million Solar masses at a redshift of one were found to decrease by a factor of slightly more than two for signals with merger as compared to signals truncated at the Schwarzchild ISCO.
Numerical modelling in non linear fracture mechanics
Directory of Open Access Journals (Sweden)
Viggo Tvergaard
2007-07-01
Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.
Lemurs and macaques show similar numerical sensitivity
Jones, Sarah M.; Pearson, John; DeWind, Nicholas K.; Paulsen, David; Tenekedjieva, Ana-Maria; Brannon, Elizabeth M.
2013-01-01
We investigated the precision of the approximate number system (ANS) in three lemur species (Lemur catta, Eulemur mongoz, and Eulemur macaco flavifrons), one Old World monkey species (Macaca mulatta) and humans (Homo sapiens). In Experiment 1, four individuals of each nonhuman primate species were trained to select the numerically larger of two visual arrays on a touchscreen. We estimated numerical acuity by modeling Weber fractions (w) and found quantitatively equivalent performance among all four nonhuman primate species. In Experiment 2, we tested adult humans in a similar procedure, and they outperformed the four nonhuman species but showed qualitatively similar performance. These results indicate that the ANS is conserved over the primate order. PMID:24068469
Discrete mathematics, discrete physics and numerical methods
Directory of Open Access Journals (Sweden)
Felice Iavernaro
2007-12-01
Full Text Available Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
Numerical wave interaction with tetrapods breakwater
Dentale, Fabio; Donnarumma, Giovanna; Carratelli, Eugenio Pugliese
2014-12-01
The paper provides some results of a new procedure to analyze the hydrodynamic aspects of the interactions between maritime emerged breakwaters and waves by integrating CAD and CFD. The structure is modeled in the numerical domain by overlapping individual three-dimensional elements (Tetrapods), very much like the real world or physical laboratory testing. Flow of the fluid within the interstices among concrete blocks is evaluated by integrating the RANS equations. The aim is to investigate the reliability of this approach as a design tool. Therefore, for the results' validation, the numerical run-up and reflection effects on virtual breakwater were compared with some empirical formulae and some similar laboratory tests. Here are presented the results of a first simple validation procedure. The validation shows that, at present, this innovative approach can be used in the breakwater design phase for comparison between several design solutions with a significant minor cost.
Numerical approach of the quantum circuit theory
Silva, J. J. B.; Duarte-Filho, G. C.; Almeida, F. A. G.
2017-03-01
In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.
Partial differential equations with numerical methods
Larsson, Stig
2003-01-01
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.
Some Experiences with Numerical Modelling of Overflows
DEFF Research Database (Denmark)
Larsen, Torben; Nielsen, L.; Jensen, B.
2007-01-01
Overflows are commonly applied in storm sewer systems to control flow and water surface level. Therefore overflows play a central role in the control of discharges of pollutants from sewer systems to the environment. The basic hydrodynamic principle of an overflow is the so-called critical flow...... across the edge of the overflow. To ensure critical flow across the edge, the upstream flow must be subcritical whereas the downstream flow is either supercritical or a free jet. Experimentally overflows are well studied. Based on laboratory experiments and Froude number scaling, numerous accurate...... the term for curvature of the water surface (the so-called Boussinesq approximation) 2. 2- and 3-dimensional so-called Volume of Fluid Models (VOF-models) based on the full Navier-Stokes equations (named NS3 and developed by DHI Water & Environment) As a general conclusion, the two numerical models show...
Intelligent numerical methods applications to fractional calculus
Anastassiou, George A
2016-01-01
In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.
Elliptic differential equations theory and numerical treatment
Hackbusch, Wolfgang
2017-01-01
This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
Multilevel Monte Carlo Approaches for Numerical Homogenization
Efendiev, Yalchin R.
2015-10-01
In this article, we study the application of multilevel Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the homogenized solutions. This is accomplished within MLMC by considering different sizes of representative volumes (RVEs). Many inexpensive computations with the smallest RVE size are combined with fewer expensive computations performed on larger RVEs. Likewise, when it comes to homogenized solutions, different levels of coarse-grid meshes are used to solve the homogenized equation. We show that, by carefully selecting the number of realizations at each level, we can achieve a speed-up in the computations in comparison to a standard Monte Carlo method. Numerical results are presented for both one-dimensional and two-dimensional test-cases that illustrate the efficiency of the approach.
Numerical methods for ordinary differential equations
Butcher, John C
2008-01-01
In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author''s pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book includeIntroductory work on differential and difference equations.A comprehensive introduction to the theory and practice of solving ordinary differential equations numeri...
Numerical approach of the quantum circuit theory
Energy Technology Data Exchange (ETDEWEB)
Silva, J.J.B., E-mail: jaedsonfisica@hotmail.com; Duarte-Filho, G.C.; Almeida, F.A.G.
2017-03-15
In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.
Numerical calculation of ion runaway distributions
Embréus, Ola; Stahl, Adam; Hirvijoki, Eero; Fülöp, Tünde
2015-01-01
Ions accelerated by electric fields (so-called runaway ions) in plasmas may explain observations in solar flares and fusion experiments, however limitations of previous analytic work have prevented definite conclusions. In this work we describe a numerical solver of the 2D non-relativistic linearized Fokker-Planck equation for ions. It solves the initial value problem in velocity space with a spectral-Eulerian discretization scheme, allowing arbitrary plasma composition and time-varying electric fields and background plasma parameters. The numerical ion distribution function is then used to consider the conditions for runaway ion acceleration in solar flares and tokamak plasmas. Typical time scales and electric fields required for ion acceleration are determined for various plasma compositions, ion species and temperatures, and the potential for excitation of toroidal Alfv\\'en eigenmodes during tokamak disruptions is considered.
Numerical aspects of 3D stellar winds
Strugarek, A; Matt, S P; Reville, V
2014-01-01
This paper explores and compares the pitfalls of modelling the three-dimensional wind of a spherical star with a cartesian grid. Several numerical methods are compared, using either uniform and stretched grid or adaptative mesh refinement (AMR). An additional numerical complication is added, when an orbiting planet is considered. In this case a rotating frame is added to the model such that the orbiting planet is at rest in the frame of work. The three-dimensional simulations are systematically compared to an equivalent two-dimensional, axisymmetric simulation. The comparative study presented here suggests to limit the rotation rate of the rotating frame below the rotating frame of the star and provides guidelines for further three-dimensional modelling of stellar winds in the context of close-in star-planet interactions.
Numerical discretization for nonlinear diffusion filter
Mustaffa, I.; Mizuar, I.; Aminuddin, M. M. M.; Dasril, Y.
2015-05-01
Nonlinear diffusion filters are famously used in machine vision for image denoising and restoration. This paper presents a study on the effects of different numerical discretization of nonlinear diffusion filter. Several numerical discretization schemes are presented; namely semi-implicit, AOS, and fully implicit schemes. The results of these schemes are compared by visual results, objective measurement e.g. PSNR and MSE. The results are also compared to a Daubechies wavelet denoising method. It is acknowledged that the two preceding scheme have already been discussed in literature, however comparison to the latter scheme has not been made. The semi-implicit scheme uses an additive operator splitting (AOS) developed to overcome the shortcoming of the explicit scheme i.e., stability for very small time steps. Although AOS has proven to be efficient, from the nonlinear diffusion filter results with different discretization schemes, examples shows that implicit schemes are worth pursuing.
Numerical implementation of isolated horizon boundary conditions
Jaramillo, J L; Limousin, F
2006-01-01
We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasi-equilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the Conformal Thin Sandwich equations. As main results, we firstly establish the consistency of including in the set of boundary conditions a "constant surface gravity" prescription, interpretable as a lapse boundary condition, and secondly we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the Conformal Transverse Traceless equations with quasi-equilibrium horizon conditions extend to the Conformal Thin Sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.
Numerical modeling in materials science and engineering
Rappaz, Michel; Deville, Michel
2003-01-01
This book introduces the concepts and methodologies related to the modelling of the complex phenomena occurring in materials processing. After a short reminder of conservation laws and constitutive relationships, the authors introduce the main numerical methods: finite differences, finite volumes and finite elements. These techniques are developed in three main chapters of the book that tackle more specific problems: phase transformation, solid mechanics and fluid flow. The two last chapters treat inverse methods to obtain the boundary conditions or the material properties and stochastic methods for microstructural simulation. This book is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics and for engineering professionals or researchers who want to get acquainted with numerical simulation to model and compute materials processing.
Efficient Numerical Evaluation of Feynman Integral
Li, Zhao; Yan, Qi-Shu; Zhao, Xiaoran
2016-01-01
Feynman loop integral is the key ingredient of high order radiation effect, which is responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing quasi-Monte Carlo method associated with the technique of CUDA/GPU. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in physical kinematic region can be evaluated in less than half minute with $\\mathcal{O}(10^{-3})$ accuracy, which makes the direct numerical approach viable for the precise investigation on the high order effect in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with finite top quark mass.
Children, algorithm and the decimal numeral system
Directory of Open Access Journals (Sweden)
Clélia Maria Ignatius Nogueira
2010-08-01
Full Text Available A large number of studies in Mathematics Education approach some possible problems in the study of algorithms in the early school years of arithmetic teaching. However, this discussion is not exhausted. In this feature, this article presents the results of a research which proposed to investigate if the arithmetic’s teaching, with emphasis in the fundamental operation’s algorithm, cooperate to build the mathematics knowledge, specifically of the Decimal Numeral System. In order to achieve this purpose, we interviewed, using the Piaget Critique Clinical Method, twenty students from a public school. The result’s analysis indicates that they mechanically reproduce the regular algorithm’s techniques without notice the relations between the techniques and the principle and the Decimal Numeral System’s properties.
Numerical Investigation on Submerged Horizontal Plate
Institute of Scientific and Technical Information of China (English)
康海贵; 王科
2001-01-01
Hydrodynamic characters on a horizontal, thin, rigid plate located beneath the free surface are numerically investigated. Assuming a linear, time-harmonic potential flow and utilizing Green identity, the governing Laplace equation can be simplified into Fredholm integral equation ofthe second kind. Supposing linear-order discontinuous elements along intersecting vertical boundaries, and by use of the boundary element method, numerical solution about source strength distribution on the plate can be changed into a series of algebraic equations. The 3D Green function is introduced to set up the integral equations, and the GMRES solver is performed for solving the large dense linear system of equations. The added-mass, damping force and exciting force are evaluated directly from the equations. It is found that the added-mass coefficient becomes negative for a range of frequencies when the plate is sufficiently close to the free surface.
Numerical solution of large Lyapunov equations
Saad, Youcef
1989-01-01
A few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix is considered. For the single input case, i.e., when the equation considered is of the form AX + XA(sup T) + bb(sup T) = 0, where b is a column vector, the existence of approximate solutions of the form X = VGV(sup T) where V is N x m and G is m x m, with m small is established. The first class of methods proposed is based on the use of numerical quadrature formulas, such as Gauss-Laguerre formulas, applied to the controllability Grammian. The second is based on a projection process of Galerkin type. Numerical experiments are presented to test the effectiveness of these methods for large problems.
Numerical Simulation of a Hypersonic Air Intake
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Soumyajit Saha
2015-05-01
Full Text Available Numerical simulations were carried out to study the unsteady flow in an intake of hypersonic air-breathing vehicle. Unsteady RANS simulations were performed to examine started flow of the intake when cowl surface is parallel to the ramp surface. Though started, the flow was unsteady due to flow separation bubbles inside intake. Intake with larger cowl opening at which intake unstarted was also simulated. Simulations indicated unstarted flow, with large pressure oscillations. The numerically simulation results match reasonably well with experimental data. Calculated unstarting Mach number was found to be 3.0-3.2 in comparison of wind tunnel data of 3.6 for the same cowl opening angle.Defence Science Journal, Vol. 65, No. 3, May 2015, pp.189-195, DOI: http://dx.doi.org/10.14429/dsj.65.8254
Numerical Noise Prediction in Fluid Machinery
Institute of Scientific and Technical Information of China (English)
Iris PANTLE; Franco MAGAGNATO; Martin GABI
2005-01-01
Numerical methods successively became important in the design and optimization of fluid machinery. However,as noise emission is considered, one can hardly find standardized prediction methods combining flow and acoustical optimization. Several numerical field methods for sound calculations have been developed. Due to the complexity of the considered flow, approaches must be chosen to avoid exhaustive computing. In this contribution the noise of a simple propeller is investigated. The configurations of the calculations comply with an existing experimental setup chosen for evaluation. The used in-house CFD solver SPARC contains an acoustic module based on Ffowcs Williams-Hawkings Acoustic Analogy. From the flow results of the time dependent Large Eddy Simulation the time dependent acoustic sources are extracted and given to the acoustic module where relevant sound pressure levels are calculated. The difficulties, which arise while proceeding from open to closed rotors and from gas to liquid are discussed.
Program Verification of Numerical Computation - Part 2
Pantelis, Garry
2014-01-01
These notes present some extensions of a formal method introduced in an earlier paper. The formal method is designed as a tool for program verification of numerical computation and forms the basis of the software package VPC. Included in the extensions that are presented here are disjunctions and methods for detecting non-computable programs. A more comprehensive list of the construction rules as higher order constructs is also presented.
Hyperbolic conservation laws and numerical methods
Leveque, Randall J.
1990-01-01
The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.
Involving human forecasters in numerical prediction systems
Directory of Open Access Journals (Sweden)
V. Homar
2006-01-01
Full Text Available Human forecasters routinely improve upon the output from numerical weather prediction models and often have keen insight to model biases and shortcomings. This wealth of knowledge about model performance is largely untapped, however, as it is used only at the end point in the forecast process to interpret the model-predicted fields. Yet there is no reason why human forecasters cannot intervene at other earlier times in the numerical weather prediction process, especially when an ensemble forecasting system is in use. Human intervention in ensemble creation may be particularly helpful for rare events, such as severe weather events, that are not predicted well by numerical models. The USA/NOAA SPC/NSSL Spring Program 2003 tested an ensemble generation method in which human forecasters were involved in the ensemble creation process. The forecaster highlighted structures of interest and, using an adjoint model, a set of perturbations were obtained and used to generate a 32-member ensemble. The results show that this experimental ensemble improves upon the operational numerical forecasts of severe weather. The human-generated ensemble is able to provide improved guidance on high-impact weather events, but lacks global dispersion and produces unreliable forecasts for non-hazardous weather events. Further results from an ensemble constructed by combining the operational ensemble perturbations with the human-generated perturbations shows promising skill for the forecast of severe weather while avoiding the problem of limited global dispersion. The value of human beings in the creation of ensembles designed to target specific high- impact weather events is potentially large. Further investigation of the value of forecasters being part of the ensemble creation process is strongly recommended. There remains a lot to learn about how to create ensembles for short-range forecasts of severe weather, and we need to make better use of the skill and experience of
Numerical simulation and nasal air-conditioning
Directory of Open Access Journals (Sweden)
Keck, Tilman
2010-01-01
Full Text Available Heating and humidification of the respiratory air are the main functions of the nasal airways in addition to cleansing and olfaction. Optimal nasal air conditioning is mandatory for an ideal pulmonary gas exchange in order to avoid desiccation and adhesion of the alveolar capillary bed. The complex three-dimensional anatomical structure of the nose makes it impossible to perform detailed in vivo studies on intranasal heating and humidification within the entire nasal airways applying various technical set-ups. The main problem of in vivo temperature and humidity measurements is a poor spatial and time resolution. Therefore, in vivo measurements are feasible only to a restricted extent, solely providing single temperature values as the complete nose is not entirely accessible. Therefore, data on the overall performance of the nose are only based on one single measurement within each nasal segment. In vivo measurements within the entire nose are not feasible. These serious technical issues concerning in vivo measurements led to a large number of numerical simulation projects in the last few years providing novel information about the complex functions of the nasal airways. In general, numerical simulations merely calculate predictions in a computational model, e.g. a realistic nose model, depending on the setting of the boundary conditions. Therefore, numerical simulations achieve only approximations of a possible real situation. The aim of this review is the synopsis of the technical expertise on the field of in vivo nasal air conditioning, the novel information of numerical simulations and the current state of knowledge on the influence of nasal and sinus surgery on nasal air conditioning.
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 topology optimization of heat sinks
Van Oevelen, Tijs; Baelmans, Martine
2014-01-01
The availability of flexible production techniques challenges their full exploitation during thermo-hydraulic design of micro heat sinks. In this context, a systematic approach capable to take advantage of the practically unlimited design freedom is highly desirable. Therefore, we propose to use topology optimization, a numerical design optimization method well-established in structural mechanics problems. In this paper, the fundamentals of topology optimization, and its application in thermo...
Mixing in modulated turbulence. Numerical results
Yang, Yuyao; Rubinstein, Robert; Bos, Wouter
2016-01-01
Direct numerical simulations are carried out to investigate scalar mixing in an isotropic turbulent flow with a time-periodic forcing. For high amplitudes of the modulation, it is shown that the average mixing rate is negatively affected at low frequencies. In this limit the mixing time scale increases, whereas the typical velocity timescale decreases. We further determine the frequency response of scalar statistics to a periodic scalar-forcing.
Fastening elements in concrete structures - numerical simulations
Ozbolt, Josko; Eligehausen, Rolf
1993-01-01
Anchoring elements such as headed and expansion studs and grouted or undercut anchors, are often used for local transfer of loads into concrete members. In order to better understand the failure mechanism, a large number of experiments have been carried out in the past. However, due to the complicated three-dimensional load transfer a very few or no numerical studies have been performed for a number of different fastening situations i.e. influence of the embedment depth, crack-width inftuence...
Photonic Crystals Mathematical Analysis and Numerical Approximation
Dörfler, Willy; Plum, Michael; Schneider, Guido; Wieners, Christian
2011-01-01
This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers. In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities, simultaneous occurrence of contin
Numerical simulation of axial flow compressors.
Jesuino Takachi Tomita
2002-01-01
This work deals with the numerical simulation of axial flow compressors, from design to performance prediction. The stage performance prediction uses the meanline flow properties. Stage-stacking is used to analyse a multi-stage compressor. A computer program, written in FORTRAN, was developed and is able to design an axial flow compressor given air mass flow, total pressure ratio, overall efficiency and design speed. All geometrical data relevant to the compressor performance prediction is ca...
The initial value problem in numerical relativity
Pfeiffer, H P
2004-01-01
The conformal method for constructing initial data for Einstein's equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages due to the recent introduction of a weight-function in the extrinsic curvature decomposition are discussed. I then describe recent progress in numerical techniques to solve the resulting elliptic equations, and explore innovative approaches toward the construction of astrophysically realistic initial data for binary black hole simulations.
Exploring New Physics Frontiers Through Numerical Relativity.
Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Sperhake, Ulrich
2015-01-01
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.
NUMERICAL SIMULATION OF SEPARATED FLOW NEAR GROYNE
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A numerical model was developed to simulate flow around non-submeged groyne in two dimensions, which was based on N-S equations with Smagorinsky's subgrid-scale turbulence model. Flow phenomenon and results measured practically agree with the calculation results very well, and this model could be used to simulate the characteristics of the eddies of upper and down reaches around spur-dikes successfully.
Numerical Simulation on CCOS Controllable Variable
Institute of Scientific and Technical Information of China (English)
CHENG Hao-bo; FENG Zhi-jing
2003-01-01
On the basis of Preston hypothesis,the motion relationship between tool and workpiece upon the tool's motion in planar model is analyzed.The effect on computer controlled optical surfacing (CCOS) caused by controllable variable is simulated except for the dwelling time,thus,some reference on theory is provided to optimize the former numerical control (NC) model,and fast manufacturing of large departure aspherics is realized.
On the numerical simulation of machining processes
Vaz Jr.,M.
2000-01-01
Numerical simulation of machining processes can be traced back to the early seventies when finite element models for continuous chip formation were proposed. The advent of fast computers and development of new techniques to model large plastic deformations have favoured machining simulation. Relevant aspects of finite element simulation of machining processes are discussed in this paper, such as solution methods, material models, thermo-mechanical coupling, friction models, chip separation an...
Automated Calibration For Numerical Models Of Riverflow
Fernandez, Betsaida; Kopmann, Rebekka; Oladyshkin, Sergey
2017-04-01
Calibration of numerical models is fundamental since the beginning of all types of hydro system modeling, to approximate the parameters that can mimic the overall system behavior. Thus, an assessment of different deterministic and stochastic optimization methods is undertaken to compare their robustness, computational feasibility, and global search capacity. Also, the uncertainty of the most suitable methods is analyzed. These optimization methods minimize the objective function that comprises synthetic measurements and simulated data. Synthetic measurement data replace the observed data set to guarantee an existing parameter solution. The input data for the objective function derivate from a hydro-morphological dynamics numerical model which represents an 180-degree bend channel. The hydro- morphological numerical model shows a high level of ill-posedness in the mathematical problem. The minimization of the objective function by different candidate methods for optimization indicates a failure in some of the gradient-based methods as Newton Conjugated and BFGS. Others reveal partial convergence, such as Nelder-Mead, Polak und Ribieri, L-BFGS-B, Truncated Newton Conjugated, and Trust-Region Newton Conjugated Gradient. Further ones indicate parameter solutions that range outside the physical limits, such as Levenberg-Marquardt and LeastSquareRoot. Moreover, there is a significant computational demand for genetic optimization methods, such as Differential Evolution and Basin-Hopping, as well as for Brute Force methods. The Deterministic Sequential Least Square Programming and the scholastic Bayes Inference theory methods present the optimal optimization results. keywords: Automated calibration of hydro-morphological dynamic numerical model, Bayesian inference theory, deterministic optimization methods.
Numerical linear algebra in data mining
Eldén, Lars
Ideas and algorithms from numerical linear algebra are important in several areas of data mining. We give an overview of linear algebra methods in text mining (information retrieval), pattern recognition (classification of handwritten digits), and PageRank computations for web search engines. The emphasis is on rank reduction as a method of extracting information from a data matrix, low-rank approximation of matrices using the singular value decomposition and clustering, and on eigenvalue methods for network analysis.
Numerical linear algebra for reconstruction inverse problems
Nachaoui, Abdeljalil
2004-01-01
Our goal in this paper is to discuss various issues we have encountered in trying to find and implement efficient solvers for a boundary integral equation (BIE) formulation of an iterative method for solving a reconstruction problem. We survey some methods from numerical linear algebra, which are relevant for the solution of this class of inverse problems. We motivate the use of our constructing algorithm, discuss its implementation and mention the use of preconditioned Krylov methods.
Conservative numerical methods for solitary wave interactions
Energy Technology Data Exchange (ETDEWEB)
Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)
2003-07-18
The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.
Exploring New Physics Frontiers Through Numerical Relativity
Cardoso, Vitor; Herdeiro, Carlos; Sperhake, Ulrich
2014-01-01
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations -- along with some spectacular results -- in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.
Efficient Numerical Inversion for Financial Simulations
Derflinger, Gerhard; Hörmann, Wolfgang; Leydold, Josef; Sak, Halis
2009-01-01
Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo. However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow. In this paper we demonstrate how our new method based on Newton interpolation and Gauss-Lobatto quadrature can be util...
Numerical Estimation in Deaf and Hearing Adults
Bull, Rebecca; Marschark, Marc; Sapere, Patty; Davidson, Wendy A.; Murphy, Derek; Nordmann, Emily
2011-01-01
Deaf students often lag behind hearing peers in numerical and mathematical abilities. Studies of hearing children with mathematical difficulties highlight the importance of estimation skills as the foundation for formal mathematical abilities, but research with adults is limited. Deaf and hearing college students were assessed on the Number-to-Position task as a measure of estimation, and completed standardised assessments of arithmetical and mathematical reasoning. Deaf students performed si...
Numerical simulation of droplet impact on interfaces
Kahouadji, Lyes; Che, Zhizhao; Matar, Omar; Shin, Seungwon; Chergui, Jalel; Juric, Damir
2015-11-01
Simulations of three-dimensional droplet impact on interfaces are carried out using BLUE, a massively-parallel code based on a hybrid Front-Tracking/Level-Set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. High resolution numerical results show fine details and features of droplet ejection, crown formation and rim instability observed under similar experimental conditions. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.
Adapting Inspection Data for Computer Numerical Control
Hutchison, E. E.
1986-01-01
Machining time for repetitive tasks reduced. Program converts measurements of stub post locations by coordinate-measuring machine into form used by numerical-control computer. Work time thus reduced by 10 to 15 minutes for each post. Since there are 600 such posts on each injector, time saved per injector is 100 to 150 hours. With modifications this approach applicable to machining of many precise holes on large machine frames and similar objects.
Ontogeny of numerical abilities in fish.
Directory of Open Access Journals (Sweden)
Angelo Bisazza
Full Text Available BACKGROUND: It has been hypothesised that human adults, infants, and non-human primates share two non-verbal systems for enumerating objects, one for representing precisely small quantities (up to 3-4 items and one for representing approximately larger quantities. Recent studies exploiting fish's spontaneous tendency to join the larger group showed that their ability in numerical discrimination closely resembles that of primates but little is known as to whether these capacities are innate or acquired. METHODOLOGY/PRINCIPAL FINDINGS: We used the spontaneous tendency to join the larger shoal to study the limits of the quantity discrimination of newborn and juvenile guppies. One-day old fish chose the larger shoal when the choice was between numbers in the small quantity range, 2 vs. 3 fish, but not when they had to choose between large numbers, 4 vs. 8 or 4 vs. 12, although the numerical ratio was larger in the latter case. To investigate the relative role of maturation and experience in large number discrimination, fish were raised in pairs (with no numerical experience or in large social groups and tested at three ages. Forty-day old guppies from both treatments were able to discriminate 4 vs. 8 fish while at 20 days this was only observed in fish grown in groups. Control experiments showed that these capacities were maintained after guppies were prevented from using non numerical perceptual variables that co-vary with numerosity. CONCLUSIONS/SIGNIFICANCE: Overall, our results suggest the ability of guppies to discriminate small numbers is innate and is displayed immediately at birth while discrimination of large numbers emerges later as a result of both maturation and social experience. This developmental dissociation suggests that fish like primates might have separate systems for small and large number representation.
Preattentive Processing of Numerical Visual Information.
Hesse, Philipp N; Schmitt, Constanze; Klingenhoefer, Steffen; Bremmer, Frank
2017-01-01
Humans can perceive and estimate approximate numerical information, even when accurate counting is impossible e.g., due to short presentation time. If the number of objects to be estimated is small, typically around 1-4 items, observers are able to give very fast and precise judgments with high confidence-an effect that is called subitizing. Due to its speed and effortless nature subitizing has usually been assumed to be preattentive, putting it into the same category as other low level visual features like color or orientation. More recently, however, a number of studies have suggested that subitizing might be dependent on attentional resources. In our current study we investigated the potentially preattentive nature of visual numerical perception in the subitizing range by means of EEG. We presented peripheral, task irrelevant sequences of stimuli consisting of a certain number of circular patches while participants were engaged in a demanding, non-numerical detection task at the fixation point drawing attention away from the number stimuli. Within a sequence of stimuli of a given number of patches (called "standards") we interspersed some stimuli of different numerosity ("oddballs"). We compared the evoked responses to visually identical stimuli that had been presented in two different conditions, serving as standard in one condition and as oddball in the other. We found significant visual mismatch negativity (vMMN) responses over parieto-occipital electrodes. In addition to the event-related potential (ERP) analysis, we performed a time-frequency analysis (TFA) to investigate whether the vMMN was accompanied by additional oscillatory processes. We found a concurrent increase in evoked theta power of similar strength over both hemispheres. Our results provide clear evidence for a preattentive processing of numerical visual information in the subitizing range.
Numerical Study of Electric Field Enhanced Combustion
Han, Jie
2016-12-26
Electric fields can be used to change and control flame properties, for example changing flame speed, enhancing flame stability, or reducing pollutant emission. The ions generated in flames are believed to play the primary role. Although experiments have been carried out to study electric field enhanced combustion, they are not sufficient to explain how the ions in a flame are affected by an electric field. It is therefore necessary to investigate the problem through numerical simulations. In the present work, the electric structure of stabilized CH4/air premixed flames at atmospheric pressure within a direct current field is studied using numerical simulations. This study consists of three parts. First, the transport equations are derived from the Boltzmann kinetic equation for each individual species. Second, a general method for computing the diffusivity and mobility of ions in a gas mixture is introduced. Third, the mechanisms for neutral and charged species are improved to give better predictions of the concentrations of charged species, based on experimental data. Following from this, comprehensive numerical results are presented, including the concentrations and fluxes of charged species, the distributions of the electric field and electric potential, and the electric current-voltage relation. Two new concepts introduced with the numerical results are the plasma sheath and dead zone in the premixed flame. A reactive plasma sheath and a Boltzmann relation sheath are discovered in the region near the electrodes. The plasma sheath penetrates into the flame gas when a voltage is applied, and penetrating further if the voltage is higher. The zone outside the region of sheath penetration is defined as the dead zone. With the two concepts, analytical solutions for the electric field, electric potential and current-voltage curve are derived. The solutions directly describe the electric structure of a premixed flame subject to a DC field. These analytical solutions
An introduction to numerical methods and analysis
Epperson, J F
2007-01-01
Praise for the First Edition "". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.""-Zentrablatt Math "". . . carefully structured with many detailed worked examples . . .""-The Mathematical Gazette "". . . an up-to-date and user-friendly account . . .""-Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or d
Numerical abilities in fish: A methodological review.
Agrillo, Christian; Miletto Petrazzini, Maria Elena; Bisazza, Angelo
2017-02-03
The ability to utilize numerical information can be adaptive in a number of ecological contexts including foraging, mating, parental care, and anti-predator strategies. Numerical abilities of mammals and birds have been studied both in natural conditions and in controlled laboratory conditions using a variety of approaches. During the last decade this ability was also investigated in some fish species. Here we reviewed the main methods used to study this group, highlighting the strengths and weaknesses of each of the methods used. Fish have only been studied under laboratory conditions and among the methods used with other species, only two have been systematically used in fish-spontaneous choice tests and discrimination learning procedures. In the former case, the choice between two options is observed in a biologically relevant situation and the degree of preference for the larger/smaller group is taken as a measure of the capacity to discriminate the two quantities (e.g., two shoals differing in number). In discrimination learning tasks, fish are trained to select the larger or the smaller of two sets of abstract objects, typically two-dimensional geometric figures, using food or social companions as reward. Beyond methodological differences, what emerges from the literature is a substantial similarity of the numerical abilities of fish with those of other vertebrates studied.
Numerical modelling in wave energy conversion systems
Energy Technology Data Exchange (ETDEWEB)
El Marjani, A. [Labo. de Turbomachines, Ecole Mohammadia d' Ingenieurs (EMI), Universite Mohammed V Agdal, Av Ibn Sina, B.P. 765 Agdal, Rabat (Morocco); Castro Ruiz, F.; Rodriguez, M.A.; Parra Santos, M.T. [Depto. de Ingenieria Energetica y Fluidomecanica, Escuela Tecnica Superior de Ingenieros Industriales, Universidad de Valladolid, Paseo del Cauce s/n, E-47011 Valladolid (Spain)
2008-08-15
This paper deals with a numerical modelling devoted to predict the flow characteristics in the components of an oscillating water column (OWC) system used for the wave energy capture. In the present paper, the flow behaviour is modelled by using the FLUENT code. Two numerical flow models have been elaborated and tested independently in the geometries of an air chamber and a turbine, which is chosen of a radial impulse type. The flow is assumed to be three-dimensional (3D), viscous, turbulent and unsteady. The FLUENT code is used with a solver of the coupled conservation equations of mass, momentum and energy, with an implicit time scheme and with the adoption of the dynamic mesh and the sliding mesh techniques in areas of moving surfaces. Turbulence is modelled with the k-{epsilon} model. The obtained results indicate that the developed models are well suitable to analyse the air flows both in the air chamber and in the turbine. The performances associated with the energy transfer processes have been well predicted. For the turbine, the numerical results of pressure and torque were compared to the experimental ones. Good agreements between these results have been observed. (author)
3D numerical design of tunnel hood
Uystepruyst, David; Monnoyer, François
2015-01-01
This paper relates to the parametric study of tunnel hoods in order to reduce the shape, i.e the temporal gradient, of the pressure wave generated by the entry of a High speed train in tunnel. This is achieved by using an in-house three-dimensional numerical solver which solves the Eulerian equations on a Cartesian and unstructured mesh. The efficiency of the numerical methodology is demonstrated through comparisons with both experimental data and empirical formula. For the tunnel hood design, three parameters, that can influence the wave shape, are considered: the shape, the section and the length of the hood. The numerical results show, (i) that a constant section hood is the most efficient shape when compared to progressive (elliptic or conical) section hoods, (ii) an optimal ratio between hood's section and tunnel section where the temporal gradient of the pressure wave can be reduced by half, (iii) a significant efficiency of the hood's length in the range of 2 to 8 times the length of the train nose. Fi...
Numerical modeling of mantle plume diffusion
Krupsky, D.; Ismail-Zadeh, A.
2004-12-01
To clarify the influence of the heat diffusion on the mantle plume evolution, we develop a two-dimensional numerical model of the plume diffusion and relevant efficient numerical algorithm and code to compute the model. The numerical approach is based on the finite-difference method and modified splitting algorithm. We consider both von Neumann and Direchlet conditions at the model boundaries. The thermal diffusivity depends on pressure in the model. Our results show that the plume is disappearing from the bottom up - the plume tail at first and its head later - because of the mantle plume geometry (a thin tail and wide head) and higher heat conductivity in the lower mantle. We study also an effect of a lateral mantle flow associated with the plate motion on the distortion of the diffusing mantle plume. A number of mantle plumes recently identified by seismic tomography seem to disappear in the mid-mantle. We explain this disappearance as the effect of heat diffusion on the evolution of mantle plume.
Numerical simulation of magmatic hydrothermal systems
Ingebritsen, S.E.; Geiger, S.; Hurwitz, S.; Driesner, T.
2010-01-01
The dynamic behavior of magmatic hydrothermal systems entails coupled and nonlinear multiphase flow, heat and solute transport, and deformation in highly heterogeneous media. Thus, quantitative analysis of these systems depends mainly on numerical solution of coupled partial differential equations and complementary equations of state (EOS). The past 2 decades have seen steady growth of computational power and the development of numerical models that have eliminated or minimized the need for various simplifying assumptions. Considerable heuristic insight has been gained from process-oriented numerical modeling. Recent modeling efforts employing relatively complete EOS and accurate transport calculations have revealed dynamic behavior that was damped by linearized, less accurate models, including fluid property control of hydrothermal plume temperatures and three-dimensional geometries. Other recent modeling results have further elucidated the controlling role of permeability structure and revealed the potential for significant hydrothermally driven deformation. Key areas for future reSearch include incorporation of accurate EOS for the complete H2O-NaCl-CO2 system, more realistic treatment of material heterogeneity in space and time, realistic description of large-scale relative permeability behavior, and intercode benchmarking comparisons. Copyright 2010 by the American Geophysical Union.
Meshless Methods Coupled with Other Numerical Methods
Institute of Scientific and Technical Information of China (English)
Y.T.GU; G.R.LIU
2005-01-01
Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as the finite element method (FEM) and the boundary element method (BEM), is naturally of great interest in many practical applications. However, the shape functions used in some MFree methods do not have the Kronecker delta function property. In order to satisfy the combined conditions of displacement compatibility, two numerical techniques, using the hybrid displacement shape function and the modified variational form, are developed and discussed in this paper. In the first technique, the original MFree shape functions are modified to the hybrid forms that possess the Kronecker delta function property. In the second technique, the displacement compatibility is satisfied via a modified variational form based on the Lagrange multiplier method. Formulations of several coupled methods are presented. Numerical examples are presented to demonstrate the effectiveness of the present coupling methods.
Numerical Modelling Of Pumpkin Balloon Instability
Wakefield, D.
Tensys have been involved in the numerical formfinding and load analysis of architectural stressed membrane structures for 15 years. They have recently broadened this range of activities into the `lighter than air' field with significant involvement in aerostat and heavy-lift hybrid airship design. Since early 2004 they have been investigating pumpkin balloon instability on behalf of the NASA ULDB programme. These studies are undertaken using inTENS, an in-house finite element program suite based upon the Dynamic Relaxation solution method and developed especially for the non-linear analysis and patterning of membrane structures. The paper describes the current state of an investigation that started with a numerical simulation of the lobed cylinder problem first studied by Calladine. The influence of material properties and local geometric deformation on stability is demonstrated. A number of models of complete pumpkin balloons have then been established, including a 64-gore balloon with geometry based upon Julian Nott's Endeavour. This latter clefted dramatically upon initial inflation, a phenomenon that has been reproduced in the numerical model. Ongoing investigations include the introduction of membrane contact modelling into inTENS and correlation studies with the series of large-scale ULDB models currently in preparation.
A Numerical Simulation of the Density Oscilator
Hernandez Zapata, Sergio; Lopez Sanchez, Erick Javier; Ruiz Chavarria, Gerardo
2016-11-01
In this work we carry out a numerical simulation for the dynamics that originates when a fluid (salty water) is located on top of another less dense fluid (pure water) in the presence of gravity. This is an unstable situation that leads to the development of intercalating lines of descending salty water and ascending pure water. Another situation is studied where the fluids are in two containers joined by a small hole. In this case a time pattern of alternating flows develops leading to an oscillator. The study of the velocity field around the hole shows than in a certain interval of time it develops intercalating lines like in the former situation. An interesting result is the fact that when a given fluid is flowing in one direction a vorticity pattern develops in the other fluid. The Navier-Stokes, continuity and salt diffusion equations, are solved numerically in cylindrical coordinates, using a finite difference scheme in the axial and radial directions and a Fourier spectral method for the angular coordinate. On the other hand, the second order Adams-Bashfort method is used for the time evolution. The results are compared to a numerical simulation of a pedestrian oscillator we developed based on the Hebling and Molnar social force model. The authors want to acknowledge support by DGAPA-UNAM (Project PAPIIT IN-115315 "Ondas y estructuras coherentes en dinámica de fluidos".
OpenPh - Numerical Physics Library
Milescu, George; Pop, Florin
2011-01-01
Numerical physics has gained a lot of importance in the last decade, its efficiency being motivated and sustained by the growth of computational power. This paper presents a concept that is to be developed in the next few years: OpenPh. OpenPh is a numerical physics library that makes use of the advantages of both open source software and MATLAB programming. Its aim is to deliver the instruments for providing numerical and graphical solutions for various physics problems. It has a modular structure, allowing the user to add new modules to the existing ones and to create its own modules according to its needs, being virtually unlimited extendable. The modules of OpenPh are implemented using MATLAB engine because it is the best solution used in engineering and science, providing a wide range of optimized methods to accomplish even the toughest jobs. Current version of OpenPh includes two modules, the first one providing tools for quantum physics and the second one for mechanics. The quantum physics module deals...
Numerical Methods for Stochastic Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Sharp, D.H.; Habib, S.; Mineev, M.B.
1999-07-08
This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National laboratory (LANL). The objectives of this proposal were (1) the development of methods for understanding and control of spacetime discretization errors in nonlinear stochastic partial differential equations, and (2) the development of new and improved practical numerical methods for the solutions of these equations. The authors have succeeded in establishing two methods for error control: the functional Fokker-Planck equation for calculating the time discretization error and the transfer integral method for calculating the spatial discretization error. In addition they have developed a new second-order stochastic algorithm for multiplicative noise applicable to the case of colored noises, and which requires only a single random sequence generation per time step. All of these results have been verified via high-resolution numerical simulations and have been successfully applied to physical test cases. They have also made substantial progress on a longstanding problem in the dynamics of unstable fluid interfaces in porous media. This work has lead to highly accurate quasi-analytic solutions of idealized versions of this problem. These may be of use in benchmarking numerical solutions of the full stochastic PDEs that govern real-world problems.
Class Generation for Numerical Wind Atlases
DEFF Research Database (Denmark)
Cutler, N.J.; Jørgensen, B.H.; Ersbøll, Bjarne Kjær;
2006-01-01
A new optimised clustering method is presented for generating wind classes for mesoscale modelling to produce numerical wind atlases. It is compared with the existing method of dividing the data in 12 to 16 sectors, 3 to 7 wind-speed bins and dividing again according to the stability of the atmos......A new optimised clustering method is presented for generating wind classes for mesoscale modelling to produce numerical wind atlases. It is compared with the existing method of dividing the data in 12 to 16 sectors, 3 to 7 wind-speed bins and dividing again according to the stability...... of the atmosphere. Wind atlases are typically produced using many years of on-site wind observations at many locations. Numerical wind atlases are the result of mesoscale model integrations based on synoptic scale wind climates and can be produced in a number of hours of computation. 40 years of twice daily NCEP....../NCAR reanalysis geostrophic wind data (approximately 200 km resolution) are represented in typically around 150 classes, each with a frequency of occurrence. The mean wind-speed and direction in each class is used as input data to force the mesoscale model, which downscales the wind to a 5 km resolution while...
KWIC index for numerical linear algebra. [Bibliography
Energy Technology Data Exchange (ETDEWEB)
Carpenter, J.A.
1982-07-01
This report is a sequel to ORNL/CSD-96 in the ongoing supplements to Professor A.S. Householder's KWIC Index for Numerical Algebra. With this supplement, the coverage has been restricted to Numerical Linear Algebra and is now roughly characterized by the American Mathematical Society's classification section 15 and 65F but with little coverage of inifinite matrices, matrices over fields of characteristics other than zero, operator theory, optimization and those parts of matrix theory primarily combinatorial in nature. Some recognition is made of the uses of graph theory in Numerical Linear Algebra, particularly as regards their use in algorithms for sparse matrix computations. The period covered by this report is roughly the calendar year 1981 as measured by the appearance of the articles in the American Mathematical Society's Contents of Mathematical Publications. The review citations are limited to the Mathematical Reviews (MR) and Das Zentralblatt fur Mathematik und Ihre Grenzgebiete (ZBL). Future reports will be made more timely by closer ovservation of the few journals which supply the bulk of the listings rather than what appears to be too much reliance on secondary sources. Some thought is being given to the physical appearance of these reports and the author welcomes comments concerning both their appearance and contents.
Avoiding numerical pitfalls in social force models
Köster, Gerta; Treml, Franz; Gödel, Marion
2013-06-01
The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.
Numerical and experimental investigations on supersonic ejectors
Energy Technology Data Exchange (ETDEWEB)
Bartosiewicz, Y.; Aidoun, Z. [CETC-Varennes, Natural Resources Canada (Canada); Desevaux, P. [CREST-UMR 6000, Belfort (France); Mercadier, Y. [Sherbrooke Univ. (Canada). THERMAUS
2005-02-01
Supersonic ejectors are widely used in a range of applications such as aerospace, propulsion and refrigeration. The primary interest of this study is to set up a reliable hydrodynamics model of a supersonic ejector, which may be extended to refrigeration applications. The first part of this work evaluated the performance of six well-known turbulence models for the study of supersonic ejectors. The validation concentrated on the shock location, shock strength and the average pressure recovery prediction. Axial pressure measurements with a capillary probe performed previously [Int. J. Turbo Jet Engines 19 (2002) 71; Conference Proc., 10th Int. Symp. Flow Visualization, Kyoto, Japan, 2002], were compared with numerical simulations while laser tomography pictures were used to evaluate the non-mixing length. The capillary probe has been included in the numerical model and the non-mixing length has been numerically evaluated by including an additional transport equation for a passive scalar, which acted as an ideal colorant in the flow. At this point, the results show that the k-omega-sst model agrees best with experiments. In the second part, the tested model was used to reproduce the different operation modes of a supersonic ejector, ranging from on-design point to off-design. In this respect, CFD turned out to be an efficient diagnosis tool of ejector analysis (mixing, flow separation), for design, and performance optimization (optimum entrainment and recompression ratios). (Author)
Correlation of Numerical Anxiety and Mathematics Performance
Directory of Open Access Journals (Sweden)
Michael Howard D. Morada
2015-12-01
Full Text Available It has been observed that most students had negative view towards mathematics and as a result, they also performed poorly.As such, it is imperative for every math teacher to understand the reasons behind this negative view to improve their student’s performance. This observation led the researcher to conduct a study on Correlation of Mathematics Performance and Anxiety of third and fourth year students for school year 2012-2013 across the different programs.This study determined the numerical anxiety level and mathematics performance of the respondents along age, gender and programs. The study revealed that students, regardless of age had passing performance. However, female and male students had fair and passing mathematics performance, respectively. Students from College of Business Education, Teacher Education and Computer Studies had fair performance while those from Marine Transportation, Criminal Justice Education and Engineering had passing performance. The study also revealed that students across different variables had moderate numerical anxiety level. Furthermore, it was found out that mathematics performance is significantly related to numerical anxiety. However, the relationship was inverse and small.
From geometry to numerics: interdisciplinary aspects in mathematical and numerical relativity
Energy Technology Data Exchange (ETDEWEB)
Jaramillo, Jose Luis [Instituto de AstrofIsica de AndalucIa, CSIC, Apartado Postal 3004, Granada 18080 (Spain); Valiente Kroon, Juan Antonio [School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom); Gourgoulhon, Eric [Laboratoire Univers et Theories, UMR 8102 du CNRS, Observatoire de Paris, Universite Paris Diderot, F-92190 Meudon (France)], E-mail: jarama@iaa.es, E-mail: j.a.valiente-kroon@qmul.ac.uk, E-mail: eric.gourgoulhon@obspm.fr
2008-05-07
This paper reviews some aspects in the current relationship between mathematical and numerical general relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial-value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed in light of the interaction between numerical and mathematical relativists. (topical review)
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
Jaramillo, J L; Gourgoulhon, E
2007-01-01
This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasilocal black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.
NUMERICAL DETERMINATION OF HORIZONTAL SETTLERS PERFORMANCE
Directory of Open Access Journals (Sweden)
M. M. Biliaiev
2015-08-01
Full Text Available Purpose.Horizontal settlers are one of the most important elements in the technological scheme of water purification. Their use is associated with the possibility to pass a sufficiently large volume of water. The important task at the stage of their designing is evaluating of their effectiveness. Calculation of the efficiency of the settler can be made by mathematical modeling. Empirical, analytical models and techniques that are currently used to solve the problem, do not allow to take into account the shape of the sump and various design features that significantly affects the loyalty to a decision on the choice of the size of the settling tank and its design features. The use of analytical models is limited only to one-dimensional solutions, does not allow accounting for nonuniform velocity field of the flow in the settler. The use of advanced turbulence models for the calculation of the hydrodynamics in the settler complex forms now requires very powerful computers. In addition, the calculation of one variant of the settler may last for dozens of hours. The aim of the paper is to build a numerical model to evaluate the effectiveness of horizontal settling tank modified design. Methodology. Numerical models are based on: 1 equation of potential flow; 2 equation of inviscid fluid vortex flow; 3 equation of viscous fluid dynamics; 4 mass transfer equation. For numerical simulation the finite difference schemes are used. The numerical calculation is carried out on a rectangular grid. For the formation of the computational domain markers are used. Findings.The models allow calculating the clarification process in the settler with different form and different configuration of baffles. Originality. A new approach to investigate the mass transfer process in horizontal settler was proposed. This approach is based on the developed CFD models. Three fluid dynamics models were used for the numerical investigation of flows and waste waters purification
Cheng, Xiaorong; Ge, Hui; Andoni, Deljfina; Ding, Xianfeng; Fan, Zhao
2015-01-01
A recent hierarchical model of numerical processing, initiated by Fischer and Brugger (2011) and Fischer (2012), suggested that situated factors, such as different body postures and body movements, can influence the magnitude representation and bias numerical processing. Indeed, Loetscher et al. (2008) found that participants' behavior in a random number generation task was biased by head rotations. More small numbers were reported after leftward than rightward head turns, i.e., a motion-numerical compatibility effect. Here, by carrying out two experiments, we explored whether similar motion-numerical compatibility effects exist for movements of other important body components, e.g., arms, and for composite body movements as well, which are basis for complex human activities in many ecologically meaningful situations. In Experiment 1, a motion-numerical compatibility effect was observed for lateral rotations of two body components, i.e., the head and arms. Relatively large numbers were reported after making rightward compared to leftward movements for both lateral head and arm turns. The motion-numerical compatibility effect was observed again in Experiment 2 when participants were asked to perform composite body movements of congruent movement directions, e.g., simultaneous head left turns and arm left turns. However, it disappeared when the movement directions were incongruent, e.g., simultaneous head left turns and arm right turns. Taken together, our results extended Loetscher et al.'s (2008) finding by demonstrating that their effect is effector-general and exists for arm movements. Moreover, our study reveals for the first time that the impact of spatial information on numerical processing induced by each of the two sensorimotor-based situated factors, e.g., a lateral head turn and a lateral arm turn, can cancel each other out.
Directory of Open Access Journals (Sweden)
Xiaorong eCheng
2015-11-01
Full Text Available A recent hierarchical model of numerical processing, initiated by Fischer and Brugger (2011 and Fisher (2012, suggested that situated factors, such as different body postures and body movements, can influence the magnitude representation and bias numerical processing. Indeed, Loetscher and colleagues (2008 found that participants’ behavior in a random number generation (RNG task was biased by head rotations. More small numbers were reported after leftward than rightward head turns, i.e. a motion–numerical compatibility effect. Here, by carrying out two experiments, we explored whether similar motion–numerical compatibility effects exist for movements of other important body components, e.g. arms, and for composite body movements as well, which are basis for complex human activities in many ecologically meaningful situations. In Experiment 1, a motion-numerical compatibility effect was observed for lateral rotations of two body components, i.e., the head and arms. Relatively large numbers were reported after making rightward compared to leftward movements for both lateral head and arm turns. The motion-numerical compatibility effect was observed again in Experiment 2 when participants were asked to perform composite body movements of congruent movement directions, e.g., simultaneous head left turns and arm left turns. However, it disappeared when the movement directions were incongruent, e.g., simultaneous head left turns and arm right turns. Taken together, our results extended Loetscher et al.'s (2008 finding by demonstrating that their effect is effector-general and exists for arm movements. Moreover, our study reveals for the first time that the impact of spatial information on numerical processing induced by each of the two sensorimotor-based situated factors, e.g., a lateral head turn and a lateral arm turn, can cancel each other out.
Directory of Open Access Journals (Sweden)
Yuan eYao
2015-05-01
Full Text Available This study examined whether long-term abacus-based mental calculation (AMC training improved numerical processing efficiency and at what stage of information processing the effect appeard. Thirty-three children participated in the study and were randomly assigned to two groups at primary school entry, matched for age, gender and IQ. All children went through the same curriculum except that the abacus group received a 2-hour/per week AMC training, while the control group did traditional numerical practice for a similar amount of time. After a two-year training, they were tested with a numerical Stroop task. Electroencephalographic (EEG and event related potential (ERP recording techniques were used to monitor the temporal dynamics during the task. Children were required to determine the numerical magnitude (NC task or the physical size (PC task of two numbers presented simultaneously. In the NC task, the AMC group showed faster response times but similar accuracy compared to the control group. In the PC task, the two groups exhibited the same speed and accuracy. The saliency of numerical information relative to physical information was greater in AMC group. With regards to ERP results, the AMC group displayed congruity effects both in the earlier (N1 and later (N2 and LPC (late positive component time domain, while the control group only displayed congruity effects for LPC. In the left parietal region, LPC amplitudes were larger for the AMC than the control group. Individual differences for LPC amplitudes over left parietal area showed a positive correlation with RTs in the NC task in both congruent and neutral conditions. After controlling for the N2 amplitude, this correlation also became significant in the incongruent condition. Our results suggest that AMC training can strengthen the relationship between symbolic representation and numerical magnitude so that numerical information processing becomes quicker and automatic in AMC children.
Yao, Yuan; Du, Fenglei; Wang, Chunjie; Liu, Yuqiu; Weng, Jian; Chen, Feiyan
2015-01-01
This study examined whether long-term abacus-based mental calculation (AMC) training improved numerical processing efficiency and at what stage of information processing the effect appeard. Thirty-three children participated in the study and were randomly assigned to two groups at primary school entry, matched for age, gender and IQ. All children went through the same curriculum except that the abacus group received a 2-h/per week AMC training, while the control group did traditional numerical practice for a similar amount of time. After a 2-year training, they were tested with a numerical Stroop task. Electroencephalographic (EEG) and event related potential (ERP) recording techniques were used to monitor the temporal dynamics during the task. Children were required to determine the numerical magnitude (NC) (NC task) or the physical size (PC task) of two numbers presented simultaneously. In the NC task, the AMC group showed faster response times but similar accuracy compared to the control group. In the PC task, the two groups exhibited the same speed and accuracy. The saliency of numerical information relative to physical information was greater in AMC group. With regards to ERP results, the AMC group displayed congruity effects both in the earlier (N1) and later (N2 and LPC (late positive component) time domain, while the control group only displayed congruity effects for LPC. In the left parietal region, LPC amplitudes were larger for the AMC than the control group. Individual differences for LPC amplitudes over left parietal area showed a positive correlation with RTs in the NC task in both congruent and neutral conditions. After controlling for the N2 amplitude, this correlation also became significant in the incongruent condition. Our results suggest that AMC training can strengthen the relationship between symbolic representation and numerical magnitude so that numerical information processing becomes quicker and automatic in AMC children.
Numerical recipes for mold filling simulation
Energy Technology Data Exchange (ETDEWEB)
Kothe, D.; Juric, D.; Lam, K.; Lally, B.
1998-07-01
Has the ability to simulate the filling of a mold progressed to a point where an appropriate numerical recipe achieves the desired results? If results are defined to be topological robustness, computational efficiency, quantitative accuracy, and predictability, all within a computational domain that faithfully represents complex three-dimensional foundry molds, then the answer unfortunately remains no. Significant interfacial flow algorithm developments have occurred over the last decade, however, that could bring this answer closer to maybe. These developments have been both evolutionary and revolutionary, will continue to transpire for the near future. Might they become useful numerical recipes for mold filling simulations? Quite possibly. Recent progress in algorithms for interface kinematics and dynamics, linear solution methods, computer science issues such as parallelization and object-oriented programming, high resolution Navier-Stokes (NS) solution methods, and unstructured mesh techniques, must all be pursued as possible paths toward higher fidelity mold filling simulations. A detailed exposition of these algorithmic developments is beyond the scope of this paper, hence the authors choose to focus here exclusively on algorithms for interface kinematics. These interface tracking algorithms are designed to model the movement of interfaces relative to a reference frame such as a fixed mesh. Current interface tracking algorithm choices are numerous, so is any one best suited for mold filling simulation? Although a clear winner is not (yet) apparent, pros and cons are given in the following brief, critical review. Highlighted are those outstanding interface tracking algorithm issues the authors feel can hamper the reliable modeling of today`s foundry mold filling processes.
Fundamental numerical methods for electrical engineering
Energy Technology Data Exchange (ETDEWEB)
Rosloniec, Stanislaw [Warsaw Univ. of Technology (Poland). Inst. of Radioelectronics
2008-07-01
The book presents fundamental numerical methods which are most frequently applied in the electrical (electronic) engineering. A scope of this book is rather wide and includes solving the sets of linear and nonlinear equations, interpolation and approximation of the functions of one variable, integration and differentation of the functions of one and two variables, integration of the ordinary differential equations, and integration the partial differential equations of two variables. All methods discussed are illustrated with real-world examples of applications. It is shown how real engineering questions can be transformed into the corresponding mathematical problems and next effectively solved by using appropriate numerical methods. Usually, for teaching reasons, mathematical problems are solved step by step, and illustrated by numerous intermediate results. Thus, it is not only explained how the problem can be solved, but the details of the solution are also demonstrated. In Chapter 7 for instance three electrical rectifying devices and a transmission-line non- homogeneous impedance transformer are analyzed in this manner. Similarly, in Chapter 8 different aspects of Laplace boundary value problem formulated for various kinds of single and coupled TEM transmission lines are presented. In other words, six standard TEM transmission lines are investigated by means of the finite difference method. It is shown how a partial differential equation of the second order can be approximated by the corresponding difference equation defined on interior and boundary nodes of the introduced grid. At the next stage, the set of linear equations, formulated in this way, is recurrently solved by using the effective SOR technique. Additionally, ideas of '' fictitious nodes '' and the '' even and odd mode excitations '' methods are explained and illustrated. All methods and computational results, presented in the book, are of significant
Quantifying Numerical Model Accuracy and Variability
Montoya, L. H.; Lynett, P. J.
2015-12-01
The 2011 Tohoku tsunami event has changed the logic on how to evaluate tsunami hazard on coastal communities. Numerical models are a key component for methodologies used to estimate tsunami risk. Model predictions are essential for the development of Tsunami Hazard Assessments (THA). By better understanding model bias and uncertainties and if possible minimizing them, a more accurate and reliable THA will result. In this study we compare runup height, inundation lines and flow velocity field measurements between GeoClaw and the Method Of Splitting Tsunami (MOST) predictions in the Sendai plain. Runup elevation and average inundation distance was in general overpredicted by the models. However, both models agree relatively well with each other when predicting maximum sea surface elevation and maximum flow velocities. Furthermore, to explore the variability and uncertainties in numerical models, MOST is used to compare predictions from 4 different grid resolutions (30m, 20m, 15m and 12m). Our work shows that predictions of particular products (runup and inundation lines) do not require the use of high resolution (less than 30m) Digital Elevation Maps (DEMs). When predicting runup heights and inundation lines, numerical convergence was achieved using the 30m resolution grid. On the contrary, poor convergence was found in the flow velocity predictions, particularly the 1 meter depth maximum flow velocities. Also, runup height measurements and elevations from the DEM were used to estimate model bias. The results provided in this presentation will help understand the uncertainties in model predictions and locate possible sources of errors within a model.
Quantum turbulence: Theoretical and numerical problems
Nemirovskii, Sergey K.
2013-03-01
The term “quantum turbulence” (QT) unifies the wide class of phenomena where the chaotic set of one dimensional quantized vortex filaments (vortex tangles) appear in quantum fluids and greatly influence various physical features. Quantum turbulence displays itself differently depending on the physical situation, and ranges from quasi-classical turbulence in flowing fluids to a near equilibrium set of loops in phase transition. The statistical configurations of the vortex tangles are certainly different in, say, the cases of counterflowing helium and a rotating bulk, but in all the physical situations very similar theoretical and numerical problems arise. Furthermore, quite similar situations appear in other fields of physics, where a chaotic set of one dimensional topological defects, such as cosmic strings, or linear defects in solids, or lines of darkness in nonlinear light fields, appear in the system. There is an interpenetration of ideas and methods between these scientific topics which are far apart in other respects. The main purpose of this review is to bring together some of the most commonly discussed results on quantum turbulence, focusing on analytic and numerical studies. We set out a series of results on the general theory of quantum turbulence which aim to describe the properties of the chaotic vortex configuration, starting from vortex dynamics. In addition we insert a series of particular questions which are important both for the whole theory and for the various applications. We complete the article with a discussion of the hot topic, which is undoubtedly mainstream in this field, and which deals with the quasi-classical properties of quantum turbulence. We discuss this problem from the point of view of the theoretical results stated in the previous sections. We also included section, which is devoted to the experimental and numerical suggestions based on the discussed theoretical models.
Numerical calculation of impurity charge state distributions
Energy Technology Data Exchange (ETDEWEB)
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.
Saccadic compression of symbolic numerical magnitude.
Directory of Open Access Journals (Sweden)
Paola Binda
Full Text Available Stimuli flashed briefly around the time of saccadic eye movements are subject to complex distortions: compression of space and time; underestimate of numerosity. Here we show that saccadic distortions extend to abstract quantities, affecting the representation of symbolic numerical magnitude. Subjects consistently underestimated the results of rapidly computed mental additions and subtractions, when the operands were briefly displayed before a saccade. However, the recognition of the number symbols was unimpaired. These results are consistent with the hypothesis of a common, abstract metric encoding magnitude along multiple dimensions. They suggest that a surprising link exists between the preparation of action and the representation of abstract quantities.
Numerical investigation of bubble nonlinear dynamics characteristics
Energy Technology Data Exchange (ETDEWEB)
Shi, Jie, E-mail: shijie@hrbeu.edu.cn; Yang, Desen; Shi, Shengguo; Hu, Bo [Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001 (China); College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China); Zhang, Haoyang; Jiang, Wei [College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China)
2015-10-28
The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.
Experimental and numerical techniques to assess catalysis
Herdrich, G.; Fertig, M.; Petkow, D.; Steinbeck, A.; Fasoulas, S.
2012-01-01
Catalytic heating can be a significant portion of the thermal load experienced by a body during re-entry. Under the auspices of the NATO Research and Technology Organisation Applied Vehicle Technologies Panel Task Group AVT-136 an assessment of the current state-of-the-art in the experimental characterization and numerical simulation of catalysis on high-temperature material surfaces has been conducted. This paper gives an extraction of the final report for this effort, showing the facilities and capabilities worldwide to assess catalysis data. A corresponding summary for the modeling activities is referenced in this article.
Numerical relativity and the early Universe
Directory of Open Access Journals (Sweden)
Mironov Sergey
2016-01-01
Full Text Available We consider numerical simulations in general relativity in ADM formalism with cosmological ansatz for the metric. This ansatz is convenient for investigations of the Universe creation in laboratory with Galileons. Here we consider toy model for the software: spherically symmetric scalar field minimally coupled to the gravity with asymmetric double well potential. We studied the dependence of radius of critical bubble on the parameters of the theory. It demonstrates the wide applicability of thin-wall approximation. We did not find any kind of stable bubble solution.
Numerical analysis method for linear induction machines.
Elliott, D. G.
1972-01-01
A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.
Numerical analysis of cross shear plate rolling
DEFF Research Database (Denmark)
Zhang, Wenqi; Bay, Niels
1997-01-01
The rolling process is widely applied for industrial production of metal plates. In conventional plate rolling the two work rolls are rotating at the same peripheral speed. By introducing a specific difference in the speed of the two work rolls, cross shear rolling is introduced forming a central...... are in the roll gap, the position and the size of the shear zone and the rolling load are calculated. Experimental results are presented verifying the calculations. The numerical analysis facilitates a better understanding of the mechanics in cross shear plate rolling....
Numerical simulations of vibrating sessile drop
Kahouadji, Lyes; Chergui, Jalel; Juric, Damir; Shin, Seungwon; Craster, Richard; Matar, Omar
2016-11-01
A vibrated drop constitutes a very rich physical system, blending both interfacial and volume phenomena. A remarkable experimental study was performed by M. Costalonga highlighting sessile drop motion subject to horizontal, vertical and oblique vibration. Several intriguing phenomena are observed such as drop walking and rapid droplet ejection. We perform three-dimensional direct numerical simulations of vibrating sessile drops where the phenomena described above are computed using the massively parallel multiphase code BLUE. EPSRC UK Programme Grant MEMPHIS (EP/K003976/1).
Efficient numerical integrators for stochastic models
De Fabritiis, G; Español, P; Coveney, P V
2006-01-01
The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.
Numerical Tests of the Improved Fermilab Action
Energy Technology Data Exchange (ETDEWEB)
Detar, C.; Kronfeld, A.S.; Oktay, M.B.
2010-11-01
Recently, the Fermilab heavy-quark action was extended to include dimension-six and -seven operators in order to reduce the discretization errors. In this talk, we present results of the first numerical simulations with this action (the OK action), where we study the masses of the quarkonium and heavy-light systems. We calculate combinations of masses designed to test improvement and compare results obtained with the OK action to their counterparts obtained with the clover action. Our preliminary results show a clear improvement.
Introduction to numerical electrostatics using MATLAB
Dworsky, Lawrence N
2014-01-01
The first of its kind uniquely devoted to the field of computational electrostatics, this book dives headfirst into the actual problems that engineers are expected to solve using method of moment (MoM), finite difference, and finite element techniques. Readers are guided step by step through specific problems and challenges, covering all aspects of electrostatics with an emphasis on numerical procedures. Focusing on practical examples, mathematical equations, and common issues with algorithms, this is an ideal text for students in engineering, physics, and electrostatics-and working engineers
Issues in Numerical Simulation of Fire Suppression
Energy Technology Data Exchange (ETDEWEB)
Tieszen, S.R.; Lopez, A.R.
1999-04-12
This paper outlines general physical and computational issues associated with performing numerical simulation of fire suppression. Fire suppression encompasses a broad range of chemistry and physics over a large range of time and length scales. The authors discuss the dominant physical/chemical processes important to fire suppression that must be captured by a fire suppression model to be of engineering usefulness. First-principles solutions are not possible due to computational limitations, even with the new generation of tera-flop computers. A basic strategy combining computational fluid dynamics (CFD) simulation techniques with sub-grid model approximations for processes that have length scales unresolvable by gridding is presented.
Argonne Code Center numerical control postprocessor inventory
Energy Technology Data Exchange (ETDEWEB)
Vollink, S. (comp.)
1977-12-21
A survey to identify numerical control postprocessors available at Department of Energy facilities is reported. The data are presented in the body of the report under the postprocessor identification. Information supplied includes the vendor name and address, the N/C and postprocessor languages, the machine tools and control unit supported, the computers used, and the identification of the DOE installation. The body of the report is followed by five indexes permitting users to refer to the postprocessor data by product number, DOE installation, machine tool, control unit, or computer. (RWR)
NUMERICAL MODELING OF COMPOUND CHANNEL FLOWS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A numerical model capable of predicting flow characteristics in a compound channel was established with the 3-D steady continuity and momentum equations along with the transport equations for turbulence kinetic energy and dissipation rate. Closure was achieved with the aid of algebraic relations for turbulent shear stresses. The above equations were discretized with implicit difference approach and solved with a step method along the flow direction. The computational results showing the lateral distribution of vertical average velocities and the latio of total flow in the compound channel agree well with the available experimental data.
Instabilities in numerical loop quantum cosmology
Rosen, J; Khanna, G; Jung, Jae-Hun; Khanna, Gaurav; Rosen, Jessica
2006-01-01
In this article we perform von Neumann analysis of the difference equations that arise as a result of loop quantum gravity being applied to models of cosmology and black holes. In particular, we study the numerical stability of Bianchi I LRS (symmetric and non-symmetric constraint) and Schwarzschild interior (symmetric constraint) models, and find that there exist domains over which there are instabilities, generically. We also present explicit evolutions of wave-packets in these models and clearly demonstrate the presence of these instabilities.
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro; Donato Trigiante
2007-01-01
Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences o...
Geometric and numerical foundations of movements
Mansard, Nicolas; Lasserre, Jean-Bernard
2017-01-01
This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.
A numerical method based on probability theory
Institute of Scientific and Technical Information of China (English)
唐立; 邹捷中; 杨文胜
2003-01-01
By using the connections between Brownian family with drift and elliptic differential equations, an efficient probabilistic computing method is given. This method is applied to a wide-range Diriehlet problem. Detail analysis and deduction of solving the problem are offered. The stochastic representation of the solution to the problem makes a 3-dimensional problem turned into a 2-dimensional problem. And an auxiliary ball is constructed. The strong Markov property and the joint distributions of the time and place of hitting spheres for Brownian family with drift are employed. Finally, good convergence of the numerical solution to the problem over domain with arbitrary boundary is obtained.
Assigning Numerical Scores to Linguistic Expressions
Directory of Open Access Journals (Sweden)
María Jesús Campión
2017-07-01
Full Text Available In this paper, we study different methods of scoring linguistic expressions defined on a finite set, in the search for a linear order that ranks all those possible expressions. Among them, particular attention is paid to the canonical extension, and its representability through distances in a graph plus some suitable penalization of imprecision. The relationship between this setting and the classical problems of numerical representability of orderings, as well as extension of orderings from a set to a superset is also explored. Finally, aggregation procedures of qualitative rankings and scorings are also analyzed.
Advanced Numerical Model for Irradiated Concrete
Energy Technology Data Exchange (ETDEWEB)
Giorla, Alain B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2015-03-01
In this report, we establish a numerical model for concrete exposed to irradiation to address these three critical points. The model accounts for creep in the cement paste and its coupling with damage, temperature and relative humidity. The shift in failure mode with the loading rate is also properly represented. The numerical model for creep has been validated and calibrated against different experiments in the literature [Wittmann, 1970, Le Roy, 1995]. Results from a simplified model are shown to showcase the ability of numerical homogenization to simulate irradiation effects in concrete. In future works, the complete model will be applied to the analysis of the irradiation experiments of Elleuch et al. [1972] and Kelly et al. [1969]. This requires a careful examination of the experimental environmental conditions as in both cases certain critical information are missing, including the relative humidity history. A sensitivity analysis will be conducted to provide lower and upper bounds of the concrete expansion under irradiation, and check if the scatter in the simulated results matches the one found in experiments. The numerical and experimental results will be compared in terms of expansion and loss of mechanical stiffness and strength. Both effects should be captured accordingly by the model to validate it. Once the model has been validated on these two experiments, it can be applied to simulate concrete from nuclear power plants. To do so, the materials used in these concrete must be as well characterized as possible. The main parameters required are the mechanical properties of each constituent in the concrete (aggregates, cement paste), namely the elastic modulus, the creep properties, the tensile and compressive strength, the thermal expansion coefficient, and the drying shrinkage. These can be either measured experimentally, estimated from the initial composition in the case of cement paste, or back-calculated from mechanical tests on concrete. If some
Numerical Ultimate Ruin Probabilities under Interest Force
Directory of Open Access Journals (Sweden)
Juma Kasozi
2005-01-01
Full Text Available This work addresses the issue of ruin of an insurer whose portfolio is exposed to insurance risk arising from the classical surplus process. Availability of a positive interest rate in the financial world forces the insurer to invest into a risk free asset. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block method in conjuction with the Simpson rule to solve the Volterra equation for ultimate ruin. This probability is arrived at by taking a linear combination of some two solutions to the Volterra integral equation. The several numerical examples given show that our results are excellent and reliable.
Numerical Quadratures for Hadamard Hypersingular Integrals
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we develop Gaussian quadrature formulas for the Hadamard finite part integrals. In our formulas, the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f(x) so that the Gaussian quadrature formulas have degree n - 1. The error estimates of the formulas are obtained. It is found from the numerical examples that the convergence rate and the accuracy of the approximation results are satisfactory. Moreover, the rate and the accuracy can be improved by choosing appropriate weight functions.
Exploring New Physics Frontiers Through Numerical Relativity
Directory of Open Access Journals (Sweden)
Vitor Cardoso
2015-09-01
Full Text Available The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein’s equations – along with some spectacular results – in various setups. We review techniques for solving Einstein’s equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.
Numerical analysis of cross shear plate rolling
DEFF Research Database (Denmark)
Zhang, Wenqi; Bay, Niels
1997-01-01
The rolling process is widely applied for industrial production of metal plates. In conventional plate rolling the two work rolls are rotating at the same peripheral speed. By introducing a specific difference in the speed of the two work rolls, cross shear rolling is introduced forming a central...... shear zone between the forward and backward slip zones in the deformation zone thus lowering the rolling load. A numerical analysis of the cross shear rolling process is carried out based on the slab method adopting Wanheim and Bay's general friction model. The pressure distribution along the contact...
Numerical Modeling of Weld Joint Corrosion
Lu, Yongxin; Jing, Hongyang; Han, Yongdian; Xu, Lianyong
2016-03-01
A numerical model is presented in this work that predicts the corrosion rate of weld joint. The model is able to track moving boundary of the corroding constituent of weld joint. The corrosion rates obtained from the model are compared with those estimated from mixed potential theory and two experimental techniques, namely immersion test and constant potential polarization test. The corrosion rate predicted using the model is within 10% of the estimate from the mixed potential theory, within 20% of that got from the immersion experiment and within 10% of that got from the constant potential polarization experiment for weld joint.
Numerical Methods for Finding Stationary Gravitational Solutions
Dias, Oscar J C; Way, Benson
2015-01-01
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly-spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS$_5\\times S^5$. We also include several tools and tricks that have been useful throughout the literature.
NUMERICAL SIMULATION OF SCOURING PROCESS UNDER SPILLWAY
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The scour problem under spillway has received a lot of attention in the past decades. For such a complicated problem, most numerical modeling presented only dealt with the water flows in equilibrium scour pools without considering the changing topography of the riverbed. In this paper, the dynamic process is handled with moving grids, and the governing equations are solved using finite volume method with colocated variable arrangement on boundary-fitted non-orthogonal grids. The results show that the given method is efficient, with which the variation of flow parameters, such as mean velocity and mean pressure, etc., can be computed correctly.
Numerical modelling of corrosion - Theoretical backgrounds -
Energy Technology Data Exchange (ETDEWEB)
Warkus, J.; Raupach, M. [ibac, RWTH Aachen (Germany); Gulikers, J. [Ministry of Transport, Rijkswaterstaat, Bouwdienst, Utrecht (Netherlands)
2006-08-15
During recent years research projects with different approaches have been carried out to develop models which are suitable to assess the metal removal rate in case of reinforcement corrosion. Some of them are based on empirical methods and correlate the corrosion rate to parameters like concrete resistivity, temperature and relative humidity. Another type of model is based on a quantification of the ongoing electrochemical processes. In this paper the theoretical backgrounds and mathematical descriptions of reinforcement corrosion with regard to a numerical modelling are presented and discussed. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Numerical simulation of nuclear pebble bed configurations
Energy Technology Data Exchange (ETDEWEB)
Shams, A., E-mail: shams@nrg.eu [Nuclear Research and Consultancy Group (NRG), Petten (Netherlands); Roelofs, F., E-mail: roelofs@nrg.eu [Nuclear Research and Consultancy Group (NRG), Petten (Netherlands); Komen, E.M.J., E-mail: komen@nrg.eu [Nuclear Research and Consultancy Group (NRG), Petten (Netherlands); Baglietto, E., E-mail: emiliob@MIT.EDU [Massachusetts Institute of Technology (MIT) (United States)
2015-08-15
Highlights: • Numerical simulations of a single face cubic centred pebble bed are performed. • Wide range of turbulence modelling techniques are used to perform these calculations. • The methods include 1-DNS, 1-LES, 3-Hybrid (RANS/LES) and 3-RANS models, respectively. • The obtained results are extensively compared to provide guidelines for such flow regimes. • These guidelines are used to perform reference LES for a limited sized random pebble bed. - Abstract: High Temperature Reactors (HTRs) are being considered all over the world. An HTR uses helium gas as a coolant, while the moderator function is taken up by graphite. The fuel is embedded in the graphite moderator. A particular inherent safety advantage of HTR designs is that the graphite can withstand very high temperatures, that the fuel inside will stay inside the graphite pebble and cannot escape to the surroundings even in the event of loss of cooling. Generally, the core can be designed using a graphite pebble bed. Some experimental and demonstration reactors have been operated using a pebble bed design. The test reactors have shown safe and efficient operation, however questions have been raised about possible occurrence of local hot spots in the pebble bed which may affect the pebble integrity. Analysis of the fuel integrity requires detailed evaluation of local heat transport phenomena in a pebble bed, and since such phenomena cannot easily be modelled experimentally, numerical simulations are a useful tool. As a part of a European project, named Thermal Hydraulics of Innovative Nuclear Systems (THINS), a benchmarking quasi-direct numerical simulation (q-DNS) of a well-defined pebble bed configuration has been performed. This q-DNS will serve as a reference database in order to evaluate the prediction capabilities of different turbulence modelling approaches. A wide range of numerical simulations based on different available turbulence modelling approaches are performed and compared with
Tornado structure interaction: a numerical simulation
Energy Technology Data Exchange (ETDEWEB)
Wilson, T.
1977-05-20
The effects of tornadoes on buildings are examined to determine the wind forces on structures. The American National Standards Institute (ANSI) has developed guidelines for building code requirements for the minimum wind loads a building must be designed to withstand. The conservatism or nonconservatism on the ANSI approach is evaluated by simulating tornado-structure interaction numerically with a two-dimensional fluid dynamics computer code and a vortex model. Only external pressures are considered. The computer calculations yield the following percentages of the ANSI design pressures: rigid frame, 50 to 90%; individual wall panels, 75 to 200%; and wall corners, 50 to 75%.
Numerically abnormal chromosome constitutions in humans
Energy Technology Data Exchange (ETDEWEB)
NONE
1993-12-31
Chapter 24, discusses numerically abnormal chromosome constitutions in humans. This involves abnormalities of human chromosome number, including polyploidy (when the number of sets of chromosomes increases) and aneuploidy (when the number of individual normal chromosomes changes). Chapter sections discuss the following chromosomal abnormalities: human triploids, imprinting and uniparental disomy, human tetraploids, hydatidiform moles, anomalies caused by chromosomal imbalance, 13 trisomy (D{sub 1} trisomy, Patau syndrome), 21 trisomy (Down syndrome), 18 trisomy syndrome (Edwards syndrome), other autosomal aneuploidy syndromes, and spontaneous abortions. The chapter concludes with remarks on the nonrandom participation of chromosomes in trisomy. 69 refs., 3 figs., 4 tabs.
Bailey, Brian N.
2017-01-01
When Lagrangian stochastic models for turbulent dispersion are applied to complex atmospheric flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behaviour in the numerical solution. Here we discuss numerical strategies for solving the non-linear Langevin-based particle velocity evolution equation that eliminate such unphysical behaviour in both Reynolds-averaged and large-eddy simulation applications. Extremely large or `rogue' particle velocities are caused when the numerical integration scheme becomes unstable. Such instabilities can be eliminated by using a sufficiently small integration timestep, or in cases where the required timestep is unrealistically small, an unconditionally stable implicit integration scheme can be used. When the generalized anisotropic turbulence model is used, it is critical that the input velocity covariance tensor be realizable, otherwise unphysical behaviour can become problematic regardless of the integration scheme or size of the timestep. A method is presented to ensure realizability, and thus eliminate such behaviour. It was also found that the numerical accuracy of the integration scheme determined the degree to which the second law of thermodynamics or `well-mixed condition' was satisfied. Perhaps more importantly, it also determined the degree to which modelled Eulerian particle velocity statistics matched the specified Eulerian distributions (which is the ultimate goal of the numerical solution). It is recommended that future models be verified by not only checking the well-mixed condition, but perhaps more importantly by checking that computed Eulerian statistics match the Eulerian statistics specified as inputs.