Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids
Housman, Jeffrey A.; Kiris, Cetin
2016-01-01
Computational aeroacoustic simulations using the structured overset grid approach and higher-order finite difference methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for slat noise predictions. The simulations are part of a collaborative study comparing noise generation mechanisms between a conventional slat and a Krueger leading edge flap. Simulation results are compared with experimental data acquired during an aeroacoustic test in the NASA Langley Quiet Flow Facility. Details of the structured overset grid, numerical discretization, and turbulence model are provided.
Mimetic finite difference method
Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail
2014-01-01
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
Implicit and fully implicit exponential finite difference methods
Indian Academy of Sciences (India)
Burgers' equation; exponential finite difference method; implicit exponential finite difference method; ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. ... Current Issue
Abstract Level Parallelization of Finite Difference Methods
Directory of Open Access Journals (Sweden)
Edwin Vollebregt
1997-01-01
Full Text Available A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”. The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automaticcode generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channel programming paradigm (e.g., message passing. This is important because message passing, unfortunately, still is the only approach that leads to acceptable performance for many more unstructured or irregular problems on parallel computers that have non-uniform memory access times. It will be shown that the use of index sets and stencils greatly simplifies the determination of which data must be exchanged between different computing processes.
Numerical methods of higher order of accuracy for incompressible flows
Czech Academy of Sciences Publication Activity Database
Kozel, K.; Louda, Petr; Příhoda, Jaromír
2010-01-01
Roč. 80, č. 8 (2010), s. 1734-1745 ISSN 0378-4754 Institutional research plan: CEZ:AV0Z20760514 Keywords : higher order methods * upwind methods * backward-facing step Subject RIV: BK - Fluid Dynamics Impact factor: 0.812, year: 2010
Higher-Order Integral Equation Methods in Computational Electromagnetics
DEFF Research Database (Denmark)
Jørgensen, Erik; Meincke, Peter
Higher-order integral equation methods have been investigated. The study has focused on improving the accuracy and efficiency of the Method of Moments (MoM) applied to electromagnetic problems. A new set of hierarchical Legendre basis functions of arbitrary order is developed. The new basis...
Multilevel Fast Multipole Method for Higher Order Discretizations
DEFF Research Database (Denmark)
Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik
2014-01-01
The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....
Improved Multilevel Fast Multipole Method for Higher-Order discretizations
DEFF Research Database (Denmark)
Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik
2014-01-01
The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion b...
Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy.
Buttler, Hans-Jurg
1995-01-01
The purpose of this paper is to evaluate numerically the semi-American callable bond by means of finite difference methods. This study implies three results. First, the numerical error is greater for the callable bond price than for the straight bond price, and too large for real applications Secondly, the numerical accuracy of the callable bond price computed for the relevant range of interest rates depends entirely on the finite difference scheme which is chosen for the boundary points. Thi...
The higher order flux mapping method in large size PHWRs
International Nuclear Information System (INIS)
Kulkarni, A.K.; Balaraman, V.; Purandare, H.D.
1997-01-01
A new higher order method is proposed for obtaining flux map using single set of expansion mode. In this procedure, one can make use of the difference between predicted value of detector reading and their actual values for determining the strength of local fluxes around detector site. The local fluxes are arising due to constant perturbation changes (both extrinsic and intrinsic) taking place in the reactor. (author)
Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model
Directory of Open Access Journals (Sweden)
Oluwaseun Egbelowo
2017-05-01
Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.
Chebyshev Finite Difference Method for Fractional Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boundary
2015-09-01
Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative
The mimetic finite difference method for elliptic problems
Veiga, Lourenço Beirão; Manzini, Gianmarco
2014-01-01
This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.
Finite-Difference Frequency-Domain Method in Nanophotonics
DEFF Research Database (Denmark)
Ivinskaya, Aliaksandra
Optics and photonics are exciting, rapidly developing fields building their success largely on use of more and more elaborate artificially made, nanostructured materials. To further advance our understanding of light-matter interactions in these complicated artificial media, numerical modeling...... is often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwell’s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers...... is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes...
Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
Directory of Open Access Journals (Sweden)
I. Amirali
2014-01-01
Full Text Available Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.
Higher order temporal finite element methods through mixed formalisms.
Kim, Jinkyu
2014-01-01
The extended framework of Hamilton's principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.
Computational electrodynamics the finite-difference time-domain method
Taflove, Allen
2005-01-01
This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.
Temperature Calculation of Annular Fuel Pellet by Finite Difference Method
Energy Technology Data Exchange (ETDEWEB)
Yang, Yong Sik; Bang, Je Geon; Kim, Dae Ho; Kim, Sun Ki; Lim, Ik Sung; Song, Kun Woo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2009-10-15
KAERI has started an innovative fuel development project for applying dual-cooled annular fuel to existing PWR reactor. In fuel design, fuel temperature is the most important factor which can affect nuclear fuel integrity and safety. Many models and methodologies, which can calculate temperature distribution in a fuel pellet have been proposed. However, due to the geometrical characteristics and cooling condition differences between existing solid type fuel and dual-cooled annular fuel, current fuel temperature calculation models can not be applied directly. Therefore, the new heat conduction model of fuel pellet was established. In general, fuel pellet temperature is calculated by FDM(Finite Difference Method) or FEM(Finite Element Method), because, temperature dependency of fuel thermal conductivity and spatial dependency heat generation in the pellet due to the self-shielding should be considered. In our study, FDM is adopted due to high exactness and short calculation time.
A parallel finite-difference method for computational aerodynamics
International Nuclear Information System (INIS)
Swisshelm, J.M.
1989-01-01
A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed. 14 refs
Higher order methods for burnup calculations with Bateman solutions
International Nuclear Information System (INIS)
Isotalo, A.E.; Aarnio, P.A.
2011-01-01
Highlights: → Average microscopic reaction rates need to be estimated at each step. → Traditional predictor-corrector methods use zeroth and first order predictions. → Increasing predictor order greatly improves results. → Increasing corrector order does not improve results. - Abstract: A group of methods for burnup calculations solves the changes in material compositions by evaluating an explicit solution to the Bateman equations with constant microscopic reaction rates. This requires predicting representative averages for the one-group cross-sections and flux during each step, which is usually done using zeroth and first order predictions for their time development in a predictor-corrector calculation. In this paper we present the results of using linear, rather than constant, extrapolation on the predictor and quadratic, rather than linear, interpolation on the corrector. Both of these are done by using data from the previous step, and thus do not affect the stepwise running time. The methods were tested by implementing them into the reactor physics code Serpent and comparing the results from four test cases to accurate reference results obtained with very short steps. Linear extrapolation greatly improved results for thermal spectra and should be preferred over the constant one currently used in all Bateman solution based burnup calculations. The effects of using quadratic interpolation on the corrector were, on the other hand, predominantly negative, although not enough so to conclusively decide between the linear and quadratic variants.
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
Modeling of NiTiHf using finite difference method
Farjam, Nazanin; Mehrabi, Reza; Karaca, Haluk; Mirzaeifar, Reza; Elahinia, Mohammad
2018-03-01
NiTiHf is a high temperature and high strength shape memory alloy with transformation temperatures above 100oC. A constitutive model based on Gibbs free energy is developed to predict the behavior of this material. Two different irrecoverable strains including transformation induced plastic strain (TRIP) and viscoplastic strain (VP) are considered when using high temperature shape memory alloys (HTSMAs). The first one happens during transformation at high levels of stress and the second one is related to the creep which is rate-dependent. The developed model is implemented for NiTiHf under uniaxial loading. Finite difference method is utilized to solve the proposed equations. The material parameters in the equations are calibrated from experimental data. Simulation results are captured to investigate the superelastic behavior of NiTiHf. The extracted results are compared with experimental tests of isobaric heating and cooling at different levels of stress and also superelastic tests at different levels of temperature. More results are generated to investigate the capability of the proposed model in the prediction of the irrecoverable strain after full transformation in HTSMAs.
A finite-difference contrast source inversion method
International Nuclear Information System (INIS)
Abubakar, A; Hu, W; Habashy, T M; Van den Berg, P M
2008-01-01
We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium
High-order finite-difference methods for Poisson's equation
van Linde, Hendrik Jan
1971-01-01
In this thesis finite-difference approximations to the three boundary value problems for Poisson’s equation are given, with discretization errors of O(H^3) for the mixed boundary value problem, O(H^3 |ln(h)| for the Neumann problem and O(H^4)for the Dirichlet problem respectively . First an operator
A finite difference method for free boundary problems
Fornberg, Bengt
2010-01-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax
A finite difference method for free boundary problems
Fornberg, Bengt
2010-04-01
Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter
2004-01-01
An efficient higher-order method of moments (MoM) solution of volume integral equations is presented. The higher-order MoM solution is based on higher-order hierarchical Legendre basis functions and higher-order geometry modeling. An unstructured mesh composed of 8-node trilinear and/or curved 27...... of magnitude in comparison to existing higher-order hierarchical basis functions. Consequently, an iterative solver can be applied even for high expansion orders. Numerical results demonstrate excellent agreement with the analytical Mie series solution for a dielectric sphere as well as with results obtained...
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
International Nuclear Information System (INIS)
Shtromberger, N.L.
1989-01-01
To design a cyclotron magnetic system the legitimacy of two-dimensional approximations application is discussed. In all the calculations the finite difference method is used, and the linearization method with further use of the gradient conjugation method is used to solve the set of finite-difference equations. 3 refs.; 5 figs
Higher order polynomial expansion nodal method for hexagonal core neutronics analysis
International Nuclear Information System (INIS)
Jin, Young Cho; Chang, Hyo Kim
1998-01-01
A higher-order polynomial expansion nodal(PEN) method is newly formulated as a means to improve the accuracy of the conventional PEN method solutions to multi-group diffusion equations in hexagonal core geometry. The new method is applied to solving various hexagonal core neutronics benchmark problems. The computational accuracy of the higher order PEN method is then compared with that of the conventional PEN method, the analytic function expansion nodal (AFEN) method, and the ANC-H method. It is demonstrated that the higher order PEN method improves the accuracy of the conventional PEN method and that it compares very well with the other nodal methods like the AFEN and ANC-H methods in accuracy
ORIGINAL ARTICLE Fitted-Stable Finite Difference Method for ...
African Journals Online (AJOL)
Gemechis
two point boundary value problems with the boundary layer at one end (left or right) ... scheme (SCD Method) and its value is obtained using the theory of singular ..... Eq. (15) at the point. N iih xxi. , ,2 ,1 ,0 ,.. = = = and taking the limit as. 0. →.
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced
Stability and non-standard finite difference method of the generalized Chua's circuit
Radwan, Ahmed G.; Moaddy, K.; Momani, Shaher M.
2011-01-01
In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well
Method of applying single higher order polynomial basis function over multiple domains
CSIR Research Space (South Africa)
Lysko, AA
2010-03-01
Full Text Available A novel method has been devised where one set of higher order polynomial-based basis functions can be applied over several wire segments, thus permitting to decouple the number of unknowns from the number of segments, and so from the geometrical...
Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method
Miyazaki, Yutaka; Tsuchiya, Takao
2012-07-01
The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.
An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs
Directory of Open Access Journals (Sweden)
Eman S. Alaidarous
2013-01-01
Full Text Available In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013. The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.
Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics
Gedney, Stephen
2011-01-01
Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to p
Wu, Zedong
2018-04-05
Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.
Compositional modeling of three-phase flow with gravity using higher-order finite element methods
Moortgat, Joachim
2011-05-11
A wide range of applications in subsurface flow involve water, a nonaqueous phase liquid (NAPL) or oil, and a gas phase, such as air or CO2. The numerical simulation of such processes is computationally challenging and requires accurate compositional modeling of three-phase flow in porous media. In this work, we simulate for the first time three-phase compositional flow using higher-order finite element methods. Gravity poses complications in modeling multiphase processes because it drives countercurrent flow among phases. To resolve this issue, we propose a new method for the upwinding of three-phase mobilities. Numerical examples, related to enhanced oil recovery and carbon sequestration, are presented to illustrate the capabilities of the proposed algorithm. We pay special attention to challenges associated with gravitational instabilities and take into account compressibility and various phase behavior effects, including swelling, viscosity changes, and vaporization. We find that the proposed higher-order method can capture sharp solution discontinuities, yielding accurate predictions of phase boundaries arising in computational three-phase flow. This work sets the stage for a broad extension of the higher-order methods for numerical simulation of three-phase flow for complex geometries and processes.
Analysis of equilibrium in a tokamak by the finite-difference method
International Nuclear Information System (INIS)
Kim, K.E.; Jeun, G.D.
1983-01-01
Ideal magnetohydrodynamic equilibrium in a Tokamak having a small radius with an elongated rectangular cross section is studied by applying the finite-difference method to the Grad-Shafranov equation to determine possible limitations for *b=8*pPsup(2)/Bsup(2). The coupled first-order differential equations resulting from the finite-difference Grad-Shafranov equation is solved by the numarical method:1)We concluded that equilibrium consideration alone gives no limitation even for *b approx.1. 2)We have obtained the equilibrium magnetic field configuration charcterized by a set of three parameters;the aspect ratio, *b,and the safety factor. (Author)
A practical implementation of the higher-order transverse-integrated nodal diffusion method
International Nuclear Information System (INIS)
Prinsloo, Rian H.; Tomašević, Djordje I.; Moraal, Harm
2014-01-01
Highlights: • A practical higher-order nodal method is developed for diffusion calculations. • The method resolves the issue of the transverse leakage approximation. • The method achieves much superior accuracy as compared to standard nodal methods. • The calculational cost is only about 50% greater than standard nodal methods. • The method is packaged in a module for connection to existing nodal codes. - Abstract: Transverse-integrated nodal diffusion methods currently represent the standard in full core neutronic simulation. The primary shortcoming of this approach is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work, an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher-order nodal methods developed some years ago. Further, a number of iteration schemes are developed around this consistent quadratic leakage approximation which yields accurate node average results in much improved calculational times. The most promising of these iteration schemes results from utilizing the consistent leakage approximation as a correction method to the standard quadratic leakage approximation. Numerical results are demonstrated on a set of benchmark problems and further applied to a realistic reactor problem, particularly the SAFARI-1 reactor, operating at Necsa, South Africa. The final optimal solution strategy is packaged into a standalone module which may simply be coupled to existing nodal diffusion codes
A new fitted operator finite difference method to solve systems of ...
African Journals Online (AJOL)
In recent years, fitted operator finite difference methods (FOFDMs) have been developed for numerous types of singularly perturbed ordinary differential equations. The construction of most of these methods differed though the final outcome remained similar. The most crucial aspect was how the difference operator was ...
Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet
2017-11-01
In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.
Higher-order schemes for the Laplace transformation method for parabolic problems
Douglas, C.
2011-01-01
In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.
The finite-difference time-domain method for electromagnetics with Matlab simulations
Elsherbeni, Atef Z
2016-01-01
This book introduces the powerful Finite-Difference Time-Domain method to students and interested researchers and readers. An effective introduction is accomplished using a step-by-step process that builds competence and confidence in developing complete working codes for the design and analysis of various antennas and microwave devices.
Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation
Prentice, J. S. C.
2012-01-01
An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…
Modeling of Nanophotonic Resonators with the Finite-Difference Frequency-Domain Method
DEFF Research Database (Denmark)
Ivinskaya, Aliaksandra; Lavrinenko, Andrei; Shyroki, Dzmitry
2011-01-01
Finite-difference frequency-domain method with perfectly matched layers and free-space squeezing is applied to model open photonic resonators of arbitrary morphology in three dimensions. Treating each spatial dimension independently, nonuniform mesh of continuously varying density can be built ea...
Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling
Fink, P. W.; Wilton, D. R.; Dobbins, J. A.
2002-01-01
In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required
Adaptive grouping for the higher-order multilevel fast multipole method
DEFF Research Database (Denmark)
Borries, Oscar Peter; Jørgensen, Erik; Meincke, Peter
2014-01-01
An alternative parameter-free adaptive approach for the grouping of the basis function patterns in the multilevel fast multipole method is presented, yielding significant memory savings compared to the traditional Octree grouping for most discretizations, particularly when using higher-order basis...... functions. Results from both a uniformly and nonuniformly meshed scatterer are presented, showing how the technique is worthwhile even for regular meshes, and demonstrating that there is no loss of accuracy in spite of the large reduction in memory requirements and the relatively low computational cost....
Higher order Godunov methods for general systems of hyperbolic conservation laws
International Nuclear Information System (INIS)
Bell, J.B.; Colella, P.; Trangenstein, J.A.
1989-01-01
We describe an extension of higher order Godunov methods to general systems of hyperbolic conservation laws. This extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields. The method constructs an approximation of the Riemann problem from local wave information. A generalization of the Engquist--Osher flux for systems is then used to compute a numerical flux based on this approximation. This numerical flux replaces the Godunov numerical flux in the algorithm, thereby eliminating the need for a global Riemann problem solution. The additional modifications to the Godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail. The method is applied to some simple model problems for which the glocal analytic structure is known. The method is also applied to the black-oil model for multiphase flow in petroleum reservoirs. copyright 1989 Academic Press, Inc
A coarse-mesh nodal method-diffusive-mesh finite difference method
International Nuclear Information System (INIS)
Joo, H.; Nichols, W.R.
1994-01-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper
Chu, Chunlei
2012-01-01
Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations. © 2011 Elsevier B.V.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Energy Technology Data Exchange (ETDEWEB)
Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
Numerical study of water diffusion in biological tissues using an improved finite difference method
International Nuclear Information System (INIS)
Xu Junzhong; Does, Mark D; Gore, John C
2007-01-01
An improved finite difference (FD) method has been developed in order to calculate the behaviour of the nuclear magnetic resonance signal variations caused by water diffusion in biological tissues more accurately and efficiently. The algorithm converts the conventional image-based finite difference method into a convenient matrix-based approach and includes a revised periodic boundary condition which eliminates the edge effects caused by artificial boundaries in conventional FD methods. Simulated results for some modelled tissues are consistent with analytical solutions for commonly used diffusion-weighted pulse sequences, whereas the improved FD method shows improved efficiency and accuracy. A tightly coupled parallel computing approach was also developed to implement the FD methods to enable large-scale simulations of realistic biological tissues. The potential applications of the improved FD method for understanding diffusion in tissues are also discussed. (note)
A comparison of different methods to implement higher order derivatives of density functionals
Energy Technology Data Exchange (ETDEWEB)
van Dam, Hubertus J.J. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2016-05-18
Density functional theory is the dominant approach in electronic structure methods today. To calculate properties higher order derivatives of the density functionals are required. These derivatives might be implemented manually,by automatic differentiation, or by symbolic algebra programs. Different authors have cited different reasons for using the particular method of their choice. This paper presents work where all three approaches were used and the strengths and weaknesses of each approach are considered. It is found that all three methods produce code that is suffficiently performanted for practical applications, despite the fact that our symbolic algebra generated code and our automatic differentiation code still have scope for significant optimization. The automatic differentiation approach is the best option for producing readable and maintainable code.
Optimized Signaling Method for High-Speed Transmission Channels with Higher Order Transfer Function
Ševčík, Břetislav; Brančík, Lubomír; Kubíček, Michal
2017-08-01
In this paper, the selected results from testing of optimized CMOS friendly signaling method for high-speed communications over cables and printed circuit boards (PCBs) are presented and discussed. The proposed signaling scheme uses modified concept of pulse width modulated (PWM) signal which enables to better equalize significant channel losses during data high-speed transmission. Thus, the very effective signaling method to overcome losses in transmission channels with higher order transfer function, typical for long cables and multilayer PCBs, is clearly analyzed in the time and frequency domain. Experimental results of the measurements include the performance comparison of conventional PWM scheme and clearly show the great potential of the modified signaling method for use in low power CMOS friendly equalization circuits, commonly considered in modern communication standards as PCI-Express, SATA or in Multi-gigabit SerDes interconnects.
Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method
Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang
2017-06-01
Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.
Directory of Open Access Journals (Sweden)
Lei Wang
2015-09-01
Full Text Available Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare with the results from the analytical method, the result from Laplace transform finite difference method turns out to be accurate. The influence factors are analyzed, including fractal dimension, fractal index, skin factor, well bore storage coefficient, energy storage ratio, interporosity flow coefficient and the adsorption factor. The calculating error of Laplace transform difference method is small. Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment results and space grid.
Two-photon or higher-order absorbing optical materials and methods of use
Marder, Seth (Inventor); Perry, Joseph (Inventor)
2012-01-01
Compositions capable of simultaneous two-photon absorption and higher order absorptivities are provided. Compounds having a donor-pi-donor or acceptor-pi-acceptor structure are of particular interest, where the donor is an electron donating group, acceptor is an electron accepting group, and pi is a pi bridge linking the donor and/or acceptor groups. The pi bridge may additionally be substituted with electron donating or withdrawing groups to alter the absorptive wavelength of the structure. Also disclosed are methods of generating an excited state of such compounds through optical stimulation with light using simultaneous absorption of photons of energies individually insufficient to achieve an excited state of the compound, but capable of doing so upon simultaneous absorption of two or more such photons. Applications employing such methods are also provided, including controlled polymerization achieved through focusing of the light source(s) used.
Applicability of higher-order TVD method to low mach number compressible flows
International Nuclear Information System (INIS)
Akamatsu, Mikio
1995-01-01
Steep gradients of fluid density are the influential factor of spurious oscillation in numerical solutions of low Mach number (M<<1) compressible flows. The total variation diminishing (TVD) scheme is a promising remedy to overcome this problem and obtain accurate solutions. TVD schemes for high-speed flows are, however, not compatible with commonly used methods in low Mach number flows using pressure-based formulation. In the present study a higher-order TVD scheme is constructed on a modified form of each individual scalar equation of primitive variables. It is thus clarified that the concept of TVD is applicable to low Mach number flows within the framework of the existing numerical method. Results of test problems of the moving interface of two-component gases with the density ratio ≥ 4, demonstrate the accurate and robust (wiggle-free) profile of the scheme. (author)
Energy stable and high-order-accurate finite difference methods on staggered grids
O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan
2017-10-01
For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.
Stability and non-standard finite difference method of the generalized Chua's circuit
Radwan, Ahmed G.
2011-08-01
In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua\\'s circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles\\' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.
Implementation of compact finite-difference method to parabolized Navier-Stokes equations
International Nuclear Information System (INIS)
Esfahanian, V.; Hejranfar, K.; Darian, H.M.
2005-01-01
The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)
A practical implicit finite-difference method: examples from seismic modelling
International Nuclear Information System (INIS)
Liu, Yang; Sen, Mrinal K
2009-01-01
We derive explicit and new implicit finite-difference formulae for derivatives of arbitrary order with any order of accuracy by the plane wave theory where the finite-difference coefficients are obtained from the Taylor series expansion. The implicit finite-difference formulae are derived from fractional expansion of derivatives which form tridiagonal matrix equations. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to that of a (6N + 2)th-order explicit formula for the first-order derivative, and (2N + 2)th-order implicit formula is nearly equivalent to (4N + 2)th-order explicit formula for the second-order derivative. In general, an implicit method is computationally more expensive than an explicit method, due to the requirement of solving large matrix equations. However, the new implicit method only involves solving tridiagonal matrix equations, which is fairly inexpensive. Furthermore, taking advantage of the fact that many repeated calculations of derivatives are performed by the same difference formula, several parts can be precomputed resulting in a fast algorithm. We further demonstrate that a (2N + 2)th-order implicit formulation requires nearly the same memory and computation as a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (6N + 2)th-order explicit formulation for the first-order derivative and that of a (4N + 2)th-order explicit method for the second-order derivative when additional cost of visiting arrays is not considered. This means that a high-order explicit method may be replaced by an implicit method of the same order resulting in a much improved performance. Our analysis of efficiency and numerical modelling results for acoustic and elastic wave propagation validates the effectiveness and practicality of the implicit finite-difference method
Wang, Yi
2016-07-21
Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.
On the Stability of the Finite Difference based Lattice Boltzmann Method
El-Amin, Mohamed; Sun, Shuyu; Salama, Amgad
2013-01-01
This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
On the Stability of the Finite Difference based Lattice Boltzmann Method
El-Amin, Mohamed
2013-06-01
This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
Directory of Open Access Journals (Sweden)
Xinfeng Ruan
2013-01-01
Full Text Available We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE of European option. The finite difference method is employed to compute the European option valuation of PIDE.
Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method
International Nuclear Information System (INIS)
Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong
2014-01-01
In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)
Lei Wang; Hongjun Yin; Xiaoshuang Yang; Chuncheng Yang; Jing Fu
2015-01-01
Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare wi...
Stability analysis of single-phase thermosyphon loops by finite difference numerical methods
International Nuclear Information System (INIS)
Ambrosini, W.
1998-01-01
In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs
Modeling 3D PCMI using the Extended Finite Element Method with higher order elements
Energy Technology Data Exchange (ETDEWEB)
Jiang, W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin W. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2017-03-31
This report documents the recent development to enable XFEM to work with higher order elements. It also demonstrates the application of higher order (quadratic) elements to both 2D and 3D models of PCMI problems, where discrete fractures in the fuel are represented using XFEM. The modeling results demonstrate the ability of the higher order XFEM to accurately capture the effects of a crack on the response in the vicinity of the intersecting surfaces of cracked fuel and cladding, as well as represent smooth responses in the regions away from the crack.
Agarwal, P.; El-Sayed, A. A.
2018-06-01
In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
Energy Technology Data Exchange (ETDEWEB)
Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, 100101 (China); Badal, José, E-mail: badal@unizar.es [Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza (Spain)
2017-05-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
International Nuclear Information System (INIS)
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José
2017-01-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
Solving the Schroedinger equation using the finite difference time domain method
International Nuclear Information System (INIS)
Sudiarta, I Wayan; Geldart, D J Wallace
2007-01-01
In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems
Analysis of multi lobe journal bearings with surface roughness using finite difference method
PhaniRaja Kumar, K.; Bhaskar, SUdaya; Manzoor Hussain, M.
2018-04-01
Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.
Finite difference applied to the reconstruction method of the nuclear power density distribution
International Nuclear Information System (INIS)
Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.
2016-01-01
Highlights: • A method for reconstruction of the power density distribution is presented. • The method uses discretization by finite differences of 2D neutrons diffusion equation. • The discretization is performed homogeneous meshes with dimensions of a fuel cell. • The discretization is combined with flux distributions on the four node surfaces. • The maximum errors in reconstruction occur in the peripheral water region. - Abstract: In this reconstruction method the two-dimensional (2D) neutron diffusion equation is discretized by finite differences, employed to two energy groups (2G) and meshes with fuel-pin cell dimensions. The Nodal Expansion Method (NEM) makes use of surface discontinuity factors of the node and provides for reconstruction method the effective multiplication factor of the problem and the four surface average fluxes in homogeneous nodes with size of a fuel assembly (FA). The reconstruction process combines the discretized 2D diffusion equation by finite differences with fluxes distribution on four surfaces of the nodes. These distributions are obtained for each surfaces from a fourth order one-dimensional (1D) polynomial expansion with five coefficients to be determined. The conditions necessary for coefficients determination are three average fluxes on consecutive surfaces of the three nodes and two fluxes in corners between these three surface fluxes. Corner fluxes of the node are determined using a third order 1D polynomial expansion with four coefficients. This reconstruction method uses heterogeneous nuclear parameters directly providing the heterogeneous neutron flux distribution and the detailed nuclear power density distribution within the FAs. The results obtained with this method has good accuracy and efficiency when compared with reference values.
Elastic frequency-domain finite-difference contrast source inversion method
International Nuclear Information System (INIS)
He, Qinglong; Chen, Yong; Han, Bo; Li, Yang
2016-01-01
In this work, we extend the finite-difference contrast source inversion (FD-CSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media and the given angular frequency, both of which are unchanged during inversion. Therefore, the matrix decomposition is performed only once at the beginning of the iteration if a direct solver is employed. This makes the inversion process relatively efficient in terms of the computational cost. In addition, the FD-CSI method automatically normalizes different parameters, which could avoid the numerical problems arising from the difference of the parameter magnitude. We exploit a parallel implementation of the FD-CSI method based on the domain decomposition method, ensuring a satisfactory scalability for large-scale problems. A simple numerical example with a homogeneous background medium is used to investigate the convergence of the elastic FD-CSI method. Moreover, the Marmousi II model proposed as a benchmark for testing seismic imaging methods is presented to demonstrate the performance of the elastic FD-CSI method in an inhomogeneous background medium. (paper)
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2011-01-01
The aim of the work described in this paper has been to investigate the use of the finite-difference time-domain method to describe the interactions between a moving object and a sound field. The main objective was to simulate oscillational instabilities that appear in single-axis acoustic...... levitation devices and to describe their evolution in time to further understand the physical mechanism involved. The study shows that the method gives accurate results for steady state conditions, and that it is a promising tool for simulations with a moving object....
A study of unstable rock failures using finite difference and discrete element methods
Garvey, Ryan J.
Case histories in mining have long described pillars or faces of rock failing violently with an accompanying rapid ejection of debris and broken material into the working areas of the mine. These unstable failures have resulted in large losses of life and collapses of entire mine panels. Modern mining operations take significant steps to reduce the likelihood of unstable failure, however eliminating their occurrence is difficult in practice. Researchers over several decades have supplemented studies of unstable failures through the application of various numerical methods. The direction of the current research is to extend these methods and to develop improved numerical tools with which to study unstable failures in underground mining layouts. An extensive study is first conducted on the expression of unstable failure in discrete element and finite difference methods. Simulated uniaxial compressive strength tests are run on brittle rock specimens. Stable or unstable loading conditions are applied onto the brittle specimens by a pair of elastic platens with ranging stiffnesses. Determinations of instability are established through stress and strain histories taken for the specimen and the system. Additional numerical tools are then developed for the finite difference method to analyze unstable failure in larger mine models. Instability identifiers are established for assessing the locations and relative magnitudes of unstable failure through measures of rapid dynamic motion. An energy balance is developed which calculates the excess energy released as a result of unstable equilibria in rock systems. These tools are validated through uniaxial and triaxial compressive strength tests and are extended to models of coal pillars and a simplified mining layout. The results of the finite difference simulations reveal that the instability identifiers and excess energy calculations provide a generalized methodology for assessing unstable failures within potentially complex
International Nuclear Information System (INIS)
Ackroyd, R.T.
1987-01-01
A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)
Finite difference method calculations of X-ray absorption fine structure for copper
Energy Technology Data Exchange (ETDEWEB)
Bourke, J.D. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia); Chantler, C.T. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)]. E-mail: chantler@physics.unimelb.edu.au; Witte, C. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)
2007-01-15
The finite difference method is extended to calculate X-ray absorption fine structure (XAFS) for solid state copper. These extensions include the incorporation of a Monte Carlo frozen phonon technique to simulate the effect of thermal vibrations under a correlated Debye-Waller model, and the inclusion of broadening effects from inelastic processes. Spectra are obtained over an energy range in excess of 300 eV above the K absorption edge-more than twice the greatest energy range previously reported for a solid state calculation using this method. We find this method is highly sensitive to values of the photoelectron inelastic mean free path, allowing us to probe the accuracy of current models of this parameter, particularly at low energies. We therefore find that experimental data for the photoelectron inelastic mean free path can be obtained by this method. Our results compare favourably with high precision measurements of the X-ray mass attenuation coefficient for copper, reaching agreement to within 3%, and improving previous results using the finite difference method by an order of magnitude.
New way for determining electron energy levels in quantum dots arrays using finite difference method
Dujardin, F.; Assaid, E.; Feddi, E.
2018-06-01
Electronic states are investigated in quantum dots arrays, depending on the type of cubic Bravais lattice (primitive, body centered or face centered) according to which the dots are arranged, the size of the dots and the interdot distance. It is shown that the ground state energy level can undergo significant variations when these parameters are modified. The results were obtained by means of finite difference method which has proved to be easily adaptable, efficient and precise. The symmetry properties of the lattice have been used to reduce the size of the Hamiltonian matrix.
Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case
International Nuclear Information System (INIS)
Hojbota, C I; Toşa, V; Mercea, P V
2013-01-01
We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food
A moving mesh finite difference method for equilibrium radiation diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
A moving mesh finite difference method for equilibrium radiation diffusion equations
International Nuclear Information System (INIS)
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-01-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation
Higher-order equation-of-motion coupled-cluster methods for ionization processes.
Kamiya, Muneaki; Hirata, So
2006-08-21
Compact algebraic equations defining the equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both alpha and beta ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and CO (with the ambiguity due to finite basis sets eliminated by extrapolation) has shown that IP-EOM-CCSD frequently accounts for orbital relaxation inadequately and displays errors exceeding a couple of eV. However, these errors can be systematically reduced to tenths or even hundredths of an eV by IP-EOM-CCSDT or CCSDTQ. Comparison of spectroscopic parameters of the FH+ and NH+ radicals between IP-EOM-CC and experiments has also underscored the importance of higher-order IP-EOM-CC treatments. For instance, the harmonic frequencies of the A 2Sigma- state of NH+ are predicted to be 1285, 1723, and 1705 cm(-1) by IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively, as compared to the observed value of 1707 cm(-1). The small adiabatic energy separation (observed 0.04 eV) between the X 2Pi and a 4Sigma- states of NH+ also requires IP-EOM-CCSDTQ for a quantitative prediction (0.06 eV) when the a 4Sigma- state has the low-spin magnetic quantum number (s(z) = 1/2). When the
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José
2017-05-01
The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational
Mustapha, K.
2017-06-03
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.
International Nuclear Information System (INIS)
Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.
1996-01-01
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)
Mustapha, K.; Furati, K.; Knio, Omar; Maitre, O. Le
2017-01-01
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.
Five-point form of the nodal diffusion method and comparison with finite-difference
International Nuclear Information System (INIS)
Azmy, Y.Y.
1988-01-01
Nodal Methods have been derived, implemented and numerically tested for several problems in physics and engineering. In the field of nuclear engineering, many nodal formalisms have been used for the neutron diffusion equation, all yielding results which were far more computationally efficient than conventional Finite Difference (FD) and Finite Element (FE) methods. However, not much effort has been devoted to theoretically comparing nodal and FD methods in order to explain the very high accuracy of the former. In this summary we outline the derivation of a simple five-point form for the lowest order nodal method and compare it to the traditional five-point, edge-centered FD scheme. The effect of the observed differences on the accuracy of the respective methods is established by considering a simple test problem. It must be emphasized that the nodal five-point scheme derived here is mathematically equivalent to previously derived lowest order nodal methods. 7 refs., 1 tab
Zhu, D.; Zhu, H.; Luo, Y.; Chen, X.
2008-12-01
We use a new finite difference method (FDM) and the slip-weakening law to model the rupture dynamics of a non-planar fault embedded in a 3-D elastic media with free surface. The new FDM, based on boundary- conforming grid, sets up the mapping equations between the curvilinear coordinate and the Cartesian coordinate and transforms irregular physical space to regular computational space; it also employs a higher- order non-staggered DRP/opt MacCormack scheme which is of low dispersion and low dissipation so that the high accuracy and stability of our rupture modeling are guaranteed. Compared with the previous methods, not only we can compute the spontaneous rupture of an arbitrarily shaped fault, but also can model the influence of the surface topography on the rupture process of earthquake. In order to verify the feasibility of this method, we compared our results and other previous results, and found out they matched perfectly. Thanks to the boundary-conforming FDM, problems such as dynamic rupture with arbitrary dip, strike and rake over an arbitrary curved plane can be handled; and supershear or subshear rupture can be simulated with different parameters such as the initial stresses and the critical slip displacement Dc. Besides, our rupture modeling is economical to be implemented owing to its high efficiency and does not suffer from displacement leakage. With the help of inversion data of rupture by field observations, this method is convenient to model rupture processes and seismograms of natural earthquakes.
A mimetic finite difference method for the Stokes problem with elected edge bubbles
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Berirao, L [DIPARTMENTO DI MATERMATICA
2009-01-01
A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.
International Nuclear Information System (INIS)
Li Bihong; Shuang Na; Liu Qingcheng
2006-01-01
The principle of finite difference method is introduced, and the radon field distribution over sandstone-type uranium deposit is narrated. The radon field distribution theory equation is established. To solve radon field distribution equation using finite difference algorithm is to provide the value computational method for forward calculation about radon field over sandstone-type uranium mine. Study on 2-D finite difference method on the center of either high anomaly radon fields in view of the character of radon field over sandstone-type uranium provide an algorithm for further research. (authors)
Need for higher order polynomial basis for polynomial nodal methods employed in LWR calculations
International Nuclear Information System (INIS)
Taiwo, T.A.; Palmiotti, G.
1997-01-01
The paper evaluates the accuracy and efficiency of sixth order polynomial solutions and the use of one radial node per core assembly for pressurized water reactor (PWR) core power distributions and reactivities. The computer code VARIANT was modified to calculate sixth order polynomial solutions for a hot zero power benchmark problem in which a control assembly along a core axis is assumed to be out of the core. Results are presented for the VARIANT, DIF3D-NODAL, and DIF3D-finite difference codes. The VARIANT results indicate that second order expansion of the within-node source and linear representation of the node surface currents are adequate for this problem. The results also demonstrate the improvement in the VARIANT solution when the order of the polynomial expansion of the within-node flux is increased from fourth to sixth order. There is a substantial saving in computational time for using one radial node per assembly with the sixth order expansion compared to using four or more nodes per assembly and fourth order polynomial solutions. 11 refs., 1 tab
Simulation of acoustic streaming by means of the finite-difference time-domain method
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2012-01-01
Numerical simulations of acoustic streaming generated by a standing wave in a narrow twodimensional cavity are presented. In this case, acoustic streaming arises from the viscous boundary layers set up at the surfaces of the walls. It is known that streaming vortices inside the boundary layer have...... directions of rotation that are opposite to those of the outer streaming vortices (Rayleigh streaming). The general objective of the work described in this paper has been to study the extent to which it is possible to simulate both the outer streaming vortices and the inner boundary layer vortices using...... the finite-difference time-domain method. To simplify the problem, thermal effects are not considered. The motivation of the described investigation has been the possibility of using the numerical method to study acoustic streaming, particularly under non-steady conditions. Results are discussed for channels...
GPU-accelerated 3D neutron diffusion code based on finite difference method
Energy Technology Data Exchange (ETDEWEB)
Xu, Q.; Yu, G.; Wang, K. [Dept. of Engineering Physics, Tsinghua Univ. (China)
2012-07-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
GPU-accelerated 3D neutron diffusion code based on finite difference method
International Nuclear Information System (INIS)
Xu, Q.; Yu, G.; Wang, K.
2012-01-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
Thermal Analysis of Ball screw Systems by Explicit Finite Difference Method
Energy Technology Data Exchange (ETDEWEB)
Min, Bog Ki [Hanyang Univ., Seoul (Korea, Republic of); Park, Chun Hong; Chung, Sung Chong [KIMM, Daejeon (Korea, Republic of)
2016-01-15
Friction generated from balls and grooves incurs temperature rise in the ball screw system. Thermal deformation due to the heat degrades positioning accuracy of the feed drive system. To compensate for the thermal error, accurate prediction of the temperature distribution is required first. In this paper, to predict the temperature distribution according to the rotational speed, solid and hollow cylinders are applied for analysis of the ball screw shaft and nut, respectively. Boundary conditions such as the convective heat transfer coefficient, friction torque, and thermal contact conductance (TCC) between balls and grooves are formulated according to operating and fabrication conditions of the ball screw. Explicit FDM (finite difference method) is studied for development of a temperature prediction simulator. Its effectiveness is verified through numerical analysis.
Directory of Open Access Journals (Sweden)
Beltrán-Prieto Juan Carlos
2016-01-01
Full Text Available The mathematical modelling of diffusion of a bleaching agent into a porous material is studied in the present paper. Law of mass conservation was applied to analize the mass transfer of a reactant from the bulk into the external surface of a solid geometrically described as a flat plate. After diffusion of the reactant, surface reaction following kinetics of first order was considered to take place. The solution of the differential equation that described the process leaded to an equation that represents the concentration profile in function of distance, porosity and Thiele modulus. The case of interfacial mass resistance is also discused. In this case, finite difference method was used for the solution of the differential equation taking into account the respective boundary conditions. The profile of concentration can be obtained after numerical especification of Thiele modulus and Biot number.
Directory of Open Access Journals (Sweden)
Mohammad Hadi Jalali
2018-01-01
Full Text Available Elastic stress analysis of rotating variable thickness annular disk made of functionally graded material (FGM is presented. Elasticity modulus, density, and thickness of the disk are assumed to vary radially according to a power-law function. Radial stress, circumferential stress, and radial deformation of the rotating FG annular disk of variable thickness with clamped-clamped (C-C, clamped-free (C-F, and free-free (F-F boundary conditions are obtained using the numerical finite difference method, and the effects of the graded index, thickness variation, and rotating speed on the stresses and deformation are evaluated. It is shown that using FG material could decrease the value of radial stress and increase the radial displacement in a rotating thin disk. It is also demonstrated that increasing the rotating speed can strongly increase the stress in the FG annular disk.
Mimetic finite difference method for the stokes problem on polygonal meshes
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA
2009-01-01
Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
International Nuclear Information System (INIS)
Park, Beom Woo; Joo, Han Gyu
2015-01-01
Highlights: • The stiffness confinement method is combined with multigroup CMFD with SENM nodal kernel. • The systematic methods for determining the shape and amplitude frequencies are established. • Eigenvalue problems instead of fixed source problems are solved in the transient calculation. • It is demonstrated that much larger time step sizes can be used with the SCM–CMFD method. - Abstract: An improved Stiffness Confinement Method (SCM) is formulated within the framework of the coarse mesh finite difference (CMFD) formulation for efficient multigroup spatial kinetics calculation. The algorithm for searching for the amplitude frequency that makes the dynamic eigenvalue unity is developed in a systematic way along with the methods for determining the shape and precursor frequencies. A nodal calculation scheme is established within the CMFD framework to incorporate the cross section changes due to thermal feedback and dynamic frequency update. The conditional nodal update scheme is employed such that the transient calculation is performed mostly with the CMFD formulation and the CMFD parameters are conditionally updated by intermittent nodal calculations. A quadratic representation of amplitude frequency is introduced as another improvement. The performance of the improved SCM within the CMFD framework is assessed by comparing the solution accuracy and computing times for the NEACRP control rod ejection benchmark problems with those obtained with the Crank–Nicholson method with exponential transform (CNET). It is demonstrated that the improved SCM is beneficial for large time step size calculations with stability and accuracy enhancement
Ping, Jing
2017-05-19
Optimal management of subsurface processes requires the characterization of the uncertainty in reservoir description and reservoir performance prediction. For fractured reservoirs, the location and orientation of fractures are crucial for predicting production characteristics. With the help of accurate and comprehensive knowledge of fracture distributions, early water/CO 2 breakthrough can be prevented and sweep efficiency can be improved. However, since the rock property fields are highly non-Gaussian in this case, it is a challenge to estimate fracture distributions by conventional history matching approaches. In this work, a method that combines vector-based level-set parameterization technique and ensemble Kalman filter (EnKF) for estimating fracture distributions is presented. Performing the necessary forward modeling is particularly challenging. In addition to the large number of forward models needed, each model is used for sampling of randomly located fractures. Conventional mesh generation for such systems would be time consuming if possible at all. For these reasons, we rely on a novel polyhedral mesh method using the mimetic finite difference (MFD) method. A discrete fracture model is adopted that maintains the full geometry of the fracture network. By using a cut-cell paradigm, a computational mesh for the matrix can be generated quickly and reliably. In this research, we apply this workflow on 2D two-phase fractured reservoirs. The combination of MFD approach, level-set parameterization, and EnKF provides an effective solution to address the challenges in the history matching problem of highly non-Gaussian fractured reservoirs.
Use of the finite-difference time-domain method in electromagnetic dosimetry
International Nuclear Information System (INIS)
Sullivan, D.M.
1987-01-01
Although there are acceptable methods for calculating whole body electromagnetic absorption, no completely acceptable method for calculating the local specific absorption rate (SAR) at points within the body has been developed. Frequency domain methods, such as the method of moments (MoM) have achieved some success; however, the MoM requires computer storage on the order of (3N) 2 , and computation time on the order of (3N) 3 where N is the number of cells. The finite-difference time-domain (FDTD) method has been employed extensively in calculating the scattering from metallic objects, and recently is seeing some use in calculating the interaction of EM fields with complex, lossy dielectric bodies. Since the FDTD method has storage and time requirements proportional to N, it presents an attractive alternative to calculating SAR distribution in large bodies. This dissertation describes the FDTD method and evaluates it by comparing its results with analytic solutions in 2 and 3 dimensions. The results obtained demonstrate that the FDTD method is capable of calculating internal SAR distribution with acceptable accuracy. The construction of a data base to provide detailed, inhomogeneous man models for use with the FDTD method is described. Using this construction method, a model of 40,000 1.31 cm. cells is developed for use at 350 MHz, and another model consisting of 5000 2.62 cm. cells is developed for use at 100 MHz. To add more realism to the problem, a ground plane is added to the FDTD software. The needed changes to the software are described, along with a test which confirms its accuracy. Using the CRAY II supercomputer, SAR distributions in human models are calculated using incident frequencies of 100 MHz and 350 MHz for three different cases: (1) A homogeneous man model in free space, (2) an inhomogeneous man model in free space, and (3) an inhomogeneous man model standing on a ground plane
Jia, Shouqing; La, Dongsheng; Ma, Xuelian
2018-04-01
The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.
Non-linear analysis of skew thin plate by finite difference method
International Nuclear Information System (INIS)
Kim, Chi Kyung; Hwang, Myung Hwan
2012-01-01
This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed
DETERMINATION OF MOISTURE DIFFUSION COEFFICIENT OF LARCH BOARD WITH FINITE DIFFERENCE METHOD
Directory of Open Access Journals (Sweden)
Qiaofang Zhou
2011-04-01
Full Text Available This paper deals with the moisture diffusion coefficient of Dahurian Larch (Larix gmelinii Rupr. by use of the Finite Difference Method (FDM. To obtain moisture distributions the dimensional boards of Dahurian Larch were dried, from which test samples were cut and sliced evenly into 9 pieces in different drying periods, so that moisture distributions at different locations and times across the thickness of Dahurian Larch were obtained with a weighing method. With these experimental data, FDM was used to solve Fick’s one-dimensional unsteady-state diffusion equation, and the moisture diffusion coefficient across the thickness at specified time was obtained. Results indicated that the moisture diffusion coefficient decreased from the surface to the center of the Dahurian Larch wood, and it decreased with decreasing moisture content at constant wood temperature; as the wood temperature increased, the moisture diffusion coefficient increased, and the effect of the wood temperature on the moisture diffusion coefficient was more significant than that of moisture content. Moisture diffusion coefficients were different for the two experiments due to differing diffusivity of the specimens.
Directory of Open Access Journals (Sweden)
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
International Nuclear Information System (INIS)
Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A
2009-01-01
A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.
Higher-order schemes for the Laplace transformation method for parabolic problems
Douglas, C.; Kim, I.; Lee, H.; Sheen, D.
2011-01-01
In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely
Xing, Yanyuan; Yan, Yubin
2018-03-01
Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.
Methods for compressible fluid simulation on GPUs using high-order finite differences
Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer
2017-08-01
We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.
Chiranjeevi, C.; Srinivas, T.
2017-11-01
Humidifier is an important component in air humidification-dehumidification desalination plant for fresh water production. Liquid to air flow rate ratio is optimization is reported for an industrial cooling towers but for an air humidifier it is not addressed. The current work is focused on the design and analysis of an air humidifier for solar desalination plant to maximize the yield with better humidification, using finite difference method (FDM). The outlet conditions of air from the humidifier are theoretically predicted by FDM with the given inlet conditions, which will be further used in the design calculation of the humidifier. Hot water to air flow rate ratio and inlet hot water temperature are identified as key operating parameters to evaluate the humidifier performance. The maximum and optimal values of mass flow rate ratio of water to air are found to be 2.15 and 1.5 respectively using packing function and Merkel Integral. The height of humidifier is constrained to 1.5 m and the diameter of the humidifier is found as 0.28m. The performance of humidifier and outlet conditions of air are simulated using FDM and compared with experimental results. The obtained results are within an agreeable range of deviation.
Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods
Diosady, Laslo T.; Murman, Scott M.
2017-02-01
A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.
Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods
Diosady, Laslo T.; Murman, Scott M.
2016-01-01
space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.
On the application of the Williams-Weizsaecker-method to higher order S-matrix-approximations
International Nuclear Information System (INIS)
Ziegelbecker, R.C.
1983-05-01
In this paper the method of quasireal processes is investigated using a special example - pair production in the stationary field of a nucleus by an incident electron. As a result, the semi-classical version of the Williams-Weizsaecker-method is confirmed on the basis of all 3sup(rd)-order Feynman-diagrams. The spectra of quasireal processes, derived from quantum field theory, can also be applied simultaneously in several vertex points on one diagram and are valid for higher photon energies than the semiclassical spectrum; the restriction #betta# [de
Doppler Radar Vital Signs Detection Method Based on Higher Order Cyclostationary.
Yu, Zhibin; Zhao, Duo; Zhang, Zhiqiang
2017-12-26
Due to the non-contact nature, using Doppler radar sensors to detect vital signs such as heart and respiration rates of a human subject is getting more and more attention. However, the related detection-method research meets lots of challenges due to electromagnetic interferences, clutter and random motion interferences. In this paper, a novel third-order cyclic cummulant (TOCC) detection method, which is insensitive to Gaussian interference and non-cyclic signals, is proposed to investigate the heart and respiration rate based on continuous wave Doppler radars. The k -th order cyclostationary properties of the radar signal with hidden periodicities and random motions are analyzed. The third-order cyclostationary detection theory of the heart and respiration rate is studied. Experimental results show that the third-order cyclostationary approach has better estimation accuracy for detecting the vital signs from the received radar signal under low SNR, strong clutter noise and random motion interferences.
Pressure transient analysis in single and two-phase water by finite difference methods
International Nuclear Information System (INIS)
Berry, G.F.; Daley, J.G.
1977-01-01
An important consideration in the design of LMFBR steam generators is the possibility of leakage from a steam generator water tube. The ensuing sodium/water reaction will be largely controlled by the amount of water available at the leak site, thus analysis methods treating this event must have the capability of accurately modeling pressure transients through all states of water occurring in a steam generator, whether single or two-phase. The equation systems of the present model consist of the conservation equations together with an equation of state for one-dimensional homogeneous flow. These equations are then solved using finite difference techniques with phase considerations and non-equilibrium effects being treated through the equation of state. The basis for water property computation is Keenan's 'fundamental equation of state' which is applicable to single-phase water at pressures less than 1000 bars and temperatures less than 1300 0 C. This provides formulations allowing computation of any water property to any desired precision. Two-phase properties are constructed from values on the saturation line. The use of formulations permits the direct calculation of any thermodynamic property (or property derivative) to great precision while requiring very little computer storage, but does involve considerable computation time. For this reason an optional calculation scheme based on the method of 'transfinite interpolation' is included to give rapid computation in selected regions with decreased precision. The conservation equations were solved using the second order Lax-Wendroff scheme which includes wall friction, allows the formation of shocks and locally supersonic flow. Computational boundary conditions were found from a method-of-characteristics solution at the reservoir and receiver ends. The local characteristics were used to interpolate data from inside the pipe to the boundary
International Nuclear Information System (INIS)
Fraysse, F.; Redondo, C.; Rubio, G.; Valero, E.
2016-01-01
This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is applied to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.
Energy Technology Data Exchange (ETDEWEB)
Fraysse, F., E-mail: francois.fraysse@rs2n.eu [RS2N, St. Zacharie (France); E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid (Spain); Redondo, C.; Rubio, G.; Valero, E. [E. T. S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Madrid (Spain)
2016-12-01
This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is applied to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.
Higher-order interactions in molecular collisions studied by a novel laser spectroscopic method
International Nuclear Information System (INIS)
Kajita, M.; Tachikawa, M.; Shimizu, T.
1986-01-01
This is the first systematic experiment to study the characteristics of the dipole-quadrupole and dipole-induced dipole interactions as well as the dipole-dipole interaction. The authors developed a new method to measure the relaxation rate constant of a weak IR transition. The absorption cell is introduced inside the CO/sub 2/ laser cavity to improve sensitivity. The transient oscillation superimposed on the cw laser output is observed when the Stark pulse is applied to the absorbing molecules. The absorption increases when the better coincidence between the laser and absorption lines is obtained by application of the Stark voltage. The absorption decreases for a larger Stark voltage. The sign of the signal depends on whether the absorption intensity increases or decreases due to the Stark field. Since pressure broadening modifies the absorption line shape, the sign of the signal changes when the pressure is increased. The relaxation rate constant can be determined by observing the sign of the signal. The experiment is performed with the frequency coincidence between the CH/sub 3/CN ν/sub 7//sup r/ R(6.6) line and the CO/sub 2/ laser 9.4-μm R(22) line. The relaxation rate constants against various foreign gas molecules (polar molecules, nonpolar linear molecules, and spherical atoms and molecules) have been determined
Emoto, K.; Saito, T.; Shiomi, K.
2017-12-01
Short-period (2 s) seismograms. We found that the energy of the coda of long-period seismograms shows a spatially flat distribution. This phenomenon is well known in short-period seismograms and results from the scattering by small-scale heterogeneities. We estimate the statistical parameters that characterize the small-scale random heterogeneity by modelling the spatiotemporal energy distribution of long-period seismograms. We analyse three moderate-size earthquakes that occurred in southwest Japan. We calculate the spatial distribution of the energy density recorded by a dense seismograph network in Japan at the period bands of 8-16 s, 4-8 s and 2-4 s and model them by using 3-D finite difference (FD) simulations. Compared to conventional methods based on statistical theories, we can calculate more realistic synthetics by using the FD simulation. It is not necessary to assume a uniform background velocity, body or surface waves and scattering properties considered in general scattering theories. By taking the ratio of the energy of the coda area to that of the entire area, we can separately estimate the scattering and the intrinsic absorption effects. Our result reveals the spectrum of the random inhomogeneity in a wide wavenumber range including the intensity around the corner wavenumber as P(m) = 8πε2a3/(1 + a2m2)2, where ε = 0.05 and a = 3.1 km, even though past studies analysing higher-frequency records could not detect the corner. Finally, we estimate the intrinsic attenuation by modelling the decay rate of the energy. The method proposed in this study is suitable for quantifying the statistical properties of long-wavelength subsurface random inhomogeneity, which leads the way to characterizing a wider wavenumber range of spectra, including the corner wavenumber.
A finite difference method for off-fault plasticity throughout the earthquake cycle
Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash
2017-12-01
We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiation-damping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic offset is accommodated by inelastic deformation ( ∼ 0.1 m per rupture, or ∼ 10% of the tectonic deformation budget).
The (G′/G-Expansion Method and Its Application for Higher-Order Equations of KdV (III
Directory of Open Access Journals (Sweden)
Huizhang Yang
2014-01-01
Full Text Available New exact traveling wave solutions of a higher-order KdV equation type are studied by the (G′/G-expansion method, where G=G(ξ satisfies a second-order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. The property of this method is that it is quite simple and understandable.
DEFF Research Database (Denmark)
Amini Afshar, Mostafa; Bingham, Harry B.
2017-01-01
. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...
Simulation model of stratified thermal energy storage tank using finite difference method
Waluyo, Joko
2016-06-01
Stratified TES tank is normally used in the cogeneration plant. The stratified TES tanks are simple, low cost, and equal or superior in thermal performance. The advantage of TES tank is that it enables shifting of energy usage from off-peak demand for on-peak demand requirement. To increase energy utilization in a stratified TES tank, it is required to build a simulation model which capable to simulate the charging phenomenon in the stratified TES tank precisely. This paper is aimed to develop a novel model in addressing the aforementioned problem. The model incorporated chiller into the charging of stratified TES tank system in a closed system. The model was developed in one-dimensional type involve with heat transfer aspect. The model covers the main factors affect to degradation of temperature distribution namely conduction through the tank wall, conduction between cool and warm water, mixing effect on the initial flow of the charging as well as heat loss to surrounding. The simulation model is developed based on finite difference method utilizing buffer concept theory and solved in explicit method. Validation of the simulation model is carried out using observed data obtained from operating stratified TES tank in cogeneration plant. The temperature distribution of the model capable of representing S-curve pattern as well as simulating decreased charging temperature after reaching full condition. The coefficient of determination values between the observed data and model obtained higher than 0.88. Meaning that the model has capability in simulating the charging phenomenon in the stratified TES tank. The model is not only capable of generating temperature distribution but also can be enhanced for representing transient condition during the charging of stratified TES tank. This successful model can be addressed for solving the limitation temperature occurs in charging of the stratified TES tank with the absorption chiller. Further, the stratified TES tank can be
Chang, Luye; Connelly, Brian S; Geeza, Alexis A
2012-02-01
Though most personality researchers now recognize that ratings of the Big Five are not orthogonal, the field has been divided about whether these trait intercorrelations are substantive (i.e., driven by higher order factors) or artifactual (i.e., driven by correlated measurement error). We used a meta-analytic multitrait-multirater study to estimate trait correlations after common method variance was controlled. Our results indicated that common method variance substantially inflates trait correlations, and, once controlled, correlations among the Big Five became relatively modest. We then evaluated whether two different theories of higher order factors could account for the pattern of Big Five trait correlations. Our results did not support Rushton and colleagues' (Rushton & Irwing, 2008; Rushton et al., 2009) proposed general factor of personality, but Digman's (1997) α and β metatraits (relabeled by DeYoung, Peterson, and Higgins (2002) as Stability and Plasticity, respectively) produced viable fit. However, our models showed considerable overlap between Stability and Emotional Stability and between Plasticity and Extraversion, raising the question of whether these metatraits are redundant with their dominant Big Five traits. This pattern of findings was robust when we included only studies whose observers were intimately acquainted with targets. Our results underscore the importance of using a multirater approach to studying personality and the need to separate the causes and outcomes of higher order metatraits from those of the Big Five. We discussed the implications of these findings for the array of research fields in which personality is studied.
Energy Technology Data Exchange (ETDEWEB)
Ahmadi, M. [Heriot Watt Univ., Edinburgh (United Kingdom)
2008-10-15
This paper described a project in which a higher order up-winding scheme was used to solve mass/energy conservation equations for simulating steam flood processes in an oil reservoir. Thermal recovery processes are among the most complex because they require a detailed accounting of thermal energy and chemical reaction kinetics. The numerical simulation of thermal recovery processes involves localized phenomena such as saturation and temperatures fronts due to hyperbolic features of governing conservation laws. A second order accurate FV method that was improved by a moving mesh strategy was used to adjust for moving coordinates on a finely gridded domain. The Finite volume method was used and the problem of steam injection was then tested using derived solution frameworks on both mixed and moving coordinates. The benefits of using a higher-order Godunov solver instead of lower-order ones were qualified. This second order correction resulted in better resolution on moving features. Preferences of higher-order solvers over lower-order ones in terms of shock capturing is under further investigation. It was concluded that although this simulation study was limited to steam flooding processes, the newly presented approach may be suitable to other enhanced oil recovery processes such as VAPEX, SAGD and in situ combustion processes. 23 refs., 28 figs.
Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data
Gibbons, T. J.; Öztürk, E.; Sims, N. D.
2018-01-01
Measuring the rotational dynamic behaviour of a structure is important for many areas of dynamics such as passive vibration control, acoustics, and model updating. Specialist and dedicated equipment is often needed, unless the rotational degree-of-freedom is synthesised based upon translational data. However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm. A key challenge with this approach is choosing the measurement spacing between the data points, an issue which has often been overlooked in the published literature. The present contribution will for the first time prove that the use of a finite difference approach can be unstable when using non-exact measured data and a small measurement spacing, for beam-like structures. Then, a generalised analytical error analysis is used to propose an optimised measurement spacing, which balances the numerical error of the finite difference equation with the propagation error from the perturbed data. The approach is demonstrated using both numerical and experimental investigations. It is shown that by obtaining a small number of test measurements it is possible to optimise the measurement accuracy, without any further assumptions on the boundary conditions of the structure.
Domain-adaptive finite difference methods for collapsing annular liquid jets
Ramos, J. I.
1993-01-01
rate increases as the Weber number, nozzle exit angle, gas concentration at the nozzle exit, and temperature of the gases enclosed by the annular liquid jet are increased, but it decreases as the Froude and Peclet numbers, and annular liquid jet's thickness-to-radius ratio at the nozzle exit are increased. It is also shown that the annular liquid jet's collapse rate increases as the Weber number, nozzle exit angle, temperature of the gases enclosed by the annular liquid jet, and pressure of the gases which surround the jet are increased, but decreases as the Froude and Peclet numbers, and annular liquid jet's thickness-toradius ratio at the nozzle exit are increased. It is also shown that both the ratio of the initial pressure of the gas enclosed by the jet to the pressure of the gas surrounding the jet and the ratio of solubilities at the annular liquid jet's inner and outer interfaces play an important role on both the steady state mass absorption rate and the jet collapse. If the product of these ratios is greater or less than one, both the pressure and the mass of the gas enclosed by the annular liquid jet decrease or increase, respectively, with time. It is also shown that the numerical results obtained with the conservative, domain-adaptive method of lines technique presented in this paper are in excellent agreement with those of a domain-adaptive, iterative, non-conservative, block-bidiagonal, finite difference method which uncouples the solution of the fluid dynamics equations from that of the convergence length.
Gyrya, V.; Lipnikov, K.
2017-11-01
We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.
Raeli, Alice; Bergmann, Michel; Iollo, Angelo
2018-02-01
We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.
Mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods
International Nuclear Information System (INIS)
Baker, A.R.
1982-07-01
A study has been performed of mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods. As the objective was to illuminate the issues, the study was performed for a 1D slab model of a reactor with one neutron-energy group for which analytical solutions were possible. A computer code SLAB was specially written to perform the finite-difference and finite-element calculations and also to obtain the analytical solutions. The standard finite-difference equations were obtained by starting with an expansion of the neutron current in powers of the mesh size, h, and keeping terms as far as h 2 . It was confirmed that these equations led to the well-known result that the criticality parameter varied with the square of the mesh size. An improved form of the finite-difference equations was obtained by continuing the expansion for the neutron current as far as the term in h 4 . In this case, the critical parameter varied as the fourth power of the mesh size. The finite-element solutions for 2 and 3 nodes per element revealed that the criticality parameter varied as the square and fourth power of the mesh size, respectively. Numerical results are presented for a bare reactive core of uniform composition with 2 zones of different uniform mesh and for a reactive core with an absorptive reflector. (author)
Directory of Open Access Journals (Sweden)
Taohua Liu
2017-01-01
Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(KlogK. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.
International Nuclear Information System (INIS)
Tokuda, Shinji; Watanabe, Tomoko.
1996-08-01
The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)
Energy Technology Data Exchange (ETDEWEB)
Sun, Yuzhou, E-mail: yuzhousun@126.com; Chen, Gensheng; Li, Dongxia [School of Civil Engineering and Architecture, Zhongyuan University of Technology, Zhengzhou (China)
2016-06-08
This paper attempts to study the application of mesh-free method in the numerical simulations of the higher-order continuum structures. A high-order bending beam considers the effect of the third-order derivative of deflections, and can be viewed as a one-dimensional higher-order continuum structure. The moving least-squares method is used to construct the shape function with the high-order continuum property, the curvature and the third-order derivative of deflections are directly interpolated with nodal variables and the second- and third-order derivative of the shape function, and the mesh-free computational scheme is establish for beams. The coupled stress theory is introduced to describe the special constitutive response of the layered rock mass in which the bending effect of thin layer is considered. The strain and the curvature are directly interpolated with the nodal variables, and the mesh-free method is established for the layered rock mass. The good computational efficiency is achieved based on the developed mesh-free method, and some key issues are discussed.
Transient analysis of printed lines using finite-difference time-domain method
Energy Technology Data Exchange (ETDEWEB)
Ahmed, Shahid [Thomas Jefferson National Accelerator Facility, 12050 Jefferson Avenue, Suite 704, Newport News, VA, 23606, USA
2012-03-29
Comprehensive studies of ultra-wideband pulses and electromagnetic coupling on printed coupled lines have been performed using full-wave 3D finite-difference time-domain analysis. Effects of unequal phase velocities of coupled modes, coupling between line traces, and the frequency dispersion on the waveform fidelity and crosstalk have been investigated in detail. To discriminate the contributions of different mechanisms into pulse evolution, single and coupled microstrip lines without (ϵ_{r} = 1) and with (ϵ_{r} > 1) dielectric substrates have been examined. To consistently compare the performance of the coupled lines with substrates of different permittivities and transients of different characteristic times, a generic metric similar to the electrical wavelength has been introduced. The features of pulse propagation on coupled lines with layered and pedestal substrates and on the irregular traces have been explored. Finally, physical interpretations of the simulation results are discussed in the paper.
Nakano, Masahiko; Yoshikawa, Takeshi; Hirata, So; Seino, Junji; Nakai, Hiromi
2017-11-05
We have implemented a linear-scaling divide-and-conquer (DC)-based higher-order coupled-cluster (CC) and Møller-Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC-based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2) TQ ]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC-based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Electron-phonon coupling from finite differences
Monserrat, Bartomeu
2018-02-01
The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.
Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.
Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray
2017-07-11
Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.
Double-grid finite-difference frequency-domain (DG-FDFD) method for scattering from chiral objects
Alkan, Erdogan; Elsherbeni, Atef
2013-01-01
This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid
Directory of Open Access Journals (Sweden)
Navnit Jha
2014-04-01
Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.
International Nuclear Information System (INIS)
Belendez, A; Pascual, C; Fernandez, E; Neipp, C; Belendez, T
2008-01-01
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient
Comparison of SAR calculation algorithms for the finite-difference time-domain method
International Nuclear Information System (INIS)
Laakso, Ilkka; Uusitupa, Tero; Ilvonen, Sami
2010-01-01
Finite-difference time-domain (FDTD) simulations of specific-absorption rate (SAR) have several uncertainty factors. For example, significantly varying SAR values may result from the use of different algorithms for determining the SAR from the FDTD electric field. The objective of this paper is to rigorously study the divergence of SAR values due to different SAR calculation algorithms and to examine if some SAR calculation algorithm should be preferred over others. For this purpose, numerical FDTD results are compared to analytical solutions in a one-dimensional layered model and a three-dimensional spherical object. Additionally, the implications of SAR calculation algorithms for dosimetry of anatomically realistic whole-body models are studied. The results show that the trapezium algorithm-based on the trapezium integration rule-is always conservative compared to the analytic solution, making it a good choice for worst-case exposure assessment. In contrast, the mid-ordinate algorithm-named after the mid-ordinate integration rule-usually underestimates the analytic SAR. The linear algorithm-which is approximately a weighted average of the two-seems to be the most accurate choice overall, typically giving the best fit with the shape of the analytic SAR distribution. For anatomically realistic models, the whole-body SAR difference between different algorithms is relatively independent of the used body model, incident direction and polarization of the plane wave. The main factors affecting the difference are cell size and frequency. The choice of the SAR calculation algorithm is an important simulation parameter in high-frequency FDTD SAR calculations, and it should be explained to allow intercomparison of the results between different studies. (note)
Application of Mass Lumped Higher Order Finite Elements
International Nuclear Information System (INIS)
J. Chen, H.R. Strauss, S.C. Jardin, W. Park, L.E. Sugiyama, G. Fu, J. Breslau
2005-01-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied
DEFF Research Database (Denmark)
Shyroki, Dzmitry; Lavrinenko, Andrei
2007-01-01
A complex-coordinate method known under the guise of the perfectly matched layer (PML) method for treating unbounded domains in computational electrodynamics is related to similar techniques in fluid dynamics and classical quantum theory. It may also find use in electronic-structure finite......-difference simulations. Straightforward transfer of the PML formulation to other fields does not seem feasible, however, since it is a unique feature of electrodynamics - the natural invariance - that allows analytic trick of complex coordinate scaling to be represented as pure modification of local material parameters...
DEFF Research Database (Denmark)
Ernst, Erik
2003-01-01
This paper introduces the notion of higher-order inheritance hierarchies. They are useful because they provide well-known benefits of object-orientation at the level of entire hierarchies-benefits which are not available with current approaches. Three facets must be adressed: First, it must be po...
Directory of Open Access Journals (Sweden)
Polshkov Yulian M.
2013-11-01
Full Text Available The article considers data on the gross domestic product, consumer expenditures, gross investments and volume of foreign trade for the national economy. It is assumed that time is a discrete variable with one year iteration. The article uses finite-difference equations. It considers models with a high degree of the regulatory function of the state with respect to the consumer market. The econometric component is based on the hypothesis that each of the above said macro-economic indicators for this year depends on the gross domestic product for the previous time periods. Such an assumption gives a possibility to engage the least-squares method for building up linear models of the pair regression. The article obtains the time series model, which allows building point and interval forecasts for the gross domestic product for the next year based on the values of the gross domestic product for the current and previous years. The article draws a conclusion that such forecasts could be considered justified at least in the short-term prospect. From the mathematical point of view the built model is a heterogeneous finite-difference equation of the second order with constant ratios. The article describes specific features of such equations. It illustrates graphically the analytical view of solutions of the finite-difference equation. This gives grounds to differentiate national economies as sustainable growth economies, one-sided, weak or being in the stage of successful re-formation. The article conducts comparison of the listed types with specific economies of modern states.
Khanday, M A; Hussain, Fida
2015-02-01
During cold exposure, peripheral tissues undergo vasoconstriction to minimize heat loss to preserve the maintenance of a normal core temperature. However, vasoconstricted tissues exposed to cold temperatures are susceptible to freezing and frostbite-related tissue damage. Therefore, it is imperative to establish a mathematical model for the estimation of tissue necrosis due to cold stress. To this end, an explicit formula of finite difference method has been used to obtain the solution of Pennes' bio-heat equation with appropriate boundary conditions to estimate the temperature profiles of dermal and subdermal layers when exposed to severe cold temperatures. The discrete values of nodal temperature were calculated at the interfaces of skin and subcutaneous tissues with respect to the atmospheric temperatures of 25 °C, 20 °C, 15 °C, 5 °C, -5 °C and -10 °C. The results obtained were used to identify the scenarios under which various degrees of frostbite occur on the surface of skin as well as the dermal and subdermal areas. The explicit formula of finite difference method proposed in this model provides more accurate predictions as compared to other numerical methods. This model of predicting tissue temperatures provides researchers with a more accurate prediction of peripheral tissue temperature and, hence, the susceptibility to frostbite during severe cold exposure. Copyright © 2014 Elsevier Ltd. All rights reserved.
Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course
Kull, Trent C.
2011-01-01
A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…
International Nuclear Information System (INIS)
Lu Jia; Zhou Huaichun
2016-01-01
To deal with the staircase approximation problem in the standard finite-difference time-domain (FDTD) simulation, the two-dimensional boundary condition equations (BCE) method is proposed in this paper. In the BCE method, the standard FDTD algorithm can be used as usual, and the curved surface is treated by adding the boundary condition equations. Thus, while maintaining the simplicity and computational efficiency of the standard FDTD algorithm, the BCE method can solve the staircase approximation problem. The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders. The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors. Moreover, the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities. (paper)
Gerke, Kirill M.
2018-01-17
Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.
Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk
2018-05-01
Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.
Bilyeu, David
This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For
DEFF Research Database (Denmark)
Hattel, Jesper; Hansen, Preben
1995-01-01
This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati....... The resulting linear algebraic equations are solved by line-Gauss-Seidel....
Directory of Open Access Journals (Sweden)
Oleg Kudryavtsev
2013-01-01
factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments.
Convergency analysis of the high-order mimetic finite difference method
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, Konstantin [Los Alamos National Laboratory; Veiga Da Beirao, L [UNIV DEGLI STUDI; Manzini, G [NON LANL
2008-01-01
We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments.
Wu, Zedong; Alkhalifah, Tariq Ali
2018-01-01
Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods
Calculation of large ion densities under HVdc transmission lines by the finite difference method
International Nuclear Information System (INIS)
Suda, Tomotaka; Sunaga, Yoshitaka
1995-01-01
A calculation method for large ion densities (charged aerosols) under HVdc transmission lines was developed considering both the charging mechanism of aerosols by small ions and the drifting process by wind. Large ion densities calculated by this method agreed well with the ones measured under the Shiobara HVdc test line on the lateral profiles at ground level up to about 70m downwind from the line. Measured values decreased more quickly than calculated ones farther downwind from the line. Considering the effect of point discharge from ground cover (earth corona) improved the agreement in the farther downwind region
Gao, Longfei
2018-02-22
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.
Directory of Open Access Journals (Sweden)
Treena Basu
2015-10-01
Full Text Available This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2 for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3 per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N and a computational cost of O(N logN per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.
Gao, Longfei; Keyes, David E.
2018-01-01
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.
International Nuclear Information System (INIS)
Morisaki, T.; Ono, H.
2005-01-01
A laser-induced liquid-crystal lens is formed by large optical non-linearity and anisotropic complex refractive indices in guest-host liquid crystals. We obtained light wave propagation characteristics of the laser-induced LC lens. Three analytical methods were used to obtain light wave propagation characteristics. Analysis by 3-dimensional heat conduction was applied to determine the refractive index in the liquid-crystal layer. Another method used was to determine light wave propagation characteristics in the laser-induced lens by means of the finite-difference tune domain (FDTD) method and diffraction theory. In this study, we draw a parallel between the experimental results and FDTD. Copyright (2003) AD-TECH - International Foundation for the Advancement of Technology Ltd
de Graaf, C.S.L.; Kandhai, D.; Sloot, P.M.A.
According to Basel III, financial institutions have to charge a credit valuation adjustment (CVA) to account for a possible counterparty default. Calculating this measure and its sensitivities is one of the biggest challenges in risk management. Here, we introduce an efficient method for the
C.S.L. de Graaf (Kees); B.D. Kandhai; P.M.A. Sloot
2017-01-01
htmlabstractAccording to Basel III, financial institutions have to charge a credit valuation adjustment (CVA) to account for a possible counterparty default. Calculating this measure and its sensitivities is one of the biggest challenges in risk management. Here, we introduce an efficient method
Ping, Jing; Al-Hinai, Omar; Wheeler, Mary F.
2017-01-01
-Gaussian in this case, it is a challenge to estimate fracture distributions by conventional history matching approaches. In this work, a method that combines vector-based level-set parameterization technique and ensemble Kalman filter (EnKF) for estimating fracture
Panczak, Tim; Ring, Steve; Welch, Mark
1999-01-01
Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.
Czech Academy of Sciences Publication Activity Database
Papáček, Š.; Matonoha, Ctirad; Štumbauer, V.; Štys, D.
2012-01-01
Roč. 82, č. 10 (2012), s. 2022-2032 ISSN 0378-4754. [Modelling 2009. IMACS Conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering /4./. Rožnov pod Radhoštěm, 22.06.2009-26.06.2009] Grant - others:CENAKVA(CZ) CZ.1.05/2.1.00/01.0024; GA JU(CZ) 152//2010/Z Institutional research plan: CEZ:AV0Z10300504 Keywords : multiscale modelling * distributed parameter system * boundary value problem * random walk * photosynthetic factory Subject RIV: EI - Biotechnology ; Bionics Impact factor: 0.836, year: 2012
A conservative finite difference method for the numerical solution of plasma fluid equations
International Nuclear Information System (INIS)
Colella, P.; Dorr, M.R.; Wake, D.D.
1999-01-01
This paper describes a numerical method for the solution of a system of plasma fluid equations. The fluid model is similar to those employed in the simulation of high-density, low-pressure plasmas used in semiconductor processing. The governing equations consist of a drift-diffusion model of the electrons, together with an internal energy equation, coupled via Poisson's equation to a system of Euler equations for each ion species augmented with electrostatic force, collisional, and source/sink terms. The time integration of the full system is performed using an operator splitting that conserves space charge and avoids dielectric relaxation timestep restrictions. The integration of the individual ion species and electrons within the time-split advancement is achieved using a second-order Godunov discretization of the hyperbolic terms, modified to account for the significant role of the electric field in the propagation of acoustic waves, combined with a backward Euler discretization of the parabolic terms. Discrete boundary conditions are employed to accommodate the plasma sheath boundary layer on underresolved grids. The algorithm is described for the case of a single Cartesian grid as the first step toward an implementation on a locally refined grid hierarchy in which the method presented here may be applied on each refinement level
DeBonis, James R.
2013-01-01
A computational fluid dynamics code that solves the compressible Navier-Stokes equations was applied to the Taylor-Green vortex problem to examine the code s ability to accurately simulate the vortex decay and subsequent turbulence. The code, WRLES (Wave Resolving Large-Eddy Simulation), uses explicit central-differencing to compute the spatial derivatives and explicit Low Dispersion Runge-Kutta methods for the temporal discretization. The flow was first studied and characterized using Bogey & Bailley s 13-point dispersion relation preserving (DRP) scheme. The kinetic energy dissipation rate, computed both directly and from the enstrophy field, vorticity contours, and the energy spectra are examined. Results are in excellent agreement with a reference solution obtained using a spectral method and provide insight into computations of turbulent flows. In addition the following studies were performed: a comparison of 4th-, 8th-, 12th- and DRP spatial differencing schemes, the effect of the solution filtering on the results, the effect of large-eddy simulation sub-grid scale models, and the effect of high-order discretization of the viscous terms.
International Nuclear Information System (INIS)
Wang Yue; Wang Jian-Guo; Chen Zai-Gao
2015-01-01
Based on conformal construction of physical model in a three-dimensional Cartesian grid, an integral-based conformal convolutional perfectly matched layer (CPML) is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain (ECT-CFDTD) method is used to simulate the wave propagation inside a perfect electric conductor (PEC) waveguide. The algorithm has the same numerical stability as the ECT-CFDTD method. For the long-time propagation problems of an evanescent wave in a waveguide, several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML. Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide. (paper)
Colera, Manuel; Pérez-Saborid, Miguel
2017-09-01
A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics -such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil- and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil-fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.
Finite-difference methods in multi-dimensional two-phase flow
International Nuclear Information System (INIS)
Travis, J.R.
1977-01-01
In the summer of 1974, the Theoretical Division of the Los Alamos Scientific Laboratory began several research programs in the area of reactor safety for the United States Nuclear Regulatory Commission. Research efforts were started in the Liquid Metal Fast Breeder (LMFBR) and the Light Water Reactor (LWR) safety programs. The character of the Theoretical Division was to develop computer codes for the safety analysis of these reactor systems. The question of whether or not, during the course of a hypothetical accident sequence in an LMFBR, the core will subside to a coolable configuration without secondary critical bursts has never been resolved. To aid the study of this question, a computer program called SIMMER (S/sub N/, Implicit, Multified, Multicomponent, Eulerian Recriticality) was to be developed to predict the dynamics of extreme hypothetical accident sequences during which extended core motion is expected. This time-dependent computer code called for combining an advanced multidimensional, multiphase fluid dynamic methodology with multidimensional neutron transport theory and improved equation-of-state technology. In the LWR program, the research emphasis was to push forward in two areas: (1) the development of advanced multiphase fluid dynamic methods and computer programs for performing basic research and analyzing areas in thermal hydraulics important to the safety of water reactors, and (2) the development of an advanced ''best estimate'' systems code called TRAC (Transient Reactor Analysis Code) for analyzing loss-of-coolant accidents and anticipated-transients-without-scram in light water reactors
Directory of Open Access Journals (Sweden)
Koichi Narahara
2012-01-01
Full Text Available Nonlinear transmission lines, which define transmission lines periodically loaded with nonlinear devices such as varactors, diodes, and transistors, are modeled in the framework of finite-difference time-domain (FDTD method. Originally, some root-finding routine is needed to evaluate the contributions of nonlinear device currents appropriately to the temporally advanced electrical fields. Arbitrary nonlinear transmission lines contain large amount of nonlinear devices; therefore, it costs too much time to complete calculations. To reduce the calculation time, we recently developed a simple model of diodes to eliminate root-finding routines in an FDTD solver. Approximating the diode current-voltage relation by a piecewise-linear function, an extended Ampere's law is solved in a closed form for the time-advanced electrical fields. In this paper, we newly develop an FDTD model of field-effect transistors (FETs, together with several numerical examples that demonstrate pulse-shortening phenomena in a traveling-wave FET.
Energy Technology Data Exchange (ETDEWEB)
Yang, Fan; Yang, Haicheng; Guo, Xueyan; Ren Dai [University of Shanghai for Science and Technology, Shanghai (China); Yan, Yonghua [Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai (China); Liu, Chaoqun [University of Texas at Arlington, Arlington (United States)
2017-06-15
Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.
Directory of Open Access Journals (Sweden)
Alexandre Bambina
2018-01-01
Full Text Available Limitation of the cloak-size reduction is investigated numerically by a finite-difference time-domain (FDTD method. A metallic pole that imitates an antenna is cloaked with an anisotropic and parameter-gradient medium against electromagnetic-wave propagation in microwave range. The cloaking structure is a metamaterial submerged in a plasma confined in a vacuum chamber made of glass. The smooth-permittivity plasma can be compressed in the radial direction, which enables us to decrease the size of the cloak. Theoretical analysis is performed numerically by comparing scattering waves in various cases; there exists a high reduction of the scattering wave when the radius of the cloak is larger than a quarter of one wavelength. This result indicates that the required size of the cloaking layer is more than an object scale in the Rayleigh scattering regime.
DEFF Research Database (Denmark)
Israelsen, Stine Møller
This PhD thesis considers higher order modes (HOMs) in optical fibers. That includes their excitation and characteristics. Within the last decades, HOMs have been applied both for space multiplexing in optical communications, group velocity dispersion management and sensing among others......-radial polarization as opposed to the linear polarization of the LP0X modes. The effect is investigated numerically in a double cladding fiber with an outer aircladding using a full vectorial modesolver. Experimentally, the bowtie modes are excited using a long period grating and their free space characteristics...... and polarization state are investigated. For this fiber, the onset of the bowtie effect is shown numerically to be LP011. The characteristics usually associated with Bessel-likes modes such as long diffraction free length and selfhealing are shown to be conserved despite the lack of azimuthal symmetry...
International Nuclear Information System (INIS)
Deupree, R.G.
1977-01-01
Finite difference techniques were used to examine the coupling of radial pulsation and convection in stellar models having comparable time scales. Numerical procedures are emphasized, including diagnostics to help determine the range of free parameters
Hajipour, Mojtaba; Jajarmi, Amin
2018-02-01
Using the Pontryagin's maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.
Sun, Qiang; Wu, Guo Xiong
2013-03-01
A mathematical model and a numerical solution procedure are developed to simulate flow field through a 3D permeable vessel with multibranches embedded in a solid tumour. The model is based on Poisseuille's law for the description of the flow through the vessels, Darcy's law for the fluid field inside the tumour interstitium, and Starling's law for the flux transmitted across the vascular walls. The solution procedure is based on a coupled method, in which the finite difference method is used for the flow in the vessels and the boundary element method is used for the flow in the tumour. When vessels meet each other at a junction, the pressure continuity and mass conservation are imposed at the junction. Three typical representative structures within the tumour vasculature, symmetrical dichotomous branching, asymmetrical bifurcation with uneven radius of daughter vessels and trifurcation, are investigated in detail as case studies. These results have demonstrated the features of tumour flow environment by the pressure distributions and flow velocity field. Copyright © 2012 John Wiley & Sons, Ltd.
International Nuclear Information System (INIS)
Garcia-Herranz, Nuria; Cabellos, Oscar; Aragones, Jose M.; Ahnert, Carol
2003-01-01
In order to take into account in a more effective and accurate way the intranodal heterogeneities in coarse-mesh finite-difference (CMFD) methods, a new equivalent parameter generation methodology has been developed and tested. This methodology accounts for the dependence of the nodal homogeneized two-group cross sections and nodal coupling factors, with interface flux discontinuity (IFD) factors that account for heterogeneities on the flux-spectrum and burnup intranodal distributions as well as on neighbor effects.The methodology has been implemented in an analytic CMFD method, rigorously obtained for homogeneous nodes with transverse leakage and generalized now for heterogeneous nodes by including IFD heterogeneity factors. When intranodal mesh node heterogeneity vanishes, the heterogeneous solution tends to the analytic homogeneous nodal solution. On the other hand, when intranodal heterogeneity increases, a high accuracy is maintained since the linear and nonlinear feedbacks on equivalent parameters have been shown to be as a very effective way of accounting for heterogeneity effects in two-group multidimensional coarse-mesh diffusion calculations
Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation
International Nuclear Information System (INIS)
Costa, Carlos A N; Campos, Itamara S; Costa, Jessé C; Neto, Francisco A; Schleicher, Jörg; Novais, Amélia
2013-01-01
Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality. (paper)
Moriyama, Eduardo H.; Zangaro, Renato A.; Lobo, Paulo D. d. C.; Villaverde, Antonio G. J. B.; Watanabe-Sei, Ii; Pacheco, Marcos T. T.; Otsuka, Daniel K.
2002-06-01
Thermal damage in dental pulp during Nd:YAG laser irradiation have been studied by several researchers; but due to dentin inhomogeneous structure, laser interaction with dentin in the hypersensitivity treatment are not fully understood. In this work, heat distribution profile on human dentine samples irradiated with Nd:YAG laser was simulated at surface and subjacent layers. Calculations were carried out using the Crank-Nicolson's finite difference method. Sixteen dentin samples with 1,5 mm of thickness were evenly distributed into four groups and irradiated with Nd:YAG laser pulses, according to the following scheme: (I) 1 pulse of 900 mJ, (II) 2 pulses of 450 mJ, (III) 3 pulses of 300 mJ, (IV) 6 pulses of 150 mJ; corresponding to a total laser energy of 900 mJ. The pulse interval was 300ms, the pulse duration of 900 ms and irradiated surface area of 0,005 mm2. Laser induced morphological changes in dentin were observed for all the irradiated samples. The heat distribution throughout the dentin layer, from the external dentin surface to the pulpal chamber wall, was calculated for each case, in order to obtain further information about the pulsed Nd:YAG laser-oral hard tissue interaction. The simulation showed significant differences in the final temperature at the pulpal chamber, depending on the exposition time and the energy contained in the laser pulse.
Energy Technology Data Exchange (ETDEWEB)
Oh, Jae-Yong, E-mail: tylor@kaeri.re.kr [Korea Atomic Energy Research Institute, Daedeok-daero 1045, Yuseong, Daejeon 305-353 (Korea, Republic of); Koo, Yang-Hyun; Lee, Byung-Ho; Tahk, Young-Wook [Korea Atomic Energy Research Institute, Daedeok-daero 1045, Yuseong, Daejeon 305-353 (Korea, Republic of)
2011-07-15
This paper evaluated the effects of porosity on the effective thermal conductivity of UO{sub 2} fuel by combining the Potts model and the finite difference method (FDM). Two types of microstructures representing irradiated UO{sub 2} microstructures were simulated by the Potts model in the three dimensional cubic system. One represented very small intragranular bubbles and a few intergranular bubbles under a low temperature condition. The other represented large intergranular bubbles under a high temperature or annealing condition. For the simulated microstructures, the effective thermal conductivities were determined by FDM calculation of the temperature distributions under steady state condition. They were compared with an experimental equation and the effect of bubble morphology was investigated by fitting a porosity shape factor in the Maxwell-Eucken equation. The simulation results showed a good agreement with an experimental equation and demonstrated the capability of the Potts model to provide information on microstructure for calculating the effective thermal conductivity of UO{sub 2} fuel.
Coco, Armando; Russo, Giovanni
2018-05-01
In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.
Y.J. Hassen (Yunus); B. Koren (Barry)
2008-01-01
textabstractIn this paper, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is
Directory of Open Access Journals (Sweden)
Richasanty Septima S
2017-03-01
Full Text Available The research in this thesis was done to examine the model of traffic flow of volcanic disaster evacuation path for uphill and downhill roads. The assessment was focused on the area of disaster evacuation path from the Pante Raya Bener Meriah intersection to Takengon. This model is assessed for two different types of time when which a disaster occurs; the disaster occurred at night and the disaster occurred during the day, especially during peak hours (working hours. The model was developed with attention to the exixtence of inflow and outflow along the evacuation route. Furthermore, the model obtained is solved numerically by using finite difference method. The chosen approach of this method is upwind scheme with time and space steps using forward difference and backward difference. The solution of this model in the form of simulated vehicle density along evacuation pathways. The research conducted is in the form of a model of traffic flow on evacuation paths and restricted to the inflow and outflow without alternative path as well as the conditions of the road which are uphill and downhill, showed a high density of vehicles either at night or during the day. Uphill road conditions resulted in decreased vehicle speed and vehicle density will increase, while downhill road conditions resulted in increased vehicle speed and vehicle density will decrease, meaning that the road conditions which are uphill and downhill will greatly affect the process of evacuation. Degree vehicles of evacuation efficiency occuring at night without an alternative pathway produces a high efficiency so that it can be interpreted that the evacuation process in the evening was successful and runs better than the evacuation process during the day, and this is caused by the existence of vehicles on the road evacuation process started thus affecting the efficiency levels.
A new time–space domain high-order finite-difference method for the acoustic wave equation
Liu, Yang; Sen, Mrinal K.
2009-01-01
A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.
A new time–space domain high-order finite-difference method for the acoustic wave equation
Liu, Yang
2009-12-01
A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.
A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...
Mehle, Nataša; Dobnik, David; Ravnikar, Maja; Pompe Novak, Maruša
2018-05-03
RNA viruses have a great potential for high genetic variability and rapid evolution that is generated by mutation and recombination under selection pressure. This is also the case of Potato virus Y (PVY), which comprises a high diversity of different recombinant and non-recombinant strains. Consequently, it is hard to develop reverse transcription real-time quantitative PCR (RT-qPCR) with the same amplification efficiencies for all PVY strains which would enable their equilibrate quantification; this is specially needed in mixed infections and other studies of pathogenesis. To achieve this, we initially transferred the PVY universal RT-qPCR assay to a reverse transcription droplet digital PCR (RT-ddPCR) format. RT-ddPCR is an absolute quantification method, where a calibration curve is not needed, and it is less prone to inhibitors. The RT-ddPCR developed and validated in this study achieved a dynamic range of quantification over five orders of magnitude, and in terms of its sensitivity, it was comparable to, or even better than, RT-qPCR. RT-ddPCR showed lower measurement variability. We have shown that RT-ddPCR can be used as a reference tool for the evaluation of different RT-qPCR assays. In addition, it can be used for quantification of RNA based on in-house reference materials that can then be used as calibrators in diagnostic laboratories.
Directory of Open Access Journals (Sweden)
Min-Jhong Gu
2014-08-01
Full Text Available This article describes the development of a suite of programs that is capable of simulating the radiation properties of a random rough surface (RRS. The fundamental approach involves the generation, by fast Fourier transform (FFT built with rigorous finite difference time domain (FDTD, as the theoretical basis for the simulation of a bidirectional reflectance distribution function (BRDF of the RRS. The results are compared with the measurements and modeling of existing work to verify the feasibility of customized programming. It was found that the results of this study were a better match to the measurement data than those achieved in other modeling work.
Cyganek, Boguslaw; Smolka, Bogdan
2015-02-01
In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.
Schultz, A.
2010-12-01
describe our ongoing efforts to achieve massive parallelization on a novel hybrid GPU testbed machine currently configured with 12 Intel Westmere Xeon CPU cores (or 24 parallel computational threads) with 96 GB DDR3 system memory, 4 GPU subsystems which in aggregate contain 960 NVidia Tesla GPU cores with 16 GB dedicated DDR3 GPU memory, and a second interleved bank of 4 GPU subsystems containing in aggregate 1792 NVidia Fermi GPU cores with 12 GB dedicated DDR5 GPU memory. We are applying domain decomposition methods to a modified version of Weiss' (2001) 3D frequency domain full physics EM finite difference code, an open source GPL licensed f90 code available for download from www.OpenEM.org. This will be the core of a new hybrid 3D inversion that parallelizes frequencies across CPUs and individual forward solutions across GPUs. We describe progress made in modifying the code to use direct solvers in GPU cores dedicated to each small subdomain, iteratively improving the solution by matching adjacent subdomain boundary solutions, rather than iterative Krylov space sparse solvers as currently applied to the whole domain.
Higher order harmonics of reactor neutron equation
International Nuclear Information System (INIS)
Li Fu; Hu Yongming; Luo Zhengpei
1996-01-01
The flux mapping method using the higher order harmonics of the neutron equation is proposed. Based on the bi-orthogonality of the higher order harmonics, the process and formulas for higher order harmonics calculation are derived via the source iteration method with source correction. For the first time, not only any order harmonics for up-to-3-dimensional geometry are achieved, but also the preliminary verification to the capability for flux mapping have been carried out
International Nuclear Information System (INIS)
Uusitupa, T M; Ilvonen, S A; Laakso, I M; Nikoskinen, K I
2008-01-01
In this paper, the anatomically realistic body model Zubal is exposed to a plane wave. A finite-difference time-domain (FDTD) method is used to obtain field data for specific-absorption-rate (SAR) computation. It is investigated how the FDTD resolution, power-loss computation method and positioning of the material voxels in the FDTD grid affect the SAR results. The results enable one to estimate the effects due to certain fundamental choices made in the SAR simulation
Directory of Open Access Journals (Sweden)
B. U. Musa
2017-04-01
Full Text Available The C++ programming language was used to implement three-dimensional (3-D finite-difference time-domain (FDTD technique to simulate radiation of high frequency electromagnetic waves in free space. To achieve any meaningful results the computational domain of interest should have to be truncated in some way and this is achieved by applying absorbing boundary conditions. A uniaxial perfectly matched layer (UPML absorbing boundary condition is used in this work. The discretised equations of the UPML in FDTD time stepping scheme were derived and has been successfully implemented using the computer program. Simulation results showed that the UPML behaves as an absorber. This was confirmed by comparing the results with another boundary condition, the Mur ABC.
International Nuclear Information System (INIS)
O'Dell, R.D.; Stepanek, J.; Wagner, M.R.
1983-01-01
The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included
International Nuclear Information System (INIS)
Fujii, A; Hayashi, S; Fujii, S; Yanagi, K
2014-01-01
This paper deals with the functional performance of optical surface texture measuring instruments on the market. It is well known that their height response curves against certain referential geometry are not always identical to each other. So, a more precise study on the optical instrument's characteristics is greatly needed. Firstly, we developed a new simulation tool using a finite-difference time-domain technique, which enables the prediction of the height response curve against the fundamental surface geometry in the case of the confocal laser scanning microscope. Secondly, by utilizing this new simulation tool, measurement results, including outliers, were compared with the analytical simulation results. The comparison showed the consistency, which indicates that necessary conditions of surface measurement standards for verifying the instrument performance can be established. Consequently, we suggest that the maximum measurable slope angle must be added to evaluation subjects as significant metrological characteristics of measuring instruments, along with the lateral period limit. Finally, we propose a procedure to determine the lateral period limit in an ISO standard. (paper)
International Nuclear Information System (INIS)
Aruchunan, E.
2015-01-01
In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods. (author)
Energy Technology Data Exchange (ETDEWEB)
Zhang, Pei, E-mail: pei.zhang@desy.de [School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom); Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, D-22607 Hamburg (Germany); Cockcroft Institute of Science and Technology, Daresbury WA4 4AD (United Kingdom); Baboi, Nicoleta [Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, D-22607 Hamburg (Germany); Jones, Roger M. [School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom); Cockcroft Institute of Science and Technology, Daresbury WA4 4AD (United Kingdom)
2014-01-11
Beam-excited higher order modes (HOMs) can be used to provide beam diagnostics. Here we focus on 3.9 GHz superconducting accelerating cavities. In particular we study dipole mode excitation and its application to beam position determinations. In order to extract beam position information, linear regression can be used. Due to a large number of sampling points in the waveforms, statistical methods are used to effectively reduce the dimension of the system, such as singular value decomposition (SVD) and k-means clustering. These are compared with the direct linear regression (DLR) on the entire waveforms. A cross-validation technique is used to study the sample independent precisions of the position predictions given by these three methods. A RMS prediction error in the beam position of approximately 50 μm can be achieved by DLR and SVD, while k-means clustering suggests 70 μm.
Zhang, P; Jones, R M
2014-01-01
Beam-excited higher order modes (HOM) can be used to provide beam diagnostics. Here we focus on 3.9 GHz superconducting accelerating cavities. In particular we study dipole mode excitation and its application to beam position determinations. In order to extract beam position information, linear regression can be used. Due to a large number of sampling points in the waveforms, statistical methods are used to effectively reduce the dimension of the system, such as singular value decomposition (SVD) and k-means clustering. These are compared with the direct linear regression (DLR) on the entire waveforms. A cross-validation technique is used to study the sample independent precisions of the position predictions given by these three methods. A RMS prediction error in the beam position of approximately 50 micron can be achieved by DLR and SVD, while k-means clustering suggests 70 micron.
Directory of Open Access Journals (Sweden)
E. A. Levchuk
2018-01-01
Full Text Available Numerical modeling of electronic state evolution due to non-uniform external electric field in the structure metal-insulator-semiconductor with solitary donor center is carried out. Considering a nanometer disc-shaped gate as a source of the electric field, the problem for the Laplace equation in multilayered medium is solved numerically to determine the distribution of the gate potential. The energy spectrum of a bound electron is calculated from the problem for the stationary Schrödinger equation. Finite difference schemes are constructed to solve both the problems. Difference scheme for the Schrödinger equation takes into account cusp condition for the wave function at the donor location. To solve the problem for the Laplace equation, asymptotic boundary conditions for approximating the external field potential at large distances from the gate in different layers are suggested. These conditions allow to reduce the calculation domain for the electrostatic problem essentially. The effect of the boundary conditions on the accuracy of calculating the potential and energies is investigated. Using the developed difference schemes, the dependences of the energy spectrum of the bound electron on the gate potential are calculated, and the values of critical potential at which the wave function of the electron is relocated are determined. It has been found on the basis of calculation results, that governing parameter for the description of electronic behavior is the potential difference between the donor and semiconductor surface. It has been shown that critical potential difference does not depend on dielectric thickness and permittivity.
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into into the numerical behavior of this rather complicated system of nonlinear PDEs....
Directory of Open Access Journals (Sweden)
Shao Yan-Lin
2014-12-01
Full Text Available This paper presents some of the efforts by the authors towards numerical prediction of springing of ships. A time-domain Higher Order Boundary Element Method (HOBEM based on cubic shape function is first presented to solve a complete second-order problem in terms of wave steepness and ship motions in a consistent manner. In order to avoid high order derivatives on the body surfaces, e.g. mj-terms, a new formulation of the Boundary Value Problem in a body-fixed coordinate system has been proposed instead of traditional formulation in inertial coordinate system. The local steady flow effects on the unsteady waves are taken into account. Double-body flow is used as the basis flow which is an appropriate approximation for ships with moderate forward speed. This numerical model was used to estimate the complete second order wave excitation of springing of a displacement ship at constant forward speeds.
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
A Paraconsistent Higher Order Logic
DEFF Research Database (Denmark)
Villadsen, Jørgen
2004-01-01
of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order...... of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens. Many non-classical logics are, at the propositional level, funny toys which work quite good, but when one wants...
Nonlocal higher order evolution equations
Rossi, Julio D.; Schö nlieb, Carola-Bibiane
2010-01-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove
Group foliation of finite difference equations
Thompson, Robert; Valiquette, Francis
2018-06-01
Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.
Energy Technology Data Exchange (ETDEWEB)
Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id [Physics Study Program, University of Mataram, Jln. Majapahit 62 Mataram, NTB (Indonesia)
2016-04-19
We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.
Merritt, M.L.
1993-01-01
The simulation of the transport of injected freshwater in a thin brackish aquifer, overlain and underlain by confining layers containing more saline water, is shown to be influenced by the choice of the finite-difference approximation method, the algorithm for representing vertical advective and dispersive fluxes, and the values assigned to parametric coefficients that specify the degree of vertical dispersion and molecular diffusion that occurs. Computed potable water recovery efficiencies will differ depending upon the choice of algorithm and approximation method, as will dispersion coefficients estimated based on the calibration of simulations to match measured data. A comparison of centered and backward finite-difference approximation methods shows that substantially different transition zones between injected and native waters are depicted by the different methods, and computed recovery efficiencies vary greatly. Standard and experimental algorithms and a variety of values for molecular diffusivity, transverse dispersivity, and vertical scaling factor were compared in simulations of freshwater storage in a thin brackish aquifer. Computed recovery efficiencies vary considerably, and appreciable differences are observed in the distribution of injected freshwater in the various cases tested. The results demonstrate both a qualitatively different description of transport using the experimental algorithms and the interrelated influences of molecular diffusion and transverse dispersion on simulated recovery efficiency. When simulating natural aquifer flow in cross-section, flushing of the aquifer occurred for all tested coefficient choices using both standard and experimental algorithms. ?? 1993.
Poppe, Leszek; Jordan, John B; Rogers, Gary; Schnier, Paul D
2015-06-02
An important aspect in the analytical characterization of protein therapeutics is the comprehensive characterization of higher order structure (HOS). Nuclear magnetic resonance (NMR) is arguably the most sensitive method for fingerprinting HOS of a protein in solution. Traditionally, (1)H-(15)N or (1)H-(13)C correlation spectra are used as a "structural fingerprint" of HOS. Here, we demonstrate that protein fingerprint by line shape enhancement (PROFILE), a 1D (1)H NMR spectroscopy fingerprinting approach, is superior to traditional two-dimensional methods using monoclonal antibody samples and a heavily glycosylated protein therapeutic (Epoetin Alfa). PROFILE generates a high resolution structural fingerprint of a therapeutic protein in a fraction of the time required for a 2D NMR experiment. The cross-correlation analysis of PROFILE spectra allows one to distinguish contributions from HOS vs protein heterogeneity, which is difficult to accomplish by 2D NMR. We demonstrate that the major analytical limitation of two-dimensional methods is poor selectivity, which renders these approaches problematic for the purpose of fingerprinting large biological macromolecules.
International Nuclear Information System (INIS)
Tzanos, C.P.
1992-01-01
A higher-order differencing method was recently proposed for the convection-diffusion equation, which even with a coarse mesh gives oscillation-free solutions that are far more accurate than those of the upwind scheme. In this paper, the performance of this method is investigated in conjunction with the performance of different iterative solvers for the solution of the Navier-Stokes equations in the vorticity-streamfunction formulation for incompressible flow at high Reynolds numbers. Flow in a square cavity with a moving lid was chosen as a model problem. Solvers that performed well at low Re numbers either failed to converge or had a computationally prohibitive convergence rate at high Re numbers. The additive correction method of Settari and Aziz and an iterative incomplete lower and upper (ILU) solver were used in a multigrid approach that performed well in the whole range of Re numbers considered (from 1000 to 10,000) and for uniform as well as nonuniform grids. At high Re numbers, point or line Gauss-Seidel solvers converged with uniform grids, but failed to converge with nonuniform grids
Higher-Order Program Generation
DEFF Research Database (Denmark)
Rhiger, Morten
for OCaml, a dialect of ML, that provides run-time code generation for OCaml programs. We apply these byte-code combinators in semantics-directed compilation for an imperative language and in run-time specialization using type-directed partial evaluation. Finally, we present an approach to compiling goal......This dissertation addresses the challenges of embedding programming languages, specializing generic programs to specific parameters, and generating specialized instances of programs directly as executable code. Our main tools are higher-order programming techniques and automatic program generation....... It is our thesis that they synergize well in the development of customizable software. Recent research on domain-specific languages propose to embed them into existing general-purpose languages. Typed higher-order languages have proven especially useful as meta languages because they provide a rich...
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
International Nuclear Information System (INIS)
Su Xiaoxing; Zhang Chuanzeng; Ma Tianxue; Wang Yuesheng
2012-01-01
When three-dimensional (3D) phononic band structures are calculated by using the finite difference time domain (FDTD) method with a relatively small number of iterations, the results can be effectively improved by post-processing the FDTD time series (FDTD-TS) based on the filter diagonalization method (FDM), instead of the classical fast Fourier transform. In this paper, we propose a way to further improve the performance of the FDM-based post-processing method by introducing a relatively large number of observing points to record the FDTD-TS. To this end, the existing scheme of FDTD-TS preprocessing is modified. With the new preprocessing scheme, the processing efficiency of a single FDTD-TS can be improved significantly, and thus the entire post-processing method can have sufficiently high efficiency even when a relatively large number of observing points are used. The feasibility of the proposed method for improvement is verified by the numerical results.
Arismendi, Ivan; Johnson, Sherri L.; Dunham, Jason B.
2015-01-01
Statistics of central tendency and dispersion may not capture relevant or desired characteristics of the distribution of continuous phenomena and, thus, they may not adequately describe temporal patterns of change. Here, we present two methodological approaches that can help to identify temporal changes in environmental regimes. First, we use higher-order statistical moments (skewness and kurtosis) to examine potential changes of empirical distributions at decadal extents. Second, we adapt a statistical procedure combining a non-metric multidimensional scaling technique and higher density region plots to detect potentially anomalous years. We illustrate the use of these approaches by examining long-term stream temperature data from minimally and highly human-influenced streams. In particular, we contrast predictions about thermal regime responses to changing climates and human-related water uses. Using these methods, we effectively diagnose years with unusual thermal variability and patterns in variability through time, as well as spatial variability linked to regional and local factors that influence stream temperature. Our findings highlight the complexity of responses of thermal regimes of streams and reveal their differential vulnerability to climate warming and human-related water uses. The two approaches presented here can be applied with a variety of other continuous phenomena to address historical changes, extreme events, and their associated ecological responses.
Velivelli, A. C.; Bryden, K. M.
2006-03-01
Lattice Boltzmann methods are gaining recognition in the field of computational fluid dynamics due to their computational efficiency. In order to quantify the computational efficiency and accuracy of the lattice Boltzmann method, it is compared with efficient traditional finite difference methods such as the alternating direction implicit scheme. The lattice Boltzmann algorithm implemented in previous studies does not approach peak performance for simulations where the data involved in computation per time step is more than the cache size. Due to this, data is obtained from the main memory and this access is much slower than access to cache memory. Using a cache-optimized lattice Boltzmann algorithm, this paper takes into account the full computational strength of the lattice Boltzmann method. The com parison is performed on both a single processor and multiple processors.
The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD
Shankar, Varun
2017-08-01
We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap parameter δ ∈ (0 , 1 ] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of stencils. We provide experimental evidence to support this generalization, and develop an automatic stabilization procedure based on local Lebesgue functions for the stable selection of stencil weights over a wide range of δ values. We provide an a priori estimate for the speedup of our method over RBF-FD that serves as a good predictor for the true speedup. We apply our method to parabolic partial differential equations with time-dependent inhomogeneous boundary conditions - Neumann in 2D, and Dirichlet in 3D. Our results show that our method can achieve as high as a 60× speedup in 3D over existing RBF-FD methods in the task of forming differentiation matrices.
Compiler-Directed Transformation for Higher-Order Stencils
Energy Technology Data Exchange (ETDEWEB)
Basu, Protonu [Univ. of Utah, Salt Lake City, UT (United States); Hall, Mary [Univ. of Utah, Salt Lake City, UT (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oliker, Leonid [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Colella, Phillip [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2015-07-20
As the cost of data movement increasingly dominates performance, developers of finite-volume and finite-difference solutions for partial differential equations (PDEs) are exploring novel higher-order stencils that increase numerical accuracy and computational intensity. This paper describes a new compiler reordering transformation applied to stencil operators that performs partial sums in buffers, and reuses the partial sums in computing multiple results. This optimization has multiple effect son improving stencil performance that are particularly important to higher-order stencils: exploits data reuse, reduces floating-point operations, and exposes efficient SIMD parallelism to backend compilers. We study the benefit of this optimization in the context of Geometric Multigrid (GMG), a widely used method to solvePDEs, using four different Jacobi smoothers built from 7-, 13-, 27-and 125-point stencils. We quantify performance, speedup, andnumerical accuracy, and use the Roofline model to qualify our results. Ultimately, we obtain over 4× speedup on the smoothers themselves and up to a 3× speedup on the multigrid solver. Finally, we demonstrate that high-order multigrid solvers have the potential of reducing total data movement and energy by several orders of magnitude.
Classical higher-order processes
DEFF Research Database (Denmark)
Montesi, Fabrizio
2017-01-01
Classical Processes (CP) is a calculus where the proof theory of classical linear logic types processes à la Π-calculus, building on a Curry-Howard correspondence between session types and linear propositions. We contribute to this research line by extending CP with process mobility, inspired...... by the Higher-Order Π-calculus. The key to our calculus is that sequents are asymmetric: one side types sessions as in CP and the other types process variables, which can be instantiated with process values. The controlled interaction between the two sides ensures that process variables can be used at will......, but always respecting the linear usage of sessions expected by the environment....
Directory of Open Access Journals (Sweden)
Julius eVerrel
2015-04-01
Full Text Available We use functional magnetic resonance imaging to investigate short-term neural effects of a brief sensorimotor intervention adapted from the Feldenkrais method, a movement-based learning method. Twenty-one participants (10 men, 19-30 years took part in the study. Participants were in a supine position in the scanner with extended legs while an experienced Feldenkrais practitioner used a planar board to touch and apply minimal force to different parts of the sole and toes of their left foot under two experimental conditions. In the local condition, the practitioner explored movement within foot and ankle. In the global condition, the practitioner focused on the connection and support from the foot to the rest of the body. Before (baseline and after each intervention (post-local, post-global, we measured brain activity during intermittent pushing/releasing with the left leg and during resting state. Independent localizer tasks were used to identify regions of interest (ROI.Brain activity during left-foot pushing did not significantly differ between conditions in sensorimotor areas. Resting state activity (regional homogeneity, ReHo increased from baseline to post-local in medial right motor cortex, and from baseline to post-global in the left supplementary/cingulate motor area. Contrasting post-global to post-local showed higher ReHo in right lateral motor cortex. ROI analyses showed significant increases in ReHo in pushing-related areas from baseline to both post-local and post-global, and this increase tended to be more pronounced post-local. The results of this exploratory study show that a short, non-intrusive sensorimotor intervention can have short-term effects on spontaneous cortical activity in functionally related brain regions. Increased resting state activity in higher-order motor areas supports the hypothesis that the global intervention engages action-related neural processes.
Collocated electrodynamic FDTD schemes using overlapping Yee grids and higher-order Hodge duals
Deimert, C.; Potter, M. E.; Okoniewski, M.
2016-12-01
The collocated Lebedev grid has previously been proposed as an alternative to the Yee grid for electromagnetic finite-difference time-domain (FDTD) simulations. While it performs better in anisotropic media, it performs poorly in isotropic media because it is equivalent to four overlapping, uncoupled Yee grids. We propose to couple the four Yee grids and fix the Lebedev method using discrete exterior calculus (DEC) with higher-order Hodge duals. We find that higher-order Hodge duals do improve the performance of the Lebedev grid, but they also improve the Yee grid by a similar amount. The effectiveness of coupling overlapping Yee grids with a higher-order Hodge dual is thus questionable. However, the theoretical foundations developed to derive these methods may be of interest in other problems.
International Nuclear Information System (INIS)
Civalek, Oemer
2005-01-01
The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation
DEFF Research Database (Denmark)
Yoon, Daeung; Zhdanov, Michael; Mattsson, Johan
2016-01-01
One of the major problems in the modeling and inversion of marine controlled-source electromagnetic (CSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward-modeling algorithms...... should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter/receiver positions. To this end, we have developed a novel 3D modeling and inversion approach, which combines the advantages of the finite-difference (FD......) and integral-equation (IE) methods. In the framework of this approach, we have solved Maxwell’s equations for anomalous electric fields using the FD approximation on a staggered grid. Once the unknown electric fields in the computation domain of the FD method are computed, the electric and magnetic fields...
I. Arismendi; S. L. Johnson; J. B. Dunham
2015-01-01
Statistics of central tendency and dispersion may not capture relevant or desired characteristics of the distribution of continuous phenomena and, thus, they may not adequately describe temporal patterns of change. Here, we present two methodological approaches that can help to identify temporal changes in environmental regimes. First, we use higher-order statistical...
Energy Technology Data Exchange (ETDEWEB)
Noguchi, K; Endo, M [Waseda University, Tokyo (Japan). School of Science and Engineering
1997-10-22
Study is made on the theory of three-dimensional modelling of TDEM (Time Domain Electromagnetic) method based on the theory of Wang and Hohmann. A difference scheme is built and investigation is conducted about calculation accuracy with attention paid especially to space and time division, and the obtained optimum value is compared with the analytical solution for a homogeneous medium. As the result, it becomes possible to have a high-accuracy TDEM response thanks to the obtained optimum parameter. In an example, a response is determined in the case of a high-resistivity body in presence near the ground surface. Calculation is performed under the given conditions of a medium 100 ohm/m in resistivity, anomalous bodies 200, 500, 1000, 2000,5000, and 10,000 ohm/m in resistivity, respectively, and a distance in the direction of depth of 20m. The result indicates that it is possible to estimate the effect of the ground surface terrain on a TDEM response. Since the effect of the ground surface terrain emerges at the initial part of a response, it is inferred that consideration of terrain is mandatory in building a model if it is for interpreting the subsurface structure in detail. 5 refs., 7 figs.
Energy Technology Data Exchange (ETDEWEB)
Lorentzen, Rolf Johan
2002-04-01
of the ensemble Kalman filter, and a comparison between the ensemble Kalman filter and the least squares approach. The concluding remarks, and future work, are summarized in Section 5. The second part comprises the following four papers: (1): Use of MUSCL type techniques in classical numerical methods for two-phase flow in pipelines and wells. In this paper the MUSCL technique, originally developed to achieve higher order of accuracy in Godunov's method, is applied to a method following a finite element approach, a predictor-corrector shooting technique and a Godunov-type scheme. This paper also demonstrates use of the no pressure wave model. (2): Under balanced Drilling: Real Time Data Interpretation and Decision Support. Here the estimation (and re-estimation) of model parameters is addressed. The estimation is performed using a least squares approach. (3): Improved modeling of two-phase flow using an ensemble Kalman filter. In this paper the ensemble Kalman filter is presented, and the robustness of the filter is addressed. The filter is tested on a set of synthetic generated measurements. (4): Under balanced and Low-head Drilling Operations: Real Time Interpretation of Measured Data and Operational Support. This paper uses the ensemble Kalman filter to estimate model parameters and physical state variables. Both synthetic and full-scale experimental measurements are utilized.
Energy Technology Data Exchange (ETDEWEB)
Dias, Gleide A.N.; Silva, Jadir C.; Rocha, Paula F.; Costa, Jorge L. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Dept. de Geologia]. E-mail: gleidalencar@hotmail.com.br; jadir@geologia.ufrj.br; ferrucio@acd.ufrj.br; jotalc@yahoo.com.br
2003-07-01
Presently the oil industry has shown the importance of defining the structural framework of reservoirs. This study intends to contribute for the solution of this problem, using synthetic models in order to evaluate the electromagnetic signal due to a certain target. Use was made of an algorithm, which is based in the Finite Difference Time Domain Methods (FDTD). The simulated results of this survey found the best parameters for the chosen frequencies. In the present study there were simulated polarization, geometry and constitutive parameters (dielectric permittivity and electric conductivity). The results, using frequencies of 50 and 100 MHz, show clearly the effects of the electromagnetic waves attenuation and their problems related with signal resolution of targets in depth. (author)
Energy Technology Data Exchange (ETDEWEB)
Bourke, J.D. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia); Chantler, C.T., E-mail: chantler@physics.unimelb.edu.a [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)
2010-07-21
X-ray Absorption Fine Structure (XAFS) is calculated for copper using the cluster based Finite Difference Method for Near-Edge Structure (FDMNES). This approach is conventionally used to produce high accuracy XAFS theory in the near edge region, however, we demonstrate that it can be readily extended to encompass an energy range of more than 1.5 keV (k{approx}20A{sup -1}) from the K absorption edge. Such calculations require extensions to FDMNES to account for thermal effects, in addition to broadening effects due to inelastic processes. Extended calculations beyond the range of near-edge structure also require consideration of technical constraints such as cluster sizes and densities. We find that with our approach, we are able to produce accurate theory ranging from the absorption edge to the smooth atom-like region at high energies, with a single consistent model that is free from any fitting parameters.
International Nuclear Information System (INIS)
Bourke, J.D.; Chantler, C.T.
2010-01-01
X-ray Absorption Fine Structure (XAFS) is calculated for copper using the cluster based Finite Difference Method for Near-Edge Structure (FDMNES). This approach is conventionally used to produce high accuracy XAFS theory in the near edge region, however, we demonstrate that it can be readily extended to encompass an energy range of more than 1.5 keV (k∼20A -1 ) from the K absorption edge. Such calculations require extensions to FDMNES to account for thermal effects, in addition to broadening effects due to inelastic processes. Extended calculations beyond the range of near-edge structure also require consideration of technical constraints such as cluster sizes and densities. We find that with our approach, we are able to produce accurate theory ranging from the absorption edge to the smooth atom-like region at high energies, with a single consistent model that is free from any fitting parameters.
International Nuclear Information System (INIS)
Lee, Deokjung; Downar, Thomas J.; Kim, Yonghee
2004-01-01
An innovative hybrid spatial discretization method is proposed to improve the computational efficiency of pin-wise heterogeneous three-dimensional light water reactor (LWR) core neutronics analysis. The newly developed method employs the standard finite difference method in the x and y directions and the well-known nodal methods [nodal expansion method (NEM) and analytic nodal method (ANM) as needed] in the z direction. Four variants of the hybrid method are investigated depending on the axial nodal methodologies: HYBRID A, NEM with the conventional quadratic transverse leakage; HYBRID B, the conventional NEM method except that the transverse-leakage shapes are obtained from a fine-mesh local problem (FMLP) around the control rod tip; HYBRID C, the same as HYBRID B except that ANM with a high-order transverse leakage obtained from the FMLP is used in the vicinity of the control rod tip; and HYBRID D, the same as HYBRID C except that the transverse leakage is determined using the buckling approximation instead of the FMLP around the control rod tip. Benchmark calculations demonstrate that all the hybrid algorithms are consistent and stable and that the HYBRID C method provides the best numerical performance in the case of rodded LWR problems with pin-wise homogenized cross sections
HIGHER ORDER THINKING IN TEACHING GRAMMAR
Directory of Open Access Journals (Sweden)
Citra Dewi
2017-04-01
Full Text Available The aim of this paper discussed about how to enhance students’ higher order thinking that should be done by teacher in teaching grammar. Usually teaching grammar was boring and has the same way to learn like change the pattern of sentence into positive, negative and introgative while the students’ need more various way to develop their thinking. The outcome of students’ competence in grammar sometimes not sufficient enough when the students’ occured some test international standart like Test of English Foreign Language, International English Language Testing. Whereas in TOEFL test it needed higher order thinking answer, so teacher should develop students’ higher order thingking in daily teaching grammar in order to make the students’ enhance their thinking are higher. The method was used in this paper by using field study based on the experience of teaching grammar. It can be shown by students’ toefl score was less in stucture and written expression. The result of this paper was after teacher gave some treatments to enhance students’ higher order thinking in teaching grammar, the students’ toefl scores are sufficient enough as a part of stucture and written expression. It can concluded that it needed some strategies to enhancce students higher order thinking by teaching grammar it can make students’ higher toefl score. Teachers should be creative and inovative to teach the students’ started from giving the students’ question or test in teaching grammar.
Tay, Wei Choon; Tan, Eng Leong
2014-07-01
In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.
Resilience and Higher Order Thinking
Directory of Open Access Journals (Sweden)
Ioan Fazey
2010-09-01
Full Text Available To appreciate, understand, and tackle chronic global social and environmental problems, greater appreciation of the importance of higher order thinking is required. Such thinking includes personal epistemological beliefs (PEBs, i.e., the beliefs people hold about the nature of knowledge and how something is known. These beliefs have profound implications for the way individuals relate to each other and the world, such as how people understand complex social-ecological systems. Resilience thinking is an approach to environmental stewardship that includes a number of interrelated concepts and has strong foundations in systemic ways of thinking. This paper (1 summarizes a review of educational psychology literature on PEBs, (2 explains why resilience thinking has potential to facilitate development of more sophisticated PEBs, (3 describes an example of a module designed to teach resilience thinking to undergraduate students in ways conducive to influencing PEBs, and (4 discusses a pilot study that evaluates the module's impact. Theoretical and preliminary evidence from the pilot evaluation suggests that resilience thinking which is underpinned by systems thinking has considerable potential to influence the development of more sophisticated PEBs. To be effective, however, careful consideration of how resilience thinking is taught is required. Finding ways to encourage students to take greater responsibility for their own learning and ensuring close alignment between assessment and desired learning outcomes are particularly important.
International Nuclear Information System (INIS)
Su Xiaoxing; Ma Tianxue; Wang Yuesheng
2011-01-01
If the band structure of a three-dimensional (3D) phononic crystal (PNC) is calculated by using the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT)-based postprocessing method, good results can only be ensured by a sufficiently large number of FDTD iterations. On a common computer platform, the total computation time will be very long. To overcome this difficulty, an excellent harmonic inversion algorithm called the filter diagonalization method (FDM) can be used in the postprocessing to reduce the number of FDTD iterations. However, the low efficiency of the FDM, which occurs when a relatively long time series is given, does not necessarily ensure an effective reduction of the total computation time. In this paper, a postprocessing method based on the FDM is proposed. The main procedure of the method is designed considering the aim to make the time spent on the method itself far less than the corresponding time spent on the FDTD iterations. To this end, the FDTD time series is preprocessed to be shortened significantly before the FDM frequency extraction. The preprocessing procedure is performed with the filter and decimation operations, which are widely used in narrow-band signal processing. Numerical results for a typical 3D solid PNC system show that the proposed postprocessing method can be used to effectively reduce the total computation time of the FDTD calculation of 3D phononic band structures.
Energy Technology Data Exchange (ETDEWEB)
Su Xiaoxing [School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044 (China); Ma Tianxue; Wang Yuesheng, E-mail: xxsu@bjtu.edu.cn [Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044 (China)
2011-10-15
If the band structure of a three-dimensional (3D) phononic crystal (PNC) is calculated by using the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT)-based postprocessing method, good results can only be ensured by a sufficiently large number of FDTD iterations. On a common computer platform, the total computation time will be very long. To overcome this difficulty, an excellent harmonic inversion algorithm called the filter diagonalization method (FDM) can be used in the postprocessing to reduce the number of FDTD iterations. However, the low efficiency of the FDM, which occurs when a relatively long time series is given, does not necessarily ensure an effective reduction of the total computation time. In this paper, a postprocessing method based on the FDM is proposed. The main procedure of the method is designed considering the aim to make the time spent on the method itself far less than the corresponding time spent on the FDTD iterations. To this end, the FDTD time series is preprocessed to be shortened significantly before the FDM frequency extraction. The preprocessing procedure is performed with the filter and decimation operations, which are widely used in narrow-band signal processing. Numerical results for a typical 3D solid PNC system show that the proposed postprocessing method can be used to effectively reduce the total computation time of the FDTD calculation of 3D phononic band structures.
Determination of finite-difference weights using scaled binomial windows
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.
Determination of finite-difference weights using scaled binomial windows
Chu, Chunlei
2012-05-01
The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.
Yang, Lei; Yan, Hongyong; Liu, Hong
2017-03-01
Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.
Finite difference order doubling in two dimensions
International Nuclear Information System (INIS)
Killingbeck, John P; Jolicard, Georges
2008-01-01
An order doubling process previously used to obtain eighth-order eigenvalues from the fourth-order Numerov method is applied to the perturbed oscillator in two dimensions. A simple method of obtaining high order finite difference operators is reported and an odd parity boundary condition is found to be effective in facilitating the smooth operation of the order doubling process
International Nuclear Information System (INIS)
Kinefuchi, K.; Funaki, I.; Shimada, T.; Abe, T.
2012-01-01
Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model. The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition.
Directory of Open Access Journals (Sweden)
Roberto Rojas
2013-03-01
Full Text Available The applicability of the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM to high Reynolds number flows about a circular cylinder is examined. Two-dimensional simulations of flows past a stationary circular cylinder are carried out for a wide range of the Reynolds number, Re, i.e., 1 ≤ Re ≤ 1×105. An immersed boundary-lattice Boltzmann method (IB-LBM is also used for comparison. Then free-falling circular cylinders are simulated to demonstrate the feasibility of predicting moving particles at high Reynolds numbers. The main conclusions obtained are as follows: (1 steady and unsteady flows about a stationary cylinder are well predicted with IB-LBM and IB-FDLBM, provided that the spatial resolution is high enough to satisfy the conditions of numerical stability, (2 high spatial resolution is required for stable IB-LBM simulation of high Reynolds number flows, (3 IB-FDLBM can stably simulate flows at very high Reynolds numbers without increasing the spatial resolution, (4 IB-FDLBM gives reasonable predictions of the drag coefficient for 1 ≤ Re ≤ 1×105, and (5 IB-FDLBM gives accurate predictions for the motion of free-falling cylinders at intermediate Reynolds numbers.
Energy Technology Data Exchange (ETDEWEB)
Kinefuchi, K. [Department of Aeronautics and Astronautics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); Funaki, I.; Shimada, T.; Abe, T. [Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan)
2012-10-15
Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model. The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition.
International Nuclear Information System (INIS)
Shen, W.
2012-01-01
Recent assessment results indicate that the coarse-mesh finite-difference method (FDM) gives consistently smaller percent differences in channel powers than the fine-mesh FDM when compared to the reference MCNP solution for CANDU-type reactors. However, there is an impression that the fine-mesh FDM should always give more accurate results than the coarse-mesh FDM in theory. To answer the question if the better performance of the coarse-mesh FDM for CANDU-type reactors was just a coincidence (cancellation of errors) or caused by the use of heavy water or the use of lattice-homogenized cross sections for the cluster fuel geometry in the diffusion calculation, three benchmark problems were set up with three different fuel lattices: CANDU, HWR and PWR. These benchmark problems were then used to analyze the root cause of the better performance of the coarse-mesh FDM for CANDU-type reactors. The analyses confirm that the better performance of the coarse-mesh FDM for CANDU-type reactors is mainly caused by the use of lattice-homogenized cross sections for the sub-meshes of the cluster fuel geometry in the diffusion calculation. Based on the analyses, it is recommended to use 2 x 2 coarse-mesh FDM to analyze CANDU-type reactors when lattice-homogenized cross sections are used in the core analysis. (authors)
El Harouny, El Hassan; Nakra Mohajer, Soukaina; Ibral, Asmaa; El Khamkhami, Jamal; Assaid, El Mahdi
2018-05-01
Eigenvalues equation of hydrogen-like off-center single donor impurity confined in polarized homogeneous hemispherical quantum dot deposited on a wetting layer, capped by insulated matrix and submitted to external uniform electric field is solved in the framework of the effective mass approximation. An infinitely deep potential is used to describe effects of quantum confinement due to conduction band offsets at surfaces where quantum dot and surrounding materials meet. Single donor ground state total and binding energies in presence of electric field are determined via two-dimensional finite difference approach and Ritz-Hassé variation principle. For the latter method, attractive coulomb correlation between electron and ionized single donor is taken into account in the expression of trial wave function. It appears that off-center single dopant binding energy, spatial extension and radial probability density are strongly dependent on hemisphere radius and single dopant position inside quantum dot. Influence of a uniform electric field is also investigated. It shows that Stark effect appears even for very small size dots and that single dopant energy shift is more significant when the single donor is near hemispherical surface.
Energy Technology Data Exchange (ETDEWEB)
Shen, W. [Candu Energy Inc., 2285 Speakman Dr., Mississauga, ON L5B 1K (Canada)
2012-07-01
Recent assessment results indicate that the coarse-mesh finite-difference method (FDM) gives consistently smaller percent differences in channel powers than the fine-mesh FDM when compared to the reference MCNP solution for CANDU-type reactors. However, there is an impression that the fine-mesh FDM should always give more accurate results than the coarse-mesh FDM in theory. To answer the question if the better performance of the coarse-mesh FDM for CANDU-type reactors was just a coincidence (cancellation of errors) or caused by the use of heavy water or the use of lattice-homogenized cross sections for the cluster fuel geometry in the diffusion calculation, three benchmark problems were set up with three different fuel lattices: CANDU, HWR and PWR. These benchmark problems were then used to analyze the root cause of the better performance of the coarse-mesh FDM for CANDU-type reactors. The analyses confirm that the better performance of the coarse-mesh FDM for CANDU-type reactors is mainly caused by the use of lattice-homogenized cross sections for the sub-meshes of the cluster fuel geometry in the diffusion calculation. Based on the analyses, it is recommended to use 2 x 2 coarse-mesh FDM to analyze CANDU-type reactors when lattice-homogenized cross sections are used in the core analysis. (authors)
Directory of Open Access Journals (Sweden)
Sebastián Otero G
2008-06-01
representa su capacidad de incorporar en el análisis el valor de la flexibilidad operativa del proyecto.In the past few years, real options, an extension of financial derivatives, have arisen as an alternative to traditional valuation methods, such as net present value (NPV. The key attribute of real options is that they take into consideration the uncertainty and flexibility involved in investment valuation. This article provides an overview of the finite difference method, by presenting an application to the real options valuation. The empirical section of the article, which makes use of the implicit finite difference method (IFD, analyzes the options of waiting, abandoning, contracting, expanding and switching, by valuing all the options involved and their possible combinations. The results are compared with those of the NPV method and the binomial tree with a logarithmic transformation (BTLT. Both methods (IFD and BTLT yield similar results, being both greater than those provided by the NPV. This difference comes to no surprise as it represents the value of the flexibility associated to an investment opportunity.
Higher order mode optical fiber Raman amplifiers
DEFF Research Database (Denmark)
Rottwitt, Karsten; Friis, Søren Michael Mørk; Usuga Castaneda, Mario A.
2016-01-01
We review higher order mode Raman amplifiers and discuss recent theoretical as well as experimental results including system demonstrations.......We review higher order mode Raman amplifiers and discuss recent theoretical as well as experimental results including system demonstrations....
Challenges in higher order mode Raman amplifiers
DEFF Research Database (Denmark)
Rottwitt, Karsten; Nielsen, Kristian; Friis, Søren Michael Mørk
2015-01-01
A higher order Raman amplifier model that take random mode coupling into account ispresented. Mode dependent gain and signal power fluctuations at the output of the higher order modeRaman amplifier are discussed......A higher order Raman amplifier model that take random mode coupling into account ispresented. Mode dependent gain and signal power fluctuations at the output of the higher order modeRaman amplifier are discussed...
International Nuclear Information System (INIS)
Priimak, Dmitri
2014-01-01
We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques
Energy Technology Data Exchange (ETDEWEB)
Priimak, Dmitri
2014-12-01
We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.
Finite difference time domain analysis of a chiro plasma
International Nuclear Information System (INIS)
Torres-Silva, H.; Obligado, A.; Reggiani, N.; Sakanaka, P.H.
1995-01-01
The finite difference time-domain (FDTD) method is one of the most widely used computational methods in electromagnetics. Using FDTD, Maxwell's equations are solved directly in the time domain via finite differences and time stepping. The basic approach is relatively easy to understand and is an alternative to the more usual frequency-domain approaches. (author). 5 refs
Higher-order ice-sheet modelling accelerated by multigrid on graphics cards
Brædstrup, Christian; Egholm, David
2013-04-01
Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Higher order cumulants in colorless partonic plasma
Energy Technology Data Exchange (ETDEWEB)
Cherif, S. [Sciences and Technologies Department, University of Ghardaia, Ghardaia, Algiers (Algeria); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria); Ahmed, M. A. A. [Department of Physics, College of Science, Taibah University Al-Madinah Al-Mounawwarah KSA (Saudi Arabia); Department of Physics, Taiz University in Turba, Taiz (Yemen); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria); Ladrem, M., E-mail: mladrem@yahoo.fr [Department of Physics, College of Science, Taibah University Al-Madinah Al-Mounawwarah KSA (Saudi Arabia); Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Kouba (Bachir El-Ibrahimi), Algiers (Algeria)
2016-06-10
Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to the thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.
Higher Order Expectations in Asset Pricing
Philippe BACCHETTA; Eric VAN WINCOOP
2004-01-01
We examine formally Keynes' idea that higher order beliefs can drive a wedge between an asset price and its fundamental value based on expected future payoffs. Higher order expectations add an additional term to a standard asset pricing equation. We call this the higher order wedge, which depends on the difference between higher and first order expectations of future payoffs. We analyze the determinants of this wedge and its impact on the equilibrium price. In the context of a dynamic noisy r...
DEFF Research Database (Denmark)
Appel, Claus; van Oostrom, Vincent; Simonsen, Jakob Grue
2010-01-01
We show that, contrary to the situation in first-order term rewriting, almost none of the usual properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order rewriting format. We show that for the particular format of simply typed applicative term rewriting...... systems modularity of confluence, normalization, and termination can be recovered by imposing suitable linearity constraints....
Difference equations in massive higher order calculations
International Nuclear Information System (INIS)
Bierenbaum, I.; Bluemlein, J.; Klein, S.; Schneider, C.
2007-07-01
The calculation of massive 2-loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter N. We report on the solution of these sums through higher order difference equations using the summation package Sigma. (orig.)
International Nuclear Information System (INIS)
Kraus, H.G.; Jones, J.L.
1986-01-01
The problem of non-linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off-normal circuit element responses, the following capabilities are included: temporal, voltage and current-dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self-mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non-linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique. (author)
Symbolic generation of finite difference formulas
International Nuclear Information System (INIS)
Keller, H.; Pereyra, V.
1978-01-01
Tables of coefficients for high order accurate, compact approximations to the first ten derivatives on and at the midpoints of uniform nets are presented. The exact rational weights are generated and tested by means of symbolic manipulation implemented through MACSYMA. These weights are required in the application of deferred corrections to new methods for solving higher order two point boundary value problems
Exact solutions to two higher order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Xu Liping; Zhang Jinliang
2007-01-01
Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)
Higher-order techniques in computational electromagnetics
Graglia, Roberto D
2016-01-01
Higher-Order Techniques in Computational Electromagnetics explains 'high-order' techniques that can significantly improve the accuracy, computational cost, and reliability of computational techniques for high-frequency electromagnetics, such as antennas, microwave devices and radar scattering applications.
Higher-order rewriting and partial evaluation
DEFF Research Database (Denmark)
Danvy, Olivier; Rose, Kristoffer H.
1998-01-01
We demonstrate the usefulness of higher-order rewriting techniques for specializing programs, i.e., for partial evaluation. More precisely, we demonstrate how casting program specializers as combinatory reduction systems (CRSs) makes it possible to formalize the corresponding program...
Implicit finite-difference simulations of seismic wave propagation
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.
Implicit finite-difference simulations of seismic wave propagation
Chu, Chunlei
2012-03-01
We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.
Electromagnetic cloaking in higher order spherical cloaks
Sidhwa, H. H.; Aiyar, R. P. R. C.; Kulkarni, S. V.
2017-06-01
The inception of transformation optics has led to the realisation of the invisibility devices for various applications, one of which is spherical cloaking. In this paper, a formulation for a higher-order spherical cloak has been proposed to reduce its physical thickness significantly by introducing a nonlinear relation between the original and transformed coordinate systems and it has been verified using the ray tracing approach. Analysis has been carried out to observe the anomalies in the variation of refractive index for higher order cloaks indicating the presence of poles in the relevant equations. Furthermore, a higher-order spherical cloak with predefined values of the material characteristics on its inner and outer surfaces has been designed for practical application.
Higher-order force gradient symplectic algorithms
Chin, Siu A.; Kidwell, Donald W.
2000-12-01
We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 103, 104, 104, and 105 better.
A simplified parsimonious higher order multivariate Markov chain model
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, a simplified parsimonious higher-order multivariate Markov chain model (SPHOMMCM) is presented. Moreover, parameter estimation method of TPHOMMCM is give. Numerical experiments shows the effectiveness of TPHOMMCM.
A tridiagonal parsimonious higher order multivariate Markov chain model
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.
Frontiers of higher order fuzzy sets
Tahayori, Hooman
2015-01-01
Frontiers of Higher Order Fuzzy Sets, strives to improve the theoretical aspects of general and Interval Type-2 fuzzy sets and provides a unified representation theorem for higher order fuzzy sets. Moreover, the book elaborates on the concept of gradual elements and their integration with the higher order fuzzy sets. This book also introduces new frameworks for information granulation based on general T2FSs, IT2FSs, Gradual elements, Shadowed sets and rough sets. In particular, the properties and characteristics of the new proposed frameworks are studied. Such new frameworks are shown to be more capable to be exploited in real applications. Higher order fuzzy sets that are the result of the integration of general T2FSs, IT2FSs, gradual elements, shadowed sets and rough sets will be shown to be suitable to be applied in the fields of bioinformatics, business, management, ambient intelligence, medicine, cloud computing and smart grids. Presents new variations of fuzzy set frameworks and new areas of applicabili...
Higher-order tensors in diffusion imaging
Schultz, T.; Fuster, A.; Ghosh, A.; Deriche, R.; Florack, L.M.J.; Lim, L.H.; Westin, C.-F.; Vilanova, A.; Burgeth, B.
2014-01-01
Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion
Analogy, higher order thinking, and education.
Richland, Lindsey Engle; Simms, Nina
2015-01-01
Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships. © 2015 John Wiley & Sons, Ltd.
Higher-Order Components for Grid Programming
Dünnweber, Jan
2009-01-01
Higher-Order Components were developed within the CoreGRID European Network of Excellence and have become an optional extension of the popular Globus middleware. This book provides the reader with hands-on experience, describing a collection of example applications from various fields of science and engineering, including biology and physics.
Higher order antibunching in intermediate states
International Nuclear Information System (INIS)
Verma, Amit; Sharma, Navneet K.; Pathak, Anirban
2008-01-01
Since the introduction of binomial state as an intermediate state, different intermediate states have been proposed. Different nonclassical effects have also been reported in these intermediate states. But till now higher order antibunching is predicted in only one type of intermediate state, which is known as shadowed negative binomial state. Recently we have shown that the higher order antibunching is not a rare phenomenon [P. Gupta, P. Pandey, A. Pathak, J. Phys. B 39 (2006) 1137]. To establish our earlier claim further, here we have shown that the higher order antibunching can be seen in different intermediate states, such as binomial state, reciprocal binomial state, hypergeometric state, generalized binomial state, negative binomial state and photon added coherent state. We have studied the possibility of observing the higher order subpoissonian photon statistics in different limits of intermediate states. The effects of different control parameters on the depth of non classicality have also been studied in this connection and it has been shown that the depth of nonclassicality can be tuned by controlling various physical parameters
Certified higher-order recursive path ordering
Koprowski, A.; Pfenning, F.
2006-01-01
The paper reports on a formalization of a proof of wellfoundedness of the higher-order recursive path ordering (HORPO) in the proof checker Coq. The development is axiom-free and fully constructive. Three substantive parts that could be used also in other developments are the formalizations of the
Higher-Order Minimal Functional Graphs
DEFF Research Database (Denmark)
Jones, Neil D; Rosendahl, Mads
1994-01-01
We present a minimal function graph semantics for a higher-order functional language with applicative evaluation order. The semantics captures the intermediate calls performed during the evaluation of a program. This information may be used in abstract interpretation as a basis for proving...
Energy Technology Data Exchange (ETDEWEB)
Sasaki, Y [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1997-05-27
To enhance the reliability of electromagnetic/magnetotelluric (MT) survey, calculation results of finite-element methods (FEMs) and finite difference methods (FDMs) were compared. Accuracy of individual methods and convergence of repitition solution were examined. As a result of the investigation, it was found that appropriate accuracy can be obtained from the edge FEM and FDM for the example of vertical magnetic dipole, and that the best accuracy can be obtained from the FDM among four methods for the example of MT survey. It was revealed that the ICBCG (incomplete Cholesky bi-conjugate gradient) method is an excellent method as a solution method of simultaneous equations from the viewpoint of accuracy and calculation time. For the joint FEM, solutions of SOR method converged for both the examples. It was concluded that the cause of error is not due to the error of numerical calculation, but due to the consideration without discontinuity of electric field. The conditions of coefficient matrix increased with decreasing the frequency, which resulted in the unstable numerical calculation. It would be required to incorporate the constraint in a certain form. 4 refs., 12 figs.
Iterative solutions of finite difference diffusion equations
International Nuclear Information System (INIS)
Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.
1981-01-01
The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)
Linear matrix differential equations of higher-order and applications
Directory of Open Access Journals (Sweden)
Mustapha Rachidi
2008-07-01
Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.
Practical implementation of a higher order transverse leakage approximation
International Nuclear Information System (INIS)
Prinsloo, Rian H.; Tomašević
2011-01-01
Transverse integrated nodal diffusion methods currently represent the standard in full core neutronic simulation. The primary shortcoming in this approach, be it via the Analytic Nodal Method or Nodal Expansion Method, is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher order nodal methods developed some years ago. In this new approach, only information relevant to describing the transverse leak- age terms in the zero-order nodal equations are obtained from the higher order formalism. The method yields accuracy comparable to full higher order methods, but does not suffer from the same computational burden which these methods typically incur. (author)
A Higher-Order Colon Translation
DEFF Research Database (Denmark)
Danvy, Olivier; Nielsen, Lasse Reichstein
2001-01-01
A lambda-encoding such as the CPS transformation gives rise to administrative redexes. In his seminal article ``Call-by-name, call-by-value and the lambda-calculus'', 25 years ago, Plotkin tackled administrative reductions using a so-called ``colon translation.'' 10 years ago, Danvy and Filinski...... integrated administrative reductions in the CPS transformation, making it operate in one pass. The technique applies to other lambda-encodings (e.g., variants of CPS), but we do not see it used in practice--instead, Plotkin's colon translation appears to be favored. Therefore, in an attempt to link both...... techniques, we recast Plotkin's proof of Indifference and Simulation to the higher-order specification of the one-pass CPS transformation. To this end, we extend his colon translation from first order to higher order...
XY model with higher-order exchange.
Žukovič, Milan; Kalagov, Georgii
2017-08-01
An XY model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model displays a quasi-long-range-order phase characterized by an algebraically decaying correlation function with the exponent η=T/[2πJ(p,α)], nonlinearly dependent on the parameters p and α that control the number of the higher-order terms and the decay rate of their intensity, respectively. At higher temperatures the system shows a crossover from the continuous Berezinskii-Kosterlitz-Thouless to the first-order transition for the parameter values corresponding to a highly nonlinear shape of the potential well. The role of topological excitations (vortices) in changing the nature of the transition is discussed.
Higher-Order and Symbolic Computation
DEFF Research Database (Denmark)
Danvy, Olivier; Mason, Ian
2008-01-01
a series of implementaions that properly account for multiple invocations of the derivative-taking opeatro. In "Adapting Functional Programs to Higher-Order Logic," Scott Owens and Konrad Slind present a variety of examples of terminiation proofs of functional programs written in HOL proof systems. Since......-calculus programs, historically. The anaylsis determines the possible locations of ambients and mirrors the temporla sequencing of actions in the structure of types....
Lagrangian procedures for higher order field equations
International Nuclear Information System (INIS)
Bollini, C.G.
1987-01-01
A Lagrangian procedure for a pedagogical way is presented for the treatment of higher order field equations. The energy-momentum tensor and the conserved density current are built. In particular the case in which the derivatives appear only in the invariant D'Alembertian operator is discussed. Some examples are discussed. The fields are quantized and the corresponding Hamilonian which is shown not to be positive defructed. Rules are given to write the causal propagators. (author) [pt
Lagrangian procedures for higher order field equations
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.
1986-01-01
We present in a pedagogical way a Lagrangian procedure for the treatment of higher order field equations. We build the energy-momentum tensor and the conserved density current. In particular we discuss the case in which the derivatives appear only in the invariant D'Alembertian operator. We discuss some examples. We quantize the fields and construct the corresponding Hamiltonian which is shown not to be positive definite. We give the rules for the causal propagators. (Author) [pt
Higher order correlations in computed particle distributions
International Nuclear Information System (INIS)
Hanerfeld, H.; Herrmannsfeldt, W.; Miller, R.H.
1989-03-01
The rms emittances calculated for beam distributions using computer simulations are frequently dominated by higher order aberrations. Thus there are substantial open areas in the phase space plots. It has long been observed that the rms emittance is not an invariant to beam manipulations. The usual emittance calculation removes the correlation between transverse displacement and transverse momentum. In this paper, we explore the possibility of defining higher order correlations that can be removed from the distribution to result in a lower limit to the realizable emittance. The intent is that by inserting the correct combinations of linear lenses at the proper position, the beam may recombine in a way that cancels the effects of some higher order forces. An example might be the non-linear transverse space charge forces which cause a beam to spread. If the beam is then refocused so that the same non-linear forces reverse the inward velocities, the resulting phase space distribution may reasonably approximate the original distribution. The approach to finding the location and strength of the proper lens to optimize the transported beam is based on work by Bruce Carlsten of Los Alamos National Laboratory. 11 refs., 4 figs
Patra, Asim
2018-03-01
This paper displays the approach of the time-splitting Fourier spectral (TSFS) technique for the linear Riesz fractional Schrödinger equation (RFSE) in the semi-classical regime. The splitting technique is shown to be unconditionally stable. Further a suitable implicit finite difference discretization of second order has been manifested for the RFSE where the Riesz derivative has been discretized via an approach of fractional centered difference. Moreover the stability analysis for the implicit scheme has also been presented here via von Neumann analysis. The L2-norm and L^{∞}-norm errors are calculated for \\vert u(x,t)\\vert2, Re(u(x,t)) and Im(u(x,t)) for various cases. The results obtained by the methods are further tabulated for the absolute errors for \\vert u(x,t)\\vert2. Furthermore the graphs are depicted showing comparison of \\vert u(x,t)\\vert2 by both techniques. The derivatives are taken here in the context of the Riesz fractional sense. Apart from that, the comparative study put forth in the following section via tables and graphs between the implicit second-order finite difference method (IFDM) and the TSFS method is for the purpose of investigating the efficiency of the results obtained. Moreover the stability analysis of the presented techniques manifesting their unconditional stability makes the proposed approach more competing and accurate.
Higher order modes of coupled optical fibres
International Nuclear Information System (INIS)
Alexeyev, C N; Yavorsky, M A; Boklag, N A
2010-01-01
The structure of hybrid higher order modes of two coupled weakly guiding identical optical fibres is studied. On the basis of perturbation theory with degeneracy for the vector wave equation expressions for modes with azimuthal angular number l ≥ 1 are obtained that allow for the spin–orbit interaction. The spectra of polarization corrections to the scalar propagation constants are calculated in a wide range of distances between the fibres. The limiting cases of widely and closely spaced fibres are studied. The obtained results can be used for studying the tunnelling of optical vortices in directional couplers and in matters concerned with information security
Ward identities of higher order Virasoro algebra
International Nuclear Information System (INIS)
Zha Chaozeng; Dolate, S.
1994-11-01
The general formulations of primary fields versus quasi-primary ones in the context of high order Virasoro algebra (HOVA) and the corresponding Ward identity are explored. The primary fields of conformal spins up to 8 are given in terms of quasi-primary fields, and the general features of the higher order expressions are also discussed. It is observed that the local fields, either primary of quasi-primary, carry the same numbers of central charges, and not all the primary fields contribute to the anomalies in the Ward identities. (author). 6 refs
DEFF Research Database (Denmark)
Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter
1995-01-01
The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention...... has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximations for the gradient at the left boundary (electrode). Under accepted assumptions one obtains the usual...... stability criteria for the classic explicit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought regarding this method....
Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.
1978-01-01
Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.
Energy Technology Data Exchange (ETDEWEB)
Sanada, Y; Ashida, Y; Sassa, K [Kyoto University, Kyoto (Japan)
1996-10-01
3-D numerical modeling by FDTD method was studied for ground penetrating radar. Radar radiates electromagnetic wave, and determines the existence and distance of objects by reflection wave. Ground penetrating radar uses the above functions for underground surveys, however, its resolution and velocity analysis accuracy are problems. In particular, propagation characteristics of electromagnetic wave in media such as heterogeneous and anisotropic soil and rock are essential. The behavior of electromagnetic wave in the ground could be precisely reproduced by 3-D numerical modeling using FDTD method. FDTD method makes precise analysis in time domain and electric and magnetic fields possible by sequentially calculating the difference equation of Maxwell`s equation. Because of the high calculation efficiency of FDTD method, more precise complicated analysis can be expected by using the latest advanced computers. The numerical model and calculation example are illustrated for surface type electromagnetic pulse ground penetrating radar assuming the survey of steel pipes of 1m deep. 4 refs., 3 figs., 1 tab.
Huang, Lianjie
2013-10-29
Methods for enhancing ultrasonic reflection imaging are taught utilizing a split-step Fourier propagator in which the reconstruction is based on recursive inward continuation of ultrasonic wavefields in the frequency-space and frequency-wave number domains. The inward continuation within each extrapolation interval consists of two steps. In the first step, a phase-shift term is applied to the data in the frequency-wave number domain for propagation in a reference medium. The second step consists of applying another phase-shift term to data in the frequency-space domain to approximately compensate for ultrasonic scattering effects of heterogeneities within the tissue being imaged (e.g., breast tissue). Results from various data input to the method indicate significant improvements are provided in both image quality and resolution.
Finding Higher Order Differentials of MISTY1
Tsunoo, Yukiyasu; Saito, Teruo; Kawabata, Takeshi; Nakagawa, Hirokatsu
MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it is recommended for Japanese e-Government ciphers by the CRYPTREC project. In this paper, we report on 12th order differentials in 3-round MISTY1 with FL functions and 44th order differentials in 4-round MISTY1 with FL functions both previously unknown. We also report that both data complexity and computational complexity of higher order differential attacks on 6-round MISTY1 with FL functions and 7-round MISTY1 with FL functions using the 46th order differential can be reduced to as much as 1/22 of the previous values by using multiple 44th order differentials simultaneously.
Three weights higher order Hardy type inequalities
Directory of Open Access Journals (Sweden)
Aigerim A. Kalybay
2006-01-01
Full Text Available We investigate the following three weights higher order Hardy type inequality (0.1 ‖g‖q,u≤ C‖Dρkg‖p,v where Dρi denotes the following weighted differential operator: {dig(tdti,i=0,1,...,m−1,di−mdti−m(p(tdmg(tdtm,i=m,m+1,...,k, for a weight function ρ(⋅. A complete description of the weights u, v and ρ so that (0.1 holds was given in [4] for the case 1
Finite difference computing with PDEs a modern software approach
Langtangen, Hans Petter
2017-01-01
This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
Higher order multipoles and splines in plasma simulations
International Nuclear Information System (INIS)
Okuda, H.; Cheng, C.Z.
1978-01-01
The reduction of spatial grid effects in plasma simulations has been studied numerically using higher order multipole expansions and the spline method in one dimension. It is found that, while keeping the higher order moments such as quadrupole and octopole moments substantially reduces the grid effects, quadratic and cubic splines in general have better stability properties for numerical plasma simulations when the Debye length is much smaller than the grid size. In particular the spline method may be useful in three-dimensional simulations for plasma confinement where the grid size in the axial direction is much greater than the Debye length. (Auth.)
Higher-order multipoles and splines in plasma simulations
International Nuclear Information System (INIS)
Okuda, H.; Cheng, C.Z.
1977-12-01
Reduction of spatial grid effects in plasma simulations has been studied numerically using higher order multipole expansions and spline method in one dimension. It is found that, while keeping the higher order moments such as quadrupole and octopole moments substantially reduces the grid effects, quadratic and cubic splines in general have better stability properties for numerical plasma simulations when the Debye length is much smaller than the grid size. In particular, spline method may be useful in three dimensional simulations for plasma confinement where the grid size in the axial direction is much greater than the Debye length
An implicit finite-difference operator for the Helmholtz equation
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.
An implicit finite-difference operator for the Helmholtz equation
Chu, Chunlei
2012-07-01
We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.
Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.
Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung
2018-01-01
A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.
Hamiltonian formulation of theory with higher order derivatives
International Nuclear Information System (INIS)
Gitman, D.M.; Lyakhovich, S.L.; Tyutin, I.V.
1983-01-01
A method of ''hamiltonization'' of a special theory with higher order derivatives is described. In a nonspecial case the result coincides with the known Ostrogradsky formulation. It is shown that in the nonspecial theory the lagrange equations of motion are reduced to the normal form
Higher-Order Hierarchical Legendre Basis Functions in Applications
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter
2007-01-01
The higher-order hierarchical Legendre basis functions have been developed for eﬀective solution of integral equations with the method of moments. They are derived from orthogonal Legendre polynomials modiﬁed to enforce normal continuity between neighboring mesh elements, while preserving a high...
Finite difference computation of Casimir forces
International Nuclear Information System (INIS)
Pinto, Fabrizio
2016-01-01
In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing
Finite difference time domain modelling of particle accelerators
International Nuclear Information System (INIS)
Jurgens, T.G.; Harfoush, F.A.
1989-03-01
Finite Difference Time Domain (FDTD) modelling has been successfully applied to a wide variety of electromagnetic scattering and interaction problems for many years. Here the method is extended to incorporate the modelling of wake fields in particle accelerators. Algorithmic comparisons are made to existing wake field codes, such as MAFIA T3. 9 refs., 7 figs
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
A Higher-Order Organizational Purpose
DEFF Research Database (Denmark)
Edgeman, Rick
2013-01-01
Six Sigma Innovation & Design (SSID) strategies and methods are discussed as a means of enabling Sustainable Enterprise Excellence along with Organizational Resilience, Robustness and Resplendence.......Six Sigma Innovation & Design (SSID) strategies and methods are discussed as a means of enabling Sustainable Enterprise Excellence along with Organizational Resilience, Robustness and Resplendence....
Analysis of Buried Dielectric Objects Using Higher-Order MoM for Volume Integral Equations
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2004-01-01
A higher-order method of moments (MoM) is applied to solve a volume integral equation for dielectric objects in layered media. In comparison to low-order methods, the higher-order MoM, which is based on higher-order hierarchical Legendre vector basis functions and curvilinear hexahedral elements,...
Adaptive approximation of higher order posterior statistics
Lee, Wonjung
2014-01-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization
Elementary introduction to finite difference equations
International Nuclear Information System (INIS)
White, J.W.
1976-01-01
An elementary description is given of the basic vocabulary and concepts associated with finite difference modeling. The material discussed is biased toward the types of large computer programs used at the Lawrence Livermore Laboratory. Particular attention is focused on truncation error and how it can be affected by zoning patterns. The principle of convergence is discussed, and convergence as a tool for improving calculational accuracy and efficiency is emphasized
Energy Technology Data Exchange (ETDEWEB)
Nascimento, E.O.; Oliveira, L.N., E-mail: lucas@ifg.edu.br [Instituto Federal de Educacao, Ciencia e Tecnologia de Goias (IFG), Goiania, GO (Brazil)
2014-11-01
Partial Differential Equations (PDE) can model natural phenomena, such as related to physics, chemistry and engineering. For these classes of equations, analytical solutions are difficult to be obtained, so a computational approach is indicted. In this context, the Finite Difference Method (FDM) can provide useful tools for the field of Medical Physics. In this study, is described the implementation of a computational mesh, in order to be used in determining the Diffusion Coefficient (DC) of the Fricke Xylenol Gel dosimeter (FXG). The initial and boundary conditions both referred by experimental factors are modelled in FDM, thus making a semi-empirical study in determining the DC. Together, the method of Reflection and Superposition (SRM) and the analysis of experimental data, served as first validation for the simulation. Such methodologies interface generated concordant results for a range of error of 3% in concentration lines for small times when compared to the analytical solution. The result for the DC was 0.43 mm{sup 2} /h. This value is in concordance with measures parameters range found in polymer gels dosimeters: 0.3-2.0 mm{sup 2} /h. Therefore, the application of computer simulation methodology supported by the FDM may be used in determining the diffusion coefficient in FXG dosimeter. (author)
Adaptive approximation of higher order posterior statistics
Lee, Wonjung
2014-02-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively. © 2013 Elsevier Inc.
Higher Order and Fractional Diffusive Equations
Directory of Open Access Journals (Sweden)
D. Assante
2015-07-01
Full Text Available We discuss the solution of various generalized forms of the Heat Equation, by means of different tools ranging from the use of Hermite-Kampé de Fériet polynomials of higher and fractional order to operational techniques. We show that these methods are useful to obtain either numerical or analytical solutions.
On higher order pyramidal finite elements
Czech Academy of Sciences Publication Activity Database
Liu, L.; Davies, K.B.; Křížek, Michal; Guan, L.
2011-01-01
Roč. 3, č. 2 (2011), s. 131-140 ISSN 2070-0733 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : pyramidal polynomial basis functions * finite element method * composite elements * three-dimensional mortar elements Subject RIV: BA - General Mathematics Impact factor: 0.750, year: 2011
The instruments of higher order thinking skills
Ahmad, S.; Prahmana, R. C. I.; Kenedi, A. K.; Helsa, Y.; Arianil, Y.; Zainil, M.
2017-12-01
This research developed the standard of instrument for measuring the High Order Thinking Skill (HOTS) ability of PGSD students. The research method used is development research with eight steps namely theoretical studies, operational definition, designation construct, dimensions and indicators, the preparation of the lattice, the preparation of grain, an analysis of legibility and Social desirability, field trials, and data analysis. In accordance with the type of data to be obtained in this study, the research instrument using validation sheet, implementation observation, and questionnaire. The results show that the instruments are valid and feasible to be used by expert and have been tested on PGSD students with 60% of PGSD students with low categorization.
Self-similarity of higher-order moving averages
Arianos, Sergio; Carbone, Anna; Türk, Christian
2011-10-01
In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).
Higher-order geodesic deviations applied to the Kerr metric
Colistete, R J; Kerner, R
2002-01-01
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a general relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this method to the problem of closed orbital motion of test particles in the Kerr metric spacetime. With a simple circular orbit in the equatorial plane taken as the initial geodesic, we obtain finite eccentricity orbits in the form of Taylor series with the eccentricity playing the role of a small parameter. The explicit expressions of these higher-order geodesic deviations are derived using successive systems of linear equations with constant coefficients, whose solutions are of harmonic oscillator type. This scheme gives best results when applied to orbits with low eccentricities, but with arbitrary possible values of (GM/Rc sup 2).
Heavy quark threshold dynamics in higher order
Energy Technology Data Exchange (ETDEWEB)
Piclum, J.H.
2007-05-15
In this work we discuss an important building block for the next-to-next-to-next-to leading order corrections to the pair production of top quarks at threshold. Specifically, we explain the calculation of the third order strong corrections to the matching coefficient of the vector current in non-relativistic Quantum Chromodynamics and provide the result for the fermionic part, containing at least one loop of massless quarks. As a byproduct, we obtain the matching coefficients of the axial-vector, pseudo-scalar and scalar current at the same order. Furthermore, we calculate the three-loop corrections to the quark renormalisation constants in the on-shell scheme in the framework of dimensional regularisation and dimensional reduction. Finally, we compute the third order strong corrections to the chromomagnetic interaction in Heavy Quark Effective Theory. The calculational methods are discussed in detail and results for the master integrals are given. (orig.)
Non Standard Finite Difference Scheme for Mutualistic Interaction Description
Gabbriellini, Gianluca
2012-01-01
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the o...
Integral and finite difference inequalities and applications
Pachpatte, B G
2006-01-01
The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.- Contains a variety of inequalities discovered which find numero
The Laguerre finite difference one-way equation solver
Terekhov, Andrew V.
2017-05-01
This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.
Higher-Order Finite Element Solutions of Option Prices
DEFF Research Database (Denmark)
Raahauge, Peter
2004-01-01
Kinks and jumps in the payoff function of option contracts prevent an effectiveimplementation of higher-order numerical approximation methods. Moreover, thederivatives (the greeks) are not easily determined around such singularities, even withstandard lower-order methods. This paper suggests...... for prices as well as for first and second order derivatives(delta and gamma). Unlike similar studies, numerical approximation errors aremeasured both as weighted averages and in the supnorm over a state space includingtime-to-maturities down to a split second.KEYWORDS: Numerical option pricing, Transformed...
Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.
2008-01-01
Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling
Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.
2008-01-01
Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling
Programming real-time executives in higher order language
Foudriat, E. C.
1982-01-01
Methods by which real-time executive programs can be implemented in a higher order language are discussed, using HAL/S and Path Pascal languages as program examples. Techniques are presented by which noncyclic tasks can readily be incorporated into the executive system. Situations are shown where the executive system can fail to meet its task scheduling and yet be able to recover either by rephasing the clock or stacking the information for later processing. The concept of deadline processing is shown to enable more effective mixing of time and information synchronized systems.
Conceptualizing and Assessing Higher-Order Thinking in Reading
Afflerbach, Peter; Cho, Byeong-Young; Kim, Jong-Yun
2015-01-01
Students engage in higher-order thinking as they read complex texts and perform complex reading-related tasks. However, the most consequential assessments, high-stakes tests, are currently limited in providing information about students' higher-order thinking. In this article, we describe higher-order thinking in relation to reading. We provide a…
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea
2013-01-01
Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.
Higher-Order Spectrum in Understanding Nonlinearity in EEG Rhythms
Directory of Open Access Journals (Sweden)
Cauchy Pradhan
2012-01-01
Full Text Available The fundamental nature of the brain's electrical activities recorded as electroencephalogram (EEG remains unknown. Linear stochastic models and spectral estimates are the most common methods for the analysis of EEG because of their robustness, simplicity of interpretation, and apparent association with rhythmic behavioral patterns in nature. In this paper, we extend the use of higher-order spectrum in order to indicate the hidden characteristics of EEG signals that simply do not arise from random processes. The higher-order spectrum is an extension Fourier spectrum that uses higher moments for spectral estimates. This essentially nullifies all Gaussian random effects, therefore, can reveal non-Gaussian and nonlinear characteristics in the complex patterns of EEG time series. The paper demonstrates the distinguishing features of bispectral analysis for chaotic systems, filtered noises, and normal background EEG activity. The bispectrum analysis detects nonlinear interactions; however, it does not quantify the coupling strength. The squared bicoherence in the nonredundant region has been estimated to demonstrate nonlinear coupling. The bicoherence values are minimal for white Gaussian noises (WGNs and filtered noises. Higher bicoherence values in chaotic time series and normal background EEG activities are indicative of nonlinear coupling in these systems. The paper shows utility of bispectral methods as an analytical tool in understanding neural process underlying human EEG patterns.
Mimetic Finite Differences for Flow in Fractures from Microseismic Data
Al-Hinai, Omar; Srinivasan, Sanjay; Wheeler, Mary F.
2015-01-01
We present a method for porous media flow in the presence of complex fracture networks. The approach uses the Mimetic Finite Difference method (MFD) and takes advantage of MFD's ability to solve over a general set of polyhedral cells. This flexibility is used to mesh fracture intersections in two and three-dimensional settings without creating small cells at the intersection point. We also demonstrate how to use general polyhedra for embedding fracture boundaries in the reservoir domain. The target application is representing fracture networks inferred from microseismic analysis.
Mimetic Finite Differences for Flow in Fractures from Microseismic Data
Al-Hinai, Omar
2015-01-01
We present a method for porous media flow in the presence of complex fracture networks. The approach uses the Mimetic Finite Difference method (MFD) and takes advantage of MFD\\'s ability to solve over a general set of polyhedral cells. This flexibility is used to mesh fracture intersections in two and three-dimensional settings without creating small cells at the intersection point. We also demonstrate how to use general polyhedra for embedding fracture boundaries in the reservoir domain. The target application is representing fracture networks inferred from microseismic analysis.
Directory of Open Access Journals (Sweden)
Lindemberg Lima Fernandes
2009-03-01
ão recomenda-se a integração de dados de superfície com os de poço, com o objetivo de obter melhor imagem dos alvos abaixo das soleiras de diabásio.This paper discusses the seismic modeling in medium with strong discontinuities in its physical properties. The approach takes in consideration the existences diffractions and multiple reflections in the analyzed medium, which, at that case, is the Amazon Basin. The stability and boundary conditions of modeling were analyzed by the method of the finite differences. Sedimentary rocks deposited since the Ordovician to the present, reaching depth up to 5 Km. The bodies of diabasic between the paleozoic sediments are layers reaching thickness of hundred meters, which add to 90.000 km3, form the geology of the Amazon Basin. The occurrence of these structures is responsible for multiple reflections during the propagation of the seismic waves, which become impossible a better imaging of horizons located bellow the layers. The representation this geological situation was performed an (synthetic acoustic velocity model. The numerical discretization scheme is based in a fourth order approximation of the acoustic wave equation in space and time The understanding of the wave propagation heterogeneous medium has improved for the application of the finite difference method. The method achieves a good resolution in the interpretation of seismic reflection events. The numerical results discusses in this paper have allowed to observed the influence of the multiple reflection in a high velocity layer. It increase a loss of energy and difficult the interpretation of the target. For this reason the integration of surface data with the well data is recommended, with the objective to get one better image of the targets below of the diabasic layer.
Higher-order automatic differentiation of mathematical functions
Charpentier, Isabelle; Dal Cappello, Claude
2015-04-01
Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.
Mixed Higher Order Variational Model for Image Recovery
Directory of Open Access Journals (Sweden)
Pengfei Liu
2014-01-01
Full Text Available A novel mixed higher order regularizer involving the first and second degree image derivatives is proposed in this paper. Using spectral decomposition, we reformulate the new regularizer as a weighted L1-L2 mixed norm of image derivatives. Due to the equivalent formulation of the proposed regularizer, an efficient fast projected gradient algorithm combined with monotone fast iterative shrinkage thresholding, called, FPG-MFISTA, is designed to solve the resulting variational image recovery problems under majorization-minimization framework. Finally, we demonstrate the effectiveness of the proposed regularization scheme by the experimental comparisons with total variation (TV scheme, nonlocal TV scheme, and current second degree methods. Specifically, the proposed approach achieves better results than related state-of-the-art methods in terms of peak signal to ratio (PSNR and restoration quality.
Higher-order techniques for some problems of nonlinear control
Directory of Open Access Journals (Sweden)
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
Higher-Order Generalized Invexity in Control Problems
Directory of Open Access Journals (Sweden)
S. K. Padhan
2011-01-01
Full Text Available We introduce a higher-order duality (Mangasarian type and Mond-Weir type for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality are derived for these pair of problems. Also, we establish few examples in support of our investigation.
Skinner-Rusk unified formalism for higher-order systems
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2012-07-01
The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, first-order and higher-order field theories, and higher-order autonomous systems. In this work we present a generalization of this formalism for higher-order non-autonomous mechanical systems.
Nil Bohr-sets and almost automorphy of higher order
Huang, Wen; Ye, Xiangdong
2016-01-01
Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d\\in \\mathbb{N} does the collection of \\{n\\in \\mathbb{Z}: S\\cap (S-n)\\cap\\ldots\\cap (S-dn)\
Finite difference time domain modeling of spiral antennas
Penney, Christopher W.; Beggs, John H.; Luebbers, Raymond J.
1992-01-01
The objectives outlined in the original proposal for this project were to create a well-documented computer analysis model based on the finite-difference, time-domain (FDTD) method that would be capable of computing antenna impedance, far-zone radiation patterns, and radar cross-section (RCS). The ability to model a variety of penetrable materials in addition to conductors is also desired. The spiral antennas under study by this project meet these requirements since they are constructed of slots cut into conducting surfaces which are backed by dielectric materials.
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
International Nuclear Information System (INIS)
Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.
2006-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)
Higher order perturbation theory - An example for discussion
International Nuclear Information System (INIS)
Lewins, J.D.; Parks, G.; Babb, A.L.
1986-01-01
Higher order perturbation theory is developed in the form of a Taylor series expansion to third order to calculate the thermal utilization of a nonuniform cell. The development takes advantage of the self-adjoint property of the diffusion operator to provide a simple development of this illustration of generalized perturbation theory employing scalar perturbation parameters. The results show how a designer might employ a second-order theory to quantify proposed design improvements, together with the limitations of second- and third-order theory. The chosen example has an exact optimization solution and thus provides a clear understanding of the role of perturbation theory at its various orders. Convergence and the computational advantages and disadvantages of the method are discussed
Higher-order force moments of active particles
Nasouri, Babak; Elfring, Gwynn J.
2018-04-01
Active particles moving through fluids generate disturbance flows due to their activity. For simplicity, the induced flow field is often modeled by the leading terms in a far-field approximation of the Stokes equations, whose coefficients are the force, torque, and stresslet (zeroth- and first-order force moments) of the active particle. This level of approximation is quite useful, but may also fail to predict more complex behaviors that are observed experimentally. In this study, to provide a better approximation, we evaluate the contribution of the second-order force moments to the flow field and, by reciprocal theorem, present explicit formulas for the stresslet dipole, rotlet dipole, and potential dipole for an arbitrarily shaped active particle. As examples of this method, we derive modified Faxén laws for active spherical particles and resolve higher-order moments for active rod-like particles.
Higher order branching of periodic orbits from polynomial isochrones
Directory of Open Access Journals (Sweden)
B. Toni
1999-09-01
Full Text Available We discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form. Using a method based on the relative cohomology decomposition of polynomial one-forms complemented with a step reduction process, we give an explicit formula for the overall upper bound of branch points of limit cycles in an arbitrary $n$ degree polynomial perturbation of the linear isochrone, and provide an algorithmic procedure to compute the upper bound at successive orders. We derive a complete analysis of the nonlinear cubic Hamiltonian isochrone and show that at most nine branch points of limit cycles can bifurcate in a cubic polynomial perturbation. Moreover, perturbations with exactly two, three, four, six, and nine local families of limit cycles may be constructed.
Higher-order structure of Saccharomyces cerevisiae chromatin
International Nuclear Information System (INIS)
Lowary, P.T.; Widom, J.
1989-01-01
We have developed a method for partially purifying chromatin from Saccharomyces cerevisiae (baker's yeast) to a level suitable for studies of its higher-order folding. This has required the use of yeast strains that are free of the ubiquitous yeast killer virus. Results from dynamic light scattering, electron microscopy, and x-ray diffraction show that the yeast chromatin undergoes a cation-dependent folding into 30-nm filaments that resemble those characteristic of higher-cell chromatin; moreover, the packing of nucleosomes within the yeast 30-nm filaments is similar to that of higher cells. These results imply that yeast has a protein or protein domain that serves the role of the histone H 1 found in higher cells; physical and genetic studies of the yeast activity could help elucidate the structure and function of H 1. Images of the yeast 30-nm filaments can be used to test crossed-linker models for 30-nm filament structure
Predictors of third and Higher order births in India
Directory of Open Access Journals (Sweden)
Payal Singh
2015-12-01
Full Text Available Background: Total fertility rate (TFR reflecting population growth is closely related to higher order parity progression. Many Indian states reached replacement level of TFR, but still states constituting nearly 40% population are with TFR ≥ 3. The predictors are the desire of son’s, poor contraceptives practices, younger age at marriage, child loss and shorter birth spacing. Objective: This analysis assessed the degree of relation of 3rd and higher order parity progression with the above mentioned predictors. Material and Methods: State/Union Territories wise proportions of women: progressing to ≥3 births, more sons desire, birth spacing <24 months, adopting modern contraception and median marriage age <18 years along with infant mortality rate (IMR were taken from NFHS-III report. Correlation matrix and stepwise forward multiple regression carried. Significance was seen at 5%. Results: Hindi speaking states constituting 38.92% nation population recorded TFR ≥3. Positive correlation of mothers progressing ≥ 3 births was highest (0.746 with those desiring more sons followed by IMR (0.445; while maximum negative correlation with those practicing modern contraceptives (-0.565 followed by median age at marriage (-0.391. Multiple regression analysis in order identified desire of more sons, practicing modern contraception and shorter birth spacing as the significant predictors and jointly explained 77.9% of the total variation with gain of 15.5% by adding modern contraceptive practice and 8.3% by adding shorter birth spacing. Conclusions: Desire of more sons appeared the most important predictor to progress ≥3 births that is governed by society culture and educational attainment, require attitudinal change. Further, mothers need motivation to practice both spacing and terminal methods once family is complete.
Higher-Order Hybrid Gaussian Kernel in Meshsize Boosting Algorithm
African Journals Online (AJOL)
In this paper, we shall use higher-order hybrid Gaussian kernel in a meshsize boosting algorithm in kernel density estimation. Bias reduction is guaranteed in this scheme like other existing schemes but uses the higher-order hybrid Gaussian kernel instead of the regular fixed kernels. A numerical verification of this scheme ...
Higher-order Jordan Osserman pseudo-Riemannian manifolds
International Nuclear Information System (INIS)
Gilkey, Peter B; Ivanova, Raina; Zhang Tan
2002-01-01
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds
Higher-order Jordan Osserman pseudo-Riemannian manifolds
Energy Technology Data Exchange (ETDEWEB)
Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)
2002-09-07
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.
Neural classifiers for learning higher-order correlations
International Nuclear Information System (INIS)
Gueler, M.
1999-01-01
Studies by various authors suggest that higher-order networks can be more powerful and biologically more plausible with respect to the more traditional multilayer networks. These architecture make explicit use of nonlinear interactions between input variables in the form of higher-order units or product units. If it is known a priori that the problem to be implemented possesses a given set of invariances like in the translation, rotation, and scale invariant recognition problems, those invariances can be encoded, thus eliminating all higher-order terms which are incompatible with the invariances. In general, however, it is a serious set-back that the complexity of learning increases exponentially with the size of inputs. This paper reviews higher-order networks and introduces an implicit representation in which learning complexity is mainly decided by the number of higher-order terms to be learned and increases only linearly with the input size
Neural Classifiers for Learning Higher-Order Correlations
Güler, Marifi
1999-01-01
Studies by various authors suggest that higher-order networks can be more powerful and are biologically more plausible with respect to the more traditional multilayer networks. These architectures make explicit use of nonlinear interactions between input variables in the form of higher-order units or product units. If it is known a priori that the problem to be implemented possesses a given set of invariances like in the translation, rotation, and scale invariant pattern recognition problems, those invariances can be encoded, thus eliminating all higher-order terms which are incompatible with the invariances. In general, however, it is a serious set-back that the complexity of learning increases exponentially with the size of inputs. This paper reviews higher-order networks and introduces an implicit representation in which learning complexity is mainly decided by the number of higher-order terms to be learned and increases only linearly with the input size.
Sidwell, Kenneth W.; Baruah, Pranab K.; Bussoletti, John E.; Medan, Richard T.; Conner, R. S.; Purdon, David J.
1990-01-01
A comprehensive description of user problem definition for the PAN AIR (Panel Aerodynamics) system is given. PAN AIR solves the 3-D linear integral equations of subsonic and supersonic flow. Influence coefficient methods are used which employ source and doublet panels as boundary surfaces. Both analysis and design boundary conditions can be used. This User's Manual describes the information needed to use the PAN AIR system. The structure and organization of PAN AIR are described, including the job control and module execution control languages for execution of the program system. The engineering input data are described, including the mathematical and physical modeling requirements. Version 3.0 strictly applies only to PAN AIR version 3.0. The major revisions include: (1) inputs and guidelines for the new FDP module (which calculates streamlines and offbody points); (2) nine new class 1 and class 2 boundary conditions to cover commonly used modeling practices, in particular the vorticity matching Kutta condition; (3) use of the CRAY solid state Storage Device (SSD); and (4) incorporation of errata and typo's together with additional explanation and guidelines.
A stable higher order space time Galerkin marching-on-in-time scheme
Pray, Andrew J.; Shanker, Balasubramaniam; Bagci, Hakan
2013-01-01
We present a method for the stable solution of time-domain integral equations. The method uses a technique developed in [1] to accurately evaluate matrix elements. As opposed to existing stabilization schemes, the method presented uses higher order
Higher order Lie-Baecklund symmetries of evolution equations
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Roy Chowdhury, K.; Paul, S.
1983-10-01
We have considered in detail the analysis of higher order Lie-Baecklund symmetries for some representative nonlinear evolution equations. Until now all such symmetry analyses have been restricted only to the first order of the infinitesimal parameter. But the existence of Baecklund transformation (which can be shown to be an overall sum of higher order Lie-Baecklund symmetries) makes it necessary to search for such higher order Lie-Baecklund symmetries directly without taking recourse to the Baecklund transformation or inverse scattering technique. (author)
The differential geometry of higher order jets and tangent bundles
International Nuclear Information System (INIS)
De Leon, M.; Rodrigues, P.R.
1985-01-01
This chapter is devoted to the study of basic geometrical notions required for the development of the main object of the text. Some facts about Jet theory are reviewed. A particular case of Jet manifolds is considered: the tangent bundle of higher order. It is shown that this jet bundle possesses in a canonical way a certain kind of geometric structure, the so called almost tangent structure of higher order, and which is a generalization of the almost tangent geometry of the tangent bundle. Another important fact examined is the extension of the notion of 'spray' to higher order tangent bundles. (Auth.)
Higher-order harmonics of general limited diffraction Bessel beams
International Nuclear Information System (INIS)
Ding De-Sheng; Huang Jin-Huang
2016-01-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m -th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. (special topic)
Higher-order harmonics of general limited diffraction Bessel beams
Ding, De-Sheng; Huang, Jin-Huang
2016-12-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).
Fischer, Christopher; Bol, Linda; Pribesh, Shana
2011-01-01
This study investigated the extent to which higher-order thinking skills are promoted in social studies classes in high schools that are implementing smaller learning communities (SLCs). Data collection in this mixed-methods study included classroom observations and in-depth interviews. Findings indicated that higher-order thinking was rarely…
Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation
International Nuclear Information System (INIS)
Ren Ji; Ruan Hangyu
2008-01-01
We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained
Multi-domain, higher order level set scheme for 3D image segmentation on the GPU
DEFF Research Database (Denmark)
Sharma, Ojaswa; Zhang, Qin; Anton, François
2010-01-01
to evaluate level set surfaces that are $C^2$ continuous, but are slow due to high computational burden. In this paper, we provide a higher order GPU based solver for fast and efficient segmentation of large volumetric images. We also extend the higher order method to multi-domain segmentation. Our streaming...
Protein scaffolds and higher-order complexes in synthetic biology
den Hamer, A.; Rosier, B.J.H.M.; Brunsveld, L.; de Greef, T.F.A.; Ryadnov, M.; Brunsveld, L.; Suga, H.
2017-01-01
Interactions between proteins control molecular functions such as signalling or metabolic activity. Assembly of proteins via scaffold proteins or in higher-order complexes is a key regulatory mechanism. Understanding and functionally applying this concept requires the construction, study, and
Generating superpositions of higher order bessel beams [Conference paper
CSIR Research Space (South Africa)
Vasilyeu, R
2009-10-01
Full Text Available An experimental setup to generate a superposition of higher-order Bessel beams by means of a spatial light modulator and ring aperture is presented. The experimentally produced fields are in good agreement with those calculated theoretically....
Higher-order curvature terms and extended inflation
International Nuclear Information System (INIS)
Wang Yun
1990-01-01
We consider higher-order curvature terms in context of the Brans-Dicke theory of gravity, and investigate the effects of these terms on extended inflationary theories. We find that the higher-order curvature terms tend to speed up inflation, although the original extended-inflation solutions are stable when these terms are small. Analytical solutions are found for two extreme cases: when the higher-order curvature terms are small, and when they dominate. A conformal transformation is employed in solving the latter case, and some of the subtleties in this technique are discussed. We note that percolation is less likely to occur when the higher-order curvature terms are present. An upper bound on α is expected if we are to avoid excessive and inadequate percolation of true-vacuum bubbles
Unambiguous formalism for higher order Lagrangian field theories
International Nuclear Information System (INIS)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn; Vankerschaver, Joris
2009-01-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Higher-order RANS turbulence models for separated flows
National Aeronautics and Space Administration — Higher-order Reynolds-averaged Navier-Stokes (RANS) models are developed to overcome the shortcomings of second-moment RANS models in predicting separated flows....
The role of formative feedback in promoting higher order thinking ...
African Journals Online (AJOL)
The role of formative feedback in promoting higher order thinking skills in ... activities, task characteristics, validating students' thinking, and providing feedback. ... Keywords: classroom environment, formative assessment, formative feedback, ...
Asymptotic Expansions for Higher-Order Scalar Difference Equations
Directory of Open Access Journals (Sweden)
Ravi P. Agarwal
2007-04-01
Full Text Available We give an asymptotic expansion of the solutions of higher-order PoincarÃƒÂ© difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.
Asymptotic Expansions for Higher-Order Scalar Difference Equations
Directory of Open Access Journals (Sweden)
Pituk Mihály
2007-01-01
Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.
Higher order aberrations of the eye: Part one
Directory of Open Access Journals (Sweden)
Marsha Oberholzer
2016-06-01
Full Text Available This article is the first in a series of two articles that provide a comprehensive literature review of higher order aberrations (HOAs of the eye. The present article mainly explains the general principles of such HOAs as well as HOAs of importance, and the measuring apparatus used to measure HOAs of the eye. The second article in the series discusses factors contributing to variable results in measurements of HOAs of the eye. Keywords: Higher order aberrations; wavefront aberrations; aberrometer
All-fiber Raman Probe using Higher Order Modes
DEFF Research Database (Denmark)
Larsen, Stine Højer Møller; Rishøj, Lars Søgaard; Rottwitt, Karsten
2013-01-01
We demonstrate the first all-fiber Raman probe utilizing higher order modes for the excitation. The spectrum of cyclohexane is measured using both the fundamental mode as well as in-fiber-generated Bessel-like modes.......We demonstrate the first all-fiber Raman probe utilizing higher order modes for the excitation. The spectrum of cyclohexane is measured using both the fundamental mode as well as in-fiber-generated Bessel-like modes....
Higher-order relativistic periastron advances and binary pulsars
International Nuclear Information System (INIS)
Damour, T.; Schafer, G.
1988-01-01
The contributions to the periastron advance of a system of two condensed bodies coming from relativistic dynamical effects of order higher than the usual first post-Newtonian (1PN) equations of motion are investigated. The structure of the solution of the orbital second post-Newtonian (2PN) equations of motion is given in a simple parametrized form. The contributions to the secular pariastron advance, and the period, of orbital 2PN effects are then explicitly worked out by using the Hamilton-Jacobi method. The spin-orbit contribution to the secular precession of the orbit in space is rederived in a streamlined way by making full use of Hamiltonian methods. These results are then applied to the theoretical interpretation of the observational data of pulsars in close eccentric binary systems. It is shown that the higher-order relativistic contributions are already of theoretical and astophysical significance for interpreting the high-precision measurement of the secular periastron advance of PSR 1913+16 achived by Taylor and coworkers. The case of extremely fast spinning (millisecond) binary pulsars is also discussed, and shown to offer an easier ground for getting new tests of general relativity, and/or, a direct measurement of the moment of inertia of a neutron star
Holographic conductivity of holographic superconductors with higher-order corrections
Energy Technology Data Exchange (ETDEWEB)
Sheykhi, Ahmad [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Ghazanfari, Afsoon; Dehyadegari, Amin [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)
2018-02-15
We analytically and numerically disclose the effects of the higher-order correction terms in the gravity and in the gauge field on the properties of s-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss-Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that, for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss-Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics makes the condensation harder. We also study the holographic conductivity of the system and disclose the effects of the Gauss-Bonnet and nonlinear parameters α and b on the superconducting gap. We observe that, for various values of α and b, the real part of the conductivity is proportional to the frequency per temperature, ω/T, as the frequency is large enough. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing temperature. (orig.)
Higher order total variation regularization for EIT reconstruction.
Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Zhang, Fan; Mueller-Lisse, Ullrich; Moeller, Knut
2018-01-08
Electrical impedance tomography (EIT) attempts to reveal the conductivity distribution of a domain based on the electrical boundary condition. This is an ill-posed inverse problem; its solution is very unstable. Total variation (TV) regularization is one of the techniques commonly employed to stabilize reconstructions. However, it is well known that TV regularization induces staircase effects, which are not realistic in clinical applications. To reduce such artifacts, modified TV regularization terms considering a higher order differential operator were developed in several previous studies. One of them is called total generalized variation (TGV) regularization. TGV regularization has been successively applied in image processing in a regular grid context. In this study, we adapted TGV regularization to the finite element model (FEM) framework for EIT reconstruction. Reconstructions using simulation and clinical data were performed. First results indicate that, in comparison to TV regularization, TGV regularization promotes more realistic images. Graphical abstract Reconstructed conductivity changes located on selected vertical lines. For each of the reconstructed images as well as the ground truth image, conductivity changes located along the selected left and right vertical lines are plotted. In these plots, the notation GT in the legend stands for ground truth, TV stands for total variation method, and TGV stands for total generalized variation method. Reconstructed conductivity distributions from the GREIT algorithm are also demonstrated.
Finite difference techniques for nonlinear hyperbolic conservation laws
International Nuclear Information System (INIS)
Sanders, R.
1985-01-01
The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references
Chu, Chunlei
2009-01-01
We analyze the dispersion properties and stability conditions of the high‐order convolutional finite difference operators and compare them with the conventional finite difference schemes. We observe that the convolutional finite difference method has better dispersion properties and becomes more efficient than the conventional finite difference method with the increasing order of accuracy. This makes the high‐order convolutional operator a good choice for anisotropic elastic wave simulations on rotated staggered grids since its enhanced dispersion properties can help to suppress the numerical dispersion error that is inherent in the rotated staggered grid structure and its efficiency can help us tackle 3D problems cost‐effectively.
Directory of Open Access Journals (Sweden)
Peng Jiang
2013-01-01
Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.
Scalar brane backgrounds in higher order curvature gravity
International Nuclear Information System (INIS)
Charmousis, Christos; Davis, Stephen C.; Dufaux, Jean-Francois
2003-01-01
We investigate maximally symmetric brane world solutions with a scalar field. Five-dimensional bulk gravity is described by a general lagrangian which yields field equations containing no higher than second order derivatives. This includes the Gauss-Bonnet combination for the graviton. Stability and gravitational properties of such solutions are considered, and we particularly emphasise the modifications induced by the higher order terms. In particular it is shown that higher curvature corrections to Einstein theory can give rise to instabilities in brane world solutions. A method for analytically obtaining the general solution for such actions is outlined. Generically, the requirement of a finite volume element together with the absence of a naked singularity in the bulk imposes fine-tuning of the brane tension. A model with a moduli scalar field is analysed in detail and we address questions of instability and non-singular self-tuning solutions. In particular, we discuss a case with a normalisable zero mode but infinite volume element. (author)
Near integrability of kink lattice with higher order interactions
Jiang, Yun-Guo; Liu, Jia-Zhen; He, Song
2017-11-01
We make use of Manton’s analytical method to investigate the force between kinks and anti-kinks at large distances in 1+1 dimensional field theory. The related potential has infinite order corrections of exponential pattern, and the coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuations around the vacuum. At the lowest order, the kink lattice represents the Toda lattice. With higher order correction terms, the kink lattice can represent one kind of generic Toda lattice. With only two sites, the kink lattice is classically integrable. If the number of sites of the lattice is larger than two, the kink lattice is not integrable but is a near integrable system. We make use of Flaschka’s variables to study the Lax pair of the kink lattice. These Flaschka’s variables have interesting algebraic relations and non-integrability can be manifested. We also discuss the higher Hamiltonians for the deformed open Toda lattice, which has a similar result to the ordinary deformed Toda. Supported by Shandong Provincial Natural Science Foundation (ZR2014AQ007), National Natural Science Foundation of China (11403015, U1531105), S. He is supported by Max-Planck fellowship in Germany and National Natural Science Foundation of China (11305235)
Higher Order Modes Excitation of Micro Cantilever Beams
Jaber, Nizar
2014-05-01
In this study, we present analytical and experimental investigation of electrically actuated micro cantilever based resonators. These devices are fabricated using polyimide and coated with chrome and gold layers from both sides. The cantilevers are highly curled up due to stress gradient, which is a common imperfection in surface micro machining. Using a laser Doppler vibrometer, we applied a noise signal to experimentally find the first four resonance frequencies. Then, using a data acquisition card, we swept the excitation frequency around the first four natural modes of vibrations. Theoretically, we derived a reduced order model using the Galerkin method to simulate the dynamics of the system. Extensive numerical analysis and computations were performed. The numerical analysis was able to provide good matching with experimental values of the resonance frequencies. Also, we proved the ability to excite higher order modes using partial electrodes with shapes that resemble the shape of the mode of interest. Such micro-resonators are shown to be promising for applications in mass and gas sensing.
Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions
Directory of Open Access Journals (Sweden)
Armando Martínez-Pérez
2017-10-01
Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.
Moving magnets in a micromagnetic finite-difference framework
Rissanen, Ilari; Laurson, Lasse
2018-05-01
We present a method and an implementation for smooth linear motion in a finite-difference-based micromagnetic simulation code, to be used in simulating magnetic friction and other phenomena involving moving microscale magnets. Our aim is to accurately simulate the magnetization dynamics and relative motion of magnets while retaining high computational speed. To this end, we combine techniques for fast scalar potential calculation and cubic b-spline interpolation, parallelizing them on a graphics processing unit (GPU). The implementation also includes the possibility of explicitly simulating eddy currents in the case of conducting magnets. We test our implementation by providing numerical examples of stick-slip motion of thin films pulled by a spring and the effect of eddy currents on the switching time of magnetic nanocubes.
Generating higher-order Lie algebras by expanding Maurer-Cartan forms
International Nuclear Information System (INIS)
Caroca, R.; Merino, N.; Salgado, P.; Perez, A.
2009-01-01
By means of a generalization of the Maurer-Cartan expansion method, we construct a procedure to obtain expanded higher-order Lie algebras. The expanded higher-order Maurer-Cartan equations for the case G=V 0 +V 1 are found. A dual formulation for the S-expansion multialgebra procedure is also considered. The expanded higher-order Maurer-Cartan equations are recovered from S-expansion formalism by choosing a special semigroup. This dual method could be useful in finding a generalization to the case of a generalized free differential algebra, which may be relevant for physical applications in, e.g., higher-spin gauge theories.
Interactions, strings and isotopies in higher order anisotropic superspaces
Vacaru, Sergiu Ion
2001-01-01
The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogeneity. The approach proceeds by developing the concept of higher order anisotropic (super)space which unifies the logical and manthematical aspects of modern Kaluza--Klein theories and generalized Lagrange and Finsler geometry and leads to modeling of physical processes on higher order fiber (super)bundles provided with nonlinear and distinguished connections and metric structures. This book can be also considered as a pedagogical survey on the mentioned subjects.
Higher-order modulation instability in nonlinear fiber optics.
Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry
2011-12-16
We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society
Higher Order Lagrange Finite Elements In M3D
International Nuclear Information System (INIS)
Chen, J.; Strauss, H.R.; Jardin, S.C.; Park, W.; Sugiyama, L.E.; Fu, G.; Breslau, J.
2004-01-01
The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles
Higher order energy transfer. Quantum electrodynamical calculations and graphical representation
International Nuclear Information System (INIS)
Jenkins, R.D.
2000-01-01
In Chapter 1, a novel method of calculating quantum electrodynamic amplitudes is formulated using combinatorial theory. This technique is used throughout instead of conventional time-ordered methods. A variety of hyperspaces are discussed to highlight isomorphism between a number of A generalisation of Pascal's triangle is shown to be beneficial in determining the form of hyperspace graphs. Chapter 2 describes laser assisted resonance energy transfer (LARET), a higher order perturbative contribution to the well-known process resonance energy transfer, accommodating an off resonance auxiliary laser field to stimulate the migration. Interest focuses on energy exchanges between two uncorrelated molecular species, as in a system where molecules are randomly oriented. Both phase-weighted and standard isotropic averaging are required for the calculations. Results are discussed in terms of a laser intensity-dependent mechanism. Identifying the applied field regime where LARET should prove experimentally significant, transfer rate increases of up to 30% are predicted. General results for three-center energy transfer are elucidated in chapter 3. Cooperative and accretive mechanistic pathways are identified with theory formulated to elicit their role in a variety of energy transfer phenomena and their relative dominance. In multichromophoric the interplay of such factors is analysed with regard to molecular architectures. The alignments and magnitudes of donor and acceptor transition moments and polarisabilities prove to have profound effects on achievable pooling efficiency for linear configurations. Also optimum configurations are offered. In ionic lattices, although both mechanisms play significant roles in pooling and cutting processes, only the accretive is responsible for sensitisation. The local, microscopic level results are used to gauge the lattice response, encompassing concentration and structural effects. (author)
The Cauchy problem for higher order abstract differential equations
Xiao, Ti-Jun
1998-01-01
This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.
Connection between weighted LPC and higher-order statistics for AR model estimation
Kamp, Y.; Ma, C.
1993-01-01
This paper establishes the relationship between a weighted linear prediction method used for robust analysis of voiced speech and the autoregressive modelling based on higher-order statistics, known as cumulants
Deformation from symmetry for Schrodinger equations of higher order on unbounded domains
Directory of Open Access Journals (Sweden)
Addolorata Salvatore
2003-06-01
Full Text Available By means of a perturbation method recently introduced by Bolle, we discuss the existence of infinitely many solutions for a class of perturbed symmetric higher order Schrodinger equations with non-homogeneous boundary data on unbounded domains.
Exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres
International Nuclear Information System (INIS)
Liu Chunping
2005-01-01
First, by using the generally projective Riccati equation method, many kinds of exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres are obtained in a unified way. Then, some relations among these solutions are revealed
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2007-01-01
The problem of electromagnetic scattering by composite metallic and dielectric objects is solved using the coupled volume-surface integral equation (VSIE). The method of moments (MoM) based on higher-order hierarchical Legendre basis functions and higher-order curvilinear geometrical elements...... with the analytical Mie series solution. Scattering by more complex metal-dielectric objects are also considered to compare the presented technique with other numerical methods....
The Role of Formative Feedback in Promoting Higher Order ...
African Journals Online (AJOL)
DrNneka
An International Multi-disciplinary Journal, Ethiopia. AFRREV ... make contribution to this research gap by proposing a theoretical feedback model that can promote higher order thinking skills in the classroom. The proposed ..... process; students provided with tasks that are novel, complex, creative, and non- algorithmic ...
Developing Higher-Order Thinking Skills through WebQuests
Polly, Drew; Ausband, Leigh
2009-01-01
In this study, 32 teachers participated in a year-long professional development project related to technology integration in which they designed and implemented a WebQuest. This paper describes the extent to which higher-order thinking skills (HOTS) and levels of technology implementation (LoTI) occur in the WebQuests that participants designed.…
First Measurements of Higher Order Optics Parameters in the LHC
Vanbavinckhove, G; Bartolini, R; Calaga, R; Giovannozzi, M; Maclean, E H; Miyamoto, R; Schmidt, F; Tomas, R
2011-01-01
Higher order effects can play an important role in the performance of the LHC. Lack of knowledge of these pa- rameters can increase the tune footprint and compromise the beam lifetime. First measurements of these parameters at injection and flattop have been conducted. Detailed sim- ulations are compared to the measurements together with discussions on the measurement limitations.
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.
2013-01-01
on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time
Meta-Logical Reasoning in Higher-Order Logic
DEFF Research Database (Denmark)
Villadsen, Jørgen; Schlichtkrull, Anders; Hess, Andreas Viktor
The semantics of first-order logic (FOL) can be described in the meta-language of higher-order logic (HOL). Using HOL one can prove key properties of FOL such as soundness and completeness. Furthermore, one can prove sentences in FOL valid using the formalized FOL semantics. To aid...
Decidable Fragments of a Higher Order Calculus with Locations
DEFF Research Database (Denmark)
Bundgaard, Mikkel; Godskesen, Jens Christian; Huttel, Hans
2009-01-01
Homer is a higher order process calculus with locations. In this paper we study Homer in the setting of the semantic finite control property, which is a finite reachability criterion that implies decidability of barbed bisimilarity. We show that strong and weak barbed bisimilarity are undecidable...
Computer-Mediated Assessment of Higher-Order Thinking Development
Tilchin, Oleg; Raiyn, Jamal
2015-01-01
Solving complicated problems in a contemporary knowledge-based society requires higher-order thinking (HOT). The most productive way to encourage development of HOT in students is through use of the Problem-based Learning (PBL) model. This model organizes learning by solving corresponding problems relative to study courses. Students are directed…
Higher-order chaotic oscillator using active bessel filter
DEFF Research Database (Denmark)
Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra
2010-01-01
A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...
Constrained variational calculus for higher order classical field theories
Energy Technology Data Exchange (ETDEWEB)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)
2010-11-12
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Constrained variational calculus for higher order classical field theories
International Nuclear Information System (INIS)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn
2010-01-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Higher-Order Separation Logic in Isabelle/HOLCF
DEFF Research Database (Denmark)
Varming, Carsten; Birkedal, Lars
2008-01-01
We formalize higher-order separation logic for a first-order imperative language with procedures and local variables in Isabelle/HOLCF. The assertion language is modeled in such a way that one may use any theory defined in Isabelle/HOLCF to construct assertions, e.g., primitive recursion, least o...
Order-sorted Algebraic Specifications with Higher-order Functions
DEFF Research Database (Denmark)
Haxthausen, Anne Elisabeth
1995-01-01
This paper gives a proposal for how order-sorted algebraic specification languages can be extended with higher-order functions. The approach taken is a generalisation to the order-sorted case of an approach given by Mller, Tarlecki and Wirsing for the many-sorted case. The main idea in the proposal...
Enhancing Higher Order Thinking Skills through Clinical Simulation
Varutharaju, Elengovan; Ratnavadivel, Nagendralingan
2014-01-01
Purpose: The study aimed to explore, describe and analyse the design and implementation of clinical simulation as a pedagogical tool in bridging the deficiency of higher order thinking skills among para-medical students, and to make recommendations on incorporating clinical simulation as a pedagogical tool to enhance thinking skills and align the…
Analysis of Scattering by Inhomogeneous Dielectric Objects Using Higher-Order Hierarchical MoM
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter
2003-01-01
An efficient technique for the analysis of electromagnetic scattering by arbitrary shaped inhomogeneous dielectric objects is presented. The technique is based on a higher-order method of moments (MoM) solution of the volume integral equation. This higher-order MoM solution comprises recently...... that the condition number of the resulting MoM matrix is reduced by several orders of magnitude in comparison to existing higher-order hierarchical basis functions and, consequently, an iterative solver can be applied even for high expansion orders. Numerical results demonstrate excellent agreement...
Higher order QCD corrections in small x physics
International Nuclear Information System (INIS)
Chachamis, G.
2006-11-01
We study higher order QCD corrections in small x Physics. The numerical implementation of the full NLO photon impact factor is the remaining necessary piece for the testing of the NLO BFKL resummation against data from physical processes, such as γ * γ * collisions. We perform the numerical integration over phase space for the virtual corrections to the NLO photon impact factor. This, along with the previously calculated real corrections, makes feasible in the near future first estimates for the γ*γ* total cross section, since the convolution of the full impact factor with the NLO BFKL gluon Green's function is now straightforward. The NLO corrections for the photon impact factor are sizeable and negative. In the second part of this thesis, we estimate higher order correction to the BK equation. We are mainly interested in whether partonic saturation delays or not in rapidity when going beyond the leading order. In our investigation, we use the so called 'rapidity veto' which forbid two emissions to be very close in rapidity, to 'switch on' higher order corrections to the BK equation. From analytic and numerical analysis, we conclude that indeed saturation does delay in rapidity when higher order corrections are taken into account. In the last part, we investigate higher order QCD corrections as additional corrections to the Electroweak (EW) sector. The question of whether BFKL corrections are of any importance in the Regge limit for the EW sector seems natural; although they arise in higher loop level, the accumulation of logarithms in energy s at high energies, cannot be dismissed without an investigation. We focus on the process γγ→ZZ. We calculate the pQCD corrections in the forward region at leading logarithmic (LL) BFKL accuracy, which are of the order of few percent at the TeV energy scale. (orig.)
Higher order QCD corrections in small x physics
Energy Technology Data Exchange (ETDEWEB)
Chachamis, G.
2006-11-15
We study higher order QCD corrections in small x Physics. The numerical implementation of the full NLO photon impact factor is the remaining necessary piece for the testing of the NLO BFKL resummation against data from physical processes, such as {gamma}{sup *}{gamma}{sup *} collisions. We perform the numerical integration over phase space for the virtual corrections to the NLO photon impact factor. This, along with the previously calculated real corrections, makes feasible in the near future first estimates for the {gamma}*{gamma}* total cross section, since the convolution of the full impact factor with the NLO BFKL gluon Green's function is now straightforward. The NLO corrections for the photon impact factor are sizeable and negative. In the second part of this thesis, we estimate higher order correction to the BK equation. We are mainly interested in whether partonic saturation delays or not in rapidity when going beyond the leading order. In our investigation, we use the so called 'rapidity veto' which forbid two emissions to be very close in rapidity, to 'switch on' higher order corrections to the BK equation. From analytic and numerical analysis, we conclude that indeed saturation does delay in rapidity when higher order corrections are taken into account. In the last part, we investigate higher order QCD corrections as additional corrections to the Electroweak (EW) sector. The question of whether BFKL corrections are of any importance in the Regge limit for the EW sector seems natural; although they arise in higher loop level, the accumulation of logarithms in energy s at high energies, cannot be dismissed without an investigation. We focus on the process {gamma}{gamma}{yields}ZZ. We calculate the pQCD corrections in the forward region at leading logarithmic (LL) BFKL accuracy, which are of the order of few percent at the TeV energy scale. (orig.)
Finite difference computing with exponential decay models
Langtangen, Hans Petter
2016-01-01
This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular. .
Finite-difference schemes for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: es@cwi.nl [Centrum Wiskunde and Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands)
2014-09-01
In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.
Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order
Directory of Open Access Journals (Sweden)
Taher S. Hassan
2016-01-01
Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t, i=1,…,n-1, with x0=x, ϕβ(u≔uβsgnu, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.
Higher order mode damping in Kaon factory RF cavities
International Nuclear Information System (INIS)
Enegren, T.; Poirier, R.; Griffin, J.; Walling, L.; Thiessen, H.A.; Smythe, W.R.
1989-05-01
Proposed designs for Kaon factory accelerators require that the rf cavities support beam currents on the order of several amperes. The beam current has Fourier components at all multiples of the rf frequency. Empty rf buckets produce additional components at all multiples of the revolution frequency. If a Fourier component of the beam coincides with the resonant frequency of a higher order mode of the cavity, which is inevitable if the cavity has a large frequency swing, significant excitation of this mode can occur. The induced voltage may then excite coupled bunch mode instabilities. Effective means are required to damp higher order modes without significantly affecting the fundamental mode. A mode damping scheme based on coupled transmission lines has been investigated and is report
Higher Order Differential Attack on 6-Round MISTY1
Tsunoo, Yukiyasu; Saito, Teruo; Nakashima, Hiroki; Shigeri, Maki
MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper reports a previously unknown higher order differential characteristic of 4-round MISTY1 with the FL functions. It also shows that a higher order differential attack that utilizes this newly discovered characteristic is successful against 6-round MISTY1 with the FL functions. This attack can recover a partial subkey with a data complexity of 253.7 and a computational complexity of 264.4, which is better than any previous cryptanalysis of MISTY1.
Higher-order risk preferences in social settings.
Heinrich, Timo; Mayrhofer, Thomas
2018-01-01
We study prudence and temperance (next to risk aversion) in social settings. Previous experimental studies have shown that these higher-order risk preferences affect the choices of individuals deciding privately on lotteries that only affect their own payoff. Yet, many risky and financially relevant decisions are made in the social settings of households or organizations. We elicit higher-order risk preferences of individuals and systematically vary how an individual's decision is made (alone or while communicating with a partner) and who is affected by the decision (only the individual or the partner as well). In doing so, we can isolate the effects of other-regarding concerns and communication on choices. Our results reveal that the majority of choices are risk averse, prudent, and temperate across social settings. We also observe that individuals are influenced significantly by the preferences of a partner when they are able to communicate and choices are payoff-relevant for both of them.
An Algorithm for Higher Order Hopf Normal Forms
Directory of Open Access Journals (Sweden)
A.Y.T. Leung
1995-01-01
Full Text Available Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit. However, the computation of high-order normal forms is usually quite complicated. This article provides an explicit formula for the normalization of nonlinear differential equations. The higher order normal form is given explicitly. Illustrative examples include a cubic system, a quadratic system and a Duffing–Van der Pol system. We use exact arithmetic and find that the undamped Duffing equation can be represented by an exact polynomial differential amplitude equation in a finite number of terms.
Practical Programming with Higher-Order Encodings and Dependent Types
DEFF Research Database (Denmark)
Poswolsky, Adam; Schürmann, Carsten
2008-01-01
, tedious, and error-prone. In this paper, we describe the underlying calculus of Delphin. Delphin is a fully implemented functional-programming language supporting reasoning over higher-order encodings and dependent types, while maintaining the benefits of HOAS. More specifically, just as representations...... for instantiation from those that will remain uninstantiated, utilizing a variation of Miller and Tiu’s ∇-quantifier [1]....
Modeling Human Behaviour with Higher Order Logic: Insider Threats
DEFF Research Database (Denmark)
Boender, Jaap; Ivanova, Marieta Georgieva; Kammuller, Florian
2014-01-01
it to the sociological process of logical explanation. As a case study on modeling human behaviour, we present the modeling and analysis of insider threats as a Higher Order Logic theory in Isabelle/HOL. We show how each of the three step process of sociological explanation can be seen in our modeling of insider’s state......, its context within an organisation and the effects on security as outcomes of a theorem proving analysis....
Higher order Bose-Einstein correlations in identical particle production
International Nuclear Information System (INIS)
Biyajima, M.
1990-01-01
A diagram technique to calculate the higher order Bose-Einstein correlations is formulated. This technique is applied to derive explicit expressions for the n-pion correlation functions for n = 2, 3, 4, and 5, and numerical predictions are given. In a comparison with the AFS and NA23 data on two-pion and three-pion Bose-Einstein correlations good agreement is obtained. 21 refs., 5 figs. (Authors)
Dynamics and phenomenology of higher order gravity cosmological models
Moldenhauer, Jacob Andrew
2010-10-01
I present here some new results about a systematic approach to higher-order gravity (HOG) cosmological models. The HOG models are derived from curvature invariants that are more general than the Einstein-Hilbert action. Some of the models exhibit late-time cosmic acceleration without the need for dark energy and fit some current observations. The open question is that there are an infinite number of invariants that one could select, and many of the published papers have stressed the need to find a systematic approach that will allow one to study methodically the various possibilities. We explore a new connection that we made between theorems from the theory of invariants in general relativity and these cosmological models. In summary, the theorems demonstrate that curvature invariants are not all independent from each other and that for a given Ricci Segre type and Petrov type (symmetry classification) of the space-time, there exists a complete minimal set of independent invariants (a basis) in terms of which all the other invariants can be expressed. As an immediate consequence of the proposed approach, the number of invariants to consider is dramatically reduced from infinity to four invariants in the worst case and to only two invariants in the cases of interest, including all Friedmann-Lemaitre-Robertson-Walker metrics. We derive models that pass stability and physical acceptability conditions. We derive dynamical equations and phase portrait analyses that show the promise of the systematic approach. We consider observational constraints from magnitude-redshift Supernovae Type Ia data, distance to the last scattering surface of the Cosmic Microwave Background radiation, and Baryon Acoustic Oscillations. We put observational constraints on general HOG models. We constrain different forms of the Gauss-Bonnet, f(G), modified gravity models with these observations. We show some of these models pass solar system tests. We seek to find models that pass physical and
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar; Salama, Amgad; Sun, Shuyu; Bao, Kai
2012-01-01
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
Modeling seismic wave propagation using staggered-grid mimetic finite differences
Directory of Open Access Journals (Sweden)
Freysimar Solano-Feo
2017-04-01
Full Text Available Mimetic finite difference (MFD approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP. In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite difference method.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar
2012-06-17
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
Higher-order Brunnian structures and possible physical realizations
DEFF Research Database (Denmark)
A. Baas, Nils; V. Fedorov, D.; S. Jensen, A.
2014-01-01
We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied...... to the binding of systems in nature. It now appears that recent generalization to higher order Brunnian structures may potentially be realized as laboratory made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms...
Development of higher order mode couplers at Cornell
International Nuclear Information System (INIS)
Amato, J.C.
1988-01-01
Higher order mode (HOM) couplers are integral parts of a superconducting accelerator cavity. The damping which the couplers must provide is dictated by the frequency and shunt impedance of the cavity modes as well as by the stability requirements of the accelerator incorporating the cavities. Cornell's 5-cell 1500 MHz elliptical cavity was designed for use in a 50 x 50 GeV electron-positron storage ring with a total beam current of 3.5 mA (CESR-II). HOM couplers for the Cornell cavity were designed and evaluated with this machine in mind. The development of these couplers is described in this paper. 8 references, 8 figures
Theory of a higher-order Sturm-Liouville equation
Kozlov, Vladimir
1997-01-01
This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.
Integrable higher order deformations of Heisenberg supermagnetic model
International Nuclear Information System (INIS)
Guo Jiafeng; Yan Zhaowen; Wang Shikun; Wu Ke; Zhao Weizhong
2009-01-01
The Heisenberg supermagnet model is an integrable supersymmetric system and has a close relationship with the strong electron correlated Hubbard model. In this paper, we investigate the integrable higher order deformations of Heisenberg supermagnet models with two different constraints: (i) S 2 =3S-2I for S is an element of USPL(2/1)/S(U(2)xU(1)) and (ii) S 2 =S for S is an element of USPL(2/1)/S(L(1/1)xU(1)). In terms of the gauge transformation, their corresponding gauge equivalent counterparts are derived.
Oscillation of solutions of some higher order linear differential equations
Directory of Open Access Journals (Sweden)
Hong-Yan Xu
2009-11-01
Full Text Available In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k}+B_{k-1}f^{(k-1}+\\cdots+B_1f'+B_0f=F$$ where $B_j(z (j=0,1,\\ldots,k-1$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li.
Squeezing of higher order Hermite-Gauss modes
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard
2008-01-01
The present paper gives an overview of the experimental generation of squeezing in higher order Hermite-Gaussian modes with an optical parametric ampli¯er (OPA). This work was awarded with The European Optical Society (EOS) price 2007. The purpose of the prize is to encourage a European dimension...... in research in pure and applied optics. The EOS prize is awarded based on the selection criteria of high professionalism, academic and technical quality. Following the EOS Prize rules, the conditions for eligibility are that the work was performed in Europe and that it is published under the auspices...
Higher-order dynamical effects in Coulomb dissociation
International Nuclear Information System (INIS)
Esbensen, H.
1994-06-01
We study the effect of higher-order processes in Coulomb dissociation of 11 Li by numerically solving the three-dimensional time-dependent Schroedinger equation for the relative motion of a di-neutron and the 9 Li core. Comparisons are made to first-order perturbation theory and to measurements. The calculated Coulomb reacceleration effects improve the agreement with experiment, but some discrepancy remains. The effects are much smaller in the dissociation of 11 Be, and they decrease with increasing beam energy. (orig.)
Inseparability inequalities for higher order moments for bipartite systems
International Nuclear Information System (INIS)
Agarwal, G S; Biswas, Asoka
2005-01-01
There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second-order moments are insufficient. We derive new inequalities involving higher order correlation, for testing entanglement in non-Gaussian states. In this context, we study an example of a non-Gaussian state, which is a bipartite entangled state of the form Ψ(x a , x b ) ∝ (αx a + βx b ) e -(x a 2 +x b 2 )/2 . Our results open up an avenue to search for new inequalities to test entanglement in non-Gaussian states
Higher-order thinking in foreign language learning
Bastos, Ascensão; Ramos, Altina
2017-01-01
A project is being conducted in English as a foreign language (EFL), involving eleventh graders in formal and non-formal learning contexts, in a Portuguese high school. The goal of this study is to examine the impact of cognitive tools and higher-order thinking processes on the learning of EFL and achievement of larger processes oriented to action, involving problem solving, decision-making and creation of new products. YouTube videos emerge as cognitive tools in the process. Final results sh...
Finite-difference time-domain analysis of time-resolved terahertz spectroscopy experiments
DEFF Research Database (Denmark)
Larsen, Casper; Cooke, David G.; Jepsen, Peter Uhd
2011-01-01
In this paper we report on the numerical analysis of a time-resolved terahertz (THz) spectroscopy experiment using a modified finite-difference time-domain method. Using this method, we show that ultrafast carrier dynamics can be extracted with a time resolution smaller than the duration of the T...
A coupled boundary element-finite difference solution of the elliptic modified mild slope equation
DEFF Research Database (Denmark)
Naserizadeh, R.; Bingham, Harry B.; Noorzad, A.
2011-01-01
The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain...
Application of Higher-Order Cumulant in Fault Diagnosis of Rolling Bearing
International Nuclear Information System (INIS)
Shen, Yongjun; Yang, Shaopu; Wang, Junfeng
2013-01-01
In this paper a new method of pattern recognition based on higher-order cumulant and envelope analysis is presented. The core of this new method is to construct analytical signals from the given signals and obtain the envelope signals firstly, then compute and compare the higher-order cumulants of the envelope signals. The higher-order cumulants could be used as a characteristic quantity to distinguish these given signals. As an example, this method is applied in fault diagnosis for 197726 rolling bearing of freight locomotive. The comparisons of the second-order, third-order and fourth-order cumulants of the envelope signals from different vibration signals of rolling bearing show this new method could discriminate the normal and two fault signals distinctly
Higher-Order Cyclostationarity Detection for Spectrum Sensing
Directory of Open Access Journals (Sweden)
Julien Renard
2010-01-01
Full Text Available Recent years have shown a growing interest in the concept of Cognitive Radios (CRs, able to access portions of the electromagnetic spectrum in an opportunistic operating way. Such systems require efficient detectors able to work in low Signal-to-Noise Ratio (SNR environments, with little or no information about the signals they are trying to detect. Energy detectors are widely used to perform such blind detection tasks, but quickly reach the so-called SNR wall below which detection becomes impossible Tandra (2005. Cyclostationarity detectors are an interesting alternative to energy detectors, as they exploit hidden periodicities present in man-made signals, but absent in noise. Such detectors use quadratic transformations of the signals to extract the hidden sine-waves. While most of the literature focuses on the second-order transformations of the signals, we investigate the potential of higher-order transformations of the signals. Using the theory of Higher-Order Cyclostationarity (HOCS, we derive a fourth-order detector that performs similarly to the second-order ones to detect linearly modulated signals, at SNR around 0 dB, which may be used if the signals of interest do not exhibit second-order cyclostationarity. More generally this paper reviews the relevant aspects of the cyclostationary and HOCS theory, and shows their potential for spectrum sensing.
Formulation of coarse mesh finite difference to calculate mathematical adjoint flux
International Nuclear Information System (INIS)
Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2002-01-01
The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)
Energy Technology Data Exchange (ETDEWEB)
Martinez-Conesa, E.J.; Estrems, M.; Miguel, V.
2010-07-01
This work develops a finite difference method to evaluate the temperature field in the heat affected zone in butt welding applied to AISI 304 stainless steel thin sheet by GTAW process. A computer program has been developed and implemented by Visual Basic for Applications (VBA) in MS-Excel spreadsheet. The results that are obtained using the numerical application foresee the thermal behaviour of arc welding processes. An experimental methodology has been developed to validate the mathematical model that allows to measure the temperature in several points close to the weld bead. The methodology is applied to a stainless steel sheet with a thickness lower than 3 mm, although may be used for other steels and welding processes as MIG/MAG and SMAW. The data which has been obtained from the experimental procedure have been used to validate the results that have been calculated by the finite differences numerical method. The mathematical model adjustment has been carried out taking into account the experimental results. The differences found between the experimental and theoretical approaches are due to the convection and radiation heat losses, which have not been considered in the simulation model.With this simple model, the designer will be able to calculate the thermal cycles that take place in the process as well as to predict the temperature field in the proximity of the weld bead. (Author). 18 refs.
On the spectral properties of random finite difference operators
International Nuclear Information System (INIS)
Kunz, H.; Souillard, B.
1980-01-01
We study a class of random finite difference operators, a typical example of which is the finite difference Schroedinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schroedinger operator with a random potential has pure point spectrum and developps no static conductivity. (orig.)
Influence of higher order modes on angled-facet amplifiers
DEFF Research Database (Denmark)
Wang, Z.; Mikkelsen, B.; Stubkjær, Kristian
1991-01-01
The influence of the first-order mode on the residual reflectivity of angled-facet amplifiers is analyzed. For a 7 degrees angled-facet ridge waveguide amplifier with a single-layer antireflective (AR) coating, a gain ripple lower than 1-dB at 25-dB gain can be obtained independent...... of the polarization, even in the presence of a first-order mode with a 15-dB gain. The tolerances for the thickness and refractive index of the AR coating are reduced by a factor of three compared to operation in the fundamental mode only. The influence of the higher order mode can virtually be suppressed...
Neutron scattering studies on chromatin higher-order structure
Energy Technology Data Exchange (ETDEWEB)
Graziano, V.; Gerchman, S.E.; Schneider, D.K.; Ramakrishnan, V. [Brookhaven National Laboratory, Upton, NY (United States)
1994-12-31
We have been engaged in studies of the structure and condensation of chromatin into the 30nm filament using small-angle neutron scattering. We have also used deuterated histone H1 to determine its location in the chromatin 30nm filament. Our studies indicate that chromatin condenses with increasing ionic strength to a limiting structure that has a mass per unit length of 6-7 nucleosomes/11 nm. They also show that the linker histone H1/H5 is located in the interior of the chromatin filament, in a position compatible with its binding to the inner face of the nucleosome. Analysis of the mass per unit length as a function of H5 stoichiometry suggests that 5-7 contiguous nucleosomes need to have H5 bound before a stable higher order structure can exist.
Minimization of heat slab nodes with higher order boundary conditions
International Nuclear Information System (INIS)
Solbrig, C.W.
1992-01-01
The accuracy of a numerical solution can be limited by the numerical approximation to the boundary conditions rather than the accuracy of the equations which describe the interior. The study presented in this paper compares the results from two different numerical formulations of the convective boundary condition on the face of a heat transfer slab. The standard representation of the boundary condition in a test problem yielded an unacceptable error even when the heat transfer slab was partitioned into over 300 nodes. A higher order boundary condition representation was obtained by using a second order approximation for the first derivative at the boundary and combining it with the general equation used for inner nodes. This latter formulation produced reasonable results when as few as ten nodes were used
MHD stability analysis using higher order spline functions
Energy Technology Data Exchange (ETDEWEB)
Ida, Akihiro [Department of Energy Engineering and Science, Graduate School of Engineering, Nagoya University, Nagoya, Aichi (Japan); Todoroki, Jiro; Sanuki, Heiji
1999-04-01
The eigenvalue problem of the linearized magnetohydrodynamic (MHD) equation is formulated by using higher order spline functions as the base functions of Ritz-Galerkin approximation. When the displacement vector normal to the magnetic surface (in the magnetic surface) is interpolated by B-spline functions of degree p{sub 1} (degree p{sub 2}), which is continuously c{sub 1}-th (c{sub 2}-th) differentiable on neighboring finite elements, the sufficient conditions for the good approximation is given by p{sub 1}{>=}p{sub 2}+1, c{sub 1}{<=}c{sub 2}+1, (c{sub 1}{>=}1, p{sub 2}{>=}c{sub 2}{>=}0). The influence of the numerical integration upon the convergence of calculated eigenvalues is discussed. (author)
Higher-order momentum distributions and locally affine LDDMM registration
DEFF Research Database (Denmark)
Sommer, Stefan Horst; Nielsen, Mads; Darkner, Sune
2013-01-01
description of affine transformations and subsequent compact description of non-translational movement in a globally nonrigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction......To achieve sparse parametrizations that allow intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper...... higher-order momentum distributions in the large deformation diffeomorphic metric mapping (LDDMM) registration framework. While the zeroth-order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local...
Higher order corrections to asymptotic-de Sitter inflation
Mohsenzadeh, M.; Yusofi, E.
2017-08-01
Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of c, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.
Neutron scattering studies on chromatin higher-order structure
International Nuclear Information System (INIS)
Graziano, V.; Gerchman, S.E.; Schneider, D.K.; Ramakrishnan, V.
1994-01-01
We have been engaged in studies of the structure and condensation of chromatin into the 30nm filament using small-angle neutron scattering. We have also used deuterated histone H1 to determine its location in the chromatin 30nm filament. Our studies indicate that chromatin condenses with increasing ionic strength to a limiting structure that has a mass per unit length of 6-7 nucleosomes/11 nm. They also show that the linker histone H1/H5 is located in the interior of the chromatin filament, in a position compatible with its binding to the inner face of the nucleosome. Analysis of the mass per unit length as a function of H5 stoichiometry suggests that 5-7 contiguous nucleosomes need to have H5 bound before a stable higher order structure can exist
Higher order statistical moment application for solar PV potential analysis
Basri, Mohd Juhari Mat; Abdullah, Samizee; Azrulhisham, Engku Ahmad; Harun, Khairulezuan
2016-10-01
Solar photovoltaic energy could be as alternative energy to fossil fuel, which is depleting and posing a global warming problem. However, this renewable energy is so variable and intermittent to be relied on. Therefore the knowledge of energy potential is very important for any site to build this solar photovoltaic power generation system. Here, the application of higher order statistical moment model is being analyzed using data collected from 5MW grid-connected photovoltaic system. Due to the dynamic changes of skewness and kurtosis of AC power and solar irradiance distributions of the solar farm, Pearson system where the probability distribution is calculated by matching their theoretical moments with that of the empirical moments of a distribution could be suitable for this purpose. On the advantage of the Pearson system in MATLAB, a software programming has been developed to help in data processing for distribution fitting and potential analysis for future projection of amount of AC power and solar irradiance availability.
Recognition of higher order patterns in proteins: immunologic kernels.
Directory of Open Access Journals (Sweden)
Robert D Bremel
Full Text Available By applying analysis of the principal components of amino acid physical properties we predicted cathepsin cleavage sites, MHC binding affinity, and probability of B-cell epitope binding of peptides in tetanus toxin and in ten diverse additional proteins. Cross-correlation of these metrics, for peptides of all possible amino acid index positions, each evaluated in the context of a ±25 amino acid flanking region, indicated that there is a strongly repetitive pattern of short peptides of approximately thirty amino acids each bounded by cathepsin cleavage sites and each comprising B-cell linear epitopes, MHC-I and MHC-II binding peptides. Such "immunologic kernel" peptides comprise all signals necessary for adaptive immunologic cognition, response and recall. The patterns described indicate a higher order spatial integration that forms a symbolic logic coordinating the adaptive immune system.
Higher-order phase transitions on financial markets
Kasprzak, A.; Kutner, R.; Perelló, J.; Masoliver, J.
2010-08-01
Statistical and thermodynamic properties of the anomalous multifractal structure of random interevent (or intertransaction) times were thoroughly studied by using the extended continuous-time random walk (CTRW) formalism of Montroll, Weiss, Scher, and Lax. Although this formalism is quite general (and can be applied to any interhuman communication with nontrivial priority), we consider it in the context of a financial market where heterogeneous agent activities can occur within a wide spectrum of time scales. As the main general consequence, we found (by additionally using the Saddle-Point Approximation) the scaling or power-dependent form of the partition function, Z(q'). It diverges for any negative scaling powers q' (which justifies the name anomalous) while for positive ones it shows the scaling with the general exponent τ(q'). This exponent is the nonanalytic (singular) or noninteger power of q', which is one of the pilar of higher-order phase transitions. In definition of the partition function we used the pausing-time distribution (PTD) as the central one, which takes the form of convolution (or superstatistics used, e.g. for describing turbulence as well as the financial market). Its integral kernel is given by the stretched exponential distribution (often used in disordered systems). This kernel extends both the exponential distribution assumed in the original version of the CTRW formalism (for description of the transient photocurrent measured in amorphous glassy material) as well as the Gaussian one sometimes used in this context (e.g. for diffusion of hydrogen in amorphous metals or for aging effects in glasses). Our most important finding is the third- and higher-order phase transitions, which can be roughly interpreted as transitions between the phase where high frequency trading is most visible and the phase defined by low frequency trading. The specific order of the phase transition directly depends upon the shape exponent α defining the stretched
Higher-order conditioning is impaired by hippocampal lesions.
Gilboa, Asaf; Sekeres, Melanie; Moscovitch, Morris; Winocur, Gordon
2014-09-22
Behavior in the real world is rarely motivated by primary conditioned stimuli that have been directly associated with potent unconditioned reinforcers. Instead, motivation and choice behavior are driven by complex chains of higher-order associations that are only indirectly linked to intrinsic reward and often exert their influence outside awareness. Second-order conditioning (SOC) [1] is a basic associative-learning mechanism whereby stimuli acquire motivational salience by proxy, in the absence of primary incentives [2, 3]. Memory-systems theories consider first-order conditioning (FOC) and SOC to be prime examples of hippocampal-independent nondeclarative memory [4, 5]. Accordingly, neurobiological models of SOC focus almost exclusively on nondeclarative neural systems that support motivational salience and reward value. Transfer of value from a conditioned stimulus to a neutral stimulus is thought to require the basolateral amygdala [6, 7] and the ventral striatum [2, 3], but not the hippocampus. We developed a new paradigm to measure appetitive SOC of tones in rats. Hippocampal lesions severely impaired both acquisition and expression of SOC despite normal FOC. Unlike controls, rats with hippocampal lesions could not discriminate between positive and negative secondary conditioned tones, although they exhibited general familiarity with previously presented tones compared with new tones. Importantly, normal rats' behavior, in contrast to that of hippocampal groups, also revealed different confidence levels as indexed by effort, a central characteristic of hippocampal relational memory. The results indicate, contrary to current systems models, that representations of intrinsic relationships between reward value, stimulus identity, and motivation require hippocampal mediation when these relationships are of a higher order. Copyright © 2014 Elsevier Ltd. All rights reserved.
A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation
Diosady, Laslo T.; Murman, Scott M.
2018-01-01
A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.
Detailed balance principle and finite-difference stochastic equation in a field theory
International Nuclear Information System (INIS)
Kozhamkulov, T.A.
1986-01-01
A finite-difference equation, which is a generalization of the Langevin equation in field theory, has been obtained basing upon the principle of detailed balance for the Markov chain. Advantages of the present approach as compared with the conventional Parisi-Wu method are shown for examples of an exactly solvable problem of zero-dimensional quantum theory and a simple numerical simulation
Principle of detailed balance and the finite-difference stochastic equation in field theory
International Nuclear Information System (INIS)
Kozhamkulov, T.A.
1986-01-01
The principle of detailed balance for the Markov chain is used to obtain a finite-difference equation which generalizes the Langevin equation in field theory. The advantages of using this approach compared to the conventional Parisi-Wu method are demonstrated for the examples of an exactly solvable problem in zero-dimensional quantum theory and a simple numerical simulation
A parallel adaptive finite difference algorithm for petroleum reservoir simulation
Energy Technology Data Exchange (ETDEWEB)
Hoang, Hai Minh
2005-07-01
Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)
Finite Difference Schemes as Algebraic Correspondences between Layers
Malykh, Mikhail; Sevastianov, Leonid
2018-02-01
For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.
Higher order aberrations in amblyopic children and their role in refractory amblyopia
Directory of Open Access Journals (Sweden)
Arnaldo Dias-Santos
2014-12-01
Full Text Available Objective: Some studies have hypothesized that an unfavourable higher order aberrometric profile could act as an amblyogenic mechanism and may be responsible for some amblyopic cases that are refractory to conventional treatment or cases of “idiopathic” amblyopia. This study compared the aberrometric profile in amblyopic children to that of children with normal visual development and compared the aberrometric profile in corrected amblyopic eyes and refractory amblyopic eyes with that of healthy eyes. Methods: Cross-sectional study with three groups of children – the CA group (22 eyes of 11 children with unilateral corrected amblyopia, the RA group (24 eyes of 13 children with unilateral refractory amblyopia and the C group (28 eyes of 14 children with normal visual development. Higher order aberrations were evaluated using an OPD-Scan III (NIDEK. Comparisons of the aberrometric profile were made between these groups as well as between the amblyopic and healthy eyes within the CA and RA groups. Results: Higher order aberrations with greater impact in visual quality were not significantly higher in the CA and RA groups when compared with the C group. Moreover, there were no statistically significant differences in the higher order aberrometric profile between the amblyopic and healthy eyes within the CA and RA groups. Conclusions: Contrary to lower order aberrations (e.g., myopia, hyperopia, primary astigmatism, higher order aberrations do not seem to be involved in the etiopathogenesis of amblyopia. Therefore, these are likely not the cause of most cases of refractory amblyopia.
Development of a Higher Order Laminate Theory for Modeling Composites with Induced Strain Actuators
Chattopadhyay, Aditi; Seeley, Charles E.
1996-01-01
A refined higher order plate theory is developed to investigate the actuation mechanism of piezoelectric materials surface bonded or embedded in composite laminates. The current analysis uses a displacement field which accurately accounts for transverse shear stresses. Some higher order terms are identified by using the conditions that shear stresses vanish at all free surfaces. Therefore, all boundary conditions for displacements and stresses are satisfied in the present theory. The analysis is implemented using the finite element method which provides a convenient means to construct a numerical solution due to the discrete nature of the actuators. The higher order theory is computationally less expensive than a full three dimensional analysis. The theory is also shown to agree well with published experimental results. Numerical examples are presented for composite plates with thicknesses ranging from thin to very thick.
Impedance Eduction in Large Ducts Containing Higher-Order Modes and Grazing Flow
Watson, Willie R.; Jones, Michael G.
2017-01-01
Impedance eduction test data are acquired in ducts with small and large cross-sectional areas at the NASA Langley Research Center. An improved data acquisition system in the large duct has resulted in increased control of the acoustic energy in source modes and more accurate resolution of higher-order duct modes compared to previous tests. Two impedance eduction methods that take advantage of the improved data acquisition to educe the liner impedance in grazing flow are presented. One method measures the axial propagation constant of a dominant mode in the liner test section (by implementing the Kumarsean and Tufts algorithm) and educes the impedance from an exact analytical expression. The second method solves numerically the convected Helmholtz equation and minimizes an objective function to obtain the liner impedance. The two methods are tested first on data synthesized from an exact mode solution and then on measured data. Results show that when the methods are applied to data acquired in the larger duct with a dominant higher-order mode, the same impedance spectra are educed as that obtained in the small duct where only the plane wave mode propagates. This result holds for each higher-order mode in the large duct provided that the higher-order mode is sufficiently attenuated by the liner.
Higher order BLG supersymmetry transformations from 10-dimensional super Yang Mills
Energy Technology Data Exchange (ETDEWEB)
Hall, John [Alumnus of Physics Department, Imperial College,South Kensington, London, SW7 2AZ (United Kingdom); Low, Andrew [Physics Department, Wimbledon High School,Mansel Road, London, SW19 4AB (United Kingdom)
2014-06-26
We study a Simple Route for constructing the higher order Bagger-Lambert-Gustavsson theory - both supersymmetry transformations and Lagrangian - starting from knowledge of only the 10-dimensional Super Yang Mills Fermion Supersymmetry transformation. We are able to uniquely determine the four-derivative order corrected supersymmetry transformations, to lowest non-trivial order in Fermions, for the most general three-algebra theory. For the special case of Euclidean three-algbera, we reproduce the result presented in arXiv:1207.1208, with significantly less labour. In addition, we apply our method to calculate the quadratic fermion terms in the higher order BLG fermion supersymmetry transformation.
Higher order effects in electroweak theory 1981-12 (KEK)
International Nuclear Information System (INIS)
Aoki, Ken-ichi
1982-01-01
This is a brief report on the higher order or loop effects in electroweak theory. The discussion is based on the Weinberg Salam model and QCD. The loop correction to weak interaction is described. The renormalization conditions were applied to physical parameters, α(QED), M(W) and M(Z). It is expected to obtain experimentally the values of M(W) and M(Z) with the accuracy of 0.1 percent. In this scheme, the parameters were fixed loop by loop. The correction was evaluated along the present on-shell scheme. The general estimation of the order of correction was performed. The evaluation of the size of terms in one-loop correction was made. The examples of one loop analysis are presented. The leading logarithmic correction such as α ln(m 2 q 2 /M 2 ) is discussed. The system was described by H(eff) with the local operator O(i), in which the propagator of heavy particles was contracted. The effective interaction was obtained as C(i) (q 2 ) O(i), where C(i)(q 2 ) satisfies a proper equation of a renormalization group. As the practical examples, μ-decay, charged current and neutral current were studied. The correction to electron neutral current and the shift of M(W) and M(Z) were numerically obtained. Comments on quark mass and the uncertainty of sin 2 (theta) from the νN reaction are presented. (Kato, T.)
Higher-order scalar interactions and SM vacuum stability
Energy Technology Data Exchange (ETDEWEB)
Lalak, Zygmunt; Lewicki, Marek; Olszewski, Paweł [Institute of Theoretical Physics, Faculty of Physics, University of Warsawul. Hoża 69, Warsaw (Poland)
2014-05-26
Investigation of the structure of the Standard Model effective potential at very large field strengths opens a window towards new phenomena and can reveal properties of the UV completion of the SM. The map of the lifetimes of the vacua of the SM enhanced by nonrenormalizable scalar couplings has been compiled to show how new interactions modify stability of the electroweak vacuum. Whereas it is possible to stabilize the SM by adding Planck scale suppressed interactions and taking into account running of the new couplings, the generic effect is shortening the lifetime and hence further destabilisation of the SM electroweak vacuum. These findings have been illustrated with phase diagrams of modified SM-like models. It has been demonstrated that stabilisation can be achieved by lowering the suppression scale of higher order operators while picking up such combinations of new couplings, which do not deepen the new minima of the potential. Our results show the dependence of the lifetime of the electroweak minimum on the magnitude of the new couplings, including cases with very small couplings (which means very large effective suppression scale) and couplings vastly different in magnitude (which corresponds to two different suppression scales)
General relativity and gauge gravity theories of higher order
International Nuclear Information System (INIS)
Konopleva, N.P.
1998-01-01
It is a short review of today's gauge gravity theories and their relations with Einstein General Relativity. The conceptions of construction of the gauge gravity theories with higher derivatives are analyzed. GR is regarded as the gauge gravity theory corresponding to the choice of G ∞4 as the local gauge symmetry group and the symmetrical tensor of rank two g μν as the field variable. Using the mathematical technique, single for all fundamental interactions (namely variational formalism for infinite Lie groups), we can obtain Einstein's theory as the gauge theory without any changes. All other gauge approaches lead to non-Einstein theories of gravity. But above-mentioned mathematical technique permits us to construct the gauge gravity theory of higher order (for instance SO (3,1)-gravity) so that all vacuum solutions of Einstein equations are the solutions of the SO (3,1)-gravity theory. The structure of equations of SO(3,1)-gravity becomes analogous to Weeler-Misner geometrodynamics one
Predicting perceptual learning from higher-order cortical processing.
Wang, Fang; Huang, Jing; Lv, Yaping; Ma, Xiaoli; Yang, Bin; Wang, Encong; Du, Boqi; Li, Wu; Song, Yan
2016-01-01
Visual perceptual learning has been shown to be highly specific to the retinotopic location and attributes of the trained stimulus. Recent psychophysical studies suggest that these specificities, which have been associated with early retinotopic visual cortex, may in fact not be inherent in perceptual learning and could be related to higher-order brain functions. Here we provide direct electrophysiological evidence in support of this proposition. In a series of event-related potential (ERP) experiments, we recorded high-density electroencephalography (EEG) from human adults over the course of learning in a texture discrimination task (TDT). The results consistently showed that the earliest C1 component (68-84ms), known to reflect V1 activity driven by feedforward inputs, was not modulated by learning regardless of whether the behavioral improvement is location specific or not. In contrast, two later posterior ERP components (posterior P1 and P160-350) over the occipital cortex and one anterior ERP component (anterior P160-350) over the prefrontal cortex were progressively modified day by day. Moreover, the change of the anterior component was closely correlated with improved behavioral performance on a daily basis. Consistent with recent psychophysical and imaging observations, our results indicate that perceptual learning can mainly involve changes in higher-level visual cortex as well as in the neural networks responsible for cognitive functions such as attention and decision making. Copyright © 2015 Elsevier Inc. All rights reserved.
Estimation of uncertainties from missing higher orders in perturbative calculations
International Nuclear Information System (INIS)
Bagnaschi, E.
2015-05-01
In this proceeding we present the results of our recent study (hep-ph/1409.5036) of the statistical performances of two different approaches, Scale Variation (SV) and the Bayesian model of Cacciari and Houdeau (CH)(hep-ph/1105.5152) (which we also extend to observables with initial state hadrons), to the estimation of Missing Higher-Order Uncertainties (MHOUs)(hep-ph/1307.1843) in perturbation theory. The behavior of the models is determined by analyzing, on a wide set of observables, how the MHOU intervals they produce are successful in predicting the next orders. We observe that the Bayesian model behaves consistently, producing intervals at 68% Degree of Belief (DoB) comparable with the scale variation intervals with a rescaling factor r larger than 2 and closer to 4. Concerning SV, our analysis allows the derivation of a heuristic Confidence Level (CL) for the intervals. We find that assigning a CL of 68% to the intervals obtained with the conventional choice of varying the scales within a factor of two with respect to the central scale could potentially lead to an underestimation of the uncertainties in the case of observables with initial state hadrons.
Higher-Order Synaptic Interactions Coordinate Dynamics in Recurrent Networks.
Directory of Open Access Journals (Sweden)
Brendan Chambers
2016-08-01
Full Text Available Linking synaptic connectivity to dynamics is key to understanding information processing in neocortex. Circuit dynamics emerge from complex interactions of interconnected neurons, necessitating that links between connectivity and dynamics be evaluated at the network level. Here we map propagating activity in large neuronal ensembles from mouse neocortex and compare it to a recurrent network model, where connectivity can be precisely measured and manipulated. We find that a dynamical feature dominates statistical descriptions of propagating activity for both neocortex and the model: convergent clusters comprised of fan-in triangle motifs, where two input neurons are themselves connected. Fan-in triangles coordinate the timing of presynaptic inputs during ongoing activity to effectively generate postsynaptic spiking. As a result, paradoxically, fan-in triangles dominate the statistics of spike propagation even in randomly connected recurrent networks. Interplay between higher-order synaptic connectivity and the integrative properties of neurons constrains the structure of network dynamics and shapes the routing of information in neocortex.
Effective description of higher-order scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Langlois, David [APC—Astroparticule et Cosmologie, Université Paris Diderot Paris 7, 75013 Paris (France); Mancarella, Michele; Vernizzi, Filippo [Institut de physique théorique, Université Paris Saclay, CEA, CNRS, 91191 Gif-sur-Yvette (France); Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: michele.mancarella@cea.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: filippo.vernizzi@cea.fr [Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Parc de Grandmont, 37200 Tours (France)
2017-05-01
Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.
Higher order mode analysis of the SNS superconducting linac
Sang Ho Kim; Dong Jeon; Sundelin, R
2001-01-01
Higher order modes (HOM's) of monopoles, dipoles, quadrupoles and sextupoles in beta =0.61 and beta =0.81 6-cell superconducting (SC) cavities for the Spallation Neutron Source (SNS) project, have been found up to about 3 GHz and their properties such as R/Q, trapping possibility, etc have been figured out concerning manufacturing imperfection. The main issues of HOM's are beam instabilities (published separately) and HOM induced power especially from TM monopoles. The time structure of SNS beam has three different time scales of pulses, which are micro-pulse, midi-pulse and macropulse. Each time structure will generate resonances. When a mode is near these resonance frequencies, the induced voltage could be large and accordingly the resulting HOM power. In order to understand the effects from such a complex beam time structure on the mode excitation and resulting HOM power, analytic expressions are developed. With these analytic expressions, the induced HOM voltage and HOM power were calculated by assuming e...
Analysis of higher order harmonics with holographic reflection gratings
Mas-Abellan, P.; Madrigal, R.; Fimia, A.
2017-05-01
Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.
Correlated stopping, proton clusters and higher order proton cumulants
Energy Technology Data Exchange (ETDEWEB)
Bzdak, Adam [AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow (Poland); Koch, Volker [Lawrence Berkeley National Laboratory, Nuclear Science Division, Berkeley, CA (United States); Skokov, Vladimir [RIKEN/BNL, Brookhaven National Laboratory, Upton, NY (United States)
2017-05-15
We investigate possible effects of correlations between stopped nucleons on higher order proton cumulants at low energy heavy-ion collisions. We find that fluctuations of the number of wounded nucleons N{sub part} lead to rather nontrivial dependence of the correlations on the centrality; however, this effect is too small to explain the large and positive four-proton correlations found in the preliminary data collected by the STAR collaboration at √(s) = 7.7 GeV. We further demonstrate that, by taking into account additional proton clustering, we are able to qualitatively reproduce the preliminary experimental data. We speculate that this clustering may originate either from collective/multi-collision stopping which is expected to be effective at lower energies or from a possible first-order phase transition, or from (attractive) final state interactions. To test these ideas we propose to measure a mixed multi-particle correlation between stopped protons and a produced particle (e.g. pion, antiproton). (orig.)
Higher order corrections to energy levels of muonic atoms
International Nuclear Information System (INIS)
Rinker, G.A. Jr.; Steffen, R.M.
1975-08-01
In order to facilitate the analysis of muonic x-ray spectra, the results of numerical computations of all higher order quantum electrodynamical corrections to the energy levels of muonic atoms are presented in tabular and graphical form. These corrections include the vacuum polarization corrections caused by emission and reabsorption of virtual electron pairs to all orders, including ''double-bubble'' and ''cracked-egg'' diagrams. An estimate of the Delbruecke scattering-type correction is presented. The Lamb-shift (second- and fourth-order vertex) corrections have been calculated including the correction for the anomalous magnetic moment of the muon. The relativistic nuclear motion (or recoil) correction as well as the correction caused by the screening of the atomic electrons is presented in graphs. For the sake of completeness a graph of the nuclear polarization as computed on the basis of Chen's approach has been included. All calculations were made with a two-parameter Fermi distribution of the nuclear charge density. 7 figures, 23 references
Higher-order scene statistics of breast images
Abbey, Craig K.; Sohl-Dickstein, Jascha N.; Olshausen, Bruno A.; Eckstein, Miguel P.; Boone, John M.
2009-02-01
Researchers studying human and computer vision have found description and construction of these systems greatly aided by analysis of the statistical properties of naturally occurring scenes. More specifically, it has been found that receptive fields with directional selectivity and bandwidth properties similar to mammalian visual systems are more closely matched to the statistics of natural scenes. It is argued that this allows for sparse representation of the independent components of natural images [Olshausen and Field, Nature, 1996]. These theories have important implications for medical image perception. For example, will a system that is designed to represent the independent components of natural scenes, where objects occlude one another and illumination is typically reflected, be appropriate for X-ray imaging, where features superimpose on one another and illumination is transmissive? In this research we begin to examine these issues by evaluating higher-order statistical properties of breast images from X-ray projection mammography (PM) and dedicated breast computed tomography (bCT). We evaluate kurtosis in responses of octave bandwidth Gabor filters applied to PM and to coronal slices of bCT scans. We find that kurtosis in PM rises and quickly saturates for filter center frequencies with an average value above 0.95. By contrast, kurtosis in bCT peaks near 0.20 cyc/mm with kurtosis of approximately 2. Our findings suggest that the human visual system may be tuned to represent breast tissue more effectively in bCT over a specific range of spatial frequencies.
Higher-order Skyrme hair of black holes
Gudnason, Sven Bjarke; Nitta, Muneto
2018-05-01
Higher-order derivative terms are considered as replacement for the Skyrme term in an Einstein-Skyrme-like model in order to pinpoint which properties are necessary for a black hole to possess stable static scalar hair. We find two new models able to support stable black hole hair in the limit of the Skyrme term being turned off. They contain 8 and 12 derivatives, respectively, and are roughly the Skyrme-term squared and the so-called BPS-Skyrme-term squared. In the twelfth-order model we find that the lower branches, which are normally unstable, become stable in the limit where the Skyrme term is turned off. We check this claim with a linear stability analysis. Finally, we find for a certain range of the gravitational coupling and horizon radius, that the twelfth-order model contains 4 solutions as opposed to 2. More surprisingly, the lowest part of the would-be unstable branch turns out to be the stable one of the 4 solutions.
Higher-order gravity and the classical equivalence principle
Accioly, Antonio; Herdy, Wallace
2017-11-01
As is well known, the deflection of any particle by a gravitational field within the context of Einstein’s general relativity — which is a geometrical theory — is, of course, nondispersive. Nevertheless, as we shall show in this paper, the mentioned result will change totally if the bending is analyzed — at the tree level — in the framework of higher-order gravity. Indeed, to first order, the deflection angle corresponding to the scattering of different quantum particles by the gravitational field mentioned above is not only spin dependent, it is also dispersive (energy-dependent). Consequently, it violates the classical equivalence principle (universality of free fall, or equality of inertial and gravitational masses) which is a nonlocal principle. However, contrary to popular belief, it is in agreement with the weak equivalence principle which is nothing but a statement about purely local effects. It is worthy of note that the weak equivalence principle encompasses the classical equivalence principle locally. We also show that the claim that there exists an incompatibility between quantum mechanics and the weak equivalence principle, is incorrect.
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, we present a simplified parsimonious higher-order multivariate Markov chain model with new convergence condition. (TPHOMMCM-NCC). Moreover, estimation method of the parameters in TPHOMMCM-NCC is give. Numerical experiments illustrate the effectiveness of TPHOMMCM-NCC.
Higher order hierarchical discretization scheme for surface integral equations for layered media
DEFF Research Database (Denmark)
Jørgensen, Erik; Kim, Oleksiy S.; Meincke, Peter
2004-01-01
This paper presents an efficient technique for the analysis of electromagnetic scattering by arbitrarily shaped perfectly conducting objects in layered media. The technique is based on a higher order method of moments (MoM) solution of the electric field, magnetic field, or combined-field integra...
Second- and Higher-Order Virial Coefficients Derived from Equations of State for Real Gases
Parkinson, William A.
2009-01-01
Derivation of the second- and higher-order virial coefficients for models of the gaseous state is demonstrated by employing a direct differential method and subsequent term-by-term comparison to power series expansions. This communication demonstrates the application of this technique to van der Waals representations of virial coefficients.…
Directory of Open Access Journals (Sweden)
Erkinjon Karimov
2017-10-01
Full Text Available In this work we discuss higher order multi-term partial differential equation (PDE with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
Erkinjon Karimov; Sardor Pirnafasov
2017-01-01
In this work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
DEFF Research Database (Denmark)
Breinbjerg, Olav
1992-01-01
An approach for including higher order edge diffraction in the equivalent edge current (EEC) method is proposed. This approach, which applies to monostatic as well as bistatic radar configurations with perfectly conducting polygonal plates, involves three distinct sets of EECs. All of these sets...
A stable higher order space time Galerkin marching-on-in-time scheme
Pray, Andrew J.
2013-07-01
We present a method for the stable solution of time-domain integral equations. The method uses a technique developed in [1] to accurately evaluate matrix elements. As opposed to existing stabilization schemes, the method presented uses higher order basis functions in time to improve the accuracy of the solver. The method is validated by showing convergence in temporal basis function order, time step size, and geometric discretization order. © 2013 IEEE.
On higher-order corrections in M theory
International Nuclear Information System (INIS)
Howe, P.S.; Tsimpis, D.
2003-01-01
A theoretical analysis of higher-order corrections to D=11 supergravity is given in a superspace framework. It is shown that any deformation of D=11 supergravity for which the lowest-dimensional component of the four-form G 4 vanishes is trivial. This implies that the equations of motion of D=11 supergravity are specified by an element of a certain spinorial cohomology group and generalises previous results obtained using spinorial or pure spinor cohomology to the fully non-linear theory. The first deformation of the theory is given by an element of a different spinorial cohomology group with coefficients which are local tensorial functions of the massless supergravity fields. The four-form Bianchi Identities are solved, to first order and at dimension -{1/2}, in the case that the lowest-dimensional component of G 4 is non-zero. Moreover, it is shown how one can calculate the first-order correction to the dimension-zero torsion and thus to the supergravity equations of motion given an explicit expression for this object in terms of the supergravity fields. The version of the theory with both a four-form and a seven-form is discussed in the presence of the five-brane anomaly-cancelling term. It is shown that the supersymmetric completion of this term exists and it is argued that it is the unique anomaly-cancelling invariant at this dimension which is at least quartic in the fields. This implies that the first deformation of the theory is completely determined by the anomaly term from which one can, in principle, read off the corrections to all of the superspace field strength tensors. (author)
Threshold resummation and higher order effects in QCD
International Nuclear Information System (INIS)
Ringer, Felix Maximilian
2015-01-01
Quantum chromodynamics (QCD) is a quantum field theory that describes the strong interactions between quarks and gluons, the building blocks of all hadrons. Thanks to the experimental progress over the past decades, there has been an ever-growing need for QCD precision calculations for scattering processes involving hadrons. For processes at large momentum transfer, perturbative QCD offers a systematic approach for obtaining precise predictions. This approach relies on two key concepts: the asymptotic freedom of QCD and factorization. In a perturbative calculation at higher orders, the infrared cancellation between virtual and real emission diagrams generally leaves behind logarithmic contributions. In many observables relevant for hadronic scattering these logarithms are associated with a kinematic threshold and are hence known as ''threshold logarithms''. They become large when the available phase space for real gluon emission shrinks. In order to obtain a reliable prediction from QCD, the threshold logarithms need to be taken into account to all orders in the strong coupling constant, a procedure known as ''threshold resummation''. The main focus of my PhD thesis is on studies of QCD threshold resummation effects beyond the next-to-leading logarithmic order. Here we primarily consider the production of hadron pairs in hadronic collisions as an example. In addition, we also consider hadronic jet production, which is particularly interesting for the phenomenology at the LHC. For both processes, we fully take into account the non-trivial QCD color structure of the underlying partonic hard- scattering cross sections. We find that threshold resummation leads to sizable numerical effects in the kinematic regimes relevant for comparisons to experimental data.
1957-2007: 50 Years of Higher Order Programming Languages
Directory of Open Access Journals (Sweden)
Alen Lovrenčić
2009-06-01
Full Text Available Fifty years ago one of the greatest breakthroughs in computer programming and in the history of computers happened -- the appearance of FORTRAN, the first higher-order programming language. From that time until now hundreds of programming languages were invented, different programming paradigms were defined, all with the main goal to make computer programming easier and closer to as many people as possible. Many battles were fought among scientists as well as among developers around concepts of programming, programming languages and paradigms. It can be said that programming paradigms and programming languages were very often a trigger for many changes and improvements in computer science as well as in computer industry. Definitely, computer programming is one of the cornerstones of computer science.Today there are many tools that give a help in the process of programming, but there is still a programming tasks that can be solved only manually. Therefore, programming is still one of the most creative parts of interaction with computers.Programmers should chose programming language in accordance to task they have to solve, but very often, they chose it in accordance to their personal preferences, their beliefs and many other subjective reasons.Nevertheless, the market of programming languages can be merciless to languages as history was merciless to some people, even whole nations. Programming languages and developers get born, live and die leaving more or less tracks and successors, and not always the best survives. The history of programming languages is closely connected to the history of computers and computer science itself. Every single thing from one of them has its reflexions onto the other. This paper gives a short overview of last fifty years of computer programming and computer programming languages, but also gives many ideas that influenced other aspects of computer science. Particularly, programming paradigms are described, their
Preparation and characterization of stable aqueous higher-order fullerenes
International Nuclear Information System (INIS)
Aich, Nirupam; Flora, Joseph R V; Saleh, Navid B
2012-01-01
Stable aqueous suspensions of nC 60 and individual higher fullerenes, i.e. C 70 , C 76 and C 84 , are prepared by a calorimetric modification of a commonly used liquid–liquid extraction technique. The energy requirement for synthesis of higher fullerenes has been guided by molecular-scale interaction energy calculations. Solubilized fullerenes show crystalline behavior by exhibiting lattice fringes in high resolution transmission electron microscopy images. The fullerene colloidal suspensions thus prepared are stable with a narrow distribution of cluster radii (42.7 ± 0.8 nm, 46.0 ± 14.0 nm, 60 ± 3.2 nm and 56.3 ± 1.1 nm for nC 60 , nC 70 , nC 76 and nC 84 , respectively) as measured by time-resolved dynamic light scattering. The ζ-potential values for all fullerene samples showed negative surface potentials with similar magnitude ( − 38.6 ± 5.8 mV, − 39.1 ± 4.2 mV, − 38.9 ± 5.8 mV and − 41.7 ± 5.1 mV for nC 60 , nC 70 , nC 76 and nC 84 , respectively), which provide electrostatic stability to the colloidal clusters. This energy-based modified solubilization technique to produce stable aqueous fullerenes will likely aid in future studies focusing on better applicability, determination of colloidal properties, and understanding of environmental fate, transport and toxicity of higher-order fullerenes. (paper)
Analysis of wheezes using wavelet higher order spectral features.
Taplidou, Styliani A; Hadjileontiadis, Leontios J
2010-07-01
. This paves the way for the use of the wavelet higher order spectral features as an input vector to an efficient classifier. Apparently, this would integrate the intrinsic characteristics of wheezes within computerized diagnostic tools toward their more efficient evaluation.
Higher-order aberrations and visual acuity after LASEK.
Urgancioglu, Berrak; Bilgihan, Kamil; Ozturk, Sertac
2008-08-01
To determine ocular higher-order aberrations (HOAs) in eyes with supernormal vision after myopic astigmatic laser subepithelial keratomileusis (LASEK) and to compare the findings with those in eyes with natural supernormal vision. Ocular HOAs were measured after LASEK in 20 eyes of 12 myopic astigmatic patients with postoperative uncorrected visual acuity (UCVA) of >20/16 (group 1). Patients who were included in the study had no visual symptoms like glare, halo or double vision. The measurements were taken 8.3 +/- 3 months after LASEK surgery. In group 2 ocular HOAs were examined in 20 eyes of 10 subjects with natural UCVA of >20/16 as a control. Measurements were taken across a pupil with a diameter of 4.0 mm and 6.0 mm. Root-mean-square (RMS) values of HOAs, Z(3)-1, Z(3)1, Z(4)0, Z(5)-1, Z(5)1 and Z(6)0 were analyzed. The mean RMS values for each order were higher in group 1 when compared with group 2 at 4.0 mm and 6.0 mm pupil diameters. There was no statistically significant difference between groups in spherical and coma aberrations (P > 0.05). Mean RMS values for total HOAs were 0.187 +/- 0.09 microm at 4.0 mm and 0.438 +/- 0.178 microm at 6.0 mm pupil in group 1 and 0.120 +/- 0.049 microm at 4.0 mm and 0.344 +/- 0.083 microm at 6.0 mm pupil in group 2. The difference between groups in total HOAs was statistically significant at 4.0 mm and 6.0 mm pupil diameters (P < 0.05). Ocular HOAs exist in eyes with supernormal vision. After LASEK, the amount of HOAs of the eye increases under both mesopic and photopic conditions. However the amount of HOA increase does not seem to be consistent with visual symptoms.
Optimized Finite-Difference Coefficients for Hydroacoustic Modeling
Preston, L. A.
2014-12-01
Responsible utilization of marine renewable energy sources through the use of current energy converter (CEC) and wave energy converter (WEC) devices requires an understanding of the noise generation and propagation from these systems in the marine environment. Acoustic noise produced by rotating turbines, for example, could adversely affect marine animals and human-related marine activities if not properly understood and mitigated. We are utilizing a 3-D finite-difference acoustic simulation code developed at Sandia that can accurately propagate noise in the complex bathymetry in the near-shore to open ocean environment. As part of our efforts to improve computation efficiency in the large, high-resolution domains required in this project, we investigate the effects of using optimized finite-difference coefficients on the accuracy of the simulations. We compare accuracy and runtime of various finite-difference coefficients optimized via criteria such as maximum numerical phase speed error, maximum numerical group speed error, and L-1 and L-2 norms of weighted numerical group and phase speed errors over a given spectral bandwidth. We find that those coefficients optimized for L-1 and L-2 norms are superior in accuracy to those based on maximal error and can produce runtimes of 10% of the baseline case, which uses Taylor Series finite-difference coefficients at the Courant time step limit. We will present comparisons of the results for the various cases evaluated as well as recommendations for utilization of the cases studied. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
ANOVA-HDMR structure of the higher order nodal diffusion solution
International Nuclear Information System (INIS)
Bokov, P. M.; Prinsloo, R. H.; Tomasevic, D. I.
2013-01-01
Nodal diffusion methods still represent a standard in global reactor calculations, but employ some ad-hoc approximations (such as the quadratic leakage approximation) which limit their accuracy in cases where reference quality solutions are sought. In this work we solve the nodal diffusion equations utilizing the so-called higher-order nodal methods to generate reference quality solutions and to decompose the obtained solutions via a technique known as High Dimensional Model Representation (HDMR). This representation and associated decomposition of the solution provides a new formulation of the transverse leakage term. The HDMR structure is investigated via the technique of Analysis of Variance (ANOVA), which indicates why the existing class of transversely-integrated nodal methods prove to be so successful. Furthermore, the analysis leads to a potential solution method for generating reference quality solutions at a much reduced calculational cost, by applying the ANOVA technique to the full higher order solution. (authors)
Optimal variable-grid finite-difference modeling for porous media
International Nuclear Information System (INIS)
Liu, Xinxin; Yin, Xingyao; Li, Haishan
2014-01-01
Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs. (paper)
A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking
Institute of Scientific and Technical Information of China (English)
ZHANG ZuTao; ZHANG JiaShu
2009-01-01
Non-Intrusive methods for eye tracking are Important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robust-ness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into today's interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty In modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and im-prove the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions.
Analysis of warping deformation modes using higher order ANCF beam element
Orzechowski, Grzegorz; Shabana, Ahmed A.
2016-02-01
Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.
International Nuclear Information System (INIS)
Waligorski, M.P.R.; Urbanczyk, K.M.
1975-01-01
The basic principles of the finite-difference approximation applied to the solution of electrostatic field distributions in gaseous proportional counters are given. Using this method, complicated two-dimensional electrostatic problems may be solved, taking into account any number of anodes, each with its own radius, and any cathode shape. A general formula for introducing the anode radii into the calculations is derived and a method of obtaining extremely accurate (up to 0.1%) solutions is developed. Several examples of potential and absolute field distributions for single rectangular and multiwire proportional counters are calculated and compared with exact results according to Tomitani, in order to discuss in detail errors of the finite-difference approximation. (author)
HEATING-7, Multidimensional Finite-Difference Heat Conduction Analysis
International Nuclear Information System (INIS)
2000-01-01
problems, surface fluxes may be plotted with H7TECPLOT which requires the proprietary software TECPLOT. HEATING 7.3 runs under Windows95 and WindowsNT on PC's. No future modifications are planned for HEATING7. See README.1ST for more information. 2 - Method of solution: Three steady-state solution techniques are available: point-successive over-relaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion.) The solution of the system of equations arising from the implicit techniques is accomplished by point-successive over-relaxation iteration and includes procedures to estimate the optimum acceleration parameter. 3 - Restrictions on the complexity of the problem: All surfaces in a model must be parallel to one of the coordinate axes which makes modeling complex geometries difficult. Transient change of phase problems can only be solved with one of the explicit techniques - an implicit change-of-phase capability has not been implemented
A higher order space-time Galerkin scheme for time domain integral equations
Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam
2014-01-01
Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.
Finite difference evolution equations and quantum dynamical semigroups
International Nuclear Information System (INIS)
Ghirardi, G.C.; Weber, T.
1983-12-01
We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)
Finite difference program for calculating hydride bed wall temperature profiles
International Nuclear Information System (INIS)
Klein, J.E.
1992-01-01
A QuickBASIC finite difference program was written for calculating one dimensional temperature profiles in up to two media with flat, cylindrical, or spherical geometries. The development of the program was motivated by the need to calculate maximum temperature differences across the walls of the Tritium metal hydrides beds for thermal fatigue analysis. The purpose of this report is to document the equations and the computer program used to calculate transient wall temperatures in stainless steel hydride vessels. The development of the computer code was motivated by the need to calculate maximum temperature differences across the walls of the hydrides beds in the Tritium Facility for thermal fatigue analysis
Higher Order Improvements for Approximate Estimators
DEFF Research Database (Denmark)
Kristensen, Dennis; Salanié, Bernard
Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such appr......Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties...... of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators......, such as simulation-based estimators. Our second bias correction is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much finer...
Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng
2004-01-01
Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair
An efficient technique for higher order fractional differential equation.
Ali, Ayyaz; Iqbal, Muhammad Asad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad; Mohyud-Din, Syed Tauseef
2016-01-01
In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.